Science

What Is Science?

Science is not a pile of facts but a method for finding out which of our ideas about the world survive contact with it. Its working parts are simple to state: notice something, guess at an explanation, work out what that guess predicts, and then look, carefully, to see whether the prediction holds. What makes the method science rather than storytelling is the last step. A claim that cannot fail any possible test is not telling you anything about the world.

The habit is older than the word. In Cairo, around 1011 to 1021, the Arab scholar Ibn al-Haytham wrote the Book of Optics, in which he settled a thousand-year argument about vision by experiment rather than authority. Most Greek thinkers had held that the eye sends out rays; Ibn al-Haytham built a dark chamber with a pinhole, showed that light from outside formed an inverted image inside, and concluded that light travels from objects into the eye. He described his procedure so that others could repeat it, which is half the point.

In 1620 Francis Bacon's Novum Organum argued that knowledge should be built upward from organised observation, and in 1660 the newly founded Royal Society in London took as its motto Nullius in verba, roughly "take nobody's word for it". The philosopher Karl Popper, writing in Vienna in 1934, sharpened the idea into a test: a scientific statement is one that could in principle be proved false. "All swans are white" is scientific because a single black swan sinks it, and in 1697 Dutch sailors in Western Australia duly found one.

The cleanest modern illustration is the eclipse of 29 May 1919. Einstein's general relativity predicted that starlight grazing the Sun would bend by about 1.75 arcseconds, twice the Newtonian figure. Arthur Eddington's expedition to Príncipe and a second team at Sobral in Brazil photographed stars near the darkened Sun and measured the shift. Had the stars sat still, the theory would have been dead. They moved by about the predicted amount, and the result made the front page of The Times.

Did you know? The word "scientist" was only coined in 1833, by William Whewell at Cambridge; before that its practitioners were "natural philosophers".

Science is also a community activity. Results are published, methods are shared, and other people try to break them, which is why peer review and replication get their own chapter. The method is not infallible: scientists are human, fashions come and go, and fraud happens. But the system is built so that errors are eventually caught, and that self-correcting machinery, more than any single discovery, is what separates science from every other way of knowing. A good scientist is someone who takes pains to find out whether they are wrong.

Observation and Measurement

Science begins with looking, but looking is not enough: the observation has to be written down, in units that someone else can use, with an honest statement of how precise it is. Measurement is what turns an impression into evidence. Aristotle thought heavy things fell faster than light ones; nobody timed them properly for nineteen centuries.

The hero of the pre-telescope age was the Danish nobleman Tycho Brahe. On the island of Hven, between 1576 and 1597, he built Uraniborg, the best-funded observatory in Europe, and filled it with huge brass quadrants and sextants read by eye. He measured the positions of 777 stars and tracked the planets night after night to an accuracy of about one arcminute, roughly a thirtieth of the Moon's width and several times better than anyone before him. Tycho never accepted that the Earth moved. His data did not care: after his death Johannes Kepler used them to discover that Mars follows an ellipse, because a circle missed Tycho's observations by eight arcminutes, and Kepler trusted the measurements over the theory.

Measurement also needs a shared ruler. In 1791 the French Academy of Sciences defined the metre as one ten-millionth of the distance from the North Pole to the Equator through Paris, and sent two astronomers, Jean-Baptiste Delambre and Pierre Méchain, to survey the meridian from Dunkirk to Barcelona; it took them six years, through a revolution and a war. A platinum-iridium bar became the standard in 1889, a count of krypton-86 wavelengths replaced it in 1960, and since 1983 the metre has been defined by the speed of light, fixed at exactly 299,792,458 metres per second.

Did you know? Until 20 May 2019 the kilogram was a platinum-iridium cylinder in a vault at Sèvres near Paris; if it gained a speck of dust, every other mass in the universe technically changed.

Some of the biggest discoveries were made by people who noticed what their instruments were telling them. In 1967 Jocelyn Bell Burnell, a Cambridge research student, spotted a quarter-inch of "scruff" on the 30 metres a day of chart-recorder paper from a radio telescope she had helped to build. The scruff repeated every 1.337 seconds; it was the first pulsar, a spinning neutron star. Chinese court astronomers had done something similar in 1054, recording a "guest star" that we now know was the supernova that left the Crab Nebula.

Today all seven SI base units are defined by constants of nature, so a laboratory in Tokyo, Nairobi or Toulouse can realise them without visiting Paris. Atomic clocks drift by less than a second in a hundred million years, and the satellite-navigation receiver in a phone depends on that. Observation tells you something happened; measurement tells you how much, and how sure you are.

The Experiment

An experiment is an observation you arrange yourself. Instead of waiting for nature to vary one thing at a time, you vary it, hold everything else steady, and watch what changes. The control, the untreated comparison, is what makes the result mean something. Without it you have an anecdote.

The naval surgeon James Lind ran what is often called the first controlled clinical trial aboard HMS Salisbury on 20 May 1747. Scurvy was killing more British sailors than the French were. Lind took twelve sick men, put them in the same quarters on the same diet, and split them into six pairs, each given a different daily remedy: a quart of cider, drops of sulphuric acid, vinegar, half a pint of seawater, a spiced paste with barley water, or two oranges and a lemon. The citrus pair were fit for duty within six days. Lind published in 1753, drew muddled conclusions, and the Admiralty took until 1795 to issue lemon juice; good experiments do not always win quickly.

The art of the control reached its peak in Paris. In 1859 Louis Pasteur boiled meat broth in flasks whose necks he had drawn out into long, downward-curving swan necks. Air could reach the broth, but dust and microbes settled in the bend. The broth stayed clear for months. Snap off the neck, or tilt the flask so the broth touched the trapped dust, and it clouded with life within days. The only variable was access to airborne particles, so spontaneous generation, the idea that life arises on its own from broth, was finished. One of Pasteur's original flasks is still sterile at the Institut Pasteur.

Did you know? The modern randomised trial was born over tea: in the 1920s Ronald Fisher tested Muriel Bristol's claim that she could taste whether milk had been poured first, using eight cups in random order. She got them all right.

Twentieth-century statisticians added two refinements. Randomisation, assigning patients to treatment or control by chance, removes the doctor's unconscious bias about who gets the new drug; the Medical Research Council's 1948 streptomycin trial for tuberculosis, designed by Austin Bradford Hill, was the first to do it properly, with 107 patients. Blinding keeps patients, and ideally doctors, from knowing who got what, because expectation alone can change a result.

Experiments now run at every scale: a physicist colliding protons 40 million times a second at CERN, an ecologist fencing off a patch of grassland, a web designer showing two versions of a page to split traffic. The logic is Lind's: change one thing, compare with the rest, and let the difference speak.

Hypotheses and Theories

A hypothesis is a specific, testable guess: if this is true, then that should happen. A theory, in science, is something much grander: a framework of ideas that has survived many tests and explains a wide range of facts. When someone says evolution is "just a theory", they have the dictionary the wrong way round. Gravity, germs and plate tectonics are theories too.

The gap between a hypothesis and a theory is the story of Ignaz Semmelweis. In 1846 he was an assistant at the Vienna General Hospital's maternity clinics. The First Clinic, staffed by doctors and medical students, lost around one mother in ten to childbed fever; the Second, run by midwives, lost about one in forty. Women begged to be admitted to the midwives. Semmelweis's colleague Jakob Kolletschka died in 1847 after being nicked by a student's scalpel during an autopsy, with symptoms like the mothers'. The doctors, Semmelweis realised, came to the wards straight from the dissecting room. His hypothesis: "cadaverous particles" on their hands carried the disease. His prediction: wash the particles off and the deaths would stop. From May 1847 he made staff scrub with chlorinated lime, and the First Clinic's mortality fell to about two per cent, then lower, matching the midwives.

It worked, and he was ignored. Semmelweis had a hypothesis with a result but no theory to explain why, and a medical establishment that believed in imbalances of the humours and bad air had no place for invisible particles. He lost his post, grew bitter, and died in an asylum in 1865. The explanation arrived with Pasteur's and Koch's germ theory in the 1860s and 1870s, which made handwashing obvious.

Did you know? Alfred Wegener's continental drift, proposed in 1912, was dismissed for fifty years largely because he could offer no mechanism; seafloor spreading supplied one and turned it into a theory in the 1960s.

Between hypothesis and theory sits the law: a regularity that holds without saying why. Boyle's law of 1662, that squeezing a gas to half its volume doubles its pressure, is a law; the kinetic theory of molecules bouncing off the walls is what explains it. Laws describe, theories explain, hypotheses propose.

A theory is never finished. Newton's gravity was the best theory in physics for two centuries, until Mercury's orbit and the 1919 eclipse showed it to be a limiting case of Einstein's. Good theories make risky predictions, invite attack, and keep standing; when they fall, they are usually absorbed rather than abolished. The right question is never whether a theory is proved, but how hard anyone has tried to break it.

Models and Simulations

A model is a deliberate simplification: a version of the world with most of the detail stripped out so that the part you care about can be reasoned about. Bohr's atom with electrons on little orbits is a model; so is a wind-tunnel wing, a map of the Tube, and the cardboard and wire double helix that Watson and Crick built in Cambridge in 1953. None of them is the thing itself. The statistician George Box put it best: all models are wrong, but some are useful.

A simulation is a model set in motion, usually inside a computer. The great example is the weather. In 1904 the Norwegian physicist Vilhelm Bjerknes argued that forecasting was a problem in physics: know the state of the atmosphere now, apply the equations of motion and heat, and compute tomorrow. The Englishman Lewis Fry Richardson tried it by hand. Working as an ambulance driver on the Western Front, he spent weeks computing a six-hour forecast for a patch of Germany on 20 May 1910, dividing the map into cells and stepping the equations forward. His answer, a pressure rise of 145 millibars, was absurd; the real change was nearly zero, and the fault lay in noisy starting data. He published anyway, in 1922, with an honest account of the failure and a vision of a "forecast factory" of 64,000 human computers in a great hall, each responsible for one cell.

The factory was built out of valves. In April 1950, on the ENIAC computer in Maryland, Jule Charney, Ragnar Fjørtoft and John von Neumann produced the first numerical weather forecasts: a 24-hour prediction took about 24 hours to run, and the results were credible. Operational computer forecasts began in Sweden in 1954 and the United States in 1955.

Did you know? Syukuro Manabe's 1967 climate model, which predicted that doubling carbon dioxide would warm the Earth by about 2 °C, earned him a share of the 2021 Nobel Prize in Physics, 54 years later.

Today the European Centre for Medium-Range Weather Forecasts runs its model on a grid of about nine kilometres across the whole planet, and runs it 51 times with slightly different starting conditions, because Edward Lorenz showed in 1963 that tiny errors grow. A spread of 51 forecasts tells you not just what will happen but how confident to be. The same technique simulates galaxies colliding, proteins folding, epidemics spreading and the crumple of a car body in a crash, which is why fewer real cars are wrecked in testing.

A simulation never proves anything on its own; it shows what follows from the model's assumptions. Its value lies in the comparison with reality afterwards. Richardson's forecast was wrong by a hundredfold, and it was still the most important forecast ever made.

Instruments That Changed Science

Every big step in science has come with a new way of seeing. The unaided eye and the memory of the unaided eye got us early astronomy and natural history; everything else has needed an instrument, and most of those instruments were made before anyone understood what they would find.

The telescope is the clearest case. In October 1608 a spectacle maker in Middelburg, Hans Lippershey, applied to the States General of the Netherlands for a patent on a tube with two lenses that made distant things appear near; it was refused because the idea was already spreading. Galileo Galilei in Padua heard of it in the summer of 1609, worked out the optics for himself, and by the end of the year had ground lenses for a tube that magnified twenty times: a convex objective at the front and a concave eyepiece that gave an upright image. He pointed it at the sky. Between 7 and 13 January 1610 he watched four points of light near Jupiter change position night by night and realised they were moons orbiting another planet, which an Earth-centred cosmos did not allow. He saw mountains on the Moon, the phases of Venus and a Milky Way made of stars, and published it all in March 1610 as Sidereus Nuncius, the Starry Messenger.

Did you know? Galileo's best telescopes had a field of view so narrow that only about a quarter of the Moon fitted in it at once; he drew the Moon in pieces.

The microscope opened the opposite door. In Delft in the 1670s a draper named Antonie van Leeuwenhoek ground tiny glass beads into single lenses that magnified up to about 270 times, better than the compound microscopes of the day, and in 1676 reported to the Royal Society the "animalcules" he saw in a drop of water: the first sight of bacteria and protozoa. The Society demanded sworn statements from witnesses before it would believe him.

The list runs on. The thermometer made heat a number; the prism and then the spectroscope of Bunsen and Kirchhoff in 1859 read the chemistry of the stars; Charles Wilson's cloud chamber of 1911 made the tracks of single subatomic particles visible as trails of droplets; X-ray diffraction revealed the double helix; the Large Hadron Collider at CERN, 27 kilometres round, found the Higgs boson in 2012; and in 2015 the LIGO detectors measured a change in length smaller than a thousandth of a proton's width and heard two black holes merge.

Each instrument extended a human sense, then showed something no sense had suspected: moons, microbes, spectra, particles, ripples in space. A hypothesis says where to look; an instrument decides what can be seen. Build a better one, and the universe gets bigger.

Error, Uncertainty and Statistics

No measurement is exact. Read a thermometer ten times and you get a scatter of values; the question is what to do with the scatter. Science's answer, worked out over three centuries, is that uncertainty can be measured too, and that an honest result is a number with a range attached: 9.81 plus or minus 0.02, never bare.

The shape of random error was found by Abraham de Moivre in 1733 and put to work by Carl Friedrich Gauss. On 1 January 1801 Giuseppe Piazzi in Palermo spotted a new object, Ceres, and tracked it for 41 days before it was lost in the Sun's glare. With only a tiny arc of sky to go on, the 24-year-old Gauss computed its orbit by a new method, least squares, which treated each observation as the truth plus a random error and found the path that made the total error smallest. On 31 December 1801 Franz von Zach found Ceres almost exactly where Gauss said it would be. The bell curve, the normal distribution, describes how such errors pile up: about 68 per cent of measurements fall within one standard deviation of the mean, 95 per cent within two, and 99.7 per cent within three.

Particle physicists will not claim a discovery below five standard deviations, where the chance of a random fluke mimicking the signal is about one in 3.5 million. That was the bar the Higgs boson cleared at CERN on 4 July 2012. Medicine and psychology have traditionally used a looser threshold, a one-in-twenty chance, the "p < 0.05" that Ronald Fisher suggested in 1925, and much of the replication crisis traces to treating it as a finishing line rather than a hint.

Did you know? The t-test was invented in 1908 by William Gosset, a brewer at Guinness in Dublin, to judge barley trials with small samples; the brewery made him publish under the name "Student".

Random error averages out; systematic error does not. In September 2011 the OPERA experiment in Italy reported neutrinos arriving from CERN 60 nanoseconds early, faster than light. Six sigma, said the collaboration, with careful caveats. By early 2012 the cause was found: a fibre-optic cable not fully screwed in, delaying the timing signal. The statistics were impeccable; the apparatus was not. Precision is how tightly your results cluster; accuracy is whether the cluster is in the right place. A clock can be precisely wrong.

The modern discipline includes error bars on every graph, propagation of uncertainties through each calculation, and the habit of stating confidence intervals rather than yes-or-no verdicts. Weather forecasts say 70 per cent; polls quote a margin of error; the kilogram's new definition carries an uncertainty of parts per billion. Doubt, properly measured, is not a weakness of science but its unit of currency.

Peer Review and Replication

A result that stays in one laboratory is not yet science. It becomes science when strangers have examined it, tried to break it, and failed. Two institutions do that work: peer review before publication and replication after.

The journal came first. On 6 March 1665 Henry Oldenburg, secretary of the Royal Society, published the first issue of Philosophical Transactions, the oldest scientific journal still running. Oldenburg was already sending manuscripts to Fellows for an opinion before printing them, and the Society's council formally vetted papers from 1752. The modern system, in which an editor sends a paper to two or three anonymous experts who recommend acceptance, revision or rejection, only became standard after the Second World War; Nature did not referee every paper until 1973. Reviewers work unpaid, catch mistakes, demand missing controls, and occasionally miss fraud entirely, because they check reasoning rather than repeat experiments.

Replication is the harder test. On 23 March 1989 Martin Fleischmann and Stanley Pons announced at a press conference in Utah that they had produced nuclear fusion in a jar of heavy water at room temperature. Within weeks, laboratories from MIT to Harwell had tried and failed to find the excess heat or the neutrons, and cold fusion collapsed before most of the papers were even published. The system worked, if noisily. The more worrying failures are quiet. In 2015 the Open Science Collaboration repeated 100 published psychology experiments; only 36 per cent gave a statistically significant result the second time, and the effects that did appear were on average about half as large. Cancer biology and economics have returned similar figures.

Did you know? Andrew Wakefield's 1998 paper linking the MMR vaccine to autism passed peer review in The Lancet and took twelve years to retract; its damage to vaccination rates is still being felt.

The causes are familiar: small samples, flexible analysis, and a publishing culture that rewards surprising positive results over careful null ones. The remedies are spreading. Pre-registration, in which the hypothesis and analysis are filed before the data are collected, removes the temptation to fish; registered reports commit a journal to publishing whatever the result; preprint servers such as arXiv, founded by Paul Ginsparg in 1991, let a paper be read and criticised by thousands before any referee sees it. Gravitational-wave physicists and the Higgs teams check each other with two independent detectors or experiments.

None of this makes any single paper true. It makes the literature self-correcting over time, which is the most that can be asked. A published claim is a promissory note; replication is when it is cashed.

Scientific Revolutions

Most of the time science moves by accumulation: one more measurement, one more species, one more decimal place. Occasionally it moves by demolition. In 1962 the physicist-turned-historian Thomas Kuhn published The Structure of Scientific Revolutions and gave the pattern a vocabulary that has stuck. A paradigm is the shared framework of theories, methods and examples that a field takes for granted. Normal science is puzzle-solving within it. Anomalies accumulate, a crisis sets in, and a new framework replaces the old one in a shift that is as much a change of vision as a change of theory.

The first and grandest case is the Copernican revolution. Nicolaus Copernicus, a canon in Frombork on the Baltic, put the Sun at the centre in De revolutionibus, printed in Nuremberg in 1543 as he lay dying. The book was initially read as a calculating device; it took Kepler's ellipses in 1609, Galileo's telescope in 1610 and Newton's gravitation in 1687 to make a moving Earth not merely convenient but compulsory.

Chemistry had its revolution in a single decade. Antoine Lavoisier in Paris, working with his wife Marie-Anne, who translated and drew the apparatus, weighed everything. Burning tin in a sealed vessel gained mass equal to the air lost, which no theory of phlogiston could explain. His Traité élémentaire de chimie of 1789 named oxygen, listed 33 elements and declared that mass is conserved. Five years later the Revolution guillotined him.

Did you know? Max Planck wrote that a new scientific truth does not triumph by convincing its opponents but because its opponents eventually die; the line is now shortened to "science advances one funeral at a time".

Darwin's On the Origin of Species in 1859 did the same for biology, and quantum theory between Planck's 1900 paper and the 1927 Solvay conference did it for physics. The most recent complete revolution is plate tectonics. Alfred Wegener's drifting continents were mocked in 1912; by 1963 Fred Vine and Drummond Matthews had shown that stripes of reversed magnetism on the seafloor record new crust spreading from mid-ocean ridges, and within five years nearly every geologist had changed sides.

Historians of science debate how clean Kuhn's picture is. Revolutions are rarely sudden, the old paradigm's data are usually kept, and Newton's mechanics still lands probes on Mars. Kuhn's word "incommensurable" suggested that scientists on either side cannot even understand each other, which overstates it. But his central insight holds: a field's deepest assumptions are invisible until they break, and the people who break them are often outsiders, young, or from the wrong department. Paradigms are not prisons; they are the scaffolding you only notice when it comes down.

What Science Cannot Tell Us

Science is the most reliable way humans have found of answering questions about how the world works. It is worth being clear about which questions it cannot answer, partly because those limits were themselves discovered scientifically, and partly because claiming too much is how a method loses trust.

The first limit is the one the Scottish philosopher David Hume noticed in 1739: no amount of description of what is tells you what ought to be. Science can tell you that a drug reduces mortality by 30 per cent, that a species will go extinct if a wetland is drained, or that the planet is warming; it cannot tell you whether to pay for the drug, save the frog or cut the carbon. Those are questions of value, and they belong to everyone. Scientists who announce that "the science says we must" have quietly smuggled in a politics.

A second set of limits was found from inside. In 1927 Werner Heisenberg showed that a particle's position and momentum cannot both be known with unlimited precision; the limit is not a fault of instruments but a property of nature. In 1963 Edward Lorenz found that a simple weather model amplified rounding errors in the fourth decimal place into completely different weather within weeks; chaos means some systems are predictable only for a while, however good the data. And in 1931 Kurt Gödel proved that any consistent system of mathematics rich enough to count contains true statements it cannot prove. Even the language of science has holes.

Did you know? Lorenz's discovery came from restarting a weather simulation from a printout that showed 0.506 instead of the stored 0.506127; the two runs diverged completely within a couple of simulated months.

A third category is questions that are not yet testable, which is different from untestable forever. Whether other universes exist, what happened before the Big Bang, and whether consciousness can be explained by physics are live scientific questions without, so far, experiments that could settle them. Scientists debate whether a theory with no possible test is still science; string theory has made the argument unusually heated.

Then there are the questions science does not even address. Why there is something rather than nothing; whether a life was well lived; what a piece of music means; whether a sunset is beautiful. Science can describe the retina's response to a sunset and the brain's response to Bach, and the description is interesting, but it is not the experience, and it does not pretend to be.

Knowing the boundary is a strength. The method works because it refuses to answer questions it has no way to test, and a culture that remembers this is less likely to be fooled by people in white coats selling certainties. Science tells us what is; the rest is up to us.

From Four Elements to Atoms

What is everything made of? For most of recorded history the answer was a short list of substances rather than a long list of particles. Around 450 BC the Sicilian philosopher Empedocles proposed four "roots", earth, water, air and fire, and Aristotle gave each a pair of qualities (hot or cold, wet or dry) so that one could change into another. It was a theory of transformation, which is why it suited alchemists so well for the next two thousand years. China had five phases instead, wood, fire, earth, metal and water, and India's Vaisheshika school, traditionally traced to the sage Kanada, taught that matter is made of indivisible particles.

The Greek alternative came from Leucippus and his pupil Democritus, around 400 BC: the world is atoms and void, and atoms are atomos, uncuttable. The idea had no experiment behind it and Aristotle rejected it; it survived mainly in a Latin poem, Lucretius's On the Nature of Things, written around 50 BC. When the Florentine book-hunter Poggio Bracciolini found a copy in a German monastery in 1417, atomism re-entered European thought.

Did you know? The Arabic alchemists did real chemistry: Jabir ibn Hayyan's school in the eighth century described distillation and crystallisation, and the words alkali, alcohol and alembic all come from Arabic.

The decisive shift was to define an element by what you could do in the laboratory rather than by philosophy. In The Sceptical Chymist of 1661, Robert Boyle in Oxford attacked the four elements and argued that an element was simply a substance that could not be broken into simpler ones. The test required a balance. Antoine Lavoisier in Paris weighed everything: he showed in 1783, with Laplace, that water was not an element at all but a compound of hydrogen and oxygen, and his Elementary Treatise on Chemistry of 1789 listed 33 substances that had resisted all attempts at decomposition. Some were wrong (he included light and heat), but the method was right, and it has given us 118 elements since.

Then John Dalton in Manchester joined the two traditions. His New System of Chemical Philosophy of 1808 took Lavoisier's elements and Democritus's atoms and said: each element is a kind of atom with its own weight, and compounds form when atoms combine in small whole-number ratios. For the first time the ancient guess made quantitative predictions a chemist could test on a balance, and the next chapter is about how it fared.

Atoms stayed hypothetical for another century. Ernst Mach refused to believe in them into the 1900s; it took Einstein's 1905 theory of Brownian motion and Jean Perrin's measurements in 1908 to make them real to the last sceptics. Today a scanning tunnelling microscope can picture single atoms, and in 1989 IBM researchers spelled the company's name with 35 xenon atoms. Empedocles's four roots turned out to be a solid, a liquid, a gas and a plasma, which is not a bad first guess at the states of matter.

Dalton's Atoms

John Dalton was a Quaker schoolteacher in Manchester who kept a weather diary for 57 years and never married. His interest in gases, how water vapour mixes with air, led him to a question the four elements could not answer: why do substances combine in fixed proportions? On 21 October 1803 he read a paper to the Manchester Literary and Philosophical Society that ended with the first table of atomic weights, and in 1808 he set out the full theory in A New System of Chemical Philosophy.

The theory had four claims. Every element consists of tiny indivisible atoms. All atoms of one element are identical in weight; atoms of different elements differ. Atoms are neither created nor destroyed in a reaction, only rearranged. And compounds form when atoms join in small whole-number ratios. The last claim made a prediction, the law of multiple proportions: if carbon forms two different oxides, the oxygen in them must come in a simple ratio. It does. For a fixed mass of carbon, carbon dioxide holds exactly twice the oxygen of carbon monoxide. Dalton drew his atoms as circles, a dot for hydrogen, an empty ring for oxygen, a black disc for carbon, and joined them into little diagrams of molecules that look like Lego.

Did you know? Dalton was colour-blind and published the first scientific account of the condition in 1794; he left his eyes to science, and a DNA test in 1995 confirmed he lacked the green-sensitive pigment.

He also made a famous mistake. Lacking any way to count atoms, Dalton assumed the simplest possible formula, so water was HO, one hydrogen to one oxygen, and oxygen's atomic weight came out at 7 instead of 16. Joseph Gay-Lussac found in 1808 that gases combine in simple ratios by volume, and Amedeo Avogadro proposed in 1811 that equal volumes of gas contain equal numbers of molecules, which fixes the formulas, but chemists ignored him for half a century. Only at the Karlsruhe Congress of 1860, when Stanislao Cannizzaro handed out a pamphlet reviving Avogadro's rule, did atomic weights settle into the values we use.

Even then atoms were a bookkeeping device to many chemists; nobody had seen one. Einstein's 1905 paper on Brownian motion, the jittering of pollen grains in water observed by Robert Brown in 1827, predicted exactly how far a grain should wander if it was being kicked by molecules, and Jean Perrin's measurements in Paris in 1908 matched. Perrin's number for the molecules in a mole, close to 6 × 10²³, won him the 1926 Nobel Prize and ended the argument.

Today atomic masses are measured to ten decimal places, and a scanning tunnelling microscope, invented in 1981, shows individual atoms as bumps on a surface. The 2019 redefinition of the mole fixed Avogadro's number at exactly 6.02214076 × 10²³. Dalton's indivisible atoms turned out to have parts, which the next chapters will dismantle, but his central claim stands: chemistry is atoms counted.

Mendeleev's Table

By 1869 chemists knew 63 elements and had no idea why there were so many or how they related. Dmitri Mendeleev, a professor in St Petersburg writing a textbook, was sorting them for his students. On 1 March 1869 (17 February in the Russian calendar) he produced a table in which the elements were arranged in order of atomic weight and lined up so that elements with similar chemistry fell in the same column. Lithium, sodium and potassium, the soft metals that fizz in water, stacked together; so did fluorine, chlorine and bromine.

Others had seen the pattern. John Newlands in London had proposed a "law of octaves" in 1865 and been laughed at; Lothar Meyer in Germany published a very similar table in 1870. What set Mendeleev apart was his nerve. Where the pattern demanded an element nobody had found, he left a gap and predicted its properties: eka-aluminium, eka-boron and eka-silicon, with atomic weights, densities and the compounds they would form. He also swapped elements out of weight order when their chemistry required it, insisting that some atomic weights must have been measured wrongly.

The predictions came true with uncomfortable precision. In 1875 Paul-Émile Lecoq de Boisbaudran in Paris discovered gallium by its spectrum; Mendeleev wrote to say the measured density was wrong and it should be about 5.9. Lecoq re-purified his sample and found 5.9. Scandium followed in 1879 in Sweden and germanium in 1886 in Freiberg, with an atomic weight of 72.6 against a predicted 72. A table that forecasts the unknown is a theory, not a filing system.

Did you know? The story that the table came to Mendeleev in a dream rests on a friend's later recollection; his surviving drafts show days of shuffling cards marked with each element's weight and properties.

The table still had puzzles. Argon, discovered in 1894 by Lord Rayleigh and William Ramsay, fitted nowhere until Ramsay found helium, neon, krypton and xenon and gave the noble gases a column of their own. And tellurium weighs more than iodine yet clearly belongs before it. The explanation came in 1913 from Henry Moseley, a 26-year-old in Manchester, who fired electrons at each element and measured the X-rays that came out. Their frequencies rose in exact steps, and the step number, the atomic number, was the count of positive charge in the nucleus. Elements are ordered by protons, not weight, and the gaps between the numbers showed exactly which elements were still missing. Moseley was killed at Gallipoli two years later.

The modern table has 118 elements, the last four named in 2016, and its shape reflects how electrons fill shells. Mendeleev knew nothing of electrons, shells or nuclei. He found the order by trusting a pattern over the data, and the pattern was right.

Discovering the Electron

The first crack in Dalton's indivisible atom appeared in a glass tube. Pump most of the air out of a tube with a metal plate at each end, apply a few thousand volts, and a faint glow streams from the negative plate, the cathode, towards the positive one. By the 1870s William Crookes in London was making these tubes and showing that the "cathode rays" cast shadows and could turn a tiny paddle wheel. Were they waves, as most German physicists thought, or particles, as the British suspected? Heinrich Hertz had tried to bend them with an electric field in 1883 and failed, which seemed to settle it for waves.

J. J. Thomson, head of the Cavendish Laboratory in Cambridge, suspected that Hertz's vacuum had been too poor: leftover gas had shielded the rays. With a better pump he tried again in 1897 and the beam bent towards the positive plate. The rays were negatively charged particles. Then he did something cleverer. He applied a magnetic field as well and adjusted it until the magnetic push exactly cancelled the electric one, which gave the particles' speed; switching the electric field off and measuring the magnetic curve then gave the ratio of charge to mass. The ratio was enormous, more than a thousand times larger than for a hydrogen ion. Either the charge was huge or the mass was tiny, and other evidence pointed to the mass. Thomson announced on 30 April 1897 that the atom contained particles, which he called "corpuscles", about two thousandths of the mass of hydrogen, and that they were the same whatever gas or metal the tube was made of.

Did you know? Thomson won the 1906 Nobel Prize for showing the electron is a particle; his son George won the 1937 prize for showing it is also a wave.

The name electron came from George Johnstone Stoney, who had coined it in 1891 for the unit of charge. The charge itself was pinned down by Robert Millikan in Chicago between 1909 and 1913. He sprayed oil droplets between two charged plates, watched single droplets through a microscope, and adjusted the voltage until each hung still against gravity. Every droplet's charge was a whole-number multiple of one value, 1.6 × 10⁻¹⁹ coulombs. Charge comes in lumps, and the electron is one lump. With charge and charge-to-mass ratio known, the mass followed: 1/1836 of a proton.

Thomson pictured the atom as a positively charged pudding with electrons stuck in it like plums; Rutherford's nucleus would demolish that in 1911. But the electron itself has never been divided. It has no measurable size, it carries every electric current, it shapes every chemical bond, and the beam that Thomson bent in a glass tube was still painting pictures on television screens a century later.

Rutherford's Nucleus

In 1909 the atom was a pudding. Thomson's model spread the positive charge evenly through a sphere about a ten-billionth of a metre across, with electrons dotted inside, and nearly everyone accepted it. Ernest Rutherford, a New Zealander running the physics department in Manchester, had a tool to test it: alpha particles, the heavy, fast, positively charged fragments thrown out by radium. Fired through thin metal, they should pass almost straight, nudged a fraction of a degree by the diffuse charge. He asked his assistant Hans Geiger and a twenty-year-old undergraduate, Ernest Marsden, to look for any that scattered through large angles. It was a job to keep a student busy.

The apparatus was simple and the work was miserable. A speck of radium emanation in a lead block sent a narrow beam of alphas at a sheet of gold leaf about 400 nanometres thick, roughly 2,000 atoms. Where an alpha struck a zinc sulphide screen it made a flash, and Geiger and Marsden sat in a darkened room for hours, eyes adapted, counting flashes through a microscope at each angle. Most alphas went straight through. But about one in 8,000 bounced back, deflected by more than 90 degrees.

Did you know? Rutherford said it was "almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you".

No pudding could do that. A diffuse positive charge cannot turn a fast, heavy alpha around; the sums give a maximum deflection of a fraction of a degree, even summed over 2,000 layers of atoms. Rutherford worked through the alternative in 1910 and published it in 1911: nearly all the atom's mass and all its positive charge sit in a tiny central nucleus, less than a hundred-thousandth of the atom's width, and the electrons orbit far outside. An alpha that happened to pass close to a nucleus felt a violent electrical repulsion and recoiled. His formula predicted exactly how the count of flashes should fall with angle, and Geiger and Marsden's 1913 measurements, more than 100,000 flashes, matched it.

The picture was almost absurd. If an atom were the size of a cathedral, its nucleus would be a fly, and the rest is empty space held open by electrical forces. Hantaro Nagaoka in Tokyo had proposed a "Saturnian" atom with a central mass in 1904, but without evidence. Rutherford's version had a problem too: orbiting electrons should radiate energy and spiral into the nucleus in a fraction of a nanosecond. Niels Bohr, visiting Manchester in 1912, fixed that the following year with quantised orbits, and the modern atom was born.

The experiment is now the template for all of particle physics: fire a beam at a target, count what scatters where, and infer the structure inside. The Large Hadron Collider is Geiger and Marsden's dark room scaled up by a factor of a billion, and the question is the same: what is in there?

Protons and Neutrons

Rutherford's nucleus was tiny, positive and heavy, and nobody knew what it was made of. The first ingredient came from Rutherford himself. In Manchester in 1917, in experiments he published in 1919, he fired alpha particles through nitrogen gas and found hydrogen nuclei flying out: an alpha had struck a nitrogen nucleus and knocked out a piece of it, turning nitrogen into oxygen. The hydrogen nucleus was evidently a building block of all nuclei, and in 1920 he named it the proton.

Protons alone did not add up. Helium has a charge of two protons but the mass of four; the extra mass had to come from something neutral. Rutherford guessed in 1920 at a neutral particle, a proton and electron bound tightly together, and his Cavendish colleague James Chadwick spent a decade failing to find it. The clue came from elsewhere. In 1930 Walther Bothe and Herbert Becker in Giessen bombarded beryllium with alpha particles and found it gave off a penetrating radiation that passed through centimetres of lead; they assumed it was gamma rays. In January 1932 Irène Curie and Frédéric Joliot in Paris put paraffin wax in its path and found that the radiation knocked protons out of the wax at high speed. They still called it gamma rays, which Chadwick thought impossible: light has no mass, and a massless ray cannot bat a proton forward like a billiard ball.

Chadwick had the beryllium source ready and worked for about a fortnight almost without sleep. He measured the recoil of nitrogen and of hydrogen nuclei struck by the radiation, applied the laws of collision, and showed that the projectile had roughly the mass of a proton and no charge. His letter to Nature, "Possible Existence of a Neutron", was dated 17 February 1932. The Nobel Prize followed in 1935.

Did you know? A free neutron is unstable: outside a nucleus it decays into a proton, an electron and an antineutrino with a half-life of about ten minutes. Inside most nuclei it lives for ever.

The neutron explained everything at once. Werner Heisenberg proposed within months that nuclei are protons and neutrons held by a new short-range force; the mass numbers worked, isotopes were simply nuclei with different neutron counts, and Enrico Fermi in Rome found in 1934 that slow neutrons, having no charge to repel them, slip into nuclei and transmute them. Four years later Otto Hahn and Fritz Strassmann in Berlin found that neutrons split uranium, and Lise Meitner and Otto Frisch, exiled in Sweden, explained the fission over Christmas 1938. Six years from a letter to a bomb.

A proton has a mass of 1.0073 atomic units, a neutron 1.0087, and the modern periodic table is a count of the first; the number of the second varies and makes the isotopes of the next chapter. Everyday matter is three particles: protons, neutrons and electrons. It took from 1897 to 1932, and the hardest one to find was the one with no charge to show.

Isotopes

Dalton said all atoms of an element were identical. They are not quite. Chlorine's atomic weight, 35.5, had bothered chemists for decades: why would nature choose a half? The answer is that chlorine is a mixture of two kinds of atom, one weighing 35 units and one 37, in a ratio of about three to one. Atoms of the same element with different masses are isotopes, from the Greek for "same place", because they occupy the same square of the periodic table.

The word was coined in 1913 by Frederick Soddy in Glasgow, who had found that radioactive decay produced substances chemically identical to known elements but with different masses and half-lives. The name itself was suggested over dinner by Margaret Todd, a doctor and family friend. The same year J. J. Thomson in Cambridge, steering beams of positive ions through electric and magnetic fields onto a photographic plate, saw neon make two parabolas, one at mass 20 and a fainter one at mass 22. His assistant Francis Aston built a far better instrument after the war, the mass spectrograph of 1919, which focused ions of each mass to a sharp line. Neon was two lines, in a ratio of about nine to one; Aston went on to find 212 of the 287 naturally occurring isotopes and won the 1922 Nobel Prize. Nearly every mass was close to a whole number, which made sense once Chadwick's neutron arrived: an isotope is a nucleus with the same protons and a different number of neutrons.

Did you know? Tin has ten stable isotopes, more than any other element, because its 50 protons form an unusually stable "magic" configuration.

Hydrogen has three. Ordinary hydrogen is a lone proton; deuterium, found by Harold Urey in 1931, adds a neutron and makes "heavy water"; tritium adds two and is radioactive. Uranium is mostly uranium-238, with 0.7 per cent uranium-235, and the whole business of enrichment is sorting those two by their 1 per cent difference in mass. Carbon-14, made in the upper atmosphere by cosmic rays, decays with a half-life of 5,730 years; Willard Libby realised in 1949 that its slow disappearance from dead wood, bone or cloth gives a clock, and radiocarbon dating has since dated the Dead Sea Scrolls, Ötzi the Iceman and the Shroud of Turin.

Stable isotopes keep records too. Water containing oxygen-18 evaporates slightly less readily than ordinary water, so the ratio in ice cores and seashells tracks ancient temperature; Willi Dansgaard read the Greenland ice this way from the 1950s. The ratio of carbon isotopes in a steak tells you whether the cow ate maize or grass; the strontium in a tooth records where a person grew up.

Medicine uses isotopes by the million. Technetium-99m, with a six-hour half-life, is injected for tens of millions of scans a year, and iodine-131 treats thyroid disease. Mass spectrometers, Aston's instrument refined, now weigh single proteins and sniff explosives at airports. Dalton's identical atoms turned out to come in several weights, and the differences are some of science's most useful handles.

Radioactivity

Radioactivity was found by accident on a cloudy day. In February 1896 Henri Becquerel in Paris was testing whether uranium salts, which glow after exposure to sunlight, also gave off the newly discovered X-rays. He wrapped a photographic plate in black paper, laid uranium crystals on it, and put the package in the sun. The plate fogged, as expected. Then the sky clouded over, and he left a prepared plate in a drawer for several days with the uranium on top. On 1 March, expecting a faint image at best, he developed it anyway and found the silhouette as strong as ever. Sunlight had nothing to do with it; the uranium was emitting something by itself, continuously, without any input of energy.

Marie Curie, a Polish student in Paris looking for a thesis topic, took up the puzzle in 1897 with an instrument her husband Pierre had designed, an electrometer that measured how strongly a sample ionised the air. She found that the effect depended only on the amount of uranium, not its chemical form, so it had to come from inside the atom, and she coined the word "radioactivity". Pitchblende ore was four times more active than its uranium content allowed. Something else was in there. By July 1898 the Curies had isolated a new element they named polonium after her homeland, and by December a second, radium, so active that it glowed in the dark. Getting a tenth of a gram of pure radium chloride took four years and tonnes of ore stirred in a leaking shed.

Did you know? Marie Curie's laboratory notebooks are still radioactive; the Bibliothèque nationale keeps them in lead-lined boxes, and readers sign a waiver.

Ernest Rutherford, then in Montreal, sorted the emissions by what stopped them. Alpha rays were blocked by a sheet of paper; beta rays needed millimetres of aluminium; gamma rays, identified by Paul Villard in 1900, penetrated centimetres of lead. Alphas turned out to be helium nuclei, betas fast electrons, gammas very energetic light. With Frederick Soddy in 1902 Rutherford established the strangest fact of all: a radioactive atom changes into an atom of a different element when it decays, and every kind of atom does so at its own fixed rate, measured by its half-life. Radium-226 takes 1,600 years for half of any sample to go; polonium-214 takes 160 microseconds; uranium-238 takes 4.5 billion years, which is why there is still uranium in the ground, and why its decay products can date the Earth.

Radioactivity turned out to be the first glimpse of the nucleus, the source of the alpha particles Rutherford used to find it, and the energy source of the Sun's slower cousin, the Earth's hot interior. Today it drives smoke alarms (americium-241), PET scans (fluorine-18, half-life 110 minutes), radiotherapy for cancer, radiocarbon dating and the thermoelectric generators on the Voyager probes. The Curies shared the 1903 Nobel Prize with Becquerel; Marie won a second, alone, in 1911, and died in 1934 of a blood disorder almost certainly caused by the element she had discovered.

Making New Elements

Nature's periodic table stops at uranium, element 92. Everything heavier decays too fast to have survived since the Earth formed, so if you want it, you have to make it, by firing one nucleus at another and hoping they stick. Since 1940 four laboratories have added 26 elements this way, and the competition between them has been one of the longest in science.

Berkeley went first. In 1940 Edwin McMillan and Philip Abelson, using the 60-inch cyclotron, bombarded uranium with neutrons and found element 93, neptunium. That winter Glenn Seaborg's team made plutonium, element 94, which two years later became the heart of a bomb. Seaborg then realised that the heavy elements formed a second row of rare earths, the actinides, and rearranged the bottom of the table accordingly; his group made americium, curium, berkelium and californium by 1950, and found einsteinium and fermium in 1952 in the debris of the first hydrogen bomb test. Element 106 was named seaborgium in 1997, while he was still alive.

The Soviet Union answered from Dubna, where Georgy Flerov founded a laboratory in 1957. The 1960s and 1970s became the "transfermium wars", with Berkeley and Dubna each claiming elements 102 to 105 and disputing the other's evidence, a quarrel not settled by the chemistry unions until 1997. Dubna's lasting contribution came from Yuri Oganessian, who worked out that firing calcium-48, a rare neutron-rich isotope, at targets of plutonium, americium and californium made nuclei that survived long enough to detect. With that method, and American targets from Livermore and Oak Ridge, Dubna produced elements 114 to 118 between 1998 and 2010; element 118, oganesson, is only the second element named after a living person.

Did you know? Seaborg could receive letters addressed entirely in element symbols: Sg (seaborgium), Lr (Lawrencium Lab), Bk (Berkeley), Cf (California), Am (America).

Germany's GSI in Darmstadt took a different route. Peter Armbruster and Gottfried Münzenberg used "cold fusion", gentle collisions of medium-weight nuclei on lead or bismuth, and a velocity filter called SHIP that picked out the single new atoms from a flood of beam. Bohrium came in 1981, meitnerium in 1982, hassium in 1984, and darmstadtium, roentgenium and copernicium between 1994 and 1996, often from a handful of atoms each.

Japan's RIKEN institute, under Kosuke Morita, spent nine years firing zinc at bismuth to make element 113, detecting three atoms in total, in 2004, 2005 and 2012. In 2016 it was named nihonium, the first element discovered in Asia, and with moscovium, tennessine and oganesson it completed the seventh row of the table.

These atoms exist for milliseconds. A few atoms of oganesson have ever been made, each lasting under a thousandth of a second, so "discovery" means a decay chain recorded in a detector, not a sample in a bottle. The prize that keeps the laboratories going is the "island of stability", a predicted region near 114 protons and 184 neutrons where superheavy nuclei might live for minutes or years. Nobody has reached it. Element 119 is being hunted at RIKEN and Dubna now.

Inside the Proton: Quarks

By 1960 the proton was supposed to be elementary, but the particle accelerators built after the war were turning up dozens of its heavier cousins, and physicists began to suspect that protons, like atoms before them, had parts. In 1964 Murray Gell-Mann at Caltech and, independently, George Zweig at CERN proposed that every such particle was built from three kinds of smaller object with the embarrassing property of fractional charge: two thirds and minus one third of the electron's. Gell-Mann called them quarks, after a line in James Joyce's Finnegans Wake, "Three quarks for Muster Mark!". A proton is two "up" quarks and one "down" (2/3 + 2/3 − 1/3 = 1); a neutron is one up and two down. Gell-Mann himself was unsure whether quarks were real or a mathematical convenience.

The evidence came from Stanford. The two-mile linear accelerator at SLAC fired electrons of 20 billion electronvolts at liquid hydrogen, and a team led by Jerome Friedman, Henry Kendall and Richard Taylor measured how the electrons scattered. If the proton were a soft blob, the electrons should glance off at small angles. In 1968 they found far too many scattering at large angles, exactly the pattern Geiger and Marsden had seen with gold foil sixty years earlier: the electrons were hitting hard, point-like lumps inside. Richard Feynman called the lumps partons; they were quarks, and the three won the 1990 Nobel Prize.

Did you know? No one has ever seen a single quark on its own, and the theory says no one ever will: pulling two apart takes so much energy that new quark pairs form, and you end up holding two particles instead of one.

What holds the quarks together is the strong force, carried by particles called gluons, described from 1973 by quantum chromodynamics. Each quark carries a kind of charge called "colour", and the force between colours does something no other force does: it gets stronger with distance, like an elastic band. Up close, quarks move almost freely, which is why SLAC could see them; pulled apart, they are confined for ever. Gluons were seen directly in 1979, as three-pronged jets of particles at the PETRA collider in Hamburg.

The proton's mass is the strangest part. Its two up quarks and one down weigh, together, about 9 million electronvolts, a hundredth of the proton's 938. The rest is the energy of the gluon field and the swarm of quark–antiquark pairs that flicker in and out of existence inside, converted to mass by E = mc². Almost everything you weigh is therefore not stuff but confined energy. Supercomputer calculations of the theory reproduce the proton's mass to within a per cent.

Quarks come in six flavours; the heaviest, the top quark, found at Fermilab in 1995, weighs as much as a gold atom and lives for a trillionth of a trillionth of a second. Whether quarks themselves have parts is unknown; at the Large Hadron Collider they behave as points down to a ten-thousandth of a proton's width. Democritus's uncuttable atom has been cut three times, and the last cut, so far, holds.

Chemical Bonds

A chemical bond is what happens when two atoms find it cheaper, in energy, to stay together than to stay apart. Atoms are electrically neutral but their outer electrons are restless, and most atoms are more stable when that outer shell is full. Sodium has one spare electron; chlorine is one short. Sodium hands its electron over, both become charged ions, and the opposite charges lock together into salt. That is an ionic bond. Two hydrogen atoms, each with one electron and each wanting two, solve the problem by sharing: a covalent bond. In a lump of copper the outer electrons belong to no atom in particular and drift through the whole crystal, a metallic bond, which is why metals conduct electricity and can be hammered into sheets.

The idea that bonds are about pairs of electrons was set out in 1916 by Gilbert Lewis at the University of California, Berkeley, in a paper titled The Atom and the Molecule. The same year Walther Kossel in Munich described the ionic case. Linus Pauling then made the picture quantitative. Working at Caltech in the 1930s he used the new quantum mechanics to explain bond lengths and angles, and in 1932 he published a scale of electronegativity, a number from about 0.7 for caesium to 4.0 for fluorine that says how greedily an atom pulls shared electrons towards itself. The gap between two atoms' numbers predicts the character of their bond.

The evidence came from X-rays. In 1913 William Henry Bragg and his son William Lawrence Bragg at Leeds and Cambridge fired X-rays through crystals of sodium chloride and read the atomic positions from the diffraction pattern. There were no molecules of salt at all, only an endless lattice in which every sodium ion is surrounded by six chloride ions. The same method, pushed much further by Dorothy Hodgkin at Oxford, revealed the bonded structure of penicillin in 1945 and of vitamin B12 in 1956, work that won her the 1964 Nobel Prize in Chemistry.

Did you know? The hydrogen bond, a weak attraction between molecules rather than a true bond, is why water boils at 100 °C instead of around minus 80 °C, which is what its small size would otherwise predict.

Bond strength can be measured as the energy needed to break it. Pulling apart one mole of hydrogen molecules takes 436 kilojoules; a carbon–carbon single bond needs about 347, and a nitrogen–nitrogen triple bond 945, which is why nitrogen gas is so inert and why making fertiliser from it is such hard work. Diamond, a single giant covalent network, is the hardest natural material; graphite, the same element arranged in sheets held together by weak forces, writes on paper.

Today bond theory is the working language of drug design, where the fit between a molecule and a protein comes down to a handful of hydrogen bonds; of materials science, where the bonding in silicon makes the transistor possible; and of every battery and catalyst in this part of the book. Chemistry, in the end, is the study of which bonds break and which ones form.

Reactions and Equations

A chemical reaction is a rearrangement. Bonds break, atoms regroup, new bonds form, and the atoms themselves survive untouched. Burn methane in air and one carbon atom with four hydrogens meets two oxygen molecules; what leaves is one molecule of carbon dioxide and two of water. Written as an equation, CH4 + 2O2 → CO2 + 2H2O, the same number of each kind of atom appears on both sides. That bookkeeping is not a convention. It is a law of nature, and it was established with a balance.

The balance belonged to Antoine Lavoisier, a Paris tax collector with a private laboratory and the most precise instruments money could buy. In the 1770s he heated tin and lead in sealed glass vessels and weighed everything before and after. The metal gained weight; the air lost exactly as much. In his 1789 textbook Traité élémentaire de chimie he stated the principle of conservation of mass: in every operation, an equal quantity of matter exists before and after. His wife Marie-Anne Paulze Lavoisier drew the apparatus, kept the laboratory notebooks and translated the English chemists he argued with. The Russian polymath Mikhail Lomonosov had argued for the same principle in 1756, though historians of science debate how widely his work was read.

Lavoisier's law made quantitative chemistry possible. Joseph Proust showed in 1799 that a compound always contains its elements in fixed proportions by mass; Jöns Jacob Berzelius introduced the letter symbols, H, O, Fe, in 1813; and the idea of the mole, a fixed count of particles, let chemists convert grams into numbers of atoms. One mole is 6.022 × 10²³ particles, so the equation for burning hydrogen, 2H2 + O2 → 2H2O, says that two grams of hydrogen need exactly sixteen grams of oxygen and give eighteen grams of water. Nothing else, and nothing left over.

Did you know? Lavoisier was guillotined in May 1794 during the Terror; the mathematician Lagrange remarked that it took an instant to cut off his head and a hundred years might not produce another like it.

Reactions also have a speed and a direction. Iron rusts over years, 4Fe + 3O2 → 2Fe2O3, while thermite, iron oxide and aluminium powder, does the reverse in seconds at over 2,000 °C, hot enough to weld railway track. Some reactions give out heat, some soak it up, and many run both ways at once until they settle at an equilibrium, an idea Claude Louis Berthollet first proposed after watching sodium carbonate crystallise on the shores of Egyptian salt lakes in 1798.

Balanced equations now run industry. The five F-1 engines of a Saturn V rocket burned around thirteen tonnes of kerosene and liquid oxygen every second in precisely metered proportions. A pharmaceutical plant calculates yield to the kilogram; a climate model counts every molecule of carbon dioxide produced per tonne of coal. Lavoisier's balance has become the ledger of the planet.

Acids and Bases

Lemon juice is sour, soap is slippery, and for most of history that was the definition. An acid tasted sharp and turned the blue dye of litmus lichen red; a base, or alkali, felt soapy and turned it back. Robert Boyle was using plant extracts as indicators in the 1660s. What acids actually were took another two centuries to pin down.

The first modern answer came from a doctoral thesis that nearly failed. In 1884 Svante Arrhenius at Uppsala proposed that salts, acids and bases split into charged ions when dissolved in water, and that an acid is anything that releases hydrogen ions, H⁺, while a base releases hydroxide, OH⁻. His examiners gave the thesis the lowest passing grade. In 1903 the same idea won him the Nobel Prize in Chemistry. In 1923 Johannes Brønsted in Copenhagen and Thomas Lowry in Cambridge independently widened the definition: an acid is any proton donor and a base any proton acceptor, which explains why ammonia, which contains no hydroxide at all, is a base. The same year Gilbert Lewis went further still and defined acids as electron-pair acceptors.

The number everyone uses came from beer. In 1909 Søren Sørensen, head of chemistry at the Carlsberg Laboratory in Copenhagen, needed a convenient way to track acidity during brewing and enzyme experiments. Hydrogen-ion concentrations ranged over many powers of ten, so he took the negative logarithm and called it pH. Each step on the scale is a tenfold change: pH 2 is ten times more acidic than pH 3, and a hundred times more than pH 4. He measured it with a hydrogen electrode; the glass electrode, invented the same year by Fritz Haber and Zygmunt Klemensiewicz, became the pH meter on every laboratory bench.

Did you know? Nobody is sure what the p in pH stands for. Sørensen wrote it as a subscript and never explained it; "power of hydrogen" and the Latin pondus hydrogenii are both later guesses.

The scale runs from roughly 0 to 14 and the familiar landmarks are vivid. Gastric juice sits around pH 1.5 to 3.5, strong enough to dissolve a nail, which is why the stomach replaces its lining every few days. Lemon juice is about 2, black coffee around 5, pure water exactly 7, blood held within a narrow band of 7.35 to 7.45, seawater about 8.1 and household bleach around 12.5. Since the industrial revolution the surface ocean has fallen by about 0.1 pH units as it absorbs carbon dioxide, which sounds small but means roughly thirty per cent more hydrogen ions, enough to trouble the corals and shellfish that build shells from carbonate.

Acids and bases run daily life. Antacid tablets are bases that neutralise excess stomach acid; baking powder is an acid and a base waiting for water; farmers add lime to sour soil and vintners measure pH before every fermentation. Sørensen's brewery shorthand turned out to be the most used number in chemistry.

Catalysts and Enzymes

Most reactions that can happen do not happen, or not quickly, because the molecules must first climb an energy hill. Hydrogen and oxygen can sit mixed in a flask for years. Strike a spark, or drop in a speck of platinum, and they combine explosively. The platinum is still there afterwards. A catalyst is a substance that speeds up a reaction without being used up, and it does so by offering an easier path over the hill, a lower activation energy.

The word was coined in 1835 by Jöns Jacob Berzelius in Stockholm, who collected a set of puzzling observations: Gottlieb Kirchhoff turning starch into sugar with a trace of acid in 1812, Johann Döbereiner's lamp of 1823 that lit a hydrogen jet by passing it over platinum sponge, and Humphry Davy's glowing platinum wires. Berzelius called the hidden power catalysis, from the Greek for loosening. Wilhelm Ostwald gave the modern definition and in 1909 won the Nobel Prize for it; his nitric acid process, passing ammonia over hot platinum gauze, is still used. Svante Arrhenius had shown in 1889 that reaction rates rise exponentially as the activation energy falls, which is why a small drop in the hill produces an enormous gain in speed.

Living things worked this out first. Every cell runs thousands of reactions at body temperature that a chemist would need heat, pressure and strong acid to force, and it does so with protein catalysts called enzymes. In 1897 Eduard Buchner in Tübingen ground up yeast, filtered out every living cell and found the juice still fermented sugar into alcohol: catalysis needed no life force, only molecules. James Sumner at Cornell crystallised the enzyme urease in 1926 and proved it was a protein, a result colleagues doubted for a decade before it earned him the 1946 Nobel Prize. Emil Fischer's 1894 lock-and-key image, refined by Daniel Koshland's induced fit in 1958, explains the selectivity: each enzyme has a pocket shaped for one substrate.

Did you know? The enzyme carbonic anhydrase in your blood processes about a million carbon dioxide molecules every second, and some enzymes speed their reactions by a factor of ten million billion.

The numbers are startling. Without catalysts, the Haber process would need temperatures that destroy the product; with iron, it runs. A car's catalytic converter, introduced in 1975 and built around platinum, palladium and rhodium, turns carbon monoxide and nitrogen oxides into carbon dioxide, nitrogen and water before they leave the exhaust. Around ninety per cent of industrial chemical processes rely on a catalyst at some stage.

Catalysts and enzymes now sit everywhere: in washing powder, where enzymes digest grass stains at 30 °C; in lactose-free milk; in the zeolites that crack crude oil into petrol; and in the engineered enzymes that make modern antidiabetic drugs in a single step. The hill is still there. Chemists have simply learned to dig tunnels through it.

Combustion and Fire

Fire is the oldest chemistry and it was among the last to be understood. For most of the eighteenth century the accepted theory held that burning things released a substance called phlogiston. The idea, from Johann Becher and Georg Stahl in Germany, explained a great deal, except that metals gained weight when they burned, which meant phlogiston would need negative mass. Chemists lived with the contradiction for seventy years.

The theory fell to a balance and a gas. In 1774 Joseph Priestley, a dissenting minister in Wiltshire, heated the red powder of mercury with a lens and collected a gas in which a candle burned with a fierce bright flame; the Swedish apothecary Carl Wilhelm Scheele had made the same gas earlier but published later. Priestley told Antoine Lavoisier about it over dinner in Paris. Lavoisier repeated and extended the experiments, weighed everything, and by 1777 had the answer: combustion is the rapid combination of a fuel with this gas, which he named oxygen, and the heat and light are released as new, stronger bonds form. Nothing leaves the fuel; something joins it. Scientists sometimes call this the chemical revolution, and it is the reason the modern list of elements begins with Lavoisier.

The best introduction to what a flame actually is remains a series of Christmas lectures for children. In 1848 Michael Faraday stood at the Royal Institution in London with a candle and showed that the wax does not burn where you think. Heat melts the wax, the wick draws it up, the flame vaporises it, and only the vapour burns. The dark zone around the wick is unburned gas; the bright yellow region glows because tiny particles of soot are heated to around 1,200 °C, incandescent like a lamp filament; the faint blue edge at the bottom is where the vapour meets enough oxygen to burn completely. Hold a cold spoon in the yellow zone and it comes out black with soot. Hold it in the blue and it comes out clean.

Did you know? In orbit, with no gravity to draw hot gas upwards, a candle flame is a dim blue sphere and burns far more slowly, as experiments on the International Space Station have shown.

Combustion needs three things, and firefighters draw them as a triangle: fuel, oxygen and heat. Remove any one and the fire stops. Water removes heat; a foam blanket or a carbon dioxide extinguisher removes oxygen; a firebreak removes fuel. Paper ignites on its own at roughly 230 °C, petrol vapour at around 250 °C, and a methane flame can reach 1,950 °C in air. Burning one kilogram of methane releases about 55 megajoules, with the equation CH4 + 2O2 → CO2 + 2H2O giving nearly three kilograms of carbon dioxide.

That last number is why combustion matters now. Around four fifths of the world's energy still comes from burning fuel, and every tonne of coal, oil or gas burned adds its carbon dioxide to the atmosphere. Lavoisier's bookkeeping has become the central problem of the century.

Electrochemistry and Batteries

A battery is a chemical reaction held apart. In any reaction where one substance gives up electrons and another takes them, you can separate the two halves, connect them with a wire and make the electrons travel the long way round. That travelling is an electric current, and the study of it is electrochemistry.

It began with a frog and an argument. In the 1780s Luigi Galvani in Bologna noticed that a dead frog's leg twitched when touched by two different metals and concluded that animals contained their own electricity. Alessandro Volta in Pavia disagreed: the metals, not the frog, were the source. To prove it he stacked discs of zinc and silver separated by cardboard soaked in brine, and in a letter to the Royal Society in London dated March 1800 described the first steady source of current, the voltaic pile. Within weeks William Nicholson and Anthony Carlisle used one to split water into hydrogen and oxygen; within seven years Humphry Davy at the Royal Institution had used a huge pile to isolate potassium, sodium, calcium and four more new elements. Michael Faraday then showed in 1834 that the mass of a substance produced at an electrode is exactly proportional to the charge that passed, and coined the words electrode, anode, cathode and ion with the help of the classicist William Whewell.

The practical battery improved step by step. John Daniell's copper-zinc cell of 1836 gave a steady 1.1 volts for telegraphs; Gaston Planté's lead-acid cell of 1859 was the first that could be recharged and still starts most cars; Georges Leclanché's 1866 zinc-carbon cell became the dry cell in every torch.

Did you know? Volta demonstrated his pile to Napoleon in Paris in 1801; the emperor made him a count, and the volt, the unit of electrical potential, is named after him.

The modern leap was lithium, the lightest metal and the most eager to give up an electron. In the 1970s Stanley Whittingham at Exxon showed lithium ions could slip in and out of layered titanium disulfide. In 1980 John Goodenough at Oxford found a far better cathode, lithium cobalt oxide, which doubled the voltage. Akira Yoshino at Asahi Kasei in Japan replaced the dangerous lithium-metal anode with carbon in 1985, and Sony sold the first commercial lithium-ion cell in 1991. The three shared the 2019 Nobel Prize in Chemistry. In such a cell, lithium ions shuttle between a graphite anode and a metal-oxide cathode through a liquid electrolyte, while a porous separator keeps the electrodes from touching. A good cell stores around 250 watt-hours per kilogram, seven times a lead-acid battery, at 3.7 volts.

Electrochemistry also runs the other way. Push current in and you can plate chrome onto steel, refine copper to 99.99 per cent, or make aluminium, which was a precious metal until Charles Hall and Paul Héroult independently electrolysed it in 1886. Every phone, electric car and grid storage bank is Volta's pile, reinvented.

Carbon: the Chemistry of Life

Carbon is the sixth element, a black smudge on a cold day and the hardest stone in a jeweller's window. It makes up only about 0.03 per cent of the Earth's crust, yet roughly ten million known compounds contain it, more than all the other elements put together. The reason is simple. A carbon atom has four outer electrons and wants four more, so it forms four strong covalent bonds, and it bonds to itself as readily as to anything else. Chains, branches, rings and sheets follow, and from those every protein, sugar, fat, fuel and plastic is built.

The study of these compounds was once a separate science, because people assumed they could only be made by living things, a doctrine called vitalism. In 1828 Friedrich Wöhler in Berlin heated ammonium cyanate, a mineral salt, and obtained urea, a substance previously found only in urine. "I must tell you that I can make urea without needing a kidney," he wrote to his teacher Berzelius. Historians of science debate how quickly the idea of a life force died, but organic chemistry had become ordinary chemistry.

The shape of carbon came next. August Kekulé in Ghent proposed in 1858 that carbon is tetravalent and forms chains, and in 1865 that benzene is a ring of six carbons. The famous story that the ring came to him in a dream of a snake biting its tail was told by Kekulé himself only in 1890, and historians treat it cautiously. In 1874 Jacobus van 't Hoff in Utrecht and Joseph Le Bel in Paris independently argued that the four bonds point to the corners of a tetrahedron, which explained why Louis Pasteur had found, in 1848, that some molecules exist as mirror-image pairs that rotate light in opposite directions. Your body is built almost entirely from one hand of each pair.

Did you know? The same carbon atoms can be a diamond or the lead in a pencil; the only difference is how they are bonded, and graphite is in fact the more stable form at room temperature.

Pure carbon alone comes in several forms. In diamond every atom bonds to four neighbours in a rigid lattice; in graphite the atoms form flat sheets of hexagons that slide over each other. In 1985 Harold Kroto from Sussex, with Robert Curl and Richard Smalley at Rice University in Texas, vaporised graphite with a laser and found a stable cluster of exactly sixty atoms arranged like a football, buckminsterfullerene. In 2004 Andre Geim and Konstantin Novoselov at Manchester peeled a single sheet of graphite from a flake with sticky tape and showed it was a material in its own right, graphene, one atom thick and about two hundred times stronger than steel by weight.

Carbon chemistry is now the chemistry of medicine, fuel and climate. The carbon cycle moves about 100 billion tonnes of the element through the air each year, and the extra eleven billion tonnes or so from fossil fuels, counted in the same molecules, are the thread connecting this chapter to the warming world.

Plastics and Polymers

A polymer is a molecule built by repetition: thousands of identical small units, called monomers, joined end to end into a chain. Cellulose, rubber, silk and DNA are polymers; so are polythene bags, nylon tights and the case of the device you may be reading this on. The chains can be straight, branched or cross-linked, and that architecture, more than the chemistry of any single unit, decides whether the material is a soft film or a bulletproof vest.

The first plastics were modified natural polymers. Alexander Parkes showed Parkesine, made from cellulose nitrate, at the 1862 International Exhibition in London; John Wesley Hyatt improved it in the United States as celluloid in 1869, a substitute for ivory in billiard balls and later the base of photographic film. The first fully synthetic plastic came from Leo Baekeland, a Belgian chemist working in Yonkers, New York, who in 1907 reacted phenol with formaldehyde under heat and pressure and got a hard, heat-resistant resin he called Bakelite. It moulded into telephones, radio cases and electrical insulators and made him rich.

Nobody yet knew what these materials were. The prevailing view was that they were clusters of small molecules held loosely together. In 1920 Hermann Staudinger at ETH Zurich argued that they were genuine giant molecules, macromolecules, with ordinary covalent bonds along a chain of thousands of atoms. Senior colleagues told him to drop the subject; he was proved right over the next decade and received the Nobel Prize in 1953. The proof came partly from Wallace Carothers at DuPont, who built polymers to order from small molecules, producing neoprene in 1930 and, in 1935, nylon, the first fully synthetic fibre. Nylon stockings went on sale in May 1940 and sold out within days.

Did you know? Polyethylene was discovered by accident at ICI in 1933, when a high-pressure experiment on ethylene leaked and left a waxy white solid; it became the most produced plastic on Earth.

The second half of the century brought precision. In 1953 Karl Ziegler in Mülheim found catalysts that joined ethylene at low pressure into strong, regular chains, and Giulio Natta in Milan used them the next year to make polypropylene; they shared the 1963 Nobel Prize. Stephanie Kwolek at DuPont produced an unexpectedly thin, cloudy solution in 1965 that spun into a fibre five times stronger than steel by weight: Kevlar. PET bottles, Teflon pans, silicone implants and acrylic paint followed.

The world now makes over 400 million tonnes of plastic a year, and only around nine per cent of what has ever been made has been recycled. Chains that resist bacteria for decades are a virtue in a water pipe and a problem in the ocean, where fragments smaller than five millimetres, microplastics, have been found from the deepest trench to Arctic snow. Chemists are now designing polymers that unzip back into their monomers on demand, which would turn Staudinger's giant molecules into a loop rather than a line.

Fertilisers and the Haber Process

Four fifths of the air is nitrogen, and almost none of it is any use to a plant. The two atoms in a nitrogen molecule are held by a triple bond, one of the strongest in chemistry, and only lightning, a few soil bacteria and, since 1909, a steel reactor can break it. Breaking it is the single most important industrial reaction on Earth, because the nitrogen in every protein in your body came through one of the three routes.

The problem was stated bluntly in 1898 by William Crookes, president of the British Association, who warned that the world's wheat fields would run out of nitrogen within a generation. The main sources at the time were guano from Peruvian islands and sodium nitrate from the Chilean desert, both finite. Fritz Haber, a chemist at the Technical University of Karlsruhe, took on the direct synthesis of ammonia from its elements. The reaction N2 + 3H2 ⇌ 2NH3 is reversible and only goes forward usefully at high pressure, yet heat, which speeds it up, also drives it backwards. Haber and his British assistant Robert Le Rossignol found the window: around 200 atmospheres, around 500 °C, a catalyst, and a loop that removes the ammonia as liquid and recirculates the unreacted gas. On 2 July 1909 their tabletop apparatus produced liquid ammonia drop by drop at a rate of roughly a cupful an hour, using an osmium catalyst.

Scaling that to a factory fell to Carl Bosch at BASF in Ludwigshafen. No steel vessel had ever held such pressure at such heat; hydrogen attacked the metal and made it brittle. Bosch's engineers designed a double-walled reactor with a soft iron liner, and Alwin Mittasch tested around 2,500 candidate catalysts in some 6,500 experiments before settling on cheap iron with traces of potassium and aluminium oxides, still used today. The plant at Oppau opened in September 1913. Haber received the Nobel Prize in 1918, Bosch in 1931.

Did you know? Roughly half of the nitrogen atoms in your body have passed through a Haber–Bosch reactor, because about half the world's food is grown with synthetic fertiliser.

The process has a dark side. The same ammonia made explosives, and Germany fought the First World War on nitrates from Oppau after the British blockade cut off Chile. Haber himself directed the first chlorine gas attack at Ypres in 1915. Today the world makes about 150 million tonnes of ammonia a year, consuming one to two per cent of global energy and releasing around 1.4 per cent of carbon dioxide emissions, mostly from making the hydrogen out of natural gas.

Fertiliser built the modern population curve. Yields of wheat, rice and maize tripled in the twentieth century, and Vaclav Smil estimates that without synthetic nitrogen the planet could feed perhaps three billion fewer people. Run-off from the same fertiliser feeds algal blooms in the Gulf of Mexico and the Baltic. Engineers are now trying to make the hydrogen with renewable electricity, so that the triple bond is broken without burning gas. The reaction is the same one Haber watched drip into his flask.

Green Chemistry

For most of its history chemistry measured success by yield: how much product came out compared with the theoretical maximum. It said nothing about what else came out. In 1991 Barry Trost at Stanford proposed a second number, atom economy: what fraction of the atoms that go into a reaction end up in the product rather than in waste. The next year Roger Sheldon in Delft published the E-factor, kilograms of waste per kilogram of product, and the figures were sobering. Oil refineries produced about 0.1 kilograms of waste per kilogram; fine chemicals 5 to 50; pharmaceuticals 25 to 100 or more. Making a kilogram of a drug could mean throwing away a hundred kilograms of solvent, salt and spent reagent.

Green chemistry is the discipline that grew from those numbers. In 1998 Paul Anastas and John Warner set out twelve principles in a slim book: prevent waste rather than treat it, maximise atom economy, use safer solvents, design for energy efficiency, prefer renewable feedstocks, use catalysts rather than stoichiometric reagents, and design products that break down harmlessly at the end of their life. None of this was new chemistry. It was a new way of judging it.

The textbook case is ibuprofen. The original Boots synthesis from the 1960s took six steps and used about forty per cent of its atoms; the rest became waste, including aluminium chloride that could not be recovered. In 1992 the BHC company, a Hoechst-Celanese venture, opened a plant in Bishop, Texas, that made the same molecule in three catalytic steps with an atom economy of seventy-seven per cent, rising to ninety-nine when the acetic acid by-product was recovered and sold. It won one of the first Presidential Green Chemistry Challenge Awards in 1997. Later examples go further: in 2010 Merck and Codexis replaced a metal-catalysed, high-pressure step in making the diabetes drug sitagliptin with an engineered enzyme working in water, cutting waste by nineteen per cent and the process to a single vessel.

Did you know? Decaffeinated coffee was once made with the solvent benzene, a known carcinogen; most is now made with supercritical carbon dioxide, which dissolves caffeine under pressure and simply evaporates afterwards.

The movement had a precedent in the atmosphere. In 1974 Mario Molina and Sherwood Rowland at Irvine calculated that chlorofluorocarbons, the inert and apparently harmless gases in fridges and aerosols, would break down in the stratosphere and destroy ozone. The Antarctic ozone hole was found in 1985; the Montreal Protocol banned the chemicals in 1987; and Molina, Rowland and Paul Crutzen shared the 1995 Nobel Prize. Designing a molecule now means asking where it goes afterwards.

Today the principles shape water-based paints, polylactic acid cups made from maize starch, enzyme-washed denim and lithium-ion recycling. The questions chemists ask have changed. Not only can we make it, and how much, but what else did we make, where will it end up, and could the same bonds be formed a cleaner way.

Galileo's Falling Bodies

Drop a cannonball and a musket ball together and they land together. That is not obvious. Aristotle had taught that heavy things fall faster in proportion to their weight, and for two thousand years almost nobody checked. In 1586 the Flemish engineer Simon Stevin and his friend Jan de Groot dropped two lead balls, one ten times heavier than the other, about ten metres from a church tower in Delft and heard them hit the boards below as a single thud. Galileo Galilei, then a young lecturer at Pisa, was reaching the same conclusion by argument: tie a light stone to a heavy one and Aristotle's rule contradicts itself.

The famous demonstration from the Leaning Tower of Pisa appears only in a biography written by Galileo's assistant Vincenzo Viviani decades after the event, and historians of science doubt it ever happened. What Galileo certainly did was slower and cleverer. Free fall is too fast to time with the instruments of 1600, so he diluted it. He cut a straight groove in a wooden beam about twelve cubits long, lined it with polished parchment, tilted it, and let a bronze ball roll down, timing it with a water clock: water ran from a tank into a cup for the duration of the roll and was then weighed. He described the work in a 1604 letter to Paolo Sarpi and published it in 1638, in Two New Sciences, written under house arrest.

The result was a pattern. In the first unit of time the ball covered one unit of distance; in the second, three; in the third, five; in the fourth, seven. The odd numbers add up to squares, 1, 4, 9, 16, so the distance fallen grows as the square of the time. The ball was not moving at constant speed but at constant acceleration, and the acceleration was the same whatever the ball's weight. Tilting the plane more steeply raised the acceleration without changing the law, so the vertical limit, free fall, must obey it too. Near the Earth's surface that acceleration is 9.8 metres per second every second.

Did you know? In August 1971 the Apollo 15 astronaut David Scott dropped a geological hammer and a falcon feather side by side on the Moon, where there is no air; they hit the dust at the same instant, on live television.

Air is the only reason a feather drifts. Its drag grows with speed until it balances the pull of gravity, which is why a skydiver stops accelerating at a terminal velocity of about 55 metres per second and a raindrop at a gentle few metres per second. Remove the air, as Robert Boyle did with his air pump in 1660, and a feather and a coin dropped inside the glass fall together.

Galileo's deeper gift was the method: idealise the problem, strip away the air, measure what can be measured and let mathematics describe the rest. Every experiment in this book descends from a bronze ball rolling down a groove.

Newton's Three Laws

In 1684 the astronomer Edmond Halley rode to Cambridge to ask Isaac Newton a question that had stumped the Royal Society: what path would a planet follow if the Sun pulled on it with a force that fell off as the square of the distance? Newton said he had already worked it out, an ellipse, but could not find the paper. Halley persuaded him to write it up, paid for the printing himself, and on 5 July 1687 the Philosophiae Naturalis Principia Mathematica appeared. Its opening pages state three laws of motion that still govern every bridge, rocket and billiard ball.

The first law says that a body keeps its state of rest or uniform straight-line motion unless a force acts on it. This is inertia, and it was the hard one, because everyday experience says the opposite: a cart stops when the horse stops. Galileo had seen that friction was the hidden force; Descartes had stated the principle in 1644; Newton made it the foundation. A puck on a frictionless rink would slide for ever. A spacecraft coasting between planets needs no engine at all.

The second law says that a force changes a body's motion in proportion to its size and in the direction it pushes. Newton wrote it in terms of change of momentum; the schoolroom form, force equals mass times acceleration, F = ma, was given by Leonhard Euler in 1750. Push twice as hard, accelerate twice as fast; push a body twice as heavy, accelerate half as much. The unit of force, the newton, is what accelerates one kilogram at one metre per second per second, roughly the weight of an apple.

The third law says that forces come in pairs: when one body pushes on another, the second pushes back equally and oppositely. The rifle recoils as the bullet leaves; the Earth rises to meet a falling stone by an imperceptible amount; a rocket climbs by hurling exhaust downwards and needs no air to push against, which is why it works in space.

Did you know? The story of the apple comes from Newton himself, who told it in old age to William Stukeley in 1726; he said he watched one fall in his mother's garden at Woolsthorpe and wondered why it fell straight down, not that it struck his head.

The laws were tested with increasing precision. In 1784 George Atwood at Cambridge hung two nearly equal masses over a pulley so that gravity's pull was almost cancelled and the acceleration could be timed by eye, confirming the second law directly. Today they are checked to extraordinary accuracy by tracking spacecraft and by the lunar laser retroreflectors left by Apollo astronauts, which measure the Moon's distance to a few millimetres.

Newton's laws fail only at the extremes: near the speed of light, where Einstein's relativity takes over, and at atomic scales, where quantum mechanics does. Everywhere in between, from a seatbelt locking in a crash to the 7.7 kilometres per second of a satellite, the three sentences of 1687 are enough.

Universal Gravitation

The idea in Newton's law of universal gravitation is that the force pulling an apple to the ground is the same force holding the Moon in its orbit, and that it acts between every pair of masses in the universe. The pull is proportional to the product of the two masses and falls off as the square of the distance between them: double the distance and the force drops to a quarter. Newton checked it against the Moon. The Moon is sixty times farther from the Earth's centre than the apple, so it should fall 3,600 times more slowly, and it does: about 1.4 millimetres every second, which is exactly the amount needed to keep it curving around the Earth instead of flying off in a straight line.

That calculation, published in the Principia in 1687, explained Kepler's elliptical orbits, the tides, the bulge of the Earth at the equator and the paths of comets. In 1705 Edmond Halley used it to predict that the comet of 1682 would return in 1758. It appeared on Christmas night 1758, sixteen years after his death.

But Newton's law contained a number nobody knew: the gravitational constant, G, the strength of the pull between two one-kilogram masses a metre apart. It is tiny, and measuring it meant detecting the gravity of a lead ball in a room. The apparatus was designed by the clergyman John Michell and, after his death, rebuilt in 1797 by Henry Cavendish, a wealthy and painfully shy chemist, in a shed at Clapham in south London. A wooden rod 1.8 metres long with a small lead ball at each end hung from a thin wire. Two 158-kilogram lead spheres were swung close to the small balls, and their gravity twisted the wire by a hair. Cavendish read the twist through a telescope from outside the room, so that his own body heat would not stir the air, and published in 1798. He expressed his result as the density of the Earth, 5.45 times that of water, within one per cent of the modern value. The Earth, it followed, weighs about six thousand billion billion tonnes.

Did you know? The gravitational pull between two people standing a metre apart is about a hundred-billionth of their weight; gravity rules the cosmos only because it adds up, and never cancels, across whole planets.

The law's reach became spectacular. In 1846 Urbain Le Verrier in Paris calculated, from wobbles in the orbit of Uranus, where an unknown planet must be; Johann Galle in Berlin found Neptune within one degree of the predicted spot the night the letter arrived. The same law guides every spacecraft.

Today G is known to about one part in fifty thousand, still the least precisely measured fundamental constant, and physicists continue to argue over discrepancies between laboratories. Newton's law itself turned out to be a superb approximation to Einstein's general relativity, which replaces the pull with curved spacetime. For the apple, the Moon and the probes leaving the solar system, the 1687 formula remains all you need.

Friction

Rub your hands together and they warm up. Slam the brakes and the car stops. Try to push a wardrobe and it refuses, then suddenly gives. All three are friction, the force that resists sliding between two surfaces in contact, and it is at once the most familiar force in daily life and one of the last to be understood at the level of atoms.

Its laws were written down twice. Leonardo da Vinci, in notebooks from around 1493, slid blocks across tables and recorded that the resistance was proportional to the load pressing the surfaces together and did not depend on how big the contact area was. He never published. Two hundred years later, in 1699, the French physicist Guillaume Amontons rediscovered both rules and presented them to the Académie des Sciences in Paris, and in 1785 Charles-Augustin de Coulomb, in a prize essay on friction in ropes and machines for the French navy, added a third: for sliding surfaces the force is roughly independent of speed. He also made clear the difference between static friction, which must be overcome to start a motion, and the smaller kinetic friction that resists it once under way. That is why the wardrobe lurches.

The rules are summed up in a single number, the coefficient of friction, which is the ratio of the friction force to the load. Rubber on dry asphalt scores about 0.8, which is why tyres grip; the same rubber on wet ice about 0.1; steel on ice around 0.03, which is why skates glide; and Teflon on Teflon about 0.04, the lowest of any solid, which is why it lines frying pans.

Did you know? Two polished steel blocks touch at so few points that their real area of contact is typically less than one ten-thousandth of what it appears to be; the rest is air.

Why area does not matter puzzled physicists until the 1930s and 1940s, when Frank Philip Bowden and David Tabor at Cambridge showed with electrical measurements that even a mirror-finished surface is, on the scale of a micrometre, a mountain range. Two surfaces meet only at the tips of their highest peaks, the asperities, which are squashed until they can carry the load. Press harder and more peaks make contact, so the real contact area grows in proportion to the load while the apparent area is irrelevant. Friction is the force needed to shear those tiny welded junctions. Lubrication works by floating the surfaces apart on a film of oil, an effect Osborne Reynolds explained mathematically in 1886 and which keeps every engine bearing alive.

Friction is now the subject of a science, tribology, with an economic weight to match: a 2017 study estimated that overcoming friction consumes about a fifth of the world's energy. Engineers reduce it with ball bearings, diamond-like coatings and air cushions, and exploit it in brakes, clutches and the soles of shoes. A force known to Leonardo is still being discovered.

Pressure and Fluids

Pressure is force spread over an area, and in a fluid it pushes equally in every direction. The air above you weighs about ten tonnes per square metre, and you do not notice because the same pressure pushes up, sideways and from inside. That the air has weight at all was discovered in a single decade of the seventeenth century, by men trying to understand why a pump could not lift water more than about ten metres.

In 1643 Evangelista Torricelli, Galileo's last assistant, filled a glass tube a metre long with mercury, upended it in a dish, and watched the column fall until it stood about 760 millimetres high, leaving an empty space above it. Nothing was pulling the mercury up, he reasoned; the weight of the atmosphere pressing on the dish was holding it up, and the space above was a vacuum. "We live submerged at the bottom of an ocean of air," he wrote later. The device was the barometer, and the height of the column, 760 millimetres of mercury, is still one way to write standard atmospheric pressure, now defined as 101,325 pascals.

Blaise Pascal saw the test. If the column is held up by the weight of air, there should be less air, and a shorter column, up a mountain. On 19 September 1648 his brother-in-law Florin Périer carried a barometer to the summit of the Puy de Dôme in central France, about a thousand metres above the town of Clermont, and watched the mercury fall by more than eight centimetres. Pascal went on to state the principle that bears his name: pressure applied to an enclosed fluid is transmitted undiminished throughout it, which is why a hydraulic jack lets a hand lift a lorry and why the brakes of a car work.

Did you know? In 1654 Otto von Guericke, mayor of Magdeburg, pumped the air from two fitted copper hemispheres and had two teams of horses try to pull them apart; the atmosphere held, and the hemispheres came apart only when he let air back in.

Robert Boyle in Oxford, with his assistant Robert Hooke, built a better pump and in 1662 published the law that a gas's pressure rises as its volume shrinks. Daniel Bernoulli in Basel showed in 1738 that in a moving fluid the pressure falls where the speed rises, the principle behind a perfume atomiser and part of the story of a wing. Pressure also grows with depth: every ten metres of seawater adds another atmosphere, so the Mariana Trench at eleven kilometres presses with about 1,100 atmospheres, and the submersibles that reach it carry their crews in spheres of titanium or thick glass.

Pressure is now measured everywhere. A blood-pressure cuff reads 120 over 80 in Torricelli's millimetres of mercury; a weather map draws lines of equal pressure to forecast storms; a car tyre holds about two atmospheres above the air outside; a pressure cooker raises the boiling point of water to 120 °C. The ocean of air that Torricelli described is still being weighed, every hour, at every weather station on Earth.

Buoyancy and Flight

A steel ship floats, a steel nail sinks, and a 560-tonne airliner climbs away from a runway on nothing but air. All three come down to the same principle: a fluid pushes harder on the underside of an object than on the top, and if the difference exceeds the object's weight, the object rises.

Archimedes of Syracuse worked out the floating case around 250 BC in On Floating Bodies. A body in a fluid is pushed upward by a force equal to the weight of the fluid it displaces. A nail displaces a thimble of water, which weighs far less than the nail; a hull displaces hundreds of tonnes of water, more than the ship, so the ship rises until the displaced water exactly balances its weight. The story that he shouted "Eureka" and ran naked from a bath after realising he could test the purity of a king's crown this way was told by the Roman architect Vitruvius two centuries later; Galileo, among others, doubted the method described would have been sensitive enough. The buoyancy principle itself, however, is exact, and it is why hot-air balloons rise: the Montgolfier brothers' balloon of 1783 displaced cold air that weighed more than the hot air inside plus the envelope and passengers.

Lift on a wing is the same force in a moving fluid. In 1799 George Cayley in Yorkshire set out the four forces of flight, lift, weight, thrust and drag, and realised a fixed wing could do the lifting while a separate engine did the pushing. Otto Lilienthal in Berlin made some two thousand glides in the 1890s and published tables of lift for curved wings; he died in a crash in 1896. Wilbur and Orville Wright, bicycle makers in Dayton, Ohio, found his numbers unreliable and in late 1901 built a wind tunnel, a wooden box 1.8 metres long with a fan, in which they tested around two hundred model wings on a delicate balance. The correct data gave them a wing that worked. On 17 December 1903 at Kitty Hawk, North Carolina, the Flyer rose for twelve seconds and 36 metres.

Did you know? The popular explanation that air over a curved wing must "catch up" with air underneath is wrong; wind-tunnel smoke shows the air above arrives at the trailing edge first, and flat-winged paper planes fly perfectly well.

What actually happens is that a wing tilted slightly into the airflow deflects air downwards. By Newton's third law the air pushes the wing up; equivalently, the air flowing over the top speeds up and its pressure falls, as Bernoulli described, while the air below slows and its pressure rises. The two descriptions are the same physics seen from two sides, and the mathematics of a circulating flow around a wing was worked out by Martin Kutta in Germany and Nikolai Zhukovsky in Russia between 1902 and 1906.

The same physics lifts a helicopter, pushes a sailing boat upwind, spins a wind turbine and makes a curved football swerve. Two thousand years apart, the bath and the wind tunnel were measuring the same push.

Momentum and Collisions

Momentum is mass times velocity, and in any collision the total momentum of the colliding bodies is the same afterwards as before. A ten-tonne lorry at walking pace carries the same momentum as a one-tonne car at ten times the speed. The rule applies to billiard balls, galaxies, and the particles in an accelerator, and it is one of the few laws of physics with no known exception.

It was settled by competition. In 1668 the newly founded Royal Society in London asked for the laws of collision, and three replies arrived within months: from the mathematician John Wallis, the architect Christopher Wren and, from The Hague, Christiaan Huygens. Wallis handled soft collisions, where bodies stick; Wren and Huygens the hard, bouncing kind. Huygens had worked it out years earlier by imagining the collision seen from a boat drifting past a canal bank at steady speed, an early use of the idea that the laws of physics look the same to any observer in uniform motion. All three agreed that the quantity of motion, mass times velocity with direction counted, was conserved. Newton built it into the Principia in 1687 as the consequence of his third law: two colliding bodies push on each other equally and oppositely, so whatever momentum one gains the other loses.

The classic demonstration is the row of steel balls on strings known as a Newton's cradle, which the French physicist Edme Mariotte was showing to the Académie in the 1670s. Lift one ball and release it; one ball flies out at the far end, and the middle ones barely stir. Lift two and two fly out. The momentum travels through the row as a compression wave, and the pattern is fixed because both momentum and, in a hard collision, kinetic energy must be conserved together.

Did you know? In 1930 Wolfgang Pauli proposed the neutrino, an invisible particle no one had detected, purely because momentum and energy seemed to go missing in radioactive beta decay; it was found in 1956.

In a soft collision kinetic energy is not conserved; it becomes heat and deformation, while momentum still is. That distinction saves lives. A car hitting a wall must lose all its momentum, and the force on the occupants depends on how quickly it happens, since force is the rate of change of momentum. The crumple zone, patented by the Hungarian engineer Béla Barényi at Mercedes-Benz in 1952, lengthens the crash from a few milliseconds to a tenth of a second and cuts the force by the same factor; seatbelts that stretch and airbags that deflate do the same job for the body inside.

Rockets are the law in reverse. Hot gas thrown backward at three or four kilometres per second carries momentum, and the rocket gains the same amount forward; Konstantin Tsiolkovsky wrote the equation for it in 1903. Every satellite launch, every recoiling gun and every tackle on a rugby pitch is settled by the answer three men sent to the Royal Society in 1668.

Circular Motion and Orbits

Swing a stone on a string and the string pulls inward all the time; let go and the stone flies off in a straight line, not outward. A body moving in a circle is constantly accelerating towards the centre, and something must supply that inward pull. Newton called it centripetal force, and the mathematics, worked out by Christiaan Huygens in 1659 and published in 1673, says the force needed grows with the square of the speed and shrinks with the radius. Take a bend twice as fast and the tyres must grip four times as hard.

Newton's great leap was to see that an orbit is nothing but a fall that keeps missing. In A Treatise of the System of the World, written in the 1680s and published in 1728, he imagined a cannon on a high mountain. Fired gently, the ball lands nearby. Fired harder, it lands farther, because the Earth's surface curves away beneath it. Fired at about eight kilometres per second, the ball falls towards the Earth exactly as fast as the ground curves away, and it never lands. The Moon is such a cannonball. It falls towards the Earth by about 1.4 millimetres every second, and in the same second its sideways motion carries it a kilometre, so the two together trace a circle.

The numbers were confirmed on 4 October 1957, when the Soviet Union's Sputnik 1 reached orbit at about 7.8 kilometres per second and circled the planet every 96 minutes. The International Space Station, at an altitude of 400 kilometres, moves at 7.66 kilometres per second and completes an orbit in 93 minutes. The astronauts inside are not beyond gravity; at that height it is still ninety per cent of its strength at the surface. They float because they and their station are falling together, and nothing presses them against the floor.

Did you know? The science-fiction writer Arthur C. Clarke proposed in 1945 that a satellite 35,786 kilometres above the equator would orbit in exactly one day and so hang motionless in the sky; the geostationary belt now carries hundreds of them.

Higher orbits are slower. At 35,786 kilometres a satellite takes 24 hours, matching the Earth's rotation, which is why a television dish can point at a fixed spot in the sky. Go faster than about 11.2 kilometres per second from the surface and no orbit closes at all; the body escapes. The Voyager probes crossed that line in 1977 and are now leaving the solar system.

Circular motion is everywhere closer to home. A washing machine's drum spins clothes against its wall and lets the water through the holes; a salad spinner does the same. A centrifuge spinning at thousands of revolutions per minute separates blood into plasma and cells, or uranium isotopes by their tiny difference in mass. And every time a car corners and you feel pushed against the door, it is the door pushing you around the bend while your body tries, as Newton's first law insists, to carry straight on.

Levers, Pulleys and Gears

"Give me a place to stand and I will move the Earth." The line attributed to Archimedes, reported by Pappus of Alexandria six centuries later, is a boast about the lever, and it is physically correct. A rigid bar pivoting on a fulcrum multiplies force in proportion to the lengths of its two arms: push down on an arm ten times longer than the other and you lift ten times your effort, though you must push ten times as far. According to Plutarch, Archimedes made the point to King Hiero of Syracuse by hauling a loaded ship across the beach single-handed with a system of ropes and pulleys, around 250 BC.

That trade is the secret of every simple machine. Force multiplied by distance is work, and no machine gives out more work than it takes in; it only exchanges a large force over a short distance for a small force over a long one, or the reverse. Hero of Alexandria listed five such machines in the first century AD: the lever, the wheel and axle, the pulley, the wedge and the screw. The ratio of the load lifted to the effort applied is the mechanical advantage. A wheelbarrow is a lever with the fulcrum at the wheel; a pair of tweezers is a lever working the other way, trading force for delicacy; a human forearm is one too, with the elbow as fulcrum and the biceps pulling close to it, which is why the hand moves fast but cannot lift much.

A pulley redirects a rope; a block with several pulleys shares the load among several lengths of it. With four ropes supporting the load, each carries a quarter of the weight and the hand pulls four metres of rope for every metre the load rises. A modern tower crane's hook block runs on multiple falls of wire for exactly the same reason.

Did you know? The Antikythera mechanism, recovered from a shipwreck in 1901 and dated to around 100 BC, contains at least thirty bronze gears cut by hand to model the motions of the Sun, Moon and planets, a thousand years ahead of any other known geared device.

Gears are levers that keep turning. Two meshed wheels trade speed for torque in the ratio of their tooth counts: a ten-tooth gear driving a thirty-tooth one turns three times for each turn of the other and delivers three times the twisting force. Clocks, mills, cars and the gearbox of a wind turbine, which steps a rotor's slow twenty turns a minute up to a generator's fifteen hundred, are all Archimedes' bar bent into a circle.

Friction takes its share, so real machines return somewhat less work than they receive, and the ancient dream of a machine that gives back more than it takes, a perpetual motion machine, violates the rule Hero never quite stated and Galileo did. The place to stand was never found. The lever, the pulley and the gear still move the world a piece at a time.

Chaos and the Limits of Prediction

Newton's laws promised that if you knew where everything was and how fast it was moving, you could compute the future. Pierre-Simon Laplace said as much in 1814. The promise is true and useless at the same time, because for most real systems the slightest error in the starting point grows until the prediction is worthless. That discovery is chaos, and it came not from new laws but from old ones computed carefully.

The first warning was Henri Poincaré's. In 1890, trying to prove the solar system stable for a prize offered by the King of Sweden, he found that three bodies pulling on one another by Newton's law could follow paths of bewildering complexity, in which a tiny change at the start produced a wholly different outcome. The idea lay dormant for seventy years.

It woke up in a weather model. In the winter of 1961 Edward Lorenz, a meteorologist at the Massachusetts Institute of Technology, was running a simplified atmosphere of twelve equations on a Royal McBee LGP-30 computer, programmed with the help of Ellen Fetter and Margaret Hamilton. Wanting to re-examine a run, he typed in the numbers from a printout, which showed three decimal places, instead of the six the machine held internally: 0.506 instead of 0.506127. The new weather tracked the old for a while, then diverged until the two were unrecognisable. The difference of one part in five thousand had grown to fill the whole system. Lorenz published Deterministic Nonperiodic Flow in 1963, with three equations whose solutions trace a shape like a pair of butterfly wings, now called the Lorenz attractor. In 1972 he gave a talk whose title, supplied by a colleague, asked whether the flap of a butterfly's wings in Brazil could set off a tornado in Texas, and the butterfly effect had its name.

Did you know? Lorenz did not say the butterfly causes the tornado. His point was that the atmosphere cannot be known precisely enough to say which small disturbance did what, so forecasts have a horizon of roughly two weeks however good the computers become.

Through the 1970s the pattern turned up everywhere. The biologist Robert May showed in 1976 that a one-line equation for an animal population could flip from steady to oscillating to chaotic as a single number was turned up. Mitchell Feigenbaum at Los Alamos found that the route to chaos through doubling periods obeys a universal constant, 4.669, the same for dripping taps, electronic circuits and heartbeats. David Ruelle and Floris Takens coined the term strange attractor in 1971, and Benoît Mandelbrot's fractals supplied the geometry.

Chaos set limits, and then taught people to work within them. Weather services now run an ensemble of fifty forecasts from slightly different starting points and report how far they agree, a method the European Centre for Medium-Range Weather Forecasts adopted in 1992. The laws are still Newton's. The future is still determined. It is simply not, beyond a point, predictable.

What Is Energy?

Ask a physicist what energy is and you may get an honest shrug. Richard Feynman told his students that physics has "no knowledge of what energy is", only a number that can be calculated for any system and that never changes while things happen inside it. That is the heart of the idea. Energy is the quantity that lets you pay for change. Lift a stone, boil a kettle, fire a neuron or launch a rocket, and a fixed sum must be handed over, drawn from one account and moved to another. The forms differ: motion, height, heat, chemical bonds, stretched springs, light, the nucleus of an atom. The currency is the same.

The idea took two centuries to settle. In 1686 Gottfried Leibniz argued that the "living force" of a moving body, his vis viva, was its mass times the square of its speed, not simply mass times speed as the followers of Descartes held. The decisive test came in Leiden around 1722, when Willem 's Gravesande dropped brass balls into soft clay from different heights. A ball travelling twice as fast made a dent four times as deep, not twice as deep. Émilie du Châtelet, working at Cirey in France, repeated and publicised the result in her Institutions de physique of 1740, and it was her account that carried the argument across Europe.

The word itself was chosen in 1807 by Thomas Young, lecturing at the Royal Institution in London, who borrowed the Greek energeia, "activity". Gaspard-Gustave Coriolis supplied the modern definition of work in 1829, force multiplied by distance, and fixed the factor of one half in the kinetic energy formula, ½mv². The unit, the joule, was adopted in 1889 and honours James Joule, who had shown that heat belonged in the ledger too.

A joule is small. Lifting an apple one metre costs about one joule. A slice of toast stores roughly 300,000 joules of chemical energy, enough to raise that apple to the height of Everest thirty times over. A family car at motorway speed carries around 700,000 joules of kinetic energy, which is why crumple zones exist. Sunlight arrives at the top of the atmosphere at 1,361 joules per second on every square metre, and a single lightning bolt releases about a billion joules in a few thousandths of a second.

Did you know? Thomas Young, who gave "energy" its scientific meaning, also made the first serious progress in deciphering the Rosetta Stone.

Today the energy ledger is kept everywhere: in the kilowatt-hours on an electricity bill, the kilocalories on a cereal box, the megajoules a battery engineer squeezes into a kilogram of lithium cells, and the joules per bit that decide how long a phone lasts. Nobody has ever seen energy itself. What we see, always, is the receipt.

Conservation of Energy

The first law of thermodynamics is bookkeeping with teeth: energy can change form but can never be created or destroyed. Pour it from motion into heat, from heat into steam, from steam into electricity and from electricity into light, and the total at the end equals the total at the start. The law sounds obvious now. In 1840 it was not even clear that heat was a form of energy at all. Most chemists still treated heat as caloric, an invisible fluid that flowed from hot bodies to cold ones and was conserved in its own right.

The idea arrived from several directions at once. In 1842 Julius Robert Mayer, a German ship's doctor who had noticed in the tropics of Java that sailors' venous blood ran unusually red, reasoned that their bodies burned less fuel in the heat, and published a paper claiming that heat and work were interchangeable at a fixed rate. Hermann von Helmholtz gave the principle its mathematical form in Berlin in 1847. But it was an amateur in Manchester who measured it.

James Prescott Joule, the son of a brewer, had the patience of a man used to waiting for beer to ferment. From 1843 he built an apparatus in which falling weights turned a brass paddle wheel inside an insulated copper vessel of water. The weights fell about 1.6 metres; he wound them back up and dropped them again, twenty times per run, while reading a thermometer he had commissioned that could be read to a two-hundredth of a degree Fahrenheit. The water warmed by barely half a degree. By 1850 he had his number: 772 foot-pounds of work raised one pound of water by one degree Fahrenheit. In modern units that is 4.15 joules per calorie, within one per cent of today's value of 4.184.

When Joule first presented his results at the British Association in Oxford in 1847, the chairman asked him to be brief and the paper was heading for silence until a young William Thomson, later Lord Kelvin, stood up and started asking questions. The two became lifelong collaborators.

Did you know? The conservation of energy is not a brute fact but a consequence of symmetry: Emmy Noether proved in 1918 that it follows from the laws of physics being the same today as tomorrow.

The law has been tested hardest where it seemed to fail. In the 1920s the electrons shot out of radioactive nuclei carried less energy than expected, and Niels Bohr was prepared to abandon conservation. Wolfgang Pauli instead proposed in 1930 an unseen particle carrying the missing share. The neutrino was detected in 1956, and the ledger balanced again. Every power station, every calorie count and every battery rating still rests on Joule's half a degree.

Heat and Temperature

Heat and temperature are not the same thing, and the difference took a century to pin down. Temperature is a measure of how vigorously the molecules of a substance are jiggling; heat is energy in transit from a hotter body to a colder one. A bathtub of warm water holds far more heat than a spark from a grinder, yet the spark is thousands of degrees hotter. Touch the bath and you are comfortable; touch the spark and you are burned only briefly, because there is so little of it.

Reliable thermometers came first. In 1714 Daniel Gabriel Fahrenheit, a glassblower working in Amsterdam, sealed mercury in a fine glass tube and produced instruments that agreed with one another, which no earlier thermometer had managed. Anders Celsius of Uppsala proposed a hundred-degree scale between the freezing and boiling points of water in 1742, though he ran it the wrong way round, with zero at boiling; the scale was inverted after his death. In 1848 William Thomson, later Lord Kelvin, argued that there must be a lowest possible temperature at which molecular motion ceases, and counted upwards from it. That absolute zero sits at minus 273.15 degrees Celsius.

The distinction between heat and temperature was the work of Joseph Black in Glasgow in the 1760s. Black noticed that a bucket of melting ice stays at zero degrees for hours while it steadily absorbs heat from the room. The energy was going somewhere without raising the temperature; he called it latent heat. Melting a kilogram of ice takes 334 kilojoules, and boiling a kilogram of water takes 2,260 kilojoules, more than five times what it took to heat the water from cold to boiling. Black also found that different substances need different amounts of heat to warm by one degree, their specific heat, and that water is unusually greedy.

What heat actually was remained open. The leading theory held it to be caloric, a weightless fluid. In Munich in 1798 Benjamin Thompson, Count Rumford, an American-born spy and administrator supervising the boring of brass cannon, noticed that a blunt borer produced heat without limit for as long as the horses kept turning it, enough to boil water in two and a half hours. A fluid that could be squeezed out endlessly was no fluid. Heat, he argued, was motion.

Did you know? The air molecules in a warm room are travelling at around 500 metres per second, faster than a rifle bullet, and collide billions of times a second.

The kinetic theory made this precise in the 1860s, when James Clerk Maxwell and Ludwig Boltzmann showed that temperature measures the average kinetic energy of molecules. Since 2019 the kelvin has been defined by fixing Boltzmann's constant exactly, so the unit of temperature now rests on the energy of molecular motion rather than any property of water. Your fever thermometer, your fridge and the cooling towers of every power station run on Black's distinction.

Engines and Thermodynamics

A heat engine turns heat into motion, and the first useful one was built to pump water out of a flooded coal mine. Thomas Newcomen's atmospheric engine of 1712, installed near Dudley in the English Midlands, filled a cylinder with steam, sprayed in cold water to condense it, and let the pressure of the atmosphere push the piston down. It was slow, enormous and wasteful: barely one per cent of the coal's heat became useful work. James Watt's separate condenser of 1765, patented in 1769, stopped the cylinder being cooled and reheated on every stroke and roughly trebled the efficiency. Watt's engines powered the mills and mines of the Industrial Revolution, and the unit of power still bears his name.

Nobody knew why engines wasted so much. The answer came from a young French army engineer, Sadi Carnot, in a slim book of 1824, Réflexions sur la puissance motrice du feu. Carnot imagined an ideal engine running an endless cycle: a gas expanding at a hot temperature, expanding further while cooling, being compressed at the cold temperature, then compressed back to the start. He proved that no engine working between two temperatures could do better than this one, and that its efficiency depended on nothing but those temperatures. In modern terms, the best possible fraction of heat turned to work is one minus the cold temperature divided by the hot, both measured in kelvin. An engine fed with steam at 550 degrees Celsius and cooled by a river at 25 can never beat about 64 per cent, whatever its design.

Carnot died of cholera in Paris in 1832, aged 36, and most of his papers were burned with his belongings. His book had sold poorly. It was rescued by Émile Clapeyron in 1834 and then by Rudolf Clausius in Germany and William Thomson in Glasgow, who in 1850 and 1851 turned Carnot's insight into the second law of thermodynamics: heat flows by itself only from hot to cold, and no engine can turn heat entirely into work. The first law says you cannot win; the second says you cannot break even.

Real engines have crept towards Carnot's ceiling ever since. Nikolaus Otto's four-stroke petrol engine of 1876 and Rudolf Diesel's compression-ignition engine of 1897 brought combustion inside the cylinder. A modern car engine converts around a third of its fuel's energy into motion; the rest leaves through the radiator and exhaust. The most efficient heat engines on Earth are combined-cycle gas turbines, which pass their hot exhaust through a steam plant and reach just over 60 per cent.

Did you know? Your refrigerator is a Carnot cycle run backwards: it uses work to pump heat from cold to hot, which is why the coils at the back are warm.

The same cycle, reversed, cools your food and heats your house. A heat pump moving warmth from the winter air into a living room delivers three or four joules of heat for every joule of electricity, the trick Carnot described on paper before anyone could build it.

Entropy and the Arrow of Time

Drop a glass and it shatters; it never reassembles. Milk stirred into coffee never unstirs. Yet every law of motion, from Newton's to Schrödinger's, runs equally well backwards. Film a planet orbiting and reverse the film, and nothing looks wrong. Film the glass and reverse it, and everyone laughs. The quantity that tells the two films apart is entropy, and the reason it always rises is, at bottom, arithmetic.

Rudolf Clausius coined the word in 1865, from the Greek for "transformation", to describe the heat an engine throws away divided by the temperature at which it throws it. His version of the second law of thermodynamics was stark: the entropy of the universe tends to a maximum. But Clausius's entropy was a bookkeeping quantity for engineers. What it meant for atoms was worked out by Ludwig Boltzmann in Vienna in 1877, in a formula later carved on his gravestone: S = k log W. Entropy equals a constant multiplied by the logarithm of W, the number of microscopic arrangements that look the same from outside.

The formula turns a law of nature into a matter of counting. Toss ten coins. There is one way to get ten heads and 252 ways to get five heads and five tails, so a random toss is 252 times more likely to look evenly mixed than perfectly ordered. Now toss a thousand million million million molecules, the number in a glass of water, and the ratio becomes so vast that "unlikely" means "never in the age of the universe". Cold milk and hot coffee mix because there are enormously more mixed arrangements than separated ones. Nothing forbids the milk from gathering back into a blob; it is simply outnumbered.

Arthur Eddington gave the effect its name in 1927, the arrow of time, and argued that entropy was the only law of physics that pointed one way. The puzzle this leaves is why the universe began in such a tidy state that it has been untidying ever since. The smooth, hot plasma of the early cosmos, revealed in the microwave background, was a low-entropy starting point whose origin scientists still debate.

Did you know? Boltzmann's tomb in Vienna's Zentralfriedhof carries S = k log W, though the formula in that exact form was first written by Max Planck.

Entropy has since escaped from physics. Claude Shannon showed in 1948 that the same formula measures information, with a bit as the unit, and Rolf Landauer found in 1961 that erasing one bit must release at least a minimum quantity of heat, which is why data centres need cooling. James Clerk Maxwell's imaginary demon, a tiny sorter who seemed able to beat the second law by watching molecules, was finally exorcised by this discovery: to forget what it has seen, the demon pays in entropy. The universe runs down because there are more ways to be messy than to be neat, and time, as far as physics can tell, is the direction in which the mess spreads.

What Is Light?

The first person to treat light as something that travels was Ibn al-Haytham, working in Cairo around 1021. Earlier Greek writers had imagined rays shooting out of the eye to feel the world; al-Haytham showed in his Book of Optics that light leaves luminous objects, bounces off everything else and enters the eye in straight lines, and he proved it with a darkened room and a pinhole, the camera obscura, where an upside-down image of the outside world appears on the far wall. What the travelling stuff actually was remained the question for 900 years.

Isaac Newton thought it was particles. His Opticks of 1704 described light as a stream of tiny "corpuscles" moving in straight lines, which neatly explained sharp shadows and reflection. Christiaan Huygens in The Hague had argued in his Traité de la Lumière of 1690 that light was a wave spreading through an invisible medium, each point on a wavefront acting as the source of a new ripple. For a century Newton's authority carried the day.

The decisive evidence came in London between 1801 and 1803. Thomas Young let sunlight through a pinhole, then through two closely spaced slits, and saw on the far screen not two bright stripes but a series of them: light added to light had produced darkness in regular bands. Only waves do that, by cancelling where crest meets trough. Young measured the spacing of the fringes and from it calculated the wavelength of light, about half a thousandth of a millimetre, a figure that still stands. In Paris in 1818 Augustin Fresnel's wave mathematics faced a famous test: Siméon Poisson pointed out that it predicted an absurd bright spot in the very centre of a round object's shadow. François Arago set up the experiment, and the spot was there.

What was waving was answered by James Clerk Maxwell in 1865. His equations of electricity and magnetism predicted waves travelling at a speed he computed from laboratory measurements of electric and magnetic constants, and the number matched the measured speed of light. Light was an electromagnetic wave, and Heinrich Hertz confirmed it in 1887 by making longer ones with a spark. The speed, 299,792,458 metres per second, is now fixed by definition and used to define the metre.

Did you know? The word "photon" was coined in 1926 by the chemist Gilbert Lewis, twenty-one years after Einstein described the particle it names.

Then the particles came back. In 1905 Albert Einstein explained why light shining on metal knocks out electrons only above a certain frequency, however bright it is: light arrives in packets of energy proportional to frequency. This photoelectric effect earned his Nobel Prize and runs every solar panel and digital camera sensor on Earth. Light is a wave when it travels and a particle when it lands, a double nature the next part of this book will take up. For now, the lesson of 900 years is that a good experiment beats a great authority.

Colour and the Spectrum

In 1666, at home in Woolsthorpe while plague closed Cambridge, Isaac Newton bored a small hole in a window shutter, let a beam of sunlight fall on a glass prism and caught the result on the far wall of the darkened room, twenty-two feet away. The beam fanned into an oblong of colour, red at one end and violet at the other. Prisms were a familiar toy; the usual explanation was that glass somehow stained the light. Newton's decisive move, his experimentum crucis, was to pass one colour from the fan through a second prism. Red stayed red. The glass added nothing. White light was a mixture, and the prism merely sorted it, bending violet more than red.

He reported the work to the Royal Society in 1672 and named seven colours, red, orange, yellow, green, blue, indigo and violet, a count chosen to match the seven notes of the musical scale rather than anything in the light itself. The spectrum is continuous. What we see depends on the eye: Thomas Young proposed in 1802, and Hermann von Helmholtz confirmed, that the retina holds three kinds of colour receptor, and in the 1960s physiologists measured the three cone pigments directly, most sensitive at roughly 420, 530 and 560 nanometres. Every screen you own exploits this by mixing just red, green and blue dots.

The spectrum turned out to be written on. In 1802 William Hyde Wollaston noticed dark gaps in the solar spectrum, and in 1814 the Bavarian glassmaker Joseph von Fraunhofer, testing prisms for the quality of his optical glass, mapped some 570 fine dark lines and labelled the strongest with letters still used today. Their meaning came in Heidelberg in 1859, when Gustav Kirchhoff and Robert Bunsen heated salts in Bunsen's new clean-burning gas flame and viewed the glow through a prism. Each element produced its own set of bright lines at fixed wavelengths, a fingerprint. Sodium's bright yellow pair sat exactly where Fraunhofer's dark D lines fell in sunlight: the Sun's atmosphere contains sodium, absorbing the same colours it would emit.

Spectroscopy was born, and the first harvest came fast. Bunsen and Kirchhoff discovered caesium in 1860 and rubidium in 1861 from lines nobody had seen before. In 1868 a yellow line in the Sun's spectrum matched no known element, and helium was named for the Sun twenty-seven years before it was found on Earth.

Did you know? Indigo is in the rainbow only because Newton wanted seven colours to match the musical scale; most people cannot pick it out at all.

Today every chemistry lab, every telescope and every satellite reads spectra. Astronomers know what distant stars are made of without leaving the ground, measure their speed from how their lines are shifted, and detect ozone and water in the atmospheres of planets orbiting other suns. Newton's hole in the shutter has become the most productive window in science.

Lenses, Mirrors and Telescopes

A lens is a piece of transparent material shaped so that light bends on the way in and the way out, and ends up converging to a point. The rule for how much it bends, the law of refraction, was written down in Baghdad in 984 by Ibn Sahl in a treatise on burning mirrors and lenses, six centuries before Willebrord Snell in Leiden derived the version that now carries his name. Reading stones, polished domes of quartz or glass laid on a page, were in use in monasteries by about 1000, and spectacles appeared in northern Italy around 1286, which is why portraits of scholars start to show them soon after.

The telescope arrived by accident and spread by rumour. In October 1608 Hans Lippershey, a spectacle maker in Middelburg in the Netherlands, applied for a patent on a tube with two lenses that made distant things look near. The patent was refused, because others claimed the same device, but news reached Venice by the following summer. Galileo Galilei ground his own lenses, pushed the magnification from three to about twenty, and in January 1610 pointed the instrument at Jupiter. Four small stars kept changing position night after night; they were moons, circling a world other than Earth. Johannes Kepler improved the design in 1611 by using two convex lenses, the layout of every refractor since.

Glass has a flaw: it bends blue light more than red, so a simple lens surrounds every bright object with coloured fringes. Isaac Newton decided the cure was to abandon lenses, and in 1668 built a telescope whose main element was a curved metal mirror only about three centimetres across. A mirror reflects all colours alike. The reflector became the astronomer's instrument once large mirrors could be made: William Herschel's 40-foot telescope at Slough in 1789, the 100-inch on Mount Wilson in California in 1917 with which Edwin Hubble found the universe expanding, and the 200-inch at Palomar in 1948.

What a telescope mostly does is not magnify but gather. A fully open human pupil is about seven millimetres across; the Hubble Space Telescope's mirror is 2.4 metres, collecting more than 100,000 times as much light. The James Webb Space Telescope, launched in 2021, unfolded a 6.5-metre mirror of eighteen gold-coated beryllium segments a million and a half kilometres from Earth, and the Extremely Large Telescope now rising in Chile's Atacama Desert will have a 39-metre mirror of 798 pieces.

Did you know? The law of refraction was stated in Baghdad in 984, six centuries before Snell, in a manuscript rediscovered only in 1990.

Lenses and mirrors also work the other way round, focusing light down rather than gathering it in. The same optics that reveal galaxies write the circuits of a microchip, where lenses project patterns a few nanometres wide, and correct the eyes of a billion people who, like Galileo's Dutch rivals, simply want to see further.

Lasers

A laser makes light in which every wave marches in step: one colour, one direction, crest aligned with crest. Ordinary light, from the Sun or a bulb, is a crowd leaving a stadium; laser light is a regiment. The trick behind it was spotted in 1917 by Albert Einstein, who showed that an atom already holding extra energy can be nudged by a passing light wave into releasing its energy as a second, identical wave. He called it stimulated emission and the acronym remembers him: light amplification by stimulated emission of radiation.

For decades it was a curiosity, because in any normal material most atoms sit in their lowest energy state and absorb light rather than amplify it. The breakthrough was to pump more atoms up than down, a "population inversion", and then let the light bounce back and forth between mirrors so that each pass stimulates more. Charles Townes did it first with microwaves and ammonia molecules at Columbia University in 1954, calling the device a maser. In 1958 Townes and Arthur Schawlow published the design for an optical version. A graduate student down the corridor, Gordon Gould, had written "LASER" in his notebook the year before and had it notarised in a sweet shop, beginning a patent fight that lasted thirty years. In Moscow, Nikolay Basov and Alexander Prokhorov had reached the same principles independently and shared the 1964 Nobel Prize with Townes.

The first working laser was built by Theodore Maiman at Hughes Research Laboratories in Malibu, California, on 16 May 1960. His design was almost domestic: a rod of synthetic ruby the size of a fingertip, its ends polished and silvered, wrapped in a coiled photographic flash lamp. When the lamp fired, the ruby emitted a pulse of deep red light at a wavelength of 694.3 nanometres. Bigger laboratories with bigger budgets had been beaten by a solid crystal and a flashbulb. The journal Physical Review Letters rejected his paper; Nature printed it in August.

Within months Ali Javan at Bell Labs had the first continuous laser, a helium-neon gas tube glowing orange-red, and in 1962 semiconductor lasers the size of a grain of sand followed. The laser's reputation as "a solution looking for a problem" did not last. The supermarket barcode scanner arrived in 1974, the compact disc in 1982, and laser light now carries almost all of the world's internet traffic through glass fibre, pulsing billions of times a second.

Did you know? The first laser's power source was an ordinary photographer's flash lamp, chosen because it was the brightest thing Maiman could buy.

Today lasers cut steel and reshape corneas, cool atoms to a billionth of a degree, and measure the distance to the Moon to within millimetres by bouncing off mirrors left by Apollo astronauts. The LIGO observatories that heard gravitational waves in 2015 are laser interferometers four kilometres long. And in December 2022 the 192 beams of the National Ignition Facility in California compressed a fuel pellet until fusion released more energy than the laser delivered, 3.15 megajoules out for 2.05 in, the first time that had happened anywhere on Earth.

Energy for a Warming World

Humanity now uses roughly 600 exajoules of primary energy a year, a number so large it needs translating: it is about 190,000 kilowatt-hours a second, around four-fifths of it from burning coal, oil and gas. The burning releases close to 37 billion tonnes of carbon dioxide annually, and the measured concentration of the gas in the air, logged continuously at Mauna Loa in Hawaii since Charles Keeling began in 1958, has passed 420 parts per million, higher than at any point in at least 800,000 years of ice-core record. The physics of why this warms the planet belongs to a later chapter. This one is about the alternatives, and how each was discovered.

The oldest is sunlight turned directly into electricity. In Paris in 1839 the nineteen-year-old Edmond Becquerel, experimenting in his father's laboratory, found that light falling on electrodes in a conducting solution produced a small current: the photovoltaic effect. Charles Fritts coated selenium with gold in New York in 1883 and made a cell that converted less than one per cent of sunlight. The modern solar cell was born at Bell Laboratories in New Jersey in 1954, when Daryl Chapin, Calvin Fuller and Gerald Pearson built a silicon cell of six per cent efficiency. Ordinary commercial panels now exceed twenty per cent, laboratory multi-junction cells have passed forty-seven, and silicon photovoltaics has become the fastest-growing source of electricity in history.

Wind power has a ceiling of its own. In 1919 the German physicist Albert Betz proved that no turbine can capture more than 59.3 per cent of the energy in the air passing through it, because the air must keep moving to get out of the way. Modern turbines approach that limit with blades longer than a jumbo jet's wingspan. Nuclear fission, demonstrated in Berlin in 1938 and harnessed for electricity at Obninsk in 1954 and Calder Hall in 1956, releases about a million times more energy per kilogram of fuel than coal.

The honest comparison is the lifetime carbon cost of each kilowatt-hour, counting mining, manufacture and fuel. The Intergovernmental Panel on Climate Change's review put coal at around 820 grams of carbon dioxide per kilowatt-hour and gas at 490, against roughly 41 to 48 for solar, 24 for hydro and about 12 each for wind and nuclear. The gap between the worst and the best is nearly a hundredfold.

Did you know? The 1954 Bell Labs solar cell was first used to power a telephone line in rural Georgia; the same silicon now lights villages the grid never reached.

Energy for a warming world is partly a problem of discovery still in progress: storage, grids that balance supply and demand across continents, cheaper electrolysis for hydrogen, and perhaps fusion. But it is mostly a problem of deployment. The science that counted the joules, and the science that measured the carbon, now sit on the same page of the ledger.

Static Electricity

Rub amber with fur and it picks up feathers. The Greeks knew this around 600 BC, and their word for amber, elektron, is where the whole subject gets its name. For two thousand years the effect stayed a party trick. In 1600 William Gilbert, physician to Elizabeth I, built a pivoting needle he called a versorium, showed that glass, sulphur, wax and gemstones all attracted it when rubbed, and coined the word "electric" for the property. Static electricity, we now know, is an imbalance of electric charge: rubbing drags electrons from one surface to another, leaving one positive and the other negative, and the charges stay put until a path lets them move.

The eighteenth century found that path. In London in 1729 Stephen Gray, a retired dyer, discovered that the "electric virtue" would travel along a damp thread for hundreds of feet, and famously along a boy suspended on silk cords, whose fingertips then attracted brass leaf. Charge could be conducted. In Paris in 1733 Charles du Fay found there were two kinds, which he called vitreous and resinous; like repelled like, and unlike attracted. Benjamin Franklin renamed them positive and negative, and his guess about which was which is why the electron, discovered in 1897, carries a negative sign.

Storing charge came by accident. In 1745 Ewald von Kleist in Pomerania, and in January 1746 Pieter van Musschenbroek in Leiden, tried to electrify water in a glass jar held in the hand. When Musschenbroek touched the wire dipping into the water he received a shock that, he wrote, he would not repeat for the whole kingdom of France. The Leyden jar, a glass bottle with metal foil inside and out, was the first capacitor; glass kept the two charges apart while the foils held them close, and a bank of jars could kill a turkey or send a jolt through 180 soldiers holding hands.

Franklin's kite experiment of June 1752 in Philadelphia drew a spark from a storm cloud into a Leyden jar, proving lightning was the same electricity. He did not wait for a strike, which would have killed him; a French team at Marly had already drawn sparks from a tall iron rod in May 1752 on his suggestion. The lightning rod followed within the year.

Did you know? Scuffing across a carpet charges you to several thousand volts, yet the spark carries so little charge that it only stings.

In 1785 Charles-Augustin de Coulomb in Paris measured the force between charged spheres with a torsion balance so sensitive that a twist of a fraction of a degree could be read, and found it fell with the square of the distance, exactly like gravity. That law still governs every photocopier, which lays toner down with charged drums, every dust-shedding air filter, and the shock that greets you at the car door. A lightning bolt is the same spark scaled up to 300 million volts, the Leyden jar's lesson written across the sky.

Current, Voltage and Resistance

A spark from a Leyden jar is over in a microsecond. What changed the world was a steady flow, and it began with a dead frog. In Bologna in the 1780s Luigi Galvani noticed that a frog's leg twitched when touched by two different metals, and concluded that animals made their own "animal electricity". His compatriot Alessandro Volta at Pavia disagreed: the frog was merely a detector, and the electricity came from the two metals meeting through a salty fluid. To prove it, Volta stacked discs of zinc and silver separated by brine-soaked cardboard, and in a letter to the Royal Society in March 1800 announced the voltaic pile. For the first time, electricity could be had on tap, hour after hour.

The pile produced a flow of charge, a current, driven by a push that we now call voltage, the energy given to each unit of charge. Within weeks of Volta's letter, William Nicholson and Anthony Carlisle in London had used a pile to split water into hydrogen and oxygen, and Humphry Davy at the Royal Institution soon isolated potassium, sodium, calcium and more with a battery of 2,000 plates. A current, it turned out, could take matter apart.

The rule linking push to flow came from a Bavarian schoolteacher. Georg Simon Ohm, teaching at the Jesuit gymnasium in Cologne, built his own thermocouples for a steady voltage and measured the deflection of a magnetic needle as current passed through wires of different lengths and thicknesses. In 1827 he published his finding: the current through a conductor is proportional to the voltage across it and inversely proportional to a property of the conductor he called resistance. In the shorthand every electrician learns, V = IR. German critics dismissed the work as "a web of naked fancies"; the Royal Society gave him its Copley Medal in 1841.

The water analogy is old but good. Voltage is the pressure in the pipe, current the flow, resistance the narrowness. Copper is a wide pipe, rubber a blocked one. A phone charger pushes about two amperes at five volts; a kettle draws about thirteen amperes from 230-volt mains in Britain; dry human skin resists with around 100,000 ohms, which is why a nine-volt battery on the tongue only tingles. Resistance turns electrical energy into heat, the principle of every toaster and the reason power lines run at hundreds of thousands of volts: for the same power, higher voltage means lower current and less waste.

Did you know? The ampere, volt and ohm were named at an international congress in Paris in 1881, honouring a Frenchman, an Italian and a German.

Every circuit designed since, from a torch to a supercomputer, is an argument in Ohm's language. Resistors set the brightness of a light-emitting diode, voltage dividers read the position of a joystick, and the heat that limits how fast a chip can run is Ohm's law at the scale of a billionth of a metre. The frog had nothing to do with it, and everything.

Magnets and the Earth's Field

A lodestone is a lump of magnetite that attracts iron, and sailors in China were hanging slivers of it from threads to find south by the late eleventh century. Shen Kuo's Dream Pool Essays of 1088 describe the floating needle and note something subtle: it did not point exactly to the pole but slightly east of it. Shen had discovered magnetic declination five centuries before Columbus noticed it mid-Atlantic. By 1269 Petrus Peregrinus, a French scholar on campaign in Italy, had mapped the field around a spherical lodestone and named its two poles, showing that cutting a magnet in half only made two smaller magnets.

Why a compass pointed north at all was answered in 1600 by William Gilbert, physician to Elizabeth I, in De Magnete, the first great experimental treatise in English science. Gilbert carved lodestones into spheres he called terrellae, little Earths, and moved a tiny compass over their surfaces. The needle dipped and swung exactly as a real compass did over the globe. His conclusion was blunt: the Earth itself is a great magnet. It also killed a popular myth, that the needle sought the Pole Star or a magnetic mountain in the Arctic.

Measuring the field as a number came from Göttingen, where Carl Friedrich Gauss in 1832 devised a way to express magnetic strength in absolute units of mass, length and time, and with Wilhelm Weber set up an international network of observatories. His 1839 analysis of their data proved that almost all of the field originates inside the planet, not in the sky. The field at the surface is weak, between 25 and 65 microtesla, a few hundredths of a fridge magnet, but it extends tens of thousands of kilometres into space.

What makes it is a dynamo. The Earth's core is iron, solid at the centre and molten around it, and the outer core, 2,900 kilometres down and hotter than the surface of the Sun, convects as the planet turns. Moving liquid metal through a magnetic field generates electric currents, which generate more field, a self-sustaining loop worked out by Walter Elsasser and Edward Bullard in the 1940s and 1950s. A permanent magnet cannot be the answer, because iron loses its magnetism above 770 degrees Celsius and the core is far hotter.

Did you know? The Earth's north magnetic pole is, in the language of magnets, a south pole; it attracts the north-seeking end of your compass.

The field is restless. The north magnetic pole, in the Canadian Arctic when first reached in 1831, has since crossed into Siberian waters at up to 50 kilometres a year. Rocks record that the whole field has flipped hundreds of times, most recently 780,000 years ago, and the magnetic stripes on the ocean floor that confirmed plate tectonics in the 1960s are that record, frozen in cooling lava. The same field steers migrating birds and sea turtles, bends the solar wind into the aurora, and keeps the atmosphere from being stripped away. Gilbert's little Earth was the right model; it just needed a molten heart.

Electromagnetism

For two centuries electricity and magnetism were separate chapters in the textbooks: one about amber and sparks, the other about lodestones and compasses. They were joined in a lecture room in Copenhagen in April 1820. Hans Christian Ørsted, demonstrating a voltaic battery to students, noticed that a compass needle lying near the wire swung aside whenever the current flowed. He had suspected a link for years; now he had it, and by July he had sent a short Latin pamphlet to every scientist he could think of. A current, it said, is surrounded by a circular magnetic field.

Paris moved fastest. André-Marie Ampère heard the news on 4 September 1820 and within a week had shown that two parallel wires carrying current attract each other when the currents flow the same way and repel when they oppose, with no magnet involved at all. Over the following years he built a complete mathematical theory in which magnetism itself is nothing but moving charge, and proposed that the magnetism of iron came from tiny circulating currents inside it, an idea that quantum physics confirmed a century later. The unit of current bears his name.

The practical device came from England. In 1825 William Sturgeon, a former soldier teaching at the military academy in Woolwich, wrapped bare copper wire round a varnished horseshoe of soft iron and found that a small battery made it lift nine pounds, twenty times its own weight, and that the magnetism vanished the moment the current stopped. Joseph Henry in Albany, New York, insulated the wire with silk so that he could wind hundreds of turns, and by 1831 his electromagnets were lifting more than a tonne. An electromagnet was a magnet with a switch.

The switch made a language possible. Samuel Morse and Alfred Vail used Henry's magnets to pull a pen against paper at the far end of a wire, and on 24 May 1844 Morse sent "What hath God wrought" from Washington to Baltimore, forty miles away, in dots and dashes. Within twenty years cables lay under the Atlantic. The same principle rings an electric bell, lifts scrap iron in a breaker's yard, and, by reversing the trick so that a current-carrying coil is pushed by a fixed magnet, turns every electric motor on Earth.

Did you know? Ørsted's compass needle did not point along the wire or towards it but sideways, at right angles, which is why the discovery baffled him at first.

The force on a moving charge in a magnetic field, written down by Hendrik Lorentz in 1895, is the rule behind the motor, the loudspeaker, the particle accelerator and the hard disk. Since 2019 the ampere has been defined by fixing the charge of the electron, so Ampère's unit now rests on counting electrons rather than measuring the pull between wires. The subject that began with a twitching needle in a lecture hall now carries, in the form of motors, about half of the electricity the world generates.

Faraday's Dynamo

If a current makes a magnetic field, can a magnetic field make a current? Michael Faraday, a blacksmith's son and former bookbinder's apprentice who had talked his way into the Royal Institution as a laboratory assistant, chased that question for a decade. The answer came on 29 August 1831. He wound two coils of wire on opposite sides of an iron ring, connected one to a battery and the other to a galvanometer, and saw the needle kick at the instant he closed the switch, then kick back when he opened it. A steady current did nothing; only a changing magnetic field pushed current through the second coil. Faraday had discovered electromagnetic induction.

He spent the autumn stripping the effect to its essentials. In October he pushed a bar magnet into a hollow coil and watched the galvanometer swing one way as it went in and the other as it came out. Then, on 28 October 1831, he mounted a copper disc so that its rim passed between the poles of a large horseshoe magnet, pressed sliding contacts against the rim and the axle, and turned the handle. A small but continuous current flowed. This was the dynamo, the first machine to turn motion into electricity, and Joseph Henry in America had been finding similar effects at almost the same moment.

Faraday's genius was for pictures rather than equations. He imagined space around a magnet filled with "lines of force", and stated the law of induction in those terms: the voltage produced in a loop equals the rate at which the lines through it are cut. Thirty years later James Clerk Maxwell turned that picture into mathematics. Faraday also discovered, in the same series of experiments, that a changing current in one coil induces a current in another, the principle of the transformer, which is why mains electricity can be stepped up for transmission and down for your kitchen.

The practical generator took time to grow. Hippolyte Pixii built a hand-cranked version in Paris in 1832; by 1858 a steam-driven dynamo was lighting the South Foreland lighthouse near Dover; and in 1882 Thomas Edison's Pearl Street station in New York was supplying 85 customers. Modern generators are Faraday's disc turned inside out: a spinning electromagnet, the rotor, sweeps its field past fixed coils, and in a large turbine the rotor turns fifty times a second to make Europe's 50-hertz mains.

Did you know? Faraday wrote no equations, having left school at thirteen; the mathematics of his lines of force was supplied by Maxwell.

The story that a politician asked Faraday what use his discovery was, and that he replied one day it might be taxed, is probably apocryphal. The honest answer would have been bigger. Every power station on Earth, whether driven by coal, water, uranium or wind, ends in a coil moving past a magnet. The dynamo on a bicycle, the alternator in a car, the pickup under a guitar string and the induction hob are all the same experiment of 28 October 1831, scaled to taste.

Maxwell's Equations

In 1861 a thirty-year-old Scottish professor at King's College London set out to turn Michael Faraday's lines of force into mathematics. James Clerk Maxwell had already explained Saturn's rings and the colours of the eye; now he built an elaborate mechanical model of space filled with spinning cells and idle wheels, and from it extracted the equations that electric and magnetic fields must obey. The model was abandoned. The equations were not.

Three of them were already known in some form. Gauss's law says that electric field lines begin and end on charges. A second law says that magnetic field lines never begin or end at all: there are no magnetic monopoles, and cutting a magnet in half gives two magnets. Faraday's law says that a changing magnetic field makes a circulating electric field, which is why a dynamo works. The fourth, Ampère's law, said that a current makes a circulating magnetic field, and here Maxwell saw that the equation was incomplete. In the gap of a charging capacitor no current flows, yet a magnetic field appears. Maxwell added a term: a changing electric field also makes a magnetic field. He called it the displacement current.

That addition closed a loop. A changing electric field makes a magnetic field; a changing magnetic field makes an electric field; and so a disturbance in one can regenerate the other and travel through empty space as a wave. Maxwell calculated its speed from two numbers measured on laboratory benches, the electric and magnetic constants, and in 1862 got about 310,000 kilometres a second. Hippolyte Fizeau had measured the speed of light in Paris in 1849 at about 315,000. The agreement, Maxwell wrote, was too close to be coincidence: light is an electromagnetic wave. His full paper, A Dynamical Theory of the Electromagnetic Field, appeared in 1865.

The four tidy equations found in every textbook are not quite Maxwell's. His Treatise of 1873 contained twenty equations in twenty variables; it was Oliver Heaviside, a self-taught former telegraph operator working alone in London, who in 1884 compressed them into the four vector equations we now write, grumbling that Maxwell's own version was "a tangle". The experimental proof came from Karlsruhe in 1887, when Heinrich Hertz made sparks jump across a gap in one loop of wire in response to sparks in another metres away, and showed the invisible waves could be reflected, focused and polarised like light.

Did you know? Maxwell died in 1879 at 48, eight years before Hertz proved his waves existed, and never knew he had been right.

Everything that uses radio, radar, microwaves, light or X-rays is an application of the four equations: the aerial in a phone, the fibre under the ocean, the magnetron in a microwave oven, the MRI scanner. Einstein kept Maxwell's portrait on his study wall, and special relativity was built to keep the equations true for every observer. Richard Feynman suggested that in the long view of history the most significant event of the nineteenth century would be Maxwell's discovery, beside which the American Civil War would fade into provincial insignificance.

The Electromagnetic Spectrum

Visible light occupies less than one octave of a keyboard that runs for more than fifty. Every band of the electromagnetic spectrum is the same thing, an oscillating electric and magnetic field travelling at the speed of light, and they differ only in wavelength: kilometres for the longest radio waves, less than a trillionth of a metre for gamma rays. Nearly all of it is invisible, and the story of the spectrum is the story of finding each band by what it did to something else.

The first invisible band was found with a thermometer. In 1800 William Herschel, the astronomer who had discovered Uranus, spread sunlight into a spectrum with a prism and laid thermometers in each colour to see which warmed most. Red warmed more than violet, and a thermometer placed just beyond the red end, where no light was visible, warmed most of all. Herschel called it "calorific rays"; we call it infrared. A year later in Jena, Johann Ritter, reasoning that the spectrum should be symmetrical, placed silver chloride beyond the violet end and watched it darken faster than in any visible colour. Ultraviolet had been found by its chemistry.

The long wavelengths needed Maxwell's theory. Heinrich Hertz generated the first radio waves at Karlsruhe in 1887 with a spark gap, measured their wavelength at a few metres and remarked that they were of no use whatsoever. Guglielmo Marconi disagreed, and in December 1901 received the letter S in Morse at St John's, Newfoundland, from Cornwall, 3,500 kilometres away. Microwaves, between radio and infrared, were tamed by the cavity magnetron that John Randall and Harry Boot built in Birmingham in 1940, the device that made wartime radar practical and now warms your soup.

The short end arrived by accident. On 8 November 1895 Wilhelm Röntgen in Würzburg noticed a screen glowing across his darkened laboratory while he ran a high-voltage discharge through a glass tube wrapped in black card. The unknown rays passed through wood, flesh and books; a photograph of his wife's hand, bones and ring plainly visible, went round the world in weeks. Paul Villard in Paris found gamma rays, shorter still, in the radiation from radium in 1900.

Did you know? Hertz, asked about the use of his radio waves, said they were "of no use whatsoever"; Marconi's company was floated ten years later.

Every band now has a job. Radio and microwaves carry broadcasts, phone calls and Wi-Fi; infrared runs remote controls and night-vision cameras and lets astronomers see through dust; ultraviolet sterilises water and gives you sunburn; X-rays image bones and luggage; gamma rays kill tumours and reveal exploding stars. Karl Jansky's discovery in 1932 that the Milky Way hisses at radio wavelengths opened astronomy to the whole keyboard, and today a single object, a black hole swallowing gas, is studied in radio, infrared, visible, X-ray and gamma light at once. Herschel's thermometer beyond the red was the first step off the one octave we were born with.

Sound Waves

Sound is a push that travels. A vibrating string or vocal cord shoves the air beside it, that air shoves the next, and a ripple of compression and rarefaction spreads outward at about 343 metres per second, faster than any sprinter and slower than any rifle bullet. Unlike light, sound needs something to push. Robert Boyle proved it in Oxford in 1660, using the air pump his assistant Robert Hooke had built: a watch hung inside a glass globe went silent as the air was drawn out and could be heard again when it was let back in. Space, as the film posters say, is quiet.

How fast sound travels was a matter of cannons. Marin Mersenne in Paris timed echoes in the 1630s and got close; in 1738 the French Academy fired guns on hills around Paris and timed the gap between flash and bang over measured distances, arriving at 332 metres per second in still air. Isaac Newton had calculated a figure from the springiness of air that came out about a sixth too low; Pierre-Simon Laplace fixed it in 1816 by noticing that the compressions happen too fast for heat to leak away. Sound goes faster in warmer air, faster still in water, about 1,480 metres per second, and nearly 6,000 in steel, which is why you hear a train through the rails before you hear it through the air.

What distinguishes a note from a noise is regularity. The pitch we hear is the frequency of the pressure ripples: a concert A is 440 waves a second, the lowest organ pipes rumble at 16, and human hearing gives out around 20,000, where a bat's begins. Joseph Fourier showed in 1822 that any repeating wave can be built from pure sine waves, which is why a violin and a flute playing the same note sound different: same fundamental, different overtones. Hermann von Helmholtz used tuned glass spheres in the 1860s to pick out those overtones by ear.

In Prague in 1842 Christian Doppler proposed that a source moving towards you should sound higher, and away from you lower, because its waves are bunched or stretched. Christophorus Buys Ballot tested it near Utrecht in 1845 by putting trumpeters on a train and musicians with perfect pitch beside the track. The Doppler effect is now how the police radar clocks you, how a sonographer hears a foetal heartbeat, and how astronomers found the universe expanding.

Did you know? The loudest sound in recorded history, the 1883 eruption of Krakatoa, was heard 4,800 kilometres away and circled the globe as a pressure wave several times.

Ultrasound, above 20,000 hertz, found its uses after the First World War, when sonar sought submarines; Ian Donald in Glasgow in 1958 used it to look inside the womb, and it is now the safest imaging in medicine. Decibels, the loudness scale, run logarithmically because the ear does, from a whisper at 30 to a jet at 140. Every one of those numbers is a measurement of how hard a crowd of molecules is pushing its neighbours.

Semiconductors and the Transistor

Between the conductors, which let electrons flow, and the insulators, which do not, sits a small family of elements that can be persuaded either way. Silicon and germanium are semiconductors: pure, they barely conduct; seeded with a few atoms of phosphorus or boron per million, they conduct by surplus electrons or by the "holes" the missing electrons leave, and a junction between the two kinds lets current pass in one direction only. The trick of using one small current to control a larger one through such a crystal is the transistor, and it was found by a team.

The team was assembled at Bell Telephone Laboratories in New Jersey by Mervin Kelly in 1945, with a clear brief: find a solid-state replacement for the bulky, hot, unreliable vacuum tubes that amplified every long-distance call. William Shockley led the group. John Bardeen, a quiet theorist, worked out why Shockley's early designs failed: electrons were trapped at the crystal's surface. Walter Brattain, an experimentalist who had grown up on a cattle ranch, built the apparatus. On 16 December 1947 Bardeen and Brattain pressed two gold contacts, cut from a strip of foil wrapped round a plastic wedge, onto a slab of germanium a thumbnail wide, and the signal through one contact came out of the other amplified. On 23 December they demonstrated it to the lab's management, speaking through it so that the gain could be heard.

Shockley, stung at being left off the key experiment, spent the next weeks designing the junction transistor, a sandwich of three layers that was more rugged and easier to make, and which became the standard. The three shared the 1956 Nobel Prize; Bardeen won a second in 1972 for superconductivity, the only person to hold two in physics. The name came from a colleague, John Pierce, who contracted "transfer resistor".

The transistor's children came fast. Texas Instruments made the first silicon transistors in 1954 and a pocket radio the same year. In 1958 Jack Kilby at Texas Instruments and in 1959 Robert Noyce at Fairchild built whole circuits on one chip, the integrated circuit. In 1959 Mohamed Atalla and Dawon Kahng at Bell Labs made the MOSFET, the field-effect design that could be shrunk almost without limit. Gordon Moore observed in 1965 that the number of transistors on a chip was doubling every year or two, and it kept doing so for half a century.

Did you know? More transistors have been manufactured than any other object in human history, well over ten sextillion, more than all the grains of sand on Earth.

A modern processor carries tens of billions of transistors, each switching billions of times a second and some only a few dozen atoms across. Every phone, pacemaker, car, satellite and solar panel is built from the germanium slab's descendants. The team that wanted a better telephone amplifier gave the century its defining machine.

Superconductors

Every wire wastes energy as heat, which is what Ohm's law says and what warms your laptop. In some materials, cooled far enough, the waste simply stops. A superconductor carries current with exactly zero resistance: a current started in a superconducting ring keeps circulating, undiminished, for as long as anyone has cared to watch, which in careful experiments has been years. It is one of the few places where quantum mechanics shows itself at the scale of a wire you can hold.

The discovery belongs to Leiden and to cold. Heike Kamerlingh Onnes had spent decades building the best low-temperature laboratory in the world and in 1908 became the first to liquefy helium, at 4.2 kelvin, within a few degrees of absolute zero. With that bath available, he began measuring how metals conducted as they chilled. On 8 April 1911 his team cooled a thread of mercury and saw its resistance fall smoothly, then, at about 4.2 kelvin, drop to nothing at all. Onnes first suspected a short circuit. It was not. He called the state "supraconductivity" and received the Nobel Prize two years later.

Zero resistance was only half of it. In 1933 Walther Meissner and Robert Ochsenfeld in Berlin found that a superconductor also expels magnetic fields from its interior, the Meissner effect, which is why a magnet hovers above a chilled superconducting disc in every science museum. Explaining both took until 1957, when John Bardeen, Leon Cooper and Robert Schrieffer in Illinois showed that below the critical temperature electrons pair up, bound by vibrations of the crystal, and the pairs move together as a single quantum wave that the atoms cannot scatter. The BCS theory earned the three a Nobel Prize and Bardeen his second.

For seventy-five years the record critical temperature crept upward to 23 kelvin and seemed stuck, which meant expensive liquid helium for every application. Then in 1986 Georg Bednorz and Alex Müller at IBM's Zurich laboratory found a brittle copper-oxide ceramic that superconducted at 35 kelvin, and within a year a yttrium-barium-copper oxide reached 93 kelvin, above the boiling point of liquid nitrogen, a coolant cheaper than milk. Why these ceramics work is still debated. Under crushing pressures, hydrogen-rich compounds have since superconducted at around 250 kelvin, close to a cold winter's day, but only inside a diamond anvil.

Did you know? The 27-kilometre Large Hadron Collider is the largest refrigerator on Earth, holding 1,232 superconducting magnets at 1.9 kelvin, colder than deep space.

Superconductors already earn their keep. The magnet in an MRI scanner is a coil of niobium-titanium wire carrying hundreds of amperes with no power supply at all, once started. The Large Hadron Collider steers protons with superconducting magnets at 8.3 tesla; Japan's maglev test trains float on them at 600 kilometres an hour; and the quantum computers of Google and IBM are built from superconducting circuits. A room-temperature superconductor at ordinary pressure, which would transform power grids and motors, remains the field's unfulfilled promise, and the claims that surface every few years have so far failed replication, the ordinary way science sorts hope from discovery.

The Speed of Light

Light is quick, but it is not instant. In a vacuum it covers 299,792,458 metres every second, a figure now fixed by definition: since 1983 the metre has been defined as the distance light travels in 1/299,792,458 of a second, so the speed of light, c, is no longer something to measure but the ruler by which other things are measured. Nothing carrying information moves faster. That one constant stitches together space, time, electricity and magnetism, and it sets the speed limit of the universe.

For most of history the question was whether light had any speed at all. Aristotle thought it filled space instantly; the Arab scholar Ibn al-Haytham argued around 1021 that it must travel. Galileo tried to time lanterns flashed between hilltops and found only that light was far too fast for a human hand. The first real number came from Jupiter. In 1676 the Danish astronomer Ole Rømer, working at the Paris Observatory, noticed that eclipses of Jupiter's moon Io ran late by some 22 minutes when Earth was on the far side of its orbit. The delay, he argued, was the time light took to cross the extra distance. His figure was roughly 220,000 kilometres per second: too low, because the size of Earth's orbit was poorly known, but of the right order and, crucially, finite.

Earth-bound measurements followed. In 1849 Hippolyte Fizeau sent a beam through the gap in a spinning toothed wheel at Suresnes to a mirror on Montmartre, 8.6 kilometres away, and sped the wheel up until the returning light was blocked by the next tooth: about 313,000 kilometres per second. Léon Foucault refined this with a rotating mirror in 1862 and got 298,000. Albert Michelson, the first American Nobel laureate in science, spent decades on the problem; in 1926 he bounced light between Mount Wilson and Mount San Antonio in California, 35 kilometres apart over a surveyed baseline, and reached 299,796 kilometres per second, within a few parts in a hundred thousand of today's value.

Did you know? In 1983 the metre was redefined in terms of c, so the speed of light now has an exact value with no uncertainty at all.

The number is enormous yet surprisingly tangible. Sunlight is eight minutes and twenty seconds old when it reaches you; moonlight 1.3 seconds. In one nanosecond light moves about 30 centimetres, which is why the computing pioneer Grace Hopper handed out foot-long pieces of wire to show why signals in a fast computer cannot cross a room in a clock tick. Light from the nearest star, Proxima Centauri, has travelled for more than four years.

The constancy of c is also the hinge on which relativity turns, and engineers live with it every day. GPS satellites broadcast time, and your receiver converts delays of a few millionths of a second into position; light in fibre-optic cables runs at about two-thirds of c, which sets the latency on the submarine links that carry the internet. The finite speed of light turns a telescope into a time machine, and a universe into a history book.

Special Relativity

Special relativity rests on two statements that sound innocent. The laws of physics are the same for every observer moving at constant speed, and the speed of light in a vacuum is the same for all of them, whatever the motion of the source or the observer. Albert Einstein, a 26-year-old examiner at the patent office in Bern, published them in June 1905 in a paper titled On the Electrodynamics of Moving Bodies. Taken together they force a strange conclusion: two observers moving relative to one another cannot agree on the length of a rod or the ticking of a clock. Space and time are not a fixed stage; they are measurements that depend on who is doing the measuring.

The ground had been prepared by a failure. Nineteenth-century physicists assumed light rippled through a stationary ether, so Earth's motion through it should alter the speed of light along different directions. In 1887, in Cleveland, Ohio, Albert Michelson and Edward Morley split a beam of light, sent the halves along perpendicular arms of an interferometer floating on a pool of mercury, and looked for a shift in the interference fringes as the apparatus turned. They expected a shift of about 0.4 of a fringe. They saw none. Hendrik Lorentz and Henri Poincaré wrote equations that could rescue the ether; Einstein simply dropped it.

The consequences are measured, not imagined. A moving clock runs slow by the Lorentz factor, which is 1.005 at a tenth of light speed and 7 at 99 per cent of it. Muons created by cosmic rays high in the atmosphere live only 2.2 microseconds on average, barely enough to travel 660 metres, yet they reach sea level in abundance. In 1941 Bruno Rossi and David Hall, and in 1963 David Frisch and James Smith on Mount Washington, counted them at altitude and at the bottom and found the survival rate that time dilation predicts. In 1971 Joseph Hafele and Richard Keating flew four caesium clocks around the world on commercial airliners; the flying clocks disagreed with those at the US Naval Observatory by tens of nanoseconds, as calculated.

Did you know? Without relativistic corrections, GPS positions would drift by around 10 kilometres per day.

Length shrinks along the direction of motion by the same factor, and simultaneity becomes relative: events that happen at the same moment for one observer happen in sequence for another. Nothing with mass can reach the speed of light, because its energy would have to be infinite. Particle accelerators confirm this daily; the protons in the Large Hadron Collider move at 99.9999991 per cent of c and never faster, however much energy is added.

Everyday life is now entangled with these corrections. The clocks on GPS satellites, orbiting at 14,000 kilometres per hour, tick about 7 microseconds a day slower than ground clocks because of their speed, and about 45 microseconds faster because of weaker gravity; engineers tune them before launch. Popular myths persist, including that Einstein failed mathematics; he did not, and the 1905 papers show it. Relativity did not make Newton wrong, only approximate: at the speeds of daily life the corrections vanish, and the old laws return.

E = mc²

Three months after his relativity paper, in September 1905, Einstein sent a three-page note to Annalen der Physik asking whether the inertia of a body depends on its energy content. His answer was yes: if a body gives off energy as radiation, its mass falls by that energy divided by the square of the speed of light. Written the modern way, E = mc². In words: mass and energy are two measures of the same thing, and the exchange rate between them is c squared, roughly 90 million billion joules per kilogram. A kilogram of anything, fully converted, would release about as much energy as 21 million tonnes of TNT. Matter is frozen energy, and it is frozen very tightly.

Because c² is so large, ordinary changes alter mass by amounts nobody can weigh. A cup of tea gains a few hundred-trillionths of a gram when heated; a wound-up spring is heavier than a slack one. Chemistry rearranges electrons and releases perhaps a billionth of a substance's mass. Only in the nucleus, where forces are a million times stronger, does the effect become large enough to matter. The missing mass of a helium nucleus compared with its separate protons and neutrons, about 0.7 per cent, is the energy that binds it.

The first direct test came in April 1932 at the Cavendish Laboratory in Cambridge. John Cockcroft and Ernest Walton accelerated protons with 700,000 volts and fired them at a lithium target. Each lithium nucleus that captured a proton split into two helium nuclei flying apart with 17 million electronvolts of energy between them. The masses of the ingredients and products were known from Francis Aston's mass spectrograph; the difference, multiplied by c², matched the energy measured, to within the few per cent of the day. In 2005 a team at MIT and the US National Institute of Standards and Technology compared the energy of gamma rays from nuclear captures with the mass lost, and confirmed the equation to 0.00004 per cent.

Did you know? The Sun converts about four million tonnes of its mass into light every second, and has done so for 4.6 billion years.

Lise Meitner and Otto Frisch used the equation on a winter walk in Sweden at Christmas 1938 to calculate that a splitting uranium nucleus should release around 200 million electronvolts, the first explanation of nuclear fission. That arithmetic runs the reactors that supply about a tenth of the world's electricity, and it ran the bombs of 1945; Einstein signed the 1939 letter that alerted President Roosevelt but took no part in the project. The equation also powers medicine quietly: in a PET scanner a positron meets an electron, both vanish, and two gamma rays of exactly 511,000 electronvolts carry away their mass as light.

E = mc² also explains why the Sun can shine for billions of years, why the proton's mass is mostly the energy of the gluons and motion inside it, and why antimatter is the most concentrated fuel imaginable. The shortest famous equation in physics says only that the ledger of mass and energy is a single column.

General Relativity

Special relativity dealt with observers moving at constant speed, and it left gravity out. Einstein's "happiest thought", in 1907, was that a person falling freely does not feel their own weight: gravity and acceleration are locally indistinguishable. Eight years of work with the mathematics of curved surfaces that Bernhard Riemann had developed led to the field equations he presented to the Prussian Academy in Berlin in November 1915. General relativity says that mass and energy curve spacetime, and that what we call gravity is objects following the straightest possible paths through that curvature. The physicist John Wheeler put it in a sentence: matter tells spacetime how to curve, and spacetime tells matter how to move.

The theory made three testable predictions. The first was already in the data. Mercury's orbit swings its closest point round the Sun by 43 arcseconds a century more than Newton's law could explain; Einstein's equations gave the figure exactly, and he wrote that the result gave him palpitations. The second was that light passing the Sun should be bent by 1.75 arcseconds, twice the Newtonian estimate. On 29 May 1919 Arthur Eddington on the island of Príncipe and Andrew Crommelin at Sobral in Brazil photographed stars near the eclipsed Sun and compared their positions with plates taken months earlier. The shift matched Einstein, and The Times of London announced a revolution in science. The third, gravitational redshift, waited until 1959, when Robert Pound and Glen Rebka measured the frequency change of gamma rays travelling 22.5 metres up a tower at Harvard: a shift of about two parts in a thousand trillion, as predicted.

Did you know? In 2010 optical clocks at NIST showed that a clock raised by just 33 centimetres runs measurably faster, so your head ages a little quicker than your feet.

The tests have never stopped. Karl Schwarzschild, serving on the Russian front in 1916, found the first exact solution and with it the radius at which escape becomes impossible: a black hole. In 2019 the Event Horizon Telescope, eight radio observatories from Hawaii to the South Pole acting as one, imaged the shadow of the 6.5-billion-solar-mass black hole in the galaxy M87, and in 2022 the one at the centre of our own Milky Way. Gravitational lensing, the warping of light from distant galaxies by nearer ones, now maps dark matter. The Gravity Probe B satellite measured the twisting of spacetime by Earth's rotation in 2011.

The theory also sits in your pocket. GPS satellite clocks run about 45 microseconds a day fast because gravity is weaker at an altitude of 20,000 kilometres, and the system would fail within minutes if the effect were ignored. General relativity remains the best description of gravity we have, passing every test for more than a century, and it still refuses to fit with quantum mechanics. Gravity, in Einstein's hands, became geometry.

Gravitational Waves

If mass curves spacetime, then mass in violent motion should send ripples through it, travelling outward at the speed of light. Einstein worked this out in 1916, then spent years doubting whether gravitational waves were real or a trick of the coordinates. They are real, but absurdly faint: by the time the waves from two colliding black holes reach Earth, they stretch and squeeze space by about one part in a thousand billion billion. A four-kilometre ruler changes length by less than a thousandth of the width of a proton.

The first evidence was indirect. In 1974, at the Arecibo radio telescope in Puerto Rico, Russell Hulse and Joseph Taylor found a pulsar orbiting another neutron star every 7.75 hours. Over the following decades the orbit shrank exactly as it should if the pair were radiating energy as gravitational waves, by about 3.5 metres a year. The agreement with Einstein's formula was better than 0.2 per cent, and it earned the 1993 Nobel Prize. The waves themselves still had to be caught. Joseph Weber's aluminium bars in the 1960s produced claims that nobody could replicate; the lesson, that a detection must be seen independently at more than one site, shaped everything that followed.

LIGO, the Laser Interferometer Gravitational-Wave Observatory, is two L-shaped instruments 3,000 kilometres apart, at Hanford in Washington State and Livingston in Louisiana. Laser light bounces hundreds of times along each 4-kilometre vacuum arm and recombines; a passing wave lengthens one arm while it shortens the other, shifting the interference pattern. On 14 September 2015 both detectors recorded the same chirp, Livingston 7 milliseconds before Hanford, rising in frequency from 35 to 250 hertz in a fifth of a second. It was the final orbit and merger of two black holes, of 36 and 29 solar masses, 1.3 billion light-years away. The remnant weighed 62 solar masses; three suns' worth of mass had become waves. The team, over a thousand scientists, announced the detection on 11 February 2016, and Rainer Weiss, Barry Barish and Kip Thorne received the 2017 Nobel Prize.

Did you know? For a fraction of a second, the merger radiated more power than all the stars in the observable universe combined.

A second kind of event, on 17 August 2017, proved the new astronomy's reach. LIGO and the Virgo detector near Pisa caught two neutron stars spiralling together; 1.7 seconds later satellites saw a gamma-ray burst from the same spot, and telescopes watched the glow of freshly made heavy elements, including an estimated several Earth masses of gold. In 2023 pulsar timing arrays, using dozens of millisecond pulsars across the sky as a galaxy-sized detector, reported a background hum of waves from supermassive black-hole pairs. KAGRA in Japan has joined the network, and the European Space Agency's LISA mission plans three spacecraft millions of kilometres apart for the 2030s. For four centuries astronomy meant light. Now the universe can also be heard.

The Quantum Leap

At the end of the nineteenth century physics had a stubborn problem with a hot oven. Classical theory predicted that a glowing cavity should pour out ever more energy at ever shorter wavelengths, an "ultraviolet catastrophe" that plainly did not happen. On 14 December 1900, in Berlin, Max Planck told the German Physical Society that the formula fitted the measurements only if the energy of the oscillators in the walls came in packets proportional to frequency, with a constant of proportionality he called h. He later called it an act of desperation. Its value, 6.626 × 10⁻³⁴ joule-seconds, is tiny, which is why the graininess of energy is invisible in everyday life and why it took so long to notice.

Einstein took the packets seriously in 1905. The photoelectric effect, in which light knocks electrons out of metal, had a puzzling feature: the energy of the ejected electrons depended on the light's colour, not its brightness, and below a threshold frequency no electrons emerged however bright the lamp. If light arrives in quanta of energy hf, that is exactly what should happen. Robert Millikan spent a decade in Chicago trying to prove Einstein wrong and in 1916 confirmed the law in detail, measuring h to within half a per cent. Einstein's 1921 Nobel Prize was for this, not for relativity.

The quantum then entered the atom. In 1913 Niels Bohr proposed that the electron in hydrogen could occupy only certain orbits, with fixed energies, and that light was emitted or absorbed only when it jumped between them. The jump is the original quantum leap: the smallest change nature allows, not the largest. The model reproduced the Balmer series, the red, blue-green and violet lines of hydrogen's spectrum, to four decimal places. In 1914 James Franck and Gustav Hertz in Berlin fired electrons through mercury vapour and found they lost energy only in steps of 4.9 electronvolts, at which point the vapour glowed with ultraviolet light of precisely the matching wavelength. Energy levels were real, and they could be counted.

Did you know? Since 2019 the kilogram has been defined by fixing Planck's constant, so the unit of mass now rests on a quantum.

Every line in every spectrum, from neon signs to the fingerprints of elements in starlight, is a quantum jump. Lasers are jumps marshalled in step; LEDs are jumps across the energy gap of a crystal, tuned by its chemistry; atomic clocks count the 9,192,631,770 oscillations of a particular jump in caesium, defining the second. Solar cells are the photoelectric effect at work on every roof. The chemistry of the whole periodic table follows from which levels electrons may fill.

Planck's constant turned out to be the hinge of a new physics in which energy, angular momentum and action come in discrete steps. The quantum leap is small, and it is everywhere.

Wave-Particle Duality

Ask whether light is a wave or a stream of particles and the honest answer is that it is neither, or both, depending on the question you put to it. The same is true of electrons, atoms and molecules. Wave-particle duality is the name for this double character: quantum objects travel like waves, spreading and interfering, but are detected like particles, arriving whole at one spot.

Thomas Young settled the wave side of light in 1801 in London. He let sunlight through a pinhole and then past two narrow slits, and on the screen behind saw not two bright bands but a comb of light and dark fringes, the signature of waves adding and cancelling. Newton's particle theory could not do this, and for a century light was a wave. Then the particle came back. Einstein's 1905 explanation of the photoelectric effect needed light quanta, and in 1923 Arthur Compton at Washington University in St Louis scattered X-rays off electrons in graphite and found their wavelength lengthened as if billiard balls had collided: the photon carried momentum, like a particle.

In 1924 a French doctoral student, Louis de Broglie, proposed the reverse: if waves can act like particles, particles should act like waves, with a wavelength equal to Planck's constant divided by momentum. Within three years it was confirmed twice. At Bell Labs in New Jersey, Clinton Davisson and Lester Germer fired electrons at a nickel crystal and found them scattering at the angles a diffracting wave would choose; in Aberdeen, George Paget Thomson passed electrons through thin metal films and photographed diffraction rings. His father, J. J. Thomson, had won a Nobel Prize for showing the electron was a particle; the son shared one for showing it was a wave.

Did you know? In 1999 a Vienna team led by Anton Zeilinger showed interference with carbon-60 molecules, footballs of sixty atoms, and by 2019 molecules of over 2,000 atoms had done the same.

The most striking demonstration sends particles through Young's two slits one at a time. In 1974 in Bologna, and most famously in 1989 at Hitachi in Tokyo, where Akira Tonomura's group filmed it, single electrons arrived as individual dots on the detector, yet as thousands accumulated the dots formed the interference fringes. Each electron, apparently, passes through both slits as a wave and lands as a particle. Put a detector at the slits to find out which one it used, and the fringes vanish.

De Broglie's wavelength is why electron microscopes see what light cannot. Electrons accelerated through 100,000 volts have a wavelength of about 4 picometres, a hundred thousand times shorter than visible light, which is enough to resolve individual atoms in a crystal. Neutron diffraction maps the positions of hydrogen atoms in proteins. Matter-wave interferometers measure gravity precisely enough to prospect for minerals. The quantum world does not choose between wave and particle; it asks which experiment you are running.

Uncertainty and Probability

Classical physics promised that, given enough information, the future could be computed. Quantum mechanics withdrew the promise, not for lack of information but as a matter of principle. Two ideas carry the change. Max Born's probability rule of 1926 says the wave that describes a particle does not tell you where it is, only the likelihood of finding it in each place when you look. Werner Heisenberg's uncertainty principle of 1927 says that certain pairs of properties, position and momentum above all, cannot both be sharply defined at once: the product of their spreads can never be smaller than Planck's constant divided by 4π.

The mathematics came first. In June 1925 Heisenberg, aged 23 and escaping hay fever on the North Sea island of Heligoland, worked out a mechanics built from tables of numbers, soon recognised in Göttingen as matrix algebra. Erwin Schrödinger produced his wave equation in Zurich in early 1926. Born, in Göttingen that summer, saw what the wave meant: its squared amplitude is a probability. Einstein's reply to Born in December 1926 contained the line that he could not believe God plays dice. Born's view prevailed, and won him the Nobel Prize in 1954. Heisenberg's uncertainty paper, written in Copenhagen in early 1927, followed from the same algebra.

A popular telling says uncertainty arises because measuring a particle disturbs it, as if a photon nudges the electron. Heisenberg used that picture, but the principle is deeper: a wave confined to a narrow region is necessarily built from many wavelengths, so a sharp position means a broad spread of momenta, with or without an observer. Experiments in Vienna in 2012, testing a formulation by Masanao Ozawa, confirmed that the disturbance picture can be beaten while the intrinsic limit cannot. Uncertainty is a property of nature, not of clumsy instruments.

Did you know? The Sun shines because protons tunnel through an electrical barrier they lack the energy to climb; without quantum uncertainty, it would be dark.

Its fingerprints are everywhere. Uncertainty is why atoms have a size: squeeze an electron closer to the nucleus and its momentum, and hence its energy, must rise, so hydrogen settles at a radius of about 53 trillionths of a metre. It is why no object can be perfectly still, even at absolute zero, and why liquid helium never freezes at normal pressure. It allows tunnelling, in which a particle appears beyond a barrier it could not classically cross. In 1981 Gerd Binnig and Heinrich Rohrer at IBM in Zurich built the scanning tunnelling microscope on exactly this effect, and produced the first images of individual atoms. Flash memory stores every photograph on your phone by tunnelling electrons through a thin insulating layer.

Probability also governs when a given radioactive nucleus decays, and quantum random-number generators sell that unpredictability to cryptographers. Physicists still argue about what the wave "really" is; they do not argue about what it predicts. Nature, at bottom, keeps a book of odds, and it has never been caught cheating.

Entanglement

Two particles that have interacted can remain linked so that measuring one instantly fixes what a measurement of the other will show, however far apart they are. Erwin Schrödinger named this entanglement in 1935 and called it not one but the characteristic trait of quantum mechanics. The same year Einstein, Boris Podolsky and Nathan Rosen at Princeton argued that it showed the theory was incomplete: surely the results were decided in advance by hidden properties the particles carried with them, like a pair of gloves posted in separate boxes. For almost thirty years that was a matter of taste, not experiment.

In 1964 John Bell, a physicist from Belfast working at CERN, turned it into arithmetic. He showed that any theory in which outcomes are fixed locally in advance must obey an inequality in the correlations between measurements made at different angles, and that quantum mechanics predicts a violation of it. In the form later used in the laboratory, local hidden variables allow a correlation score of at most 2; quantum theory allows up to about 2.83. The question could now be settled by counting.

Counting began in 1972 at Berkeley, where John Clauser and Stuart Freedman measured the polarisations of photon pairs from excited calcium atoms and found the quantum value. In 1982 at Orsay, near Paris, Alain Aspect's team switched the analysers while the photons were in flight, so that no signal travelling at light speed could pass between them. In 2015 three groups, in Delft, Vienna and Boulder, closed the remaining loopholes: at Delft, entangled electrons in diamonds 1.3 kilometres apart violated Bell's inequality with every pair detected. Clauser, Aspect and Anton Zeilinger shared the 2022 Nobel Prize. The gloves-in-boxes picture is wrong; the correlations are not written down anywhere before the measurement is made.

Did you know? In 2017 China's Micius satellite sent entangled photon pairs to ground stations 1,200 kilometres apart, the longest-distance Bell test yet.

Entanglement does not send messages faster than light. Each observer sees only random outcomes; the correlation appears only when the two lists are compared, and that comparison travels by ordinary means. What it does offer is a resource. Quantum key distribution, proposed by Charles Bennett and Gilles Brassard in 1984 and in an entanglement form by Artur Ekert in 1991, lets two parties share a secret key and detect any eavesdropper, because listening disturbs the correlations. Quantum teleportation, demonstrated with photons in Innsbruck in 1997, transfers a quantum state using entanglement plus two ordinary bits. Quantum computers depend on entangling many qubits at once; that is what makes them hard to simulate and hard to build.

Entangled atoms sharpen atomic clocks and interferometers beyond the usual noise limit, and entangled photon pairs are used to calibrate detectors and to image with light that never touched the object. Einstein called the effect "spooky action at a distance". The spookiness survived every test; the distance turned out not to matter.

The Standard Model

The Standard Model is the inventory of everything matter is made of and the forces that act on it, bar gravity. It lists twelve particles of matter, six quarks and six leptons; four force carriers, the photon, the gluon and the W and Z bosons; and the Higgs boson, which gives the others their mass. Written out as a single equation it covers a page, and it has predicted the outcome of every particle experiment for half a century. Nothing in physics has been tested more thoroughly, and nobody believes it is the last word.

It was assembled rather than discovered in one piece. Murray Gell-Mann and George Zweig proposed quarks in 1964 to tidy the zoo of particles pouring out of accelerators; in 1968 electrons fired at protons at Stanford scattered as if off hard points inside. Sheldon Glashow, Abdus Salam and Steven Weinberg unified electromagnetism with the weak force between 1961 and 1967, and the theory of the strong force, quantum chromodynamics, arrived in 1973 with David Gross, Frank Wilczek and David Politzer. Each piece came with a prediction that could kill it.

The predictions kept coming true. In November 1974 teams led by Samuel Ting at Brookhaven and Burton Richter at Stanford found the charm quark on the same day. In 1983 Carlo Rubbia and Simon van der Meer's experiment at CERN saw the W and Z bosons at the masses the theory demanded. The top quark, as heavy as an atom of gold, turned up at Fermilab near Chicago in 1995 after a twenty-year hunt. The last piece was the Higgs boson, proposed in 1964 by Peter Higgs, and separately by François Englert and Robert Brout, and announced on 4 July 2012 by the ATLAS and CMS collaborations at the Large Hadron Collider, with a mass of 125 gigaelectronvolts. Each collaboration numbers around 3,000 physicists from more than forty countries, and the collider is a 27-kilometre ring beneath the French–Swiss border.

Did you know? The theory predicts the electron's magnetic moment to twelve decimal places, and experiment agrees: the most precise match in all of science.

The model has known holes. It says nothing about gravity or dark matter, and in its original form the neutrino has no mass; yet in 1998 the Super-Kamiokande detector in Japan, and in 2001 the Sudbury Neutrino Observatory in Canada, showed neutrinos changing type in flight, which requires mass. It cannot explain why the universe contains matter rather than equal amounts of matter and antimatter. Measurements of the muon's magnetism at Fermilab in 2021 and 2023 hinted at something extra, though theorists debate the prediction.

Its everyday reach is larger than the headlines suggest. PET scanners, cancer therapy with proton beams, the World Wide Web written at CERN in 1989, and the superconducting magnets in MRI machines all trace back to particle physics. The Standard Model is science's most successful theory and its most complete confession of what remains unknown.

Deep Time

Stand at Siccar Point on the Berwickshire coast and you can see two sets of rock meeting at an angle: near-vertical grey layers below, gently tilted red sandstone above. In June 1788 James Hutton rowed there with John Playfair and James Hall and read the junction as a story. The lower beds had been laid down flat on a seabed, tilted, raised, worn away over an unimaginable span, then buried again under new sediment. Playfair wrote that "the mind seemed to grow giddy by looking so far into the abyss of time". Hutton's conclusion, that the Earth showed "no vestige of a beginning, no prospect of an end", is the founding idea of deep time: the planet is old beyond ordinary intuition, and its rocks are a clock.

Reading that clock took another century and a half. Archbishop Ussher had set creation at 4004 BC in 1650; by the 1860s the physicist William Thomson, later Lord Kelvin, calculated from the Earth's cooling that it could be no more than a few hundred million years old, and later squeezed that to about 20 million. Geologists and Darwin's supporters protested that erosion and evolution needed far longer, but had no number of their own. The way out came from a discovery Kelvin could not have known: radioactivity. In 1904 Ernest Rutherford, lecturing at the Royal Institution with Kelvin in the audience, pointed out that the steady decay of uranium into lead was a timer with no need to be wound.

The English geologist Arthur Holmes made the method rigorous. In 1911, aged 21, he dated a Devonian rock at 370 million years by its uranium and lead; his 1913 book The Age of the Earth argued for at least 1.6 billion. The decisive measurement came in 1956. Clair Patterson at Caltech, using a mass spectrometer and lead from the Canyon Diablo iron meteorite, which formed with the solar system, obtained 4.55 billion years, give or take 70 million. Lead contamination from petrol and paint was so pervasive that he had to build one of the first ultra-clean laboratories to make the measurement at all; the experience turned him into the scientist who later forced lead out of fuel.

Did you know? If Earth's 4.54 billion years were compressed into one day, modern humans would appear in the final six seconds.

The modern figure, 4.54 billion years, has barely moved since. The oldest surviving rocks, the Acasta Gneiss of northern Canada, are about 4.0 billion years old; zircon crystals from the Jack Hills of Western Australia reach 4.4 billion, and their oxygen chemistry hints that liquid water existed almost from the start. Dozens of radioactive clocks now cross-check one another: potassium–argon for volcanic ash, rubidium–strontium and samarium–neodymium for ancient crust, carbon-14 for the last 50,000 years.

Deep time underpins the search for oil and ore, the reconstruction of past climates, and the timing of mass extinctions, such as the asteroid impact dated to 66.0 million years ago. The giddiness Playfair felt has become a routine measurement. The abyss has a depth, and it is 4.54 billion years.

Fossils and the Rock Record

A cliff face is a book with the oldest pages at the bottom. The Danish anatomist Nicolas Steno set out the rules in Florence in 1669: sediments settle in horizontal layers, each layer is younger than the one beneath, and a layer originally extended sideways until something cut it off. Three years earlier, dissecting the head of a great white shark, he had realised that the "tongue stones" found in Maltese rock were ancient shark teeth, turned to stone. Fossils were not sports of nature but remains of once-living things, and the layers that held them were a record of time.

William Smith, a canal surveyor, turned that record into a map. Digging cuttings across England in the 1790s he noticed that each stratum carried its own characteristic fossils, always in the same order, so a bed in Somerset could be matched with one in Yorkshire by its ammonites alone. His 1815 geological map of England and Wales, hand-coloured and two and a half metres tall, was the first of a whole country. On the Dorset coast, meanwhile, Mary Anning was finding the creatures themselves: a complete ichthyosaur skeleton dug out in 1812 when she was twelve, the first plesiosaur in 1823, a flying pterosaur in 1828. She sold them to make a living, taught herself anatomy, and was never permitted to join the Geological Society that discussed her finds. In Paris, Georges Cuvier compared mammoth bones with living elephants and in 1796 argued that species could vanish entirely: extinction was real.

Fossilisation is rare and biased. An organism must be buried quickly, usually in water, away from scavengers and oxygen, and most fossils are shells and bones of marine animals; soft bodies survive only in exceptional deposits. The Burgess Shale in the Canadian Rockies, found by Charles Walcott in 1909, preserves 508-million-year-old animals complete with gut and gills; the Chengjiang beds of Yunnan, from 518 million years ago, do the same. Ash layers between beds can be dated by radioactive decay, pinning the sequence to a calendar.

Did you know? In 2004 Neil Shubin's team found Tiktaalik, a fish with a neck and wrist bones, by searching 375-million-year-old rocks on Ellesmere Island chosen for exactly that age.

The record now runs from 3.5-billion-year-old microbial mats to yesterday's pollen. It documents five mass extinctions, including the end-Permian loss of about 90 per cent of marine species 252 million years ago, and the transitions Darwin hoped for: fish with limbs, dinosaurs with feathers, whales with legs. Index fossils such as trilobites, ammonites and graptolites still date rocks for oil geologists, and microscopic foraminifera from drill cores record the temperature of ancient seas in the chemistry of their shells.

Steno's principles remain the first lesson of every geology course. Read downward, a cliff is a journey into the past; read upward, it is the history of life.

Continental Drift to Plate Tectonics

Look at a map and South America tucks into Africa. Alfred Wegener, a German meteorologist, was not the first to notice, but in January 1912, in a lecture in Frankfurt, he was the first to build a case. The coastlines matched; so did rock formations and fossils on either side, including the fern Glossopteris and the freshwater reptile Mesosaurus, found in Brazil and South Africa and nowhere between. Ancient glacial scratches in India, Australia and Africa made sense only if those lands had once huddled near the South Pole. His 1915 book proposed continental drift: a single supercontinent, Pangaea, had broken up and its pieces had wandered.

Most geologists rejected it, and with some reason. Wegener could not say what force moved continents through solid ocean floor, and his suggested mechanisms were feeble. He died on the Greenland ice sheet in 1930 with the idea still a heresy. The answer lay under the sea. Arthur Holmes proposed in 1931 that slow convection in the hot mantle might carry continents like rafts. After the Second World War, sonar built for submarine hunting mapped the ocean floors, and in New York the geologist Marie Tharp, converting soundings into profiles, found in 1952 that a deep valley ran along the crest of the Mid-Atlantic Ridge: a rift, as if the floor were being pulled apart. Her colleague Bruce Heezen at first dismissed it as "girl talk", then saw that earthquake epicentres followed the rift exactly.

Harry Hess of Princeton put the pieces together in 1962 as seafloor spreading: new crust forms at the ridges and moves outward, returning to the mantle at deep ocean trenches. The proof was magnetic. The Earth's field reverses polarity every few hundred thousand years, and lava records the field as it cools. In 1963 Fred Vine and Drummond Matthews in Cambridge, and independently Lawrence Morley in Canada, showed that the ocean floor is striped with alternating magnetisation, symmetrical about the ridge: a tape recorder of spreading. Tuzo Wilson added transform faults and hotspot chains such as Hawaii, and by 1968 Jason Morgan, Dan McKenzie, Xavier Le Pichon and others had assembled the theory of plate tectonics: a dozen or so rigid plates, 100 kilometres thick, moving over a softer mantle.

Did you know? The Atlantic widens by about 2.5 centimetres a year, roughly the rate your fingernails grow, and GPS stations measure it directly.

The theory explains why earthquakes and volcanoes trace plate edges, why the Himalaya rise where India has pushed into Asia for 50 million years, why Iceland is splitting, and why the Pacific is ringed with fire. It guides the search for copper and oil, the siting of nuclear plants and the forecasting of tsunamis. Satellite positioning now watches the plates move in real time, Nazca sliding under South America at some 7 centimetres a year.

Wegener's continents do drift, though not as he imagined: they ride on plates, and the ocean floor is the engine. A heresy in 1912 became the organising principle of geology within sixty years.

Seismology: Listening to the Earth

Nobody has drilled more than 12 kilometres into the Earth, yet we know the planet has a solid inner core 1,220 kilometres in radius, a liquid outer core and a rocky mantle 2,890 kilometres deep. The knowledge comes from earthquakes. A large quake rings the planet like a bell, and the waves that pass through it bend, speed up, slow down or vanish according to what they meet. Seismology is the art of reading those waves, and most of the Earth's interior was mapped by it in the space of thirty years.

The instrument came first. In Japan in the 1880s the British engineer John Milne and his colleagues built the first reliable seismographs, pendulums that trace ground motion on smoked paper, and by 1900 Milne had set up a global network. Two kinds of wave travel through the body of the Earth: P waves, which compress and stretch the rock like sound, and slower S waves, which shake it from side to side. S waves cannot pass through liquid. In 1906 Richard Oldham noticed that P waves from distant quakes arrived late in a zone on the far side of the globe, as if something dense had slowed them: the first evidence of a core. In 1909, studying a quake near Zagreb, Andrija Mohorovičić found that waves arriving from below the crust travelled faster, revealing the boundary now called the Moho. Beno Gutenberg fixed the top of the core at 2,900 kilometres in 1914, and in 1936 the Danish seismologist Inge Lehmann, puzzling over faint P waves that should not have reached the shadow zone, showed that a solid inner core must be reflecting them.

Magnitude came next. Charles Richter at Caltech devised his logarithmic scale in 1935; each whole number means ten times more ground motion and about 32 times more energy. Seismologists now prefer the moment magnitude of 1979, which measures the fault's area and slip. The largest ever recorded, Chile in 1960, reached 9.5; the Tōhoku quake of 2011, at 9.0 to 9.1, shifted Japan's coast several metres eastward and launched the tsunami that wrecked Fukushima.

Did you know? Inge Lehmann kept her seismic readings on cards stored in oatmeal boxes, and worked out the inner core from the timings alone.

Today thousands of digital stations feed computers that tomographically image the mantle, revealing sinking slabs of old ocean floor and rising plumes beneath Hawaii and Iceland. Because P waves travel faster than the destructive surface waves, early-warning systems in Japan, Mexico and California send alerts seconds before the shaking arrives, enough to stop trains and shut valves. The same network polices the nuclear test ban, distinguishing an explosion from an earthquake by the shape of its waves. Seismology even reached Mars, where NASA's InSight lander recorded marsquakes from 2019 to 2022 and measured that planet's core.

The Earth cannot be opened, but it can be heard. Every earthquake is an X-ray of the planet.

The Atmosphere

The air weighs about five million billion tonnes, and every square metre of ground carries ten tonnes of it. That was the discovery of 1643, when Evangelista Torricelli in Florence inverted a tube of mercury into a dish and found that the column stood 76 centimetres high, held up by nothing but the weight of the atmosphere pressing on the dish. Five years later Blaise Pascal sent his brother-in-law up the Puy de Dôme with such a barometer; the mercury fell 8 centimetres on the climb, proving that the ocean of air thins with height.

It thins quickly. Half the atmosphere's mass lies below 5.5 kilometres, and three-quarters within the troposphere, the lowest layer, 8 kilometres deep at the poles and 18 at the equator, where almost all weather happens and temperature falls by about 6.5 degrees per kilometre. In 1902 Léon Teisserenc de Bort, flying unmanned balloons from Trappes near Paris, found that above about 11 kilometres the cooling stopped: the stratosphere, calm and layered, warming with height because its ozone absorbs ultraviolet light. Above 50 kilometres the mesosphere cools again to minus 90 degrees, where meteors burn; beyond 85 kilometres the thermosphere thins into the aurora and the orbit of the International Space Station at 400 kilometres. The conventional edge of space, the Kármán line, is set at 100 kilometres.

By volume the dry air is 78 per cent nitrogen, 21 per cent oxygen, 0.9 per cent argon and 0.04 per cent carbon dioxide, with water vapour varying from almost nothing to 4 per cent. None of this was given. The oxygen was put there by photosynthesis, beginning around 2.4 billion years ago with the Great Oxidation Event, and the ozone layer that lets life survive on land is a by-product of it. Gordon Dobson at Oxford began measuring ozone in the 1920s, and the unit of ozone column still bears his name.

Did you know? The ozone hole was found in 1985 by three British Antarctic Survey scientists using a 1950s instrument at Halley Bay, after satellites had been programmed to discard such low readings as errors.

That ozone record produced the atmosphere's most consequential discovery. Joe Farman, Brian Gardiner and Jonathan Shanklin reported in Nature in 1985 that springtime ozone over Antarctica had fallen by a third since the 1970s. Chlorofluorocarbons from aerosols and refrigerators, as Mario Molina and Sherwood Rowland had warned in 1974, were releasing chlorine that destroyed ozone on the surfaces of polar stratospheric clouds. The Montreal Protocol of 1987 phased them out, and the hole is slowly healing, with recovery expected around the 2060s.

The atmosphere is also the stage of weather forecasting, now run on supercomputers that take in satellite soundings, aircraft and 1,000 radiosonde balloons released twice daily around the globe, and of the greenhouse effect that the next chapters follow. It is a thin film: scaled to a schoolroom globe, it would be thinner than the varnish.

Ocean Currents

The sea is not still. A parcel of water that sinks off Greenland today will surface in the Indian or Pacific Ocean roughly a thousand years from now, having crept along the bottom of the Atlantic and round Antarctica. Ocean currents carry heat, salt, carbon and life around the planet, and they are the reason Britain is milder than Labrador at the same latitude.

The first scientific chart was a postal matter. In 1769 Benjamin Franklin, then deputy postmaster for the American colonies, learned from his cousin Timothy Folger, a Nantucket whaling captain, that mail ships took two weeks longer westward because they fought a strong current the whalers knew well. Franklin had the Gulf Stream engraved on a chart and measured its warmth with a thermometer on crossings. Matthew Maury of the US Navy gathered ships' logs into the first global wind and current charts in the 1850s, and the Challenger expedition of 1872 to 1876 sounded the deep oceans and found cold water at the bottom of the tropics, which could only have come from the poles.

Physics explained the pattern. The Swedish oceanographer Vagn Walfrid Ekman showed in 1905 that wind and the Earth's rotation make surface water move at an angle to the wind, driving the great gyres that circle each basin. Henry Stommel explained in 1948 why those gyres pile up on their western edges into narrow, fast jets like the Gulf Stream and Japan's Kuroshio. The Gulf Stream carries about 30 million cubic metres a second through the Florida Straits, swelling to over 100 million off Newfoundland, more than a hundred times the flow of all the world's rivers.

Did you know? A message in a bottle, or a container of plastic ducks lost overboard in 1992, can circle the North Pacific gyre in about three years.

The deep circulation is driven by density. In the North Atlantic, surface water cooled by Arctic winds and made saltier by sea-ice formation becomes dense enough to sink several kilometres; around Antarctica the same happens with even colder, heavier water. Wallace Broecker named the resulting global loop the "great ocean conveyor" in 1987 and warned that it could switch off. Since 2004 the RAPID array of moorings across the Atlantic at 26 degrees north has measured the overturning at around 17 million cubic metres a second, with large swings from year to year. Some 4,000 Argo floats, drifting at depth and surfacing every ten days to report temperature and salinity, have watched the oceans since 2000.

The currents also set the climate's rhythms. El Niño, the warming of the eastern Pacific every few years that Jacob Bjerknes linked to the trade winds in 1969, shifts rainfall from Indonesia to Peru and droughts across Australia. The ocean has absorbed about 90 per cent of the extra heat trapped by greenhouse gases and a quarter of the carbon dioxide; its currents decide where that heat goes. Franklin's postal shortcut turned out to be the planet's central heating.

Ice Ages

Twenty thousand years ago an ice sheet three kilometres thick covered Canada, another buried Scandinavia and the sea stood 120 metres lower than today, so that Britain was a peninsula of Europe. These were not legends but the last of dozens of ice ages, and discovering them meant first accepting that ice could carve a landscape. In 1837 the Swiss naturalist Louis Agassiz, prompted by the mountain engineer Ignaz Venetz and the salt-mine director Jean de Charpentier, told a startled meeting at Neuchâtel that the boulders strewn across the Jura and the scratched bedrock of the Alps were the work of vanished glaciers. Within a decade geologists in Scotland, Scandinavia and North America recognised the same signs. The Earth had once been far colder.

Why? In 1864 the Scottish janitor-turned-physicist James Croll proposed that slow changes in Earth's orbit altered the sunlight reaching high latitudes. The Serbian mathematician Milutin Milanković worked the idea out by hand between 1912 and 1941, computing how three cycles combine: the stretch of the orbit over about 100,000 years, the tilt of the axis over 41,000 years, and the wobble of the axis over around 23,000 years. When northern summers were weak, snow survived and ice grew. His curves predicted the timing of the glaciations, but geologists had no record precise enough to test them.

The record came from the sea floor. The oxygen in the shells of foraminifera carries a signature of how much water was locked in ice when they grew, and in 1976 James Hays, John Imbrie and Nicholas Shackleton, analysing cores from the Indian Ocean, found the 100,000-, 41,000- and 23,000-year rhythms in the data, with Milanković's cycles as the "pacemaker of the ice ages". Ice itself soon spoke. The Soviet Vostok core from Antarctica, published in 1987, reached back 160,000 years; the European EPICA core at Dome C, finished in 2004, covers 800,000 years and eight glacial cycles. Trapped bubbles show carbon dioxide swinging between about 180 and 280 parts per million in step with temperature, an amplifier that turned small orbital nudges into global change.

Did you know? Lake Agassiz, a meltwater lake on the edge of the retreating ice sheet, held more water than all the Great Lakes combined, and its sudden drainage may have cooled the climate for a thousand years.

Ice ages shaped the modern world. They scoured the Great Lakes and the Norwegian fjords, dumped the boulder clay of England and the loess soils of China, and dropped sea level enough to let humans walk from Siberia to Alaska. Far older events went further: around 700 million years ago glaciers reached the equator in a "Snowball Earth". We live in an interglacial that began 11,700 years ago; by orbital reckoning the next glaciation would be some 50,000 years off, though the carbon dioxide now in the air, at over 420 parts per million, is outside anything in the ice-core record. Croll's orbital clock still ticks, but we have changed the amplifier.

The Greenhouse Effect

Without its atmosphere the Earth would average about minus 18 degrees Celsius, a frozen ball. Its actual average is near plus 15. The 33-degree difference is the greenhouse effect: sunlight passes freely through the air and warms the ground, but the infrared heat the ground radiates back is absorbed by water vapour, carbon dioxide and a few other gases, which re-emit much of it downward. The name is a loose analogy, since a real greenhouse mostly works by stopping warm air escaping; the physics is radiation.

Joseph Fourier, in Paris in 1824, was the first to calculate that the Earth should be colder than it is and to suggest that the air traps heat. In 1856 the American scientist Eunice Foote filled glass cylinders with different gases, set them in the sun and found that the one with carbon dioxide grew hottest and cooled slowest; her paper was read for her at a scientific meeting in Albany, New York, and forgotten until 2011. Three years later John Tyndall at the Royal Institution in London built an instrument to measure how gases absorb infrared and showed that nitrogen and oxygen are transparent while water vapour and carbon dioxide absorb strongly. He grasped the consequence: change those gases and the climate changes.

Svante Arrhenius put numbers to it. In Stockholm in 1896, after a year of hand calculation, he estimated that halving carbon dioxide would cool the Earth by 4 to 5 degrees, enough for an ice age, and doubling it would warm it by 5 to 6. In 1938 the English engineer Guy Callendar showed that both carbon dioxide and global temperature had already risen, and in 1958 Charles Keeling began measuring the gas on the summit of Mauna Loa in Hawaii: 315 parts per million then, over 420 now, rising with a sawtooth as the northern forests breathe in each spring. In 1967 Syukuro Manabe and Richard Wetherald built the first computer model that handled radiation and convection together; it gave about 2.3 degrees of warming for doubled carbon dioxide, close to the modern range, and earned Manabe a share of the 2021 Nobel Prize.

Did you know? Venus, with an atmosphere 96 per cent carbon dioxide, has a surface temperature of about 465 degrees, hot enough to melt lead, though it receives less sunlight at the ground than Earth does.

The budget balances to within a few watts. Of the roughly 340 watts per square metre of sunlight arriving on average, about 100 are reflected by clouds, ice and air, 80 are absorbed in the atmosphere and 160 reach the surface. The surface radiates nearly 400 watts upward, but receives some 340 back from the sky; only 240 escape to space, matching what came in. Adding carbon dioxide raises the height from which heat finally escapes to colder, thinner air, so less gets out until the whole system warms enough to restore the balance.

Satellites now measure the outgoing infrared and see the carbon dioxide absorption band deepening year on year, a fingerprint Tyndall would recognise. The greenhouse effect is what makes the planet habitable; the argument of the past century has been about how much more of it we want.

Measuring Climate Change

A single thermometer tells you about a garden. To say the planet has warmed by 1.1 degrees since the late nineteenth century, you need an observing system that spans the globe, reaches into the deep ocean and back into the deep past, and checks itself constantly. Measuring climate change is the work of thousands of instruments and several independent teams, and the picture they agree on is now one of the best-tested results in science.

The anchor is the Keeling curve. Charles Keeling's measurements on Mauna Loa, begun in 1958 and continued through funding crises by his son Ralph, show carbon dioxide climbing from 315 to over 420 parts per million. Temperature records go back further. Land stations and ship logs since 1850 are assembled by the Met Office Hadley Centre and the University of East Anglia in Britain, by NASA and NOAA in the United States, by the Japan Meteorological Agency and, since 2012, by Berkeley Earth, a project begun by the physicist Richard Muller to test whether the others had got it wrong; it found they had not. All agree that the decade 2011 to 2020 was about 1.1 degrees warmer than 1850 to 1900, and that the warming has accelerated.

The ocean holds more than 90 per cent of the extra heat, so it is where the signal is clearest. Around 4,000 Argo floats have profiled the upper two kilometres since 2000; tide gauges since the 1800s and the TOPEX/Poseidon and Jason altimetry satellites since 1992 show the sea rising about 20 centimetres since 1900 and currently 3.7 millimetres a year. The GRACE satellites, flying in formation from 2002 and weighing the Earth by the pull on their orbits, found Greenland losing roughly 270 billion tonnes of ice a year. Ice cores, tree rings, corals and lake sediments extend the record thousands of years back, which is how Michael Mann and colleagues drew the 1998 "hockey stick" showing recent warming as unusual in a millennium.

Did you know? The stratosphere has cooled while the surface warmed, a pattern a brighter Sun could not produce but added carbon dioxide must, which is why it counts as a fingerprint.

Attribution is the final step. Nights have warmed faster than days, winters faster than summers, the stratosphere has cooled, and the carbon in the air carries the isotopic signature of fossil fuels. Each pattern is a fingerprint that natural causes cannot match. The Intergovernmental Panel on Climate Change, founded in 1988, has summarised the evidence in six assessment reports; the 2021 report called human influence on the climate "unequivocal".

The system has gaps, in the deep ocean below two kilometres, over Africa and the poles, and in the clouds that remain the largest uncertainty. But its strength is redundancy: satellites, buoys, balloons, thermometers and ice agree. Kelvin said that to measure is to know. The planet has been measured.

Earth from Space

The first photograph of the Earth from space was taken on 24 October 1946 by a 35-millimetre camera bolted into a captured German V-2 rocket fired from White Sands, New Mexico. At 105 kilometres it caught a grainy curve of horizon above cloud. The camera smashed on landing but the film, in a steel cassette, survived. Within a generation the view from above had become the main way of watching the planet: its weather, its ice, its forests and its slow, measurable changes.

The weather came first. TIROS-1, launched on 1 April 1960, sent back 23,000 television pictures of cloud systems in 78 days, and forecasters saw for the first time the spiral of a storm as a whole. Geostationary satellites from 1975 onward hung over the equator and made the looping cloud animation of the evening news possible; today no hurricane goes unseen from birth. On 24 December 1968 Apollo 8's Bill Anders photographed the Earth rising over the Moon's grey limb, and on 7 December 1972 the crew of Apollo 17 took the "Blue Marble", the whole sunlit disc with Africa and Antarctica. Both became icons of the environmental movement.

Science followed the pictures. Landsat 1, launched in July 1972, began the longest continuous record of the land surface, now more than fifty years of images at 30-metre resolution, free to anyone since 2008: deforestation in the Amazon, the shrinking of the Aral Sea, the spread of cities, all measured rather than argued over. Nimbus 7 mapped ozone from 1978; TOPEX/Poseidon measured sea level from 1992 to within a few centimetres by radar; the twin GRACE satellites from 2002 weighed groundwater, glaciers and ice sheets by sensing the tug on their orbits. Europe's Copernicus programme, with its Sentinel satellites launched from 2014, now images every point on Earth every few days.

Did you know? On 14 February 1990, six billion kilometres away, Voyager 1 turned its camera home and recorded Earth as a "pale blue dot" less than a pixel wide.

The orbital view has practical consequences on every scale. Weather satellites give days of warning of cyclones that once killed hundreds of thousands. Radar from Sentinel-1 maps floods through cloud and night and measures ground sinking in cities by millimetres. Infrared sensors spot wildfires within minutes, and sulphur dioxide instruments track volcanic plumes for aviation. GPS, itself a constellation of 31 satellites, has become the invisible infrastructure of transport, finance and farming.

Astronauts speak of an "overview effect", the shift that comes from seeing a world with no visible borders and a wafer-thin atmosphere. The instruments report the same thing in numbers: one planet, measured as a whole, changing within a human lifetime. The V-2's blurry horizon turned into a mirror.