Conservation Laws
What Nature Refuses to Lose
Totals That Never Change
Some quantities in nature are never made and never lost. Add one of them up over everything in a closed space, one that nothing enters or leaves and nothing outside pushes or pulls on, and the total stays the same, whatever happens inside. Four such totals are kept exactly, in every measurement and by the laws themselves: energy, momentum, angular momentum (the amount of turning motion) and electric charge. Two more, met below, have never been seen to change either, but nothing deep in the laws guards them.
They are kept in a stricter way, too: from place to place. Charge cannot vanish here and appear on the Moon at the same instant, even though the total would come out right. Seen from a passing rocket, the two would not happen at the same instant, and for a while the total would be wrong. Charge can only flow, across every border on the way. So can energy and momentum, and the fields between things carry their share: light crossing empty space carries both, and pushes on whatever it lands on.
Energy changes form the most. A ball held up above the ground stores energy, together with the Earth, because of the height between them; let it go, and that energy turns into motion. When a moving block of atoms runs into one at rest and the two stick, much of the motion turns into a jiggle of their atoms, each in a direction of its own, which we feel as warmth. None of the energy is lost. It only becomes harder to see, and harder to get back.
Momentum cannot hide that way. The jiggle runs every way at once and adds up to none, so the pair glides on, keeping the momentum the moving block had. Its balance point, the ring of light that marks out each second in the picture, never changes pace.
Each of these is kept because the laws of physics stay the same in some way. They are the same at every moment, so energy is kept; the same everywhere, so momentum is kept; the same in every direction, so angular momentum is kept; the same at every steady speed, so that balance point keeps a steady speed in a straight line. A quieter sameness in the quantum fields keeps charge. Where a sameness fails, its total is no longer kept. Universe as a whole is stretching, and over the whole of it no single total of energy stays the same: light that crosses it for billions of years arrives with less energy than it set out with, and the difference need not have gone anywhere. Some physicists balance the books with an energy of gravity, but it can be counted in more than one way. Inside anything held together by its own forces, from an atom to a galaxy, every one of these is kept as strictly as ever.
The Ending Without the Story
A kept total tells you how something ends without following how it happens. Let a ball roll down a track, gripping it without slipping, with nothing rubbing. The energy of its height turns into energy of motion, part of it in the ball’s spin, and at the bottom it moves exactly as fast as its drop allows, whatever the track’s shape. A track that drops early gets it there sooner, and one that drops late gets it there later, but both deliver the same speed.
A roller coaster runs on this rule. On one with a single chain lift and nothing else to push it, every later hill has to be lower than the first: nothing pays for climbing higher, and the wheels and the air turn a little of its energy into warmth all the way round.
Momentum settles collisions the same way. A car that runs into an identical car standing with its brakes off, and locks onto it, moves off at half its speed, however the metal crumples. Energy then says where the rest went: half the energy of motion has turned into warmth and bent metal, the jiggle of the picture above. A rocket in empty space has no ground or air to push on. It pushes its exhaust backward, the exhaust pushes it forward, and the two momenta still add up to what they were before.
A spinning skater who pulls in their arms spins faster: the turning motion is kept while the mass comes closer to the axis. The faster spin carries more energy, and the arms supply it, pulling the hands in against their swing.
Kept totals also say what can never happen. No machine can keep doing work forever with nothing feeding it, or give out more energy than it takes in. Patent offices know it: the United States one does not normally ask an inventor for a working model, except of a machine claimed to run forever.
Mass Is Not a Total of Its Own
For a long time mass seemed to be kept as a total of its own. Chemists held that every chemical change leaves as much matter as it found. Sealed flasks, weighed before and after reactions inside them, showed no change, to better than one part in ten million.
But energy has mass. Anything that gives out energy, as heat, light or anything else, gets lighter by that energy divided by the square of the speed of light, a huge number. The flasks did get lighter once the heat of the reaction had passed out through the glass, but by less than a billionth of their weight, far below what the scales could see. A flask that let no heat out would weigh just what it weighed before. A charged phone weighs more than a flat one, by about half a billionth of a gram.
What is not kept is the mass of the pieces. Four hydrogen atoms weigh about 0.7 percent more than the one helium atom they become when they fuse, and the difference leaves as light and neutrinos. That is how the Sun shines, and the light it sends out alone takes about 4 million tonnes a second from its mass. Physicists have weighed silicon and sulfur atoms against the lighter atoms and the neutron that build them, and measured the ray of light given out when such an atom takes in a neutron. The mass that went missing matched the ray’s energy to 4 parts in 10 million.
So mass is not a separate total. It is the energy a thing has at rest, counted in kilograms: a closed space keeps its mass because it keeps its energy, while its pieces need not add up to it. Most of the mass of a proton is not the mass of its quarks at all, but the energy of the gluon field inside it, and of the quarks moving in that field.
Why Anything Lasts
Kept totals also decide what lasts. A particle can break up only into lighter ones, since the mass of what it leaves behind has to be paid for out of its own. And the pieces must carry the totals it had: the same charge, and the same two counts that no experiment has yet seen change. One is the count of quarks; the other is the count of leptons, the electron’s family, which includes the neutrinos. An antiparticle counts as minus one.
That rule sorts the particles. The electron is the lightest particle with an electric charge, so it has nothing lighter to pass its charge to. If charge is kept, an electron lasts forever. A detector under a mountain in Italy watched for an electron turning into a neutrino and a flash of light, and saw none. An electron lasts longer than 6.6 × 10²⁸ years, some five billion billion times the age of universe.
Quarks are never found alone. They come in bundles: three, as in the proton; a quark with an antiquark, whose count is zero; and rarer bundles of four or five, whose counts come out to zero or three. So nothing lighter can take over a count of three, and the proton, the lightest bundle with a count of three, lasts as long as the count of quarks is kept. One way many theories favor for it to break up, into a positron and a lighter particle called a pion, would take longer than 2.4 × 10³⁴ years, if it happens at all.
A neutron weighs a little more than a proton and an electron together, so it can turn into a proton, an electron and an antineutrino: one lepton and one antilepton, together none. Alone, it does, in about a quarter of an hour on average. Inside the nuclei of ordinary, stable atoms it does not, because there the change would cost energy instead of releasing it, so a neutron there lasts as long as the count of quarks is kept.
Particles are made under the same rules. A ray of light passing close to a nucleus can turn into an electron and its antiparticle, the positron: charge minus one and plus one, together zero, as before. It needs the nucleus. For its energy, a ray of light carries more momentum than any electron and positron could carry off together, and the nucleus takes up the rest. Whatever is made and whatever decays, the chains end in electrons, protons, neutrinos and light, or their antiparticles; the charged ones last only until they meet matter. That is why the world around us is built from electrons, protons and the neutrons held in nuclei.
The Books That Would Not Balance
Once, the energy books seemed not to balance. Some radioactive atoms throw out a heavy piece, an alpha particle. Atoms of one kind throw it out with the same energy every time (or one of a few), as they must. The atom changes by a fixed amount, and when anything splits in two, the pieces fly apart with equal and opposite momentum; so they can share a fixed amount of energy in only one way. Atoms that give out electrons instead, in what is called beta decay, do not. Their electrons come out with every energy from almost nothing up to the full amount the change releases.
The picture sorts the electrons with a magnet. A magnet bends a moving electron into a half circle, wider the faster it goes, back onto a plate where it lands. An electron with the whole energy released would land at the far mark. None does: each lands short of it, by an amount of its own.
Perhaps the missing energy left as rays the instruments missed. To test that, physicists put a sample of one such element, bismuth-210, inside a heat meter that would catch anything its atoms gave out short of passing through the walls. The heat matched the average electron’s energy, about a third of the full amount. The rest was not hiding in the sample. It had left without a trace.
Some physicists were ready to give up the conservation of energy for single atoms, keeping it only on average. The other way out looked desperate: a particle with no charge, so light and so shy of matter that no one had noticed it, leaving each decay with the energy the electron lacked. It also solved a second puzzle, about the spins of some atomic nuclei. It was named the neutrino, the little neutral one, and a theory of beta decay was soon built around it.
Later, measurements of the atoms recoiling from the decay showed that momentum went missing too, just as such a particle would carry it off. Neutrinos themselves were caught beside a nuclear reactor 26 years after they were proposed. When a kept total seems to fail, the first suspect is something nobody has seen yet. But not every rule passes such a test. The rule that a process and its mirror image are equally likely, called parity, failed outright, broken by the weak force.
Counts Still on Trial
The two counts are kept for now, but nothing deep guards them. Charge is kept by a sameness of the laws. The counts of quarks and of leptons hold today only because the one known process that can change them, a rare act of the weak force, is too slow ever to have been seen. The theory of the known particles predicts that in the young universe, hotter than a million billion degrees, it changed both counts all the time, nine quarks and three leptons at a time.
A finer count has already broken. Physicists once kept separate counts of the electron’s type of lepton and of its two heavier cousins’, the muon and the tau. Then two underground detectors, one in Japan and one in Canada, showed neutrinos turning from one type into another on their way. The one in Japan counted neutrinos made high in the air, where cosmic rays strike it. Those of the muon type coming down from the sky overhead arrived in full number. Of those coming up through the whole Earth, about half had turned into another type on the long way. A neutrino travels as a blend of three waves of slightly different masses. On the way they drift out of step, and the chance of catching it as each type rises and falls.
Only neutrinos have been caught at it. No muon has been seen turning into an electron and a flash of light; if it happens at all, it happens in fewer than one decay in 6.7 trillion.
The whole count of leptons is being tested with a rare kind of decay. Xenon-136 cannot turn one neutron into a proton, because cesium-136, which that would make, weighs more. It can turn two at once, giving out two electrons and two antineutrinos, so seldom that half its atoms would take about 2 × 10²¹ years to go. If a neutrino is its own antiparticle, the brief stir in the neutrino field made by one change could be taken up by the other, and the decay would give out no neutrinos at all, only two electrons carrying its whole energy: two leptons made from none.
A detector in Japan, watching xenon dissolved in a tank of liquid, has seen no such decay. In a tonne of xenon-136 the ordinary double decay happens about 1.4 million times a year; the kind without neutrinos, if it happens at all, about eight times at most. Larger experiments are being prepared, among them one that will watch a tonne of germanium-76. Electrons sharing the whole energy, seen even a few times, would show that the count of leptons can change, and that a neutrino is its own antiparticle.
It matters beyond bookkeeping. Universe is made of matter, with almost no antimatter left, and for that the young universe needed some way to change the count of quarks. One favored idea starts with the count of leptons, changed by neutrinos far heavier than ours, and the weak force passing that change on to the quarks. The totals that guard the world we know may be the very ones that, once, had to break to make it.
The Total of All Chances
Quantum physics adds one more kept total. It cannot say for certain what a single particle will do, only how likely each outcome is, and those chances always add up to exactly one: something certainly happens.
A half mirror shows it with light. Send it one photon at a time, with a detector on each side, and no one can say which detector will catch the next. Each photon’s wave goes both ways, but with perfect detectors, each photon is caught whole by one detector or the other, never by both and never by neither. The chances are half and half; for a mirror with a thinner coating, four in five and one in five. Either way they add to one.
The chances add to one because of a deeper rule, called unitarity. As a closed system changes, its wave keeps its overall size, which holds the total chance at one, and two different starting states never turn into one. So nothing is truly lost, and its equations, run backward, bring every earlier state back. Whether a measurement itself breaks the rule is still argued over.
This total made a prediction of its own. Without the Higgs boson, the theory of the weak force gave two W bosons meeting head-on a chance of bouncing off each other that grows with their energy. Once they collided with between one and two trillion electron volts, it would pass 100 percent. So something new had to appear by that energy, the Higgs boson or something else. The Large Hadron Collider was built to reach it, and it found the Higgs boson, at 125 billion electron volts.
Black holes are the other place this rule is argued over. Quantum physics predicts that a black hole slowly glows away, and at first the glow seemed to carry nothing of what fell in. The chances would still add to one, but running the equations backward could never bring back what fell in. In the last few years, calculations in simplified models have found signs that what fell in does come out with the glow. Most physicists now expect that nothing is lost, but no calculation yet shows how it gets out, and nothing has been observed.
