Symmetry
Why Nature Repeats Itself
A Change Nothing Can Notice
Turn a cube a quarter of the way round, and it looks just as it did. Turn a ball by any amount at all, and it looks the same. That is what symmetry means in physics: a change you can make that nothing can notice. The ball’s kind is the more powerful. It works for any amount, however small, and that will matter.
Physics cares most about a bigger kind: symmetries of its laws, not of things. Move an experiment from Tokyo to Buenos Aires, turn it to face east instead of north, run it again next year, or run it on a train gliding smoothly along, and it comes out the same, once local things such as the Earth’s pull are counted in. The laws have no favorite place, direction, moment or steady speed.
None of this had to be so, and it is tested. Two kinds of atomic clock depend on the strength of the electric force in different ways, so if that strength drifted, their ticking would drift apart. Compared over years, they show it has not changed by more than a few parts in 10¹⁹ a year. Atoms in a galaxy so far away that we see it as it was eight billion years ago leave the same pattern of colors in light as atoms here, to about a millionth. The stretch of space on the way moves every color by the same proportion. A change in the electric force would move some colors more than others.
Every Symmetry Hides a Law
The mathematician Emmy Noether proved that every symmetry of the ball’s kind comes with a quantity that can never change. The laws are the same everywhere, so momentum is kept. They are the same in every direction, so angular momentum, the amount of turning motion, is kept. They are the same at every moment, so energy is kept. And they are the same at every steady speed, so the balance point of all the energy in a system left to itself moves in a straight line at a steady speed.
The reason is easiest to see for place. A ball rolls down a hill because the ground ahead is lower: the world is not the same from one spot to the next, and that difference pushes. Where the world stays the same along some line, nothing in it can favor one way along that line over the other. So the total motion along it, counted over everything that takes part, never changes. A single body can lose some only by handing it to something else, as a puck sliding on ice hands its share to the ice.
Time works the same way. If gravity were weaker on Mondays, you could lift a weight on a Monday, let it fall on a Tuesday, and get back more energy than you spent. Laws that never change rule that out, and that is where the conservation of energy comes from.
Where a symmetry fails, its quantity is no longer kept. A slope is not the same from one spot to the next, so a ball rolling down it gains momentum; the Earth takes up just as much the other way, since the laws themselves are still the same everywhere. Universe as a whole is stretching, so the stage itself is not the same from one time to the next, and over the whole of it no single total of energy stays the same. Light that crosses it for billions of years arrives stretched to redder colors, carrying less energy. With no single total to keep, the difference need not have gone anywhere, though some physicists balance the books with an energy of gravity, which can be counted in more than one way. Inside an atom, a planet or a galaxy, held together by its own forces, nothing stretches, and energy is kept as strictly as ever.
A Freedom That Needs a Field
Some symmetries have nothing to do with space or time. An electron is a ripple in the electron field, and at every point that ripple is at some stage of its rise and fall, called its phase. Draw the phase as a pointer turned round a circle. Only differences in phase between places can ever be measured. Turn every pointer in universe by the same amount, and nothing can tell.
That symmetry works for any amount, so by Noether’s rule it keeps something. What it keeps is electric charge. That is why the total charge never changes: charges are only passed along, or made and destroyed in plus-and-minus pairs. Every field takes part in the same turn, each pointer at a rate set by its charge: an up quark’s turns two thirds as fast as an electron’s, and the other way, and a neutrino’s does not turn at all.
Now ask for more freedom: let the pointer at each point turn by an amount of its own. That ought to show, because the differences between neighbors change, and differences are what experiments see. It cannot show only if something between the points takes up each difference: a field that records how far the pointer turns from one place to the next. Write down rules that keep this freedom, and that field comes out as the electromagnetic field. Its ripples are light.
The same idea carries over to symmetries that turn one kind of particle into another. A quark carries one of three kinds of strong charge, called colors, though they have nothing to do with the colors we see. A freedom to turn the three into any blend of one another, by any amount, demands eight gluons, the carriers of the strong force. A freedom to turn an electron into its neutrino, or a down quark into an up quark, demands the carriers of the weak force. This freedom touches only left-handed particles and right-handed antiparticles (handedness is, roughly, which way the spin turns round the direction of motion). That is why the W bosons, the carriers that change one kind of particle into another, act on those alone. Once a freedom is chosen, its force comes with it and is not added separately. Which freedoms nature has is read from experiment. Gravity rests on a freedom of a similar kind, in how places and moments are labeled, together with the fact that everything falls alike. It has not yet been joined to quantum physics.
There was a catch. These rules make every carrier massless, like light: a carrier with mass would make the field between the points cost energy to turn, and then the pointers’ turns would show. Yet the weak force reaches only a tiny distance, which takes heavy carriers. The way out came from the next idea. It passed its first great test when the W and Z bosons turned up at the masses it had foretold; the Higgs boson, found much later, confirmed the field behind it.
Symmetric Laws, Lopsided World
A pencil balanced on its tip has no reason to fall one way rather than another, yet it falls. Gravity pulls straight down and favors no direction along the table, yet the fallen pencil points one way. A symmetry can hold in the laws and be missing from what they produce. Physicists call this spontaneous symmetry breaking.
A magnet does the same. Above 770 degrees Celsius the tiny magnets of iron’s atoms point every which way. As the iron cools, neighbors line up, and each patch settles on one of the directions its crystal allows; which one, nothing in the laws decides.
This is the way out for the weak force. The Higgs field’s lowest energy is not at zero but in a trough around it, and the field sits in the trough. Its rules keep the symmetry; its value does not, and that hides the symmetry from view. The weak freedom turns out to be knit together with a second, simpler phase freedom, a close cousin of the electric one, with four carriers between them. The field in the trough sorts them: three become the heavy W and Z, and one combination stays massless, the photon, whose freedom is the electric one. Calculations with the known particles say the field settled there gradually as universe cooled, not in a sudden snap. Undiscovered particles could change that, and a sudden snap could have left ripples in space itself, gravitational waves, for future detectors to find. And unlike a magnet’s, the way it settled cannot be measured at all. This freedom holds at every point, so every point of the trough is the same universe, described another way; what is real is that the field is not zero. How strongly it holds each matter particle, the electron or each quark, is required by no symmetry. Each strength is read from the particle’s mass, and so far it has been checked directly only for the heaviest few.
The Mirrors That Crack
Some symmetries cannot be applied a little at a time. A mirror reflection is all or nothing, and so are two others: swapping every particle for its antiparticle, and running events backward in time. Noether’s rule does not reach these. Where the first two hold, they still keep something, by another route: a plus or minus sign that some particles, and groups of them, carry. But no deeper law requires any of them, and only experiment can say whether nature keeps them.
Experiment says no. The weak force breaks the mirror, and it breaks the mirror combined with the swap of matter for antimatter too. In particles called kaons, a decay and its matter-antimatter mirror image differ by a few parts in a thousand. In heavier B mesons they can differ by tens of percent, and the difference has recently been seen in the proton’s own family too, at about 2.5 percent. Time reversal has been caught broken directly, in B mesons.
One combination is far harder to break: all three at once, mirror, antimatter and time together. It can be proved that any theory obeying both relativity and quantum physics keeps it, as long as nothing in it acts at a distance. It requires an antiparticle to have exactly its particle’s mass, and an anti-atom to glow with exactly the same colors. So far it holds. An antiproton’s charge, divided by its mass, is a proton’s with the sign reversed, to 16 parts in a trillion, and antihydrogen takes up exactly the ultraviolet light that hydrogen does, to two parts in a trillion.
The cracked mirrors matter because universe is made of matter, with almost no antimatter left. The differences found so far are some ten billion times too small to explain that, so physicists look for a larger one, in neutrinos and elsewhere. And cracked mirrors are not enough. The young universe also needed a way to change the number of protons and neutrons, which no experiment has yet seen happen, and a time out of balance, when reactions running backward could not undo the gain.
A Bigger Symmetry, Not Yet Seen
The three forces of particle physics come from three separate symmetries. Many physicists suspect that these are pieces of one larger symmetry, broken like the Higgs field’s. Two clues point that way. The three forces’ strengths grow closer as the energy of a collision rises, though with the known particles alone they do not quite meet. And a proton’s charge matches an electron’s, sign reversed, to better than one part in 10²¹. A larger symmetry would make that match exact.
A larger symmetry would make quarks and electrons members of one family, and that has a price. A proton could turn into a positron and lighter particles, so matter would slowly decay. Nothing deep forbids it. Electric charge is guarded by a symmetry with a field of its own, the one whose ripples are light; the number of protons and neutrons is guarded by no such symmetry. Today the weak force changes it so seldom that it has never been seen. The theory of the known particles predicts that in the very hot young universe it changed that count all the time. The simplest version gave protons a life of no more than about 10³¹ years, and experiments have ruled it out. A tank of 50,000 tonnes of water in a mine in Japan, watched for decades, has seen no proton decay that way. That puts their life beyond 2.4 × 10³⁴ years.
Larger versions survive, with longer lives. A tank five times larger is due to start in 2028 and could see protons decay if they live up to nearly 10³⁵ years. A single clear decay would show that the count of protons and neutrons can change, and the way protons decay would point strongly to the forces once being one. Seeing none would rule out many of the favorite versions, but not the idea that the forces were once one.
