Symmetry is easily recognizable in art, architecture, even anatomy. But the concept of symmetry in physics is hard to wrap one’s head around. Yet it is here that symmetry has played one of its most important roles, unlocking the secrets of the forces in nature and of the fundamental particles that inhabit our universe. “The biggest conceptual change over the last 100 years in the way physicists think about the world is symmetry,” says theoretical physicist Lawrence Krauss of Arizona State University.
Mathematical symmetry, which Krauss describes as a kind of rule book of nature, has guided scientists to discover the quarks that make up the protons and neutrons in atoms, the gluons that bind them, and eventually the current crowning achievement of particle physics: the Higgs boson that explains how particles get their mass. It has allowed researchers to unify some of the forces in nature—for instance uniting electricity and magnetism into electromagnetism and later adding the weak force to make the electroweak interaction.
In his new book, The Greatest Story Ever Told—So Far: Why Are We Here? (March 2017, Simon & Schuster), Krauss details how symmetries have led the way to the major breakthroughs of modern particle physics. Scientific American spoke to Krauss about the meaning of symmetry in science, how symmetry got “broken” in important ways during the history of the universe and what role it could play in both future research and the fate of our entire cosmos.
[An edited transcript of the interview follows.]
When physicists talk about symmetry, they mean something particular. What is scientific symmetry and why is it so important?
Symmetry does mean something different for physicists than for members of the public. It means that an object or a theory does not change when you make some transformation—either rotating or moving it or doing something to the equations. For a physicist or a mathematician, the most symmetrical object you could think about would be a sphere, because it looks identical no matter what you do to it, however you rotate it in any given direction.
Symmetries are the playing field on which the physical world works and which determine the rules of the game. The symmetries of nature determine for us things that remain constant, that can’t be changed. Those are the guideposts in physics, the quantities like energy and momentum. For instance, energy is conserved, we now understand, because there is a symmetry of nature that tells us the laws of physics don’t change over time.
You call a certain type of symmetry, gauge symmetry, the most important symmetry of nature. What is gauge symmetry?
The fact that you have to ask that question is important. There’s been a total transformation in the way we think about the fundamental physical world because of gauge symmetry, but no one knows about it. It happened between about 1960 and 1975, which from a theoretical perspective was the most revolutionary period of the 20th century in understanding the universe. All the laws of physics have this symmetry and it guides us in looking for new laws.
Gauge symmetry starts simply with a symmetry that most people are familiar with. That is the conservation of electric charge, the fact that whenever I produce a positive charge I have to have a negative charge to balance it if the system is neutral. Electrons have what is called negative charge, but negative charge is just a human term—it doesn’t mean anything physically. We might have called electrons the positive charges. So the sign of charge is an arbitrary thing. We could change the sign of every electric charge in nature and the world would look identical. That’s symmetry.
But that’s not gauge symmetry.
Right. The term itself—“gauge” symmetry—is something of a misnomer that has absolutely no meaning in its application to forces of nature. The “gauge” part comes from work in 1918 by the mathematician Hermann Weyl, who was examining geometric symmetries in general relativity. Weyl discussed changes in scale as changes in “gauge”—a reference to the gauges that measure the distance between the rails of a train track.
Back to your question: “What is gauge symmetry?” Again, symmetries imply laws that don’t change—like everything staying the same if every positive charge turned into a negative charge and vice versa. Well, gauge symmetry expresses a deeper, really weird symmetry, in which you can show equivalence between two things—“positive” and “negative,” for instance—by defining what is “positive” and “negative” locally, by setting certain conditions that map the two together. It’s a very subtle idea that has required us to stretch our minds to their limits, but it’s important to know about, because it actually helps constrain theorists and ensure that our mathematics are consistent and make sense.
I’m not sure I understand…
So, imagine the universe as a big chessboard. I could change every white square on a chessboard to a black square and every black square to a white square and the game would be exactly the same. That’s the simple kind of symmetry. Now I can turn it into a gauge symmetry by making it much trickier. I can say, “Let me just change locally, whenever I want, a white square to a black square or a black square to a white square. Not everywhere but place to place." Now the chessboard doesn’t look the same at all, so the game can’t be the same unless I also have a rule book—a coordinate system for what happens at every point—containing rules for the pieces of the chessboard to follow to keep the game the same, rules that account for everywhere I have changed the color of a square. That becomes a very weird symmetry.
As I explain in the book, this sort of symmetry tells you how to go from the conservation of charge to the theory of electromagnetism. It says, “I could change the sign of each electric charge in nature locally. But I have to have a rule book.” What's the rule book? In this case, it’s the electromagnetic field. Even though gauge symmetry is something that most people find obscure, it’s the most visible thing in the world—and if you don’t have it, things fall apart in surprising ways. Whenever you look at a lightbulb, you're able to see light because nature has this weird symmetry.
When did physicists realize how important gauge symmetry was?
All of this was discovered after the fact. Maxwell developed his equations of electromagnetism in the 1800s. But people began to recognize this symmetry once again when it came to Einstein’s general relativity, which was guided by another kind of gauge symmetry. Now this became really interesting because the two most fundamental theories that we knew of in nature at the time—electromagnetism and gravity—are suddenly determined by this weird mathematical symmetry. That leads to the question: If there are other forces in nature, are they determined by this same kind of symmetry?
But if you’d asked these questions in the 1930s through the early ‘50s, you still wouldn’t have heard physicists talking about gauge symmetry as the guiding principle. It was only after the fact they began to realize how useful it was. One of the reasons I wanted to write this book, and the reason it’s called The Greatest Story Ever Told, is if it were easy, it wouldn’t be the greatest story ever told. I wanted to show the long and convoluted path that people took to enlightenment. It’s a tremendous story because it involves great leaps of the imagination, great failures, great blind alleys and red herrings. In any case, the real heart of the idea is to understand that the world we live in and the other forces in nature was a search to ultimately apply this idea of gauge symmetry to these other forces.
How did the idea of “broken symmetry” fit into this search?
Some symmetries exist in the fundamental world, but when we look around we don’t see them. What’s happened is that as an accident of our circumstances, the symmetry isn’t manifested. We say it’s broken. An example is sitting down at a round banquet table and not knowing which water glass is mine. Say there are eight chairs at the table and it looks identical. There’s a symmetry because the glasses to the left and the right look exactly the same. But the first person to sit at the table and pick up a glass of water determines for everyone else which glass they have to pick up. That means they break the symmetry.
This idea of broken symmetry turns out to be the fundamental key that solves a problem with the other forces in nature—the weak and the strong forces—which don’t behave like electromagnetism. The weak force and the strong force both only operate on subatomic scales and they’re very, very different. Physicists eventually realized that in an underlying way those theories might actually look identical to electromagnetism and have a gauge symmetry that determines their nature, but some accident of our circumstances hides that fact from us.
An example is ice on a window on a cold day. Ice crystals are pointing in every different direction on the window. But if you were a civilization that lived on that ice crystal, then the direction along which the ice crystal pointed would be a very special direction. It would be a fundamental aspect of your universe. What would be hidden to you is the fact that the direction of the ice crystal is irrelevant, that the laws of physics are the same independent of this direction.
And this realization helped explain why these other forces behave differently than electromagnetism?
Let’s say we’re living in something very much like an ice crystal, and due to an accident of our circumstances some weird field froze into existence that fills empty space. If that’s the case, the particles that interact with that field act like they’re very heavy even if in reality they are weightless. Then you could understand the weak force because you could say that at a fundamental level, the particles that convey the weak force really are massless just like the photons that convey electromagnetism. In the world in which we live, those particles act like they’re massive, so the force we see is very different than it would be if we didn’t live in this accidental universe. The world of our experience is an illusion in which the forces are very different, but that’s only because there’s this invisible field that exists everywhere that affects the properties of certain particles and not the properties of other particles.
And this invisible field you’re talking about is the Higgs field, which is linked to the famous Higgs boson and which we think explains mass?
This is what physicist Steven Weinberg did, was say, “Maybe it’s not just the mass of these weird particles that convey the weak force, but maybe it’s the mass of all particles we see,” that certain particles interact more strongly with that background field and they behave heavier. Other particles interact less strongly with that background field and behave lighter. Some particles like the photon don’t interact at all. If that’s the case, then the universe of our existence is really a total illusion, because mass itself is not fundamental. If it weren’t for this weird accident that we live in this universe with this background field that’s frozen into existence, there would be no massive objects. There would be no stars, no galaxies, no planets, no people, no Scientific American, no Scientific American reporters. It would be a much less interesting world.
What kind of accident could have created this field?
We think symmetry has been broken in the past as the universe has cooled down in the aftermath of the big bang, causing the Higgs field to freeze in the state it did. It’s like the ice crystals on the window—and when the sun comes out, those crystals melt. Suddenly, the universe that those people thought they lived in disappears. The question then becomes, why did it settle into the configuration it did in the early universe? Why does it have the properties it has? None of that is explained within the theory.
And what's going to happen to that field in the future? It’s not fundamental. It’s the preferred state for that field to be in now. But maybe as the universe evolves, that field will either melt or another field may freeze. That would change the fundamental nature of the forces in the universe. If the Higgs field were to melt, then all particles become massless and everything we see would disappear. Or it could be that the Higgs field will freeze into a different configuration where the masses of particles will change completely and again, neutral stable matter will disappear. In some sense we’re at the hairy edge of a universe that might be unstable. The Higgs field probably won’t melt tomorrow—but in the far future, it might. We're lucky to be here to be able to ask these questions. We should enjoy our moment in the sun.