Trespassing on Einstein's Lawn (23 page)

If you look carefully at what the Higgs field is doing, you'll notice that something strange is happening to time. When a left-handed electron interacts with the Higgs field, it comes out a right-handed antipositron. And an antipositron is nothing other than an electron viewed in a different frame—namely, a frame in which time's arrow has been reversed.

Two observers will always agree on the time ordering of events, so long as they occur in regions where their light cones overlap. They might not agree on
when
the events occur, but they'll always agree on the order. For overlapping observers, “before” and “after” are invariant. But relative to some observer outside my light cone, those words lose all meaning. My before could be her after, her cause my effect. You wouldn't think you'd have to worry about that, given the fact that the two of us could never compare notes. But that's not quite true once quantum mechanics comes into play. According to the uncertainty principle, a particle that should be outside my light cone always has some nonzero probability of showing up inside it, skirting the laws of relativity. In doing so, it would appear to be traveling faster than light—which is to say, it would appear to be traveling backward in time.

It was Wheeler who first realized that an antiparticle is just an ordinary particle for which time's arrow has been reversed. Antiparticles have to exist to account for the fact that, for some observers, a
particle might look like it hitched a ride in a DeLorean. Particles and antiparticles—they're not two different things. They're two different points of view.

It's no coincidence that the Higgs field has just the right properties to patch up the differences created by our changing reference frames, because the Higgs field, it now dawned on me, isn't something that exists out there in ultimate reality. Like gravity, electromagnetism, and the nuclear forces, the Higgs is fictitious—it's something we're forced to add to our
description
of reality to ensure that we can treat all reference frames equally and don't confuse different views for different things.

That's what physics does, I realized. Every time we break the world apart with our reference frames, physics offers a way to piece it back together. Reverse the direction of each spatial coordinate, turning the universe into its mirror image, and physics changes. Reverse charges, swapping every particle for its antiparticle, and physics changes. Reverse the arrow of time, trading future for past, and again, physics changes. But do all three at once and physics remains the same. CPT symmetry, as the triplicate invariance is known, is a direct consequence of the Lorentz symmetry of spacetime. Charge, parity (or handedness), and the arrow of time work together to maintain the structural equivalence of reference frames, to ensure that we can't mistake different descriptions for different realities.

CPT symmetry revealed a deep connection between the structure of spacetime and the structure of matter. Whenever I'd asked physicists to define a particle, they'd say it was an “irreducible representation of the Poincaré symmetry group”—which, I figured, sounded better than saying it was “a little ball.” But now I finally understood what they meant. They meant that the symmetry of spacetime defines everything in it. Poincaré symmetry is the symmetry of the flat, gravity-free spacetime of special relativity, the symmetry that enforces an equivalence between inertial frames that are rotated relative to one another or that are moving at different uniform velocities or whose origins are at different locations. What we call “particles” are the most basic invariant structures that, in flat spacetime, won't disappear in any frame.

That reference frames matter so much—that they define what was beginning to seem like all of physics—was all Einstein's doing. The limits he imposed with a finite speed of light and the relativity of space and time meant that different observers have different views of the same ultimate reality. In Newtonian physics, where space was absolute and the speed of light was infinite, you didn't have to think about what different observers see, because they'd all see the same thing. Not in Einstein's world. In Einstein's world, you need rules for comparing different frames, for filtering out the artifacts of perspective. You need Lorentz and diffeomorphism transformations; you need gauge forces. In Einstein's world, our individual points of view shatter the unity of reality. Physics pieces it back together. It has to. Because reality is never really broken—it only appears that way.

Suddenly, the moral of the story about that falling pencil became clear to me. A paradigm of spontaneous symmetry breaking, I had read again and again, the pencil balanced on its tip can be knocked over by the slightest breeze, landing in one of an infinite number of equivalent ground states that encircle it, states of the lowest possible energy, where there's nowhere left to fall. The ground states, the story always goes, do not exhibit the original rotational symmetry of the vertical pencil—the symmetry has been broken.

But I now saw that the ground states are
gauges.
They're points of view. Which means
the pencil never really falls
—it only looks like it has fallen from the vantage point of an observer stuck in a gauge on the ground. From such a vantage point, the pencil casts a horizontal shadow, a shadow we mistake for the real thing, a shadow that doesn't enjoy the original rotational symmetry. To see the full symmetry, you'd need a God's-eye view from which you could see the pencil from every point around its circumference simultaneously. Since that's impossible, we're stuck having to infer the rotational symmetry from our limited vantage point. And we can do it by traveling 360 degrees around the pencil, transforming from one reference frame to the next as we go, gauge after gauge, remembering to account for the slight shifts in angle required to keep the pencil in view as we make our way around the circle. Gauge symmetry ensures that such transformations are possible. Gauge forces do the shifting.

Wilczek had suggested that perhaps spontaneous symmetry breaking created the universe by shattering the symmetry of nothing. That explanation had bugged me, though, because it wasn't really an explanation at all—by invoking some kind of preexisting quantum breeze, it violated Smolin's slogan: “The first principle of cosmology must be ‘There is nothing outside the universe.' ” But if the pencil never really falls, maybe the universe never really begins. Maybe it just looks like it did from here inside it.

In and of themselves, symmetries don't break—they just appear broken when our reference frames are finite and the full symmetries of ultimate reality can't fit within our view. If you could see the whole of spacetime from some Archimedean point outside the universe, every wavefunction's phase would be aligned and every angle of the pencil would be simultaneously visible. Symmetry would reign. Forces would disappear. And what would be left behind, invariant? That, I knew, was the ultimate question. The answer, whatever it was, was the ultimate reality.

Here—inside the universe, under the covers, stateside—I was left to view things through a funhouse mirror, hoping to reconstruct a single reality from a deceptive multiplicity. Still, I had to admit the distortions were pretty extraordinary. Spin, charge, handedness, speed, causality, mass … they all fit together in precisely the right way to keep reality intact despite our fractured viewpoints, and in doing so give rise to the world. From afar, physics looks so messy, so replete with ingredients, with so many arbitrary parameters. Only the truth is, none of it is arbitrary. It's all working toward the same goal: to account for how some singular reality appears from every possible point of view.

That was what I loved about physics—that moment of pure surprise when you suddenly realize that what you had thought was one thing is really something else, or that two things that seemed so different are really two ways of looking at the very same thing. It was the perennial comfort that comes from discovering that the world is not remotely what it seems.

I had grown pretty adept at faking the stuff of everyday living, but I had never been very good at it. At paying bills or doing dishes, at
meeting for coffee or making small talk, at any of the daily proceedings that constitute life here on the surface of things. Sometimes I'd walk down the street feeling like everyone else was gliding past me, unfettered, like my feet were somehow heavier than theirs and I could feel the ground buckling beneath me, like I might plunge through at any moment, like I would give anything to plunge through, only you're not allowed to, because life is here on the surface and you just have to hang on and try not to slip through the cracks. It was a feeling that on some days left me wondering whether I was a trespasser not only at physics conferences and editorial meetings but here in the world, on the surface, too. Then, on nights like tonight, I'd catch a glimpse of the underlying structure, of the world beneath the world, the truth below the surface. I'd see the way everything was so perfectly connected to everything else, the way it was all governed by simple notions of singularity and symmetry—and it was just so fucking beautiful.
“I believe that nature is a perfect structure,” Einstein wrote. Lying there in bed in the dark, I was beginning to understand exactly what he meant.

“I've been thinking more about invariance and its relation to symmetry,” my dad said, passing the syrup across the table. We had come to IHOP for a late breakfast. “Noether's theorem says that for every continuous symmetry there's some conserved quantity—an invariant. If we're hunting for invariants, the symmetries will help us find them.”

“That makes sense,” I said. “Symmetries tell you what remains the same when you transform between frames.” I couldn't decide which to dig into first, the omelette or the pancakes. They looked symmetrically delicious. Wasn't this how some philosophical donkey starved to death? Buridan's ass?

“Right. A snowflake has 60-degree rotational symmetry because if you rotate it by any multiple of 60 degrees it looks the same as the original. But that's a discrete symmetry—there are still reference frames, say a rotation by 64 degrees, in which its appearance isn't invariant. That's why you need a continuous symmetry to find real invariance, so that there's no possible frame in which the thing changes.”

“Okay,” I said, “so let's look at continuous symmetries.” I went for the pancakes. Symmetry broken. No asses were going to starve today.

“Well, the translational symmetry of space gives you conservation of momentum, and the rotational symmetry of space conserves angular momentum,” my father said. “Time translation conserves energy. Rotational symmetry of four-dimensional spacetime conserves spacetime intervals. And gauge symmetry conserves charge.”

“All right, that gives us some candidates for what's real. Let's make a list,” I said, digging a pen out of my purse. On my napkin I wrote,
Ingredients of ultimate reality.
“Let's just list anything that could possibly be real, and then we'll look at them more closely. Let's see … space, time, spacetime, gravity, electromagnetism, the nuclear forces, mass, energy, momentum, angular momentum, charge … what else?”

“How about the number of dimensions?” my dad asked. I wrote it down. “Or particles? We should assume particles are real, right?”

“Unless they're strings,” I said.

“Well, particles are excitations of fields, so particles and fields really should go together. And the fields are defined in terms of the vacuum.”

I nodded, adding them to the list.
Particles/​fields/​vacuum. Strings.
“How about the universe? You'd hope that was real. Maybe that goes without saying?”

My dad shook his head. “Nothing in physics goes without saying.”

I added
universe
to the list. I paused, then added
multiverse
, too.

“The speed of light,” my dad said, pointing to the list as he took a sip of coffee. “That's the ultimate invariant.”

I wrote it down.
Speed of light.

“Bostrom would say that we need to question the reality of reality,” I said. “But I think adding it to the list could send us into some kind of turtle-laden vortex.”

“Skip it.” He nodded. “It would be like listing cake as an ingredient in cake.”

“Okay, so let's see,” I said, turning the napkin so that we could both read the list. “Based on relativity, we can cross off space and time. They're both observer-dependent.”

“You can cross off gravity,” my dad said. “And the other forces.
They're all fictitious. What about mass? Mass is invariant, right? Or at least rest mass?”

I swallowed a gulp of coffee and shook my head. “It's not. Rest mass is invariant in special relativity, but in general relativity it's not well defined. In order to define it you have to break general covariance—you have to choose a time coordinate, and that sets a preferred frame. Mass is only defined within specified frames, and since E = mc
²
transforms mass into energy, the same goes for energy. They're observer-dependent.” I crossed them off the list. “And momentum and angular momentum are defined in terms of mass, so they become observer-dependent under general relativity, too.”

“Even in quantum field theory mass changes with scale,” my dad said. “With the resolution at which it's measured.”

I nodded. “The standard model says that all particles are ultimately massless—mass only arises as a consequence of symmetry breaking or the structure of the vacuum at low energies or interaction with the Higgs field. At high enough energies, mass disappears.”

“Should we have put the Higgs on the list?”

“I think ‘particles/​fields/​vacuum' covers it.”

“Okay,” my father said, scanning down to the next item on the napkin. “What about charge? Isn't charge conservation violated in some kinds of weak nuclear decay?”