Trespassing on Einstein's Lawn (22 page)

When it comes to the quantum forces, the “things” are no longer space and time but quantum wavefunctions. And the key thing about wavefunctions is that, like all waves, they have a phase.

“Let's say you have some kind of matter particle, like an electron,” I said. “It's described by a wavefunction, which has a phase. But the phase isn't a physical thing. It's just a measure of how far along the wave is in its cycle—whether it's halfway up its peak or heading down its trough, or whatever—
relative
to some measuring apparatus. To some observer. If you're watching a wave go by and you take a step to the left, you've now changed its phase, so obviously phase can't be an intrinsic feature of the wave; it's observer-dependent.” Of course, phase
differences
mattered—that was the source of the interference pattern in the double-slit experiment. But phase in and of itself had no intrinsic meaning.

“The phase defines a reference frame,” my father said.

“Exactly! So imagine that this electron's wavefunction is spread throughout all of space. I mean, its amplitude is probably peaked around a specific location, but technically it extends forever because of the uncertainty principle—it can't have zero probability of being in any location. So you're looking at this electron and you take two steps to the left. You've changed its phase. But you haven't changed its phase throughout all space, because your perspective only spans your own light cone. Shifting the phase of the entire wavefunction everywhere in the universe at once would require moving faster than light. If you could, that would be like making a Lorentz transformation or something. But you can't. You're only shifting a local portion of it. So now you have a portion that's shifted and a portion that isn't—the phases don't line up properly. They're mismatched, like a curve and a line. So you need to introduce a force to account for the mismatch. You have to bend things in just the right way so that the phases match up smoothly—like a diffeomorphism transformation.”

“You need the equivalent of gravity.”

“Exactly. And in the case of the electron, the equivalent of gravity is electromagnetism.”

Electromagnetism is a gauge force.
Gauge
is just another word for phase. It's a point of view, a reference frame. Like Einstein's principle of general covariance, the principle of gauge symmetry demands that all gauges are created equal; no reference frame is truer than the next. But local gauge shifts—shifts in points of view—leave a wavefunction with misaligned phases. To account for the mismatch and keep all reference frames on equal footing, you need a gauge force.

Many of the books and articles I had read claimed that forces affect particles by changing the phase of their wavefunction, but really it was the other way around: a change in reference frames creates misaligned phases, which
produces
a force. In other words, the mismatched reference frames
are
the force. In the case of the electron, the force that arises from its mismatched phase is electromagnetism; its particle excitations are photons.

The electromagnetic force ensures that we don't confuse two different
descriptions
of one electron for two different electrons, just as gravity ensures that we don't confuse two different descriptions of spacetime for two different universes. The strong and weak nuclear forces are gauge forces, too, existing solely to account for the way that the phase of a quark's wavefunction can appear misaligned when seen from another point of view. And the similarity of gauge transformations to the diffeomorphisms of general relativity was no coincidence: gravity is a gauge force.

I had learned about the nuclear forces back when I was writing my quark-gluon plasma article, but I hadn't appreciated the deeper significance of gauge theory until my epiphany about the link between invariance and reality. Because the point is, gauge forces aren't invariant. Just like the falling roofer, you can find reference frames in which they disappear. In fact, in any single reference frame, they don't even exist. They only
appear
to exist when you compare one frame with another. They're observer-dependent.
They're not real.

“They're fictitious,” my father said, excited.

“Right! They're not real.”

“No, I mean they're fictitious forces,” he said, leaning forward in his chair.

“That's a thing?”

“Let's say you're stuck at a red light. It turns green, you press your foot down on the gas, and as the car lurches forward you feel like there's a force pushing you back into your seat. Physicists call that a fictitious force—like the centrifugal force that seems like it's pushing you toward the side of the car when you careen around a corner. The forces aren't real—they're artifacts of being in an accelerated reference frame and not knowing it. Take the first example, when you step on the gas, and look at it from the perspective of a guy standing on the sidewalk watching. He's in an inertial frame, right? He sees your car jolt forward and sees you collide with your seat, but according to him the explanation is simply that the car is accelerating and it's trying to carry you along with it. From his point of view you're not being pushed back into your seat, your seat is pushing forward on you. But from inside the car, you have no way of knowing you're really accelerating.”

“Well, I can see that I'm moving faster and faster away from the stuff outside my window,” I said.

“But for all you know you could be at rest and everything outside could be rushing faster and faster away from you. And if you covered up all the windows, you could assume that you weren't moving at all, because relative to you, everything inside the car, including your seat, isn't moving. You would have every right to assume you're at rest, in which case it would be really strange to suddenly be thrown back into your seat. The only way to explain it would be to assume that a force is pushing you.”

“But it's not a real force.… ”

“Right, it's fictitious, because it disappears when you switch to the point of view of the inertial guy on the sidewalk. For him there's no force; there's just an accelerating car. Physicists call it fictitious because you can switch frames and make it go away. But really, based on what you're saying,
all
the forces, even the ones we thought were real, are fictitious.”

“Yes, exactly! Gravity, electromagnetism, the nuclear forces … they're all fictitious. They're gauge-dependent, which is just another way of saying observer-dependent. They're not invariant. But you said the fictitious force arises because you're ‘really' accelerating even though you don't know it. Isn't the point of relativity that you can't say
that you're ‘really' accelerating? You might be in an inertial frame with a force or you might be in an accelerating frame with no force, but they're equivalent. You can't privilege the sidewalk guy's frame as the ‘real' one—every observer's view is equally valid.”

“That's absolutely right.” My father nodded. “The idea of fictitious forces comes from Newtonian physics, where the inertial guy on the sidewalk is considered to be in the absolute space relative to which the car is accelerating. Einstein made the sidewalk guy's frame and the driver's frame equivalent.”

“By making space and time observer-dependent!”

We discussed the issue for a few hours until the jet lag was tugging on my eyelids.

“Come sleep with me, girly!” I said to Cassidy as I headed toward my old bedroom. She started to follow me but then turned around, headed back down the hallway, and lay down at the entryway to my parents' bedroom, keeping guard. “I see how it is,” I told her, shaking my head. “Traitor.”

Lying in bed that night, happy to be in a room large enough to be governed by the laws of classical physics, I thought about ultimate reality. Einstein had said,
“Physics is an attempt conceptually to grasp reality as it is thought independently of its being observed. In this sense one speaks of physical reality.” “Real,” to Einstein, meant observer-independent, and the only way to figure out what was observer-independent was to compare all possible viewpoints and hope to find those rare keystones that don't change from one to the next.
What's real is what's invariant.

It is a philosophical truth that everybody already knows, at least instinctively. If we see something so strange that we can't believe our eyes and we want to make sure that we haven't lost our minds or been served a dosed cocktail, what do we do? We turn to the guy next to us and ask, “Do you see that, too?” If he says no, then we know that the thing's not invariant across reference frames, and that it's probably time to panic.

As a newly enlisted structural realist, I knew I had to be careful to disentangle our stories about physics from its underlying mathematical structure, to not mistake different
descriptions
for different
things.
And now with invariance as my sole criterion for ultimate reality, I understood that the descriptions are what vary from one reference frame to the next—only structure has the potential to be invariant.

Ladyman had been right to turn structural realism into an ontological claim—structure, stripped of the baggage of our individual perceptions, was the only candidate for reality that stood a chance. Because the point was, there are infinitely many ways of looking at the same thing, of describing the same structure. That was obvious from general relativity alone. You could describe a curved world line in a flat spacetime or a straight world line in a curved spacetime. You could talk about a warped manifold with a simple grid-like metric or a distorted metric and no manifold at all. You could describe the cosmos with non-Euclidean geometry or you could stick with Euclid and toss in some extra forces. You could label and relabel spacetime points in infinitely varied ways. And none of it made any difference. The underlying structure was always the same. Our creativity for describing reality is probably boundless. The trick is to know what's mere description and what's the real thing underneath.

Luckily, I had discovered a simple rule of thumb: anything that serves to uphold gauge symmetry is mere description. And yet, mere
descriptions
give rise to what seem like very real and often dramatic physics. Simply shifting from one point of view to another can transform space into time, make gravity disappear, or produce an electromagnetic force. It can spark a nuclear reaction. It can cause the Sun to shine.

In addition to the four fundamentally fictitious forces, there's one more thing you need in order to preserve gauge symmetry: a Higgs field.

All particles have a property called spin, a kind of intrinsic rotation, which accounts for how the particles look from different reference frames. I liked to picture it as a beach ball flying past me, with different partial views consecutively coming into sight as it approaches
and then recedes, making it appear to be rotating, even though in its own reference frame it's not rotating at all. Of course, it doesn't make any sense to ask whether the ball is “really” rotating, because motion is relative. An observer walking 360 degrees around an object that's standing still and an observer who is standing still while the object rotates by 360 degrees are two equivalent descriptions of the same thing.

A particle's spin is described as either right- or left-handed—right if it is spinning in the same direction in which it's moving through space and left if it is spinning opposite its direction of motion. But handedness is relative, too: if you have a particle that's spinning to the right, you can always run faster than it, turn around, and you'll see it spinning to the left. Handedness depends on the reference frame from which it's viewed.

That's a problem. Handedness is an observer-dependent property, which means it's not real. There's no true difference between left- and right-handed particles. And yet experiments in the late 1950s had proven that the weak nuclear force, which acts on quarks and electrons, acts differently on left-handed particles than on right-handed ones, in direct defiance of Einstein's governing principle and its incarnation in the mandate of gauge symmetry. Swap spacetime for its mirror image, interchanging left and right, and you'll see a different world. As if left and right actually mean something. As if they're invariant. Why would the weak force see handedness as invariant when it's really observer-dependent?

There was only one possibility: if the particles move at the speed of light, no one can ever outrun them, which means there's no possible reference frame in which their handedness appears reversed. Even though handedness is still fundamentally observer-dependent, it will always
appear
to be invariant. A left-handed particle traveling at light speed will be left-handed in
every
reference frame.

It seemed like an easy enough fix: just have all quarks and electrons travel at the speed of light. But there was a major snag in that plan, namely, that quarks and electrons have mass. You can't have mass and travel at light speed—the tiniest bit of heft will slow you down. If the particles move slower than light, however, there's no way to explain the weak force's preference for left-handed particles without violating gauge symmetry.

Unless you have a Higgs field. Physicists hypothesized
^*
that there exists a space-filling field constructed in such a way that when a left-handed particle interacts with it, the particle comes out right-handed, and vice versa. So while the weak force
thinks
it's only acting on left-handed particles, the Higgs field is there in the background swapping left and right, so that the weak force is really acting on left- and right-handed particles equally. Now you can swap spacetime for its mirror image and the world will appear unchanged. Thanks to the Higgs field, particles like quarks and electrons can have mass without violating gauge symmetry.