Trespassing on Einstein's Lawn (21 page)

My mother plunked the salad bowl on the table, along with plates and forks.

Cassidy whined. I looked down to find her staring up at me, her tongue hanging out of her mouth in what looked uncannily like a smile. She offered me her paw.

“Really?” I asked her. “Salad?”

I tossed a piece of lettuce into the air; her jaws snapped shut around it. My mother flashed me a disapproving look.

That evening, I dug some books and papers out of my suitcase, then headed toward our physics library. In the hallway, my mother was lying on the floor with the dog, nuzzling her face into Cassidy's and whispering in motherese.
Yes
,
I love you. Yes
,
I do.

“Still hate dogs?” I asked.

“Yes, I do,” she cooed as Cassidy licked her nose.

In the library, my father was lounging in his leather chair, flipping through a book. I made myself comfortable on the couch.

My mother rendered powerless by Cassidy's charm
W. Gefter

“Check out this paper,” I said. It was written by Max Born, one of the founders of quantum mechanics, published in the
Philosophical Quarterly
in 1953,
and entitled “Physical Reality.” I read the first line aloud.
“ ‘The notion of reality in the physical world has become, during the last century, somewhat problematic.' ”

My dad laughed. “You think?”

I continued to read aloud, and my father listened intently.

Cut a circle from a piece of cardboard, Born wrote, hold it in the light of a distant lamp, and observe its shadow on the wall.

“ ‘The shadow of the circle will appear in general as an ellipse, and by turning your cardboard figure you can give to the length of an axis of the elliptical shadow any value between almost zero and a maximum. That is the exact analogue of the behavior of length in relativity which in different states of motion may have any value between zero and a maximum.… It is evident that the simultaneous observation of the shadows on several different planes suffices to ascertain the fact that the original cardboard figure is a circle and to determine uniquely its radius. This radius is what mathematicians call an invariant.' ”

“That's basically how a CT scan works,” my father mused.

I continued to read.
“ ‘The projection (the shadow in our example) is defined in relation to a system of reference (the walls, on which the shadow may be thrown). There are in general many equivalent systems of reference.… Invariants are quantities having the same value for any system of reference.' ”

“They're observer-independent.”

“Exactly. And here's the kicker,” I said, continuing.
“ ‘The main advances in the conceptual structure of physics consist in the discovery that some quantity which was regarded as the property of a thing is in fact only the property of a projection.' ”

“That's a really interesting point,” my father said. “Progress in physics comes from realizing that things once believed to be invariant are really just observer-dependent. Shadows.”

“Yup. Born goes on to say,
‘I think the idea of invariant is the clue to a rational concept of reality.' Then he talks about quantum mechanics, arguing that a measurement is a projection onto some reference system, the measuring apparatus. And he ends by saying, ‘Invariants are the concepts of which science speaks in the same way as ordinary language speaks of “things.” … The feature which suggests reality is
always some kind of invariance of a structure independent of the aspect, the projection.' ”

“What's real is what's invariant.”

I nodded. “What's real is what's invariant. It almost sounds too obvious, like it's trivial, but it's incredibly profound.”

“I can see that,” my dad said, flipping through a book of Einstein's collected papers. “It's the whole idea behind relativity. Listen to this. Einstein was thinking about electricity and magnetism. If you move a magnet, you generate an electric field, and if you move an electron, you generate a magnetic field. But how can you say what's really moving? Motion is relative—are you stationary to the frame of the electron or to the frame of the magnet? He wrote,
‘That these were two, in principle different cases was unbearable for me. The difference between the two, I was convinced, could only be a difference in choice of viewpoint and not a real difference. Judged from the [moving] magnet, there was certainly no electric field present. Judged from the [ether state of rest], there certainly was one present. Thus the existence of the electric field was a relative one, according to the state of motion of the coordinate system used, and only the electric and magnetic field together could be ascribed a kind of objective reality, apart from the state of motion of the observer or the coordinate system. The phenomenon of magneto-electric induction compelled me to postulate the (special) principle of relativity.' ”

As my father read Einstein's words, I realized that of all the things for which physicists had Einstein to thank, they probably owed him most for demonstrating the deep connection between invariance and reality.

Because motion is relative and yet the laws of electromagnetism required light waves to move at 186,000 miles per second, space and time themselves had to vary from one reference frame to the next. That is, space and time were observer-dependent. They weren't real.

By weeding out what was observer-dependent, however, Einstein had discovered what
was
real: the unified, four-dimensional spacetime. Different observers could slice spacetime in different ways, calling some bits “space” and others “time,” but they were just different ways of looking at the same invariant thing. If you had a world line that spanned,
say, ten units of spacetime, I might call five of those units space and the other five time. From another reference frame, my father might call seven units space and only three time, which means two of the units that he sees as space, I see as time. Light calls all ten units space and has zero left for time. That's why you can't go faster than light. You can't allocate less than zero units of spacetime for time. If you did, you'd have a negative number—you'd be traveling backward in time.

The point was, no matter how you slice it, spacetime is spacetime. It's invariant.

That's why Hermann Minkowski said, “Henceforth space by itself and time by itself are doomed to fade away into mere shadows and only a kind of union of the two will preserve an independent reality.” Space and time were shadows on the wall; spacetime was the cardboard.

Einstein thought the latter point was more important than the former—he was not so concerned with what was relative as with what was invariant, because he knew that what's invariant is what's
real.
In fact, he regretted having called his theory a theory of relativity, wishing instead that he had named it
invariantentheorie:
the theory of invariance.

The thing is, we can never see spacetime. Like prisoners in Plato's cave, we are compelled to experience the world through its shadows, a universe broken into pieces of three-dimensional space and one-dimensional time. But by spotting the invariant in Einstein's equations—the spacetime interval that holds steady through Lorentz transformations from one inertial frame to the next—we can glimpse the true reality behind appearances. Spacetime is a symmetry, but the universe of our perception is a symmetry broken. We are living among the shards.

Things got even more observer-dependent when Einstein upgraded from special to general relativity. People say that his inspiration—what Einstein described as his “happiest thought”—came when he saw a workman fall off the roof of a building near the patent office. That makes Einstein sound like kind of an asshole. But it's probably not true. Either way, it occurred to him that a man falling off a roof would, while in free fall, experience weightlessness, as if gravity had somehow disappeared. It was his happiest thought because it contained an unbelievable epiphany: if gravity could disappear in one observer's reference
frame, then it couldn't be a fundamental ingredient of reality. It had to be an artifact of perspective.

From the ill-fated roofer's perspective, he's in an ordinary inertial frame, a frame without gravity. It's not that he's delusional—from his point of view, he
really is
in a gravity-free inertial frame, and if he bothered to do some quick science experiments on the way down, they would all confirm it. If, for instance, he took his keys from his pocket and dropped them, they would not fall toward his feet, as gravity would have it, but simply hover alongside him, since they're falling at the same rate. The only thing out of the ordinary would be the massive planet that happened to be accelerating toward his face.

An inertial observer traces a straight trajectory through spacetime. But from the perspective of the onlookers pointing and laughing on the ground, the falling man is crossing more and more space in less and less time as he plummets toward the Earth. According to them, he's accelerating, his world line tracing a curve. So which is it? Line or curve?

Einstein knew the answer had to be
both
, since the line and the curve are merely different descriptions of the same falling man. But how can they both be right? How can a curve also be a straight line?
To turn a curve into a line
,
you have to bend the paper.
Equating the roofer's perspective with the onlookers' requires a diffeomorphism transformation. It requires spacetime to be curved. It requires gravity.

Einstein's principle of general covariance demanded that all observers see the same laws of physics. Gravity upholds general covariance at the edges of mismatched reference frames; it turns curves into lines. “We are able to ‘produce' a gravitational field merely by changing the system of coordinates,” Einstein wrote. “The requirement of general covariance … takes away from space and time the last remnant of physical objectivity.”

Newton had believed in the reality of absolute space because without it acceleration didn't mean anything—acceleration relative to what? But Einstein's general theory of relativity had shown that what looks like an accelerated frame from one point of view looks from another like an inertial frame with gravity. There's no ontological difference between accelerated and inertial frames, which in turn meant that you didn't need absolute space. That is, you didn't need space to be
real.

It also explained what had always been a curious fact, one that I assumed would have the girl from my philosophy class foaming at the mouth: if you dropped two balls off the Leaning Tower of Pisa, say a bowling ball and a Ping-Pong ball, they'd hit the ground at the exact same time, assuming they were falling in an airless vacuum. You'd think the heavier one would fall faster, but it doesn't. Because if heavier things fell faster than lighter things, you'd be able to tell whether you were in an accelerated frame or an inertial frame with gravity.

How? If you found yourself in a windowless elevator and felt your weight being pulled toward the floor, you might wonder whether the elevator was accelerating upward, causing the floor to push up against your feet, or the elevator was at rest on a planet with a strong gravitational pull. To find out, you could drop a really heavy vagina and a really light vagina at the same time. If the heavy one hit the floor first, you'd know you were in a gravitational field. If they hit the floor simultaneously, you'd know that the elevator was accelerating upward, so the floor rose up to meet the hovering vaginas at the same time.

It's only because vaginas of different weights fall at the same speed that Einstein's equivalence principle holds: you can never tell the difference between acceleration and gravitation. If you could, “space” would mean something. It would be real. But it's not.

“Special relativity shows that space and time aren't real—they're observer-dependent,” I said to my father. “And general relativity shows that gravity isn't real, because it disappears in certain frames. But here's the crazy thing—it doesn't stop with Einstein. It applies to all the forces. None of the so-called ‘fundamental' forces is real!”

There are three forces in addition to gravity. Electromagnetism is the most familiar, since it operates on the scales of our everyday lives. The other two are more remote, governing subatomic matter. The strong nuclear force binds quarks into the protons and neutrons at the heart of every atom. The weak nuclear force swaps protons for neutrons, and vice versa, by changing the flavors of their constituent quarks, mediating radioactive decay and allowing the Sun to shine.

Despite all the talk of gravity being the odd man out in a world governed by quantum mechanics, all the forces arise in essentially the
same way—specifically, to account for the fact that things appear differently in different reference frames.