Trespassing on Einstein's Lawn (7 page)

But I was sick of being patted on the head and told not to worry about understanding it. The quantum works in mysterious ways? Really,
science
?

After reading enough so-called explanations of the theory, it was clear to me that any hope I had for understanding quantum mechanics hinged on a single experiment: the double slit. It went something like this.

Physicists shine a laser at a screen with two parallel slits. The light travels through the slits and hits a photographic plate on the other side,
so you can see where it lands. If light was made of particles—and Einstein had already proven that it was—you'd expect to see two blobs of light opposite each slit. But you don't. Instead you see a series of light and dark vertical stripes, like a barcode.

Physicists realized that they could make sense of the barcode if the photons en masse were traveling as a wave, which splits apart at the screen, travels through both slits, then recombines on the other side. When it recombines, it's partially out of phase. In spots where the two waves are in phase—crests line up with crests and the troughs line up with troughs—they reinforce each other, producing a bright strip of light on the screen. Where they are out of phase—crests align with troughs and troughs with crests—they cancel out, leaving only stripes of darkness.

Okay, that was kind of strange, but it was nothing compared to what happens next. The physicists repeat the experiment, turning down the intensity of the laser until it shoots a single photon at a time. They fire off one photon and see a single bit of light register on the plate—just like you'd expect. They fire another, and another dot appears. They fire another and another and another and slowly but surely a pattern begins to emerge. One by one, the individual photons build up the same interference pattern of light and dark stripes.

The books all concluded that the interference showed that light was “both a particle and a wave”—the so-called wave-particle duality—but when you measure it, light is
always
a particle. A single photon will invariably show up as a single spot of light. It's only when you map out the probability for the particle to land at any given spot on the plate that you find a wave.

The wave that describes the quantum particle is a mathematical wave, a wavefunction. Whereas physical waves carry energy in their amplitudes, mathematical wavefunctions carry probability. Square the amplitude at any point along a wavefunction mapped out in position space and you get the probability of finding the particle there. Make enough measurements and the dots of light will map out the whole distribution.

As far as I could tell, it wasn't so weird that a particle's probability distribution could be mapped as a wave. What
was
weird was the interference
pattern that shows up photon by single photon. The probability distribution mapped out by the bright and dark stripes is not the distribution encoded in the wavefunction of a single photon—it's the distribution that results from the interference of
two
wavefunctions. It's as if the single photon travels through both slits and its wavefunction splits in two. When the pieces recombine on the other side, they are out of phase and they interfere with each other to form a new wavefunction. The individual photons then land only at positions that are allowed by the probability distribution encoded in the combined wavefunction. Hence the stripes.

If you close the second slit and run the experiment again, shooting one photon at a time at the screen, the interference pattern disappears. Now the spots that show up on the plate are only those allowed by the wavefunction of a single photon, which is always in phase with itself. It's only when both slits are open that the stripes appear.

Finally, the books all told me, there's one more version of the experiment that physicists run in an attempt to catch the photon traveling through both slits at once. They keep both slits open but this time they rig them with detectors that will trigger when a photon passes through. Then they turn on the laser and shoot off one photon at a time. Two open slits always show interference. But not this time. This time there's just the distribution of a single photon's wavefunction on the plate. It's as if the photon knows it's being watched.

Okay, I thought. This was what they had warned me about: the smell of my neurons sizzling. It
knows
when it's being watched?

Obviously the photon doesn't
know
anything. But how do you explain what's going on? Is the photon really in two places at once when no one's watching and in one when someone is? What does it mean for us to be watching? Why should our watching make any difference at all?

Double slit boils down to this
, I wrote in my notebook.
Why do the probability distributions of single photons trace out an interference pattern
,
as if the photons are traveling two paths simultaneously? And why does the interference pattern disappear when you try to measure which path the photon takes?

Different physicists viewed the situation differently. Feynman, for
instance, said that when we're not watching, the particle really does take multiple paths. Bohr, on the other hand, argued that if we're not watching, we have no right to say anything about the particle at all. Until we measure it, Bohr said, the particle has no position. Until we measure it, it's not even a particle. It's not anything. But if particles aren't particles until you measure them, what exactly is the interference pattern interference of? Stark stripes of counterfactuals? A scattered pile of mere could-have-beens that never quite were?

Clearly
something
happens when we make a measurement—observe which path the photon takes and the interference pattern disappears. But quantum theory itself doesn't describe any such thing. It never breathes a word about measurement at all. According to the theory,
everything
is described by wavefunctions: the photon, the slits, the detectors, the photographic plate, even the physicist performing the experiment. According to the theory, when the photon passes through a detector-rigged slit, its wavefunction superposes and interferes with the wavefunction of the detector; no single event registers. The combined system of photon-plus-detector is now described by their combined wavefunction, hovering in a simultaneous state of yes-the-photon-took-this-path and no-it-didn't. According to the theory, when the physicist checks the detector's readout, his wavefunction superposes with the combined photon-plus-detector wavefunction, a mangled heap of probability, a haze of parallel would-be realities: the-physicist-sees-that-detector-A-registered-a-photon and the-physicist-sees-that-detector-A-did-not.

The universe, according to quantum theory, is just superpositions piled atop superpositions, yet we never see even one. Sure, we see their remnants in paradoxical stripes of interference. But I'd never once found myself in Manhattan
and
Brooklyn, or checked someone's coat only to find it hanging on multiple hangers. If the world was really so quantum, where were all the simultaneously alive-and-dead cats?

Physicists called it the measurement problem: the wavefunction encodes a host of possible states and yet we only ever measure one. What happens in the course of a measurement that collapses the wavefunction's probability distribution down to a single outcome? Given the many positions allowed by the photon's probability distribution,
how does it choose one? The choice appears to be truly random—an effect with no cause. Was the universe at bottom truly random? Einstein didn't buy it, but the universe didn't seem to care.

Bohr argued that quantum phenomena, like particles, have real properties only after they are measured; it makes no sense to even ask about their pre-measurement state. There's no mysterious collapse, he said, because there's nothing to collapse. Bohr didn't believe that observers magically influence the outcomes of experiments or create reality through their minds—it was just that a measurement outcome was objectively relative to the frame of reference of a measuring device, be it a detector or a photographic plate or a human eye.

That's not to say he didn't realize how seriously weird the whole thing was, requiring, as he wrote,
“a radical revision of our attitude toward the problem of physical reality.” But in some sense the fact that properties were relative to observers wasn't that different from Einstein's relativity, a fact that Bohr happily pointed out after Einstein had insisted that quantum theory couldn't be a complete description of reality. “I like to think that the moon is there even if I'm not looking at it,” Einstein had said. In response, Bohr wrote that quantum theory
“may be paralleled with the fundamental modification of all ideas regarding the absolute character of physical phenomena brought about by the general theory of relativity.” In other words,
Sure
,
quantum theory fucks with reality
,
but you started it.

Then again, there was something distinctly weirder about quantum mechanics than relativity. At least in relativity there was some basic reality—the unified four-dimensional spacetime—that simply
looked
different relative to different observers, and Einstein had kindly offered up tools such as Lorentz and diffeomorphism transformations to translate between different points of view. But what was the basic reality in quantum theory? It was as if there was no reality at all until someone made a measurement.

Of course, if that was true, you couldn't have an observer to make the measurement in the first place. The observer's got to live in some kind of reality. That was the problem with Bohr's view. If measurement is the arbiter of reality, then the measuring device has to sit outside reality—which, even within the bizarro universe of quantum mechanics,
is downright impossible. Besides, any measuring device, human or otherwise, is ultimately made up of subatomic particles, so drawing some kind of ontological line between the two was just plain schizophrenic.

The assertion that a particle doesn't have any “real” attributes until someone measures them becomes particularly weird when you realize that certain attributes can't be measured at the same time. Which means that certain attributes can't
exist
at the same time. Take position and momentum. There's no conceivable experiment that can measure both a particle's position and momentum to perfect accuracy. If you want to accurately measure position, you need a rigidly fixed measuring device that won't move when the particle hits it; otherwise its movement will smear out the position measurement. But if you want to accurately measure momentum, your device had better move easily when hit, so that its recoil can register the amount of momentum imparted by the particle.

No matter how you set it up, the two measurements are mutually exclusive. The more accurately you know position, the less accurately you know momentum. And it's not merely a practical matter. It's not just that you can't measure both at once. It's that the particle doesn't
have
both at once. The uncertainty relation between position and momentum is built into the mathematical structure of the theory. A particle's position wavefunction and its momentum wavefunction are Fourier transforms of each other—two equally true but mutually exclusive ways of looking at the same thing. Choose to look at one and you obliterate the other. The probability distributions encoded in the wavefunctions reflect this mutual exclusivity. If you were to assume that the particle had both attributes at the same time, your probability distribution wouldn't match up with experiment. In other words, you can pretend the whole thing is merely a pragmatic problem, a reflection of the limits of measurement rather than the limits of reality, but you'll get the wrong answer.

So here was the situation. A particle can't have a well-defined position and momentum, yet an observer can measure either one with perfect accuracy and is free to choose which one to measure. The moral of the story was clear: there's no normal reality lurking behind the
quantum scene, no objective Einsteinian world that sits idly by regardless of who's looking. There's just the stuff we measure. The whole thing reeked of paradox, but as Feynman said,
“The ‘paradox' is only a conflict between reality and your feeling of what reality ‘ought to be.' ”

It was clear to me that in our hunt for ultimate reality, my father and I needed to be prepared for the ground to give way beneath our feet. Reality according to quantum theory was not the run-of-the-mill, steady-mooned world we thought we knew. But it was also clear that Bohr and his followers didn't have the last word on the theory's interpretation—because the distinction between observer and observed would never hold up. If that presumably false dividing line marked the very birthplace of reality, it was going to be crucial to figure out what happens to reality when it blurs.

It was also clear that we needed to give careful consideration to the meaning and role of “observers” in general. Both relativity and quantum theory had changed the role observers played in physics—not observers as in humans or conscious creatures, but observers as in points of view. Relativity taught us that we can't talk about space or time without first specifying a frame of reference. Independent of observers, those terms lose all meaning, since one observer's time is another's space. Quantum mechanics taught us that we can't talk about properties of matter without first specifying what we're measuring—its position, for example, or its momentum. At the heart of both theories was a single epiphany: perspective matters. For some as-yet-unknown reason, points of view determine not only how we
see
things, but how things
are.

That was what they had in common, anyway. So what was really at the heart of their incompatibility? Why couldn't those two crazy kids make it work?

Summer had descended on New York when I finally met Fotini Markopoulou. We had agreed to meet in the lounge of the Tribeca Grand Hotel. I figured we could find a quiet spot to talk, and that it would be air-conditioned—a luxury I had grown to appreciate. My Brooklyn
apartment didn't have any such luxury, and I had taken to reading and writing in the bathtub to stay cool.