How to Teach Physics to Your Dog (12 page)

The most disturbing element of the Copenhagen interpretation by far, for a physicist at least, is the lack of a mathematical
procedure for describing what happens when you make a measurement of some quantity. The Schrödinger equation allows you to calculate what happens to the wavefunction between measurements, but at the instant of a measurement the Copenhagen interpretation says that normal physics stops, and something happens to select a single outcome in a way that does not involve any known mathematical equation.

The ad hoc nature of the Copenhagen interpretation, with its arbitrary division between microscopic and macroscopic physics and its mysterious “wavefunction collapse,” is tremendously disturbing, because the whole project of modern theoretical physics is to find a single consistent mathematical description of the world. The unexplained process of wavefunction collapse is like the famous Sidney Harris cartoon of a scientist who has written “Then a miracle occurs” as the second step of a problem. Normal science has no room for miracles, and the Copenhagen collapse idea is a little too miraculous for comfort.

Most physicists (particularly experimentalists) are content to use the idea of wavefunction collapse as a calculational shortcut and go about the business of predicting and measuring the physical world, for which regular quantum theory works astound-ingly well. In this “shut up and calculate” interpretation, the problem of finding a consistent explanation for quantum measurement is pushed aside to be dealt with by philosophers. Some better theory may eventually come along, but until then, we should do what we can with what we’ve got (which turns out to be an awful lot).

The nature of measurement has been a problem from the first days of quantum theory, though, and a few physicists have always chosen to think deeply about these issues. Many of these physicists think that the lack of a clear explanation for the “collapse” of the wavefunction indicates that the Copenhagen interpretation is fundamentally flawed. Thus, they have always searched for some alternative interpretation.

In 1957, a graduate student at Princeton named Hugh Everett III suggested a solution to the “collapse” problem that’s breathtaking in its simplicity. The reason there is no mathematical method to describe the collapse of the wavefunction, Everett said, is because there is no such thing as the collapse of the wavefunction. The wavefunction always and everywhere evolves according to the Schrödinger equation, but we only see a small piece of the larger wavefunction of the universe.

Let’s return to the previous chapter’s example of dog treats in sealed boxes to see how this works. If we imagine that we have one dog treat in two boxes, the Copenhagen picture says that we initially have a wavefunction for the treat that consists of two pieces at the same time. This wavefunction changes in time according to the Schrödinger equation. When we open a box and let the dog look inside, the wavefunction instantaneously collapses into only one of those two states, with the treat in either the left-hand box or the right-hand box. We predict future changes by starting over with the Schrödinger equation using the new one-part wavefunction.

In the Everett picture, there is no collapse. The wavefunction starts out in a superposition, a two-part wavefunction with pieces corresponding to the treat in both left-hand and right-hand boxes, and when we open a box that superposition just becomes a little bigger. Now the superposition includes not just the apparatus but also the dog measuring the position of the treat. One piece is “treat in the left-hand box plus a dog who knows the treat is in the left-hand box,” and the other is “treat in the right-hand box plus a dog who knows the treat is in the right-hand box.” This process continues as you move into the future. If the next step in the experiment involves the
dog either eating the treat or not (a low probability outcome, but it’s possible), the wavefunction contains four pieces: a dog who ate the treat from the left-hand box; a dog who didn’t eat the treat from the left-hand box; a dog who didn’t eat the treat from the right-hand box, and a dog who ate the treat from the right-hand box.

The increase in complexity is even more striking in mathematical notation. We start with a two-component wavefunction for just the treat:

where the angled brackets represent wavefunctions for the treat being in the left or right boxes. Then we bring in the dog:

and finally, the decision to eat the treat or not:

As you can see, this gets very complicated very quickly, but its evolution is always described by the Schrödinger equation.

“You know, I’m not getting a lot out of these equations.”

“You’re not supposed to understand them in detail. They’re just there to illustrate the increasing complexity of the wave-function in a more compact manner.”

“So, basically, they’re just supposed to look scary?”

“Pretty much.”

“Oh. Good job, then.”

• • •

The Everett picture doesn’t immediately appear to be an improvement. The mysterious “collapse” is removed, but at the price of a wavefunction that’s expanding exponentially. At first glance, it also seems to defy reality, as we never see systems in more than one state. If all these extra pieces of the wavefunction are running around, why don’t we perceive objects as being in multiple states at the same time?

The answer, according to Everett, is that we can’t separate the observer from the wavefunction. The observer is included with the rest of the system—the components are things like “treat in the left-hand box plus a dog who knows the treat is in the left-hand box”—and as a consequence, we only perceive our own small part of the overall wavefunction. This branching is the origin of the quantum randomness that Einstein and others found so troubling: the wavefunction always evolves in a smooth and continuous way, but we only experience one branch of the wave-function at a time, and which branch we see is a random choice. Other versions of ourselves exist in the other branches, experiencing different outcomes (for this reason, the interpretation is sometimes referred to as the “many-minds” interpretation).

None of the myriad other branches have any detectable influence over the events in our branch, and our branch has no detectable influence over the events in any of the others. For all intents and purposes, those other branches are self-contained parallel universes, completely inaccessible from our universe. This is the origin of the name “many-worlds” for the theory: it’s as if the universe forks every time a measurement is made, and is constantly spawning new parallel universes with slightly different histories.

These noninteracting branches present a serious but subtle problem for the many-worlds interpretation. Every other two-part wavefunction we’ve seen has led to some sort of interference phenomenon. So, why don’t we see interference around us all the time if there are all these extra branches to the wave-function? What is it that seals these “parallel universes” off from us?

The answer is a process called decoherence, which prevents the different branches of the wavefunction from interacting with one another. Decoherence is the result of random, fluctuating interactions with a larger environment, which destroy the possibility of interference between different branches of the wave-function, and make the world we experience look classical. Decoherence doesn’t just occur in the many-worlds interpretation of quantum mechanics—it’s a real physical process, compatible with any interpretation
*
—but it’s particularly important in the modern view of many-worlds (which is sometimes called “decoherent histories” as a result—the interpretation has almost as many names as universes
^†
).

Decoherence is absolutely critical to the modern view of quantum mechanics and quantum interpretations. The most common semiclassical explanations of decoherence leave a lot to be desired, though, as they are inaccurate, and often somewhat circular. The real theory of decoherence is subtle and difficult to understand. As with the uncertainty principle (
chapter 2
, page
40), though, it’s worth some effort to unpack it, because it provides a much richer understanding of the way the universe works.

To understand the idea of decoherence, let’s think about the concrete example of a simple interferometer, a device consisting of two beam splitters that split a beam of light in half and a couple of mirrors that bring it back together again.
*
Interferometers like this are extremely important in physics, not only for demonstrating quantum effects, but because they form the basis for the world’s most sensitive detectors of rotation, acceleration, and gravity. These allow the measurement of tiny forces in physics experiments, and also find application in submarine navigation.

Light enters the interferometer when it strikes a beam splitter, which passes half of the light through without perturbing it and reflects the other half off at a 90° angle. These two beams separate from each other, and then are steered back together using two mirrors, and recombined on a second beam splitter. The second beam splitter is lined up so that the transmitted light from one beam and the reflected light from the other follow exactly the same path and interfere with each other before falling on one of two detectors.

You might think that each of the two detectors would detect exactly half of the light, because each detector receives one-quarter of the original beam from each of the two paths (¼ + ¼ = ½). Each detector can actually see anything from no light at all up to the full intensity of the initial beam, though, because the waves that took different paths interfere with each other, like the waves in the double-slit experiment in
chapter 1
(page 18).

If the paths followed by the two beams have exactly the same length, the two light waves undergo the same number of oscillations en route to Detector 2, and interfere constructively, giving
a bright spot—all of the light entering the interferometer hits that detector.
*
On the other hand, if one path is longer than the other by one half of the wavelength of the light, the light along that path undergoes an extra half-oscillation, and the two waves interfere destructively: the crests of the wave hitting Mirror 1 line up with the troughs of the wave hitting Mirror 2, and they cancel out, giving no light at Detector 2. If we increase the length difference to one full wavelength, the peaks align again, and we get another bright spot, and so on. Between
those two extremes we get some intermediate amount of light. We can generate an interference pattern by repeating the experiment many times, and changing the length of one path slightly. This will give us a pattern of alternating light and dark spots on Detector 2.