The Sciences

From Eternity to Book Club: Chapter Eleven

Cosmic VarianceBy Sean CarrollMar 23, 2010 2:27 PM

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Welcome to this week's installment of the From Eternity to Herebook club. Part Three of the book concludes with Chapter Eleven, "Quantum Time." Excerpt:

This distinction between “incomplete knowledge” and “intrinsic quantum indeterminacy” is worth dwelling on. If the wave function tells us there is a 75 percent chance of observing the cat under the table and a 25 percent chance of observing her on the sofa, that does not mean there is a 75 percent chance that the cat is under the table and a 25 percent chance that she is on the sofa. There is no such thing as “where the cat is.” Her quantum state is described by a superposition of the two distinct possibilities we would have in classical mechanics. It’s not even that “they are both true at once”; it’s that there is no “true” place where the cat is. The wave function is the best description we have of the reality of the cat. It’s clear why this is hard to accept at first blush. To put it bluntly, the world doesn’t look anything like that. We see cats and planets and even electrons in particular positions when we look at them, not in superpositions of different possibilities described by wave functions. But that’s the true magic of quantum mechanics: What we see is not what there is. The wave function really exists, but we don’t see it when we look; we see things as if they were in particular ordinary classical configurations.

Title notwithstanding, the point of the chapter is not that there's some "quantum" version of time that we have to understand. Some people labor under the impression that the transition from classical mechanics to quantum mechanics ends up "quantizing" everything, and turning continuous parameters into discrete ones, perhaps even including time. It doesn't work that way; the conventional formalism of quantum mechanics (such as the Schrödinger equation) implies that time should be a continuous parameter. Things could conceivably change when we eventually understand quantum gravity, but they just as conceivably might not. In fact, I'd argue that the smart money is on time remaining continuous once all is said and done. (As a small piece of evidence, the context in which we understand quantum gravity the best is probably the AdS/CFT correspondence, where the Schrödinger equation is completely conventional and time is perfectly continuous.) However, we still need to talk about quantum mechanics for the purposes of this book, for one very good reason: we've been making a big deal about how the fundamental laws of physics are reversible, but wave function collapse (under the textbook Copenhagen interpretation) is an apparent counterexample. Whether it's a real counterexample, or simply an artifact of an inadequate interpretation of quantum mechanics, is a matter of much debate. I personally come down on the side that believes that there's no fundamental irreversibility, only apparent irreversibility, in quantum mechanics. That's basically the many-worlds interpretation, so I felt the book needed a chapter on what that was all about. Along the way, I get to give my own perspective on what quantum mechanics really means. Unlike certain parts of the book, I'm pretty happy with how this one came out -- feel free to correct me if you don't completely agree. Quantum mechanics can certainly be tricky to understand, for the basic reason that what we see isn't the same as what there is. I'm firmly convinced that most expositions of the subject make it seem even more difficult than it should be, by speaking as if "what we see" really does reflect "what there is," even if we should know better.

So I present a number of colorful examples of two-state systems involving cats and dogs. Experts will recognize very standard treatments of the two-slit experiment and the EPR experiment, but in very different words. Things that seem very forbidding when phrased in terms of interference fringes and electron spins hopefully become a bit more accessible when we're asking whether the cat is on the sofa or under the table. I did have to treat complicated macroscopic objects with many moving parts as if they could be described as very simple systems, but I judged that to be a worthwhile compromise in the interests of pedagogy. And no animals were harmed in the writing of this chapter! Let me know how you think the strategy worked.

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