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What if Time Really Exists?

Cosmic Variance
By Sean Carroll
Nov 24, 2008 11:01 PMNov 5, 2019 8:18 AM


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The Foundational Questions Institute is sponsoring an essay competition on "The Nature of Time." Needless to say, I'm in. It's as if they said: "Here, you keep talking about this stuff you are always talking about anyway, except that we will hold out the possibility of substantial cash prizes for doing so." Hard to resist. The deadline for submitting an entry is December 1, so there's still plenty of time (if you will), for anyone out there who is interested and looking for something to do over Thanksgiving. They are asking for essays under 5000 words, on any of various aspects of the nature of time, pitched "between the level of Scientific American and a review article in Science or Nature." That last part turns out to be the difficult one -- you're allowed to invoke some technical concepts, and in fact the essay might seem a little thin if you kept it strictly popular, but hopefully it should be accessible to a large range of non-experts. Most entries seem to include a few judicious equations while doing their best to tell a story in words. All of the entries are put online here, and each comes with its own discussion forum where readers can leave comments. A departure from the usual protocols of scientific communication, but that's a good thing. (Inevitably there is a great deal of chaff along with the wheat among the submitted essays, but that's the price you pay.) What is more, in addition to a judging by a jury of experts, there is also a community vote, which comes with its own prizes. So feel free to drop by and vote for mine if you like -- or vote for someone else's if you think it's better. There's some good stuff there.

My essay is called "What if Time Really Exists?" A lot of people who think about time tend to emerge from their contemplations and declare that time is just an illusion, or (in modern guise) some sort of semi-classical approximation. And that might very well be true. But it also might not be true; from our experiences with duality in string theory, we have explicit examples of models of quantum gravity which are equivalent to conventional quantum-mechanical systems obeying the time-dependent Schrödinger equation with the time parameter right there where Schrödinger put it. And from that humble beginning -- maybe ordinary quantum mechanics is right, and there exists a formulation of the theory of everything that takes the form of a time-independent Hamiltonian acting on a time-dependent quantum state defined in some Hilbert space -- you can actually reach some sweeping conclusions. The fulcrum, of course, is the observed arrow of time in our local universe. When thinking about the low-entropy conditions near the Big Bang, we tend to get caught up in the fact that the Bang is a singularity, forming a boundary to spacetime in classical general relativity. But classical general relativity is not right, and it's perfectly plausible (although far from inevitable) that there was something before the Bang. If the universe really did come into existence out of nothing 14 billion years ago, we can at least imagine that there was something special about that event, and there is some deep reason for the entropy to have been so low. But if the ordinary rules of quantum mechanics are obeyed, there is no such thing as the "beginning of time"; the Big Bang would just be a transitional stage, for which our current theories don't provide an adequate spacetime interpretation. In that case, the observed arrow of time in our local universe has to arise dynamically according to the laws of physics governing the evolution of a wave function for all eternity. Interestingly, that has important implications. If the quantum state evolves in a finite-dimensional Hilbert space, it evolves ergodically through a torus of phases, and will exhibit all of the usual problems of Boltzmann brains and the like (as Dyson, Kleban, and Susskind have emphasized). So, at the very least, the Hilbert space (under these assumptions) must be infinite-dimensional. In fact you can go a bit farther than that, and argue that the spectrum of energy eigenvalues must be arbitrarily closely spaced -- there must be at least one accumulation point. Sexy, I know. The remarkable thing is that you can say anything at all about the Hilbert space of the universe just by making a few simple assumptions and observing that eggs always turn into omelets, never the other way around. Turning it into a respectable cosmological model with an explicit spacetime interpretation is, admittedly, more work, and all we have at the moment are some very speculative ideas. But in the course of the essay I got to name-check Parmenides, Heraclitus, Lucretius, Augustine, and Nietzsche, so overall it was well worth the effort.

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