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Q & A: entropy and the fate of the universe

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Most recent answer: 01/17/2013
Assuming the fate of the universe is thermal equilibrium, or total entropy: At universal thermal equilibrium, the wave-function would not be subject to entropy, and without an observer to cause apparent wave-function collapse, and without quantum decoherence due to other individual quantum states creating entanglement interactions that make the wave-function "conform" to its surroundings, the wave-function would not collapse for infinite quantum states separated by infinite space; and since the wave-function before collapse represents all possible eigenvalues, the probability of all matter in in these conditions leading to a singularity is non-zero given infinite time. Is there anything to point me towards that will illuminate more on my hypothesis? I'm deeply interested in physics; while I am competent at math, physics equations are difficult to grasp. I'm really just trying to see if I'm on the right track or if I've misunderstood/assumed anything.
- Matthew Spencer, AA (age 25)
Ann Arbor. MI, USA
I'm glad you asked for pointers rather than an explanation, which would have been beyond our capacities.

I'd start with a book by Sean Carroll, From Eternity to Here. Roughly, the picture it gives for the long-term fate of our universe is that it gets very cold and flat and empty as black holes ultimately evaporate. However, this blank universe sheds new universes via quantum fluctuations, so it never becomes really environment-free. I believe that finesses the problem of decoherence without environments.

If you're feeling mathematically adventurous you could try tackling a paper by Bousso and Susskind, . My summary of it will be even less competent than my summary of Carroll. They propose that certain cosmic horizons provide a permanent outside, again removing the issue of environment-free decoherence.

So long as there is some environment which cannot be included in the expression for the quantum state (e.g. because it lies outside a cosmic horizon), then one needs a density matrix rather than a pure state, so that there's some entropy.

Mike W.

(published on 01/15/2013)

Follow-Up #1: entropy in the multiverse

So if I'm understanding Carroll right, entropy is responsible for the flow of time, the big bang was a very low entropy state at singularity, and higher entropy states will exist near the end of the universe and therefore create new singularities that spawn new universes through the process of quantum fluctuations? It seems I was on the right track. Bousso and Susskind's paper was more confusing and raised more questions however. Are they trying to say that in specially controlled "multiverses" (their "hats") where conditions are exact that their two postulates would succeed, thereby making wave-function collapse or decoherence implausible for those conditions?
- Matthew Spencer (age 25)
Ann Arbor. MI, USA
I'd adjust that picture a little. Probably our universe didn't quite start with a singularity. The singularity arises in solutions of the general relativistic equation, but that's presumed to break down on the Planck scale, where quantum gravity should become important. Since the universe may be infinite it may not be quite accurate to speak of whether the universe as high or low entropy, although we do talk that way. When we're being more careful, we talk of something more like the entropy per energy, a sort of entropy density. That grows as the universe ages, basically along the lines you outline. Carroll discusses this much more carefully. If I understand right, he's not saying that the cold flat universe is better, in any region, at shedding new ones than our current universe. It's just that it has a lot of space (maybe also infinite) and forever to do so. His key point is that the birth of a new low-entropy universe actually increases the net entropy from a global point of view that includes both the old and new pieces. From the point of view of somebody who evolves after a while in the new piece, it seems as if everything was born in a low-entropy state.

I think that Bousso and Susskind are saying something significantly different than what you gathered. They really aren't considering wave function collapse as a serious ingredient of quantum mechanics at all. They assume that the unitarity of all quantum field theories is exact, i.e. there's no collapse. With regard to decoherence, I think they're saying that there are bound to be branches of the multiverse in which decoherence is intrinsic due to horizons rather than just being a somewhat arbitrary consequence of the line drawn between "system' and "environment". But here you have to put big error bars on my understanding.

Mike W.

(published on 01/17/2013)

Follow-up on this answer.