Physics Question (kinda long)

Factual Questions
1

I was fascinated to read this article about entropy and the “arrow of time,” in the context of new work by several different scientists.

Sean Carroll and Alan Guth are collaborating on one of the papers under discussion. Carroll is quoted as saying (referring to another paper/model),
“I think basically any time you have a finite collection of particles in a really big space you’ll get this kind of generic behavior they describe.”

And Guth said, “If we assume there is no maximum possible entropy for the universe, then any state can be a state of low entropy. That may sound dumb, but I think it really works, and I also think it’s the secret of the Barbour et al construction. If there’s no limit to how big the entropy can get, then you can start anywhere, and from that starting point you’d expect entropy to rise as the system moves to explore larger and larger regions of phase space. Eternal inflation is a natural context in which to invoke this idea, since it looks like the maximum possible entropy is unlimited in an eternally inflating universe.”

Here’s my question: From Guth’s quote, I understand that in an endlessly expanding universe, entropy can always be (relatively) low because at any given time the particles therein can always be much farther apart than they currently are, which would then result in higher entropy.

And Carroll’s quote I assume to imply (partly) that there is (postulated to be) a finite amount of matter present within the universe. So in these guys’ model, that same finite amount of matter was all present at the Big Bang, has clumped and coagulated together some on its way to getting farther apart as space began to expand, and will continue to break down and spread apart as space expands infinitely?

Also, I understand that this model is for the purpose of explaining “time’s arrow,” i.e., a process in the past that resulted in the perceived directionality of time. But I’m wondering about the future in such a model, and about inflation in general. Is inflation something that is happening in all of space, except the space between particles? In other words, are the strong and weak forces inside an atom stronger than the expansion of inflation? Is the expectation that all bodies of matter will eventually break down into their constituent particles as the result of natural processes, and then those particles will end up getting infinitely further apart?

2

No … that would imply that any part of a galaxy that was undergoing some sort of compression should suffer a reversal of direction of time… doesn’t happen.

I don’t see how the movement of matter is affecting time.
People take the entropy as defined by thermodynamics and then try to apply that to like, the mechanics of the expansion of the universe… No, because the system the thermodynamics entropy applies to is not a gravitational well… The entropy of this question is some other entropy, which is trying to measure the effect involving many gravitational systems (galaxies, solar systems, and so on… )… totally different physics at work… not the same entropy.

Or to put that another way, Entropy is a measure of the results of time in a thermodynamics context, but it is not saying that entropy drives time… correlation is not causation.

3

Well, the whole business of “time’s arrow” is a tenuous one, and I have issues with the idea of time as a “thing” anyway.

But what I’m curious about is inflation, and how it affects matter.

4

Like, is the space between, say, the nucleus and its electrons also part of “space” as we think of it? Is it expanding too?

5

We don’t know the answer to this for certain, since nobody knows what is causing inflation, let alone how to test whether it works differently on large scales and on small scales. All we know at this point is that there is something that’s causing a constant acceleration of the Universe on large scales. In the lack of evidence otherwise, it seems like the simplest hypothesis to assume it works the same way on all scales, but that’s an assumption born from a desire for simplicity (Occam and all that.)

This is a scenario that people have thought about, and is known as the Big Rip. Very roughly speaking, in this scenario the “force” between two objects due to the cosmic acceleration grows with time, and so as the Universe evolves, objects that are more and more tightly bound to each other get pulled apart. First galactic clusters get pulled apart; then the galaxies themselves, then solar systems, then molecules, then atoms, then protons and neutrons. It’s a pretty grisly scenario.

However, this is another question where we don’t know enough about what’s causing the cosmic acceleration to know whether this will happen or not. In the simplest possible models of dark energy, it doesn’t happen; the force between objects a given distance apart is (effectively) constant with time, and so it just acts as a slight correction to things like the radius of an electron’s orbit. In principle, the electron might orbit slightly closer to (farther from?) the atom if it existed in a Universe without dark energy. But we can’t just pop over to that Universe and measure the radius there, so it’s kind of a moot point.

6

First of all, “eternal inflation” doesn’t describe the Universe we observe ourselves to be in. Our Universe is one with a positive cosmological constant, which will therefore (to the best of our knowledge) expand forever. Inflation is qualtitatively like that, but turned up [del]to 11[/del] past a googol. We know (or at least are pretty sure) that our Universe underwent a period of inflation in its early history, but that… something… happened to stop the inflation, leading to the more sedate sort of expansion we have now.

The current best models for this change are similar to a supercritical phase transition. For example, if you put bottled water in a freezer, and leave it there long enough undisturbed, you can get liquid water at a temperature below the freezing point. Give it the slightest disturbance, like jostling it as you take it out of the freezer, and it’ll suddenly “realize” that it’s not supposed to be liquid, and freeze with crystals growing before your eyes. The colder you get, the smaller the necessary disturbance, until eventually you reach a point where it happens effectively spontaneously: The liquid water can persist for a while, but it’s unstable.

The inflationary state is similarly believed to be unstable: Give it the appropriate nudge, and it’ll start growing “crystals” of what we think of as ordinary space. So at some point in our history, something nudged the Universe, and it “solidified”.

Except that the “crystals” can only expand at the speed of light. This is where the concept of eternal inflation comes in: Even if you do get a “crystallization” started in a small region of an inflationary universe, that crystal is going to grow much slower than other regions of the same initial size that didn’t “crystallize”. So even if something did nudge our Universe out of the unstable state, one would expect that there’s still far more space, way out there somewhere, that is still inflating, than there is non-inflationary space.

Eternal inflation takes this concept to the logical conclusion: It posits that the vast majority of existence is, and always has been, in an inflationary state. It’s unstable, and so occasionally bubbles of non-inflationary space arise, but they don’t matter on the large scale, because everything else expands faster than them. What we know as our Universe, then, is just one of these bubbles.

Now, on to this paper, it looks like they’re addressing one of the objections to this model. Eternal inflation posits that the inflationary bulk must be stationary (which is not the same thing as static): That is to say, if you look at it at any one time, and then look at it at some later time, it should look basically the same. Details like where the bubbles are and how big each one is might change, but the density of bubbles, and the distribution of their sizes, should be unchanging. But, one might object, what about entropy? Surely, if you look at a later snapshot of this inflationary bulk, it should have a higher entropy than in an earlier snapshot? It looks like Carroll and Guth are addressing this by pointing out that such a space has no maximum (nor minimum) entropy, and thus there’s no point to use as a fixed point of any entropy scale.