Boundaries of Time in The Evolution of The Universe

[Quantizer]

Given The Hawking-Hartle state is an initial state of the very early universe

If the universe very far in the future asymptotically approaches 0K, what is the name of this final state of Maximum Entropy

Does time stop at Maximum Entropy final state of the universe

Given the assumption that the Arrow of Time is a function of Entropy

 

[PeterDonis]

Does time stop at Maximum Entropy final state of the universe

No, because there is no such "final state". More precisely, if the universe will expand forever, then its entropy will also increase forever; it will never reach a maximum because there is no maximum, i.e., there is no upper bound to how large it can get.

 

[marcus]

Our U apparently began expansion with very low entropy. Peter, how might that have happened (if it did) from prior high entropy conditions such as you imagine? Any thoughts on this recent paper?
http://arxiv.org/abs/1406.3706
Our Universe from the cosmological constant
Aurelien Barrau, Linda Linsefors
(Submitted on 14 Jun 2014)
In this article, we consider a bouncing Universe, as described for example by Loop Quantum Cosmology. If the current acceleration is due to a true cosmological constant, this constant is naturally conserved through the bounce and the Universe should also be in a (contracting) de Sitter phase in the remote past. We investigate here the possibility that the de Sitter temperature in the contracting branch fills the Universe with radiation and causes the bounce and the subsequent inflation and reheating. We also consider the possibility that this gives rise to a cyclic model of the Universe and suggest some possible tests.
5 pages

My comment: The standard LambdaCDM cosmic model assumes a positive cosmological constant Lambda. What Barrau Linsefors say is if that is true (which it seems likely to be) then putting that with other conventional assumptions together with the LQC cosmological bounce (quantum corrections akin to the Heisenberg uncertainty principle make gravity repel at extreme density and cause a rebound instead a singularity), you get that a low entropy beginning of expansion is NOT improbable.
On the contrary one eventually must occur---is in fact inevitable---somewhere.

 

[PeterDonis]

Our U apparently began expansion with very low entropy. Peter, how might that have happened (if it did) from prior high entropy conditions such as you imagine?

I wasn't imagining that our universe came from a prior high entropy condition. (Neither was the OP, as far as I can tell.) I'll have to read through the paper you link to, but just from the excerpts you post, one obvious question I have is how the contracting de Sitter phase came into existence. I don't see any obvious way for our current expanding de Sitter phase to turn into a contracting de Sitter phase.

 

[Chronos]

This may not be the proper place to bring this up, but, how do you get a contracting universe without violating the cosmological principle?

 

[marcus]

This may not be the proper place to bring this up, but, how do you get a contracting universe without violating the cosmological principle?

Astute question! You should write immediately to Linda Linsefors and ask her.
I decided that they just go ahead and let the universe violate homogeneity when it gets a huge tract of empty space which is effectively deSitter. Makes sense to me.

But why not ask? Linda is a postdoc, how much correspondence does she get? What would be the harm? If she answers please let me know what she says. AFAICS homogeneity is a vague scale-dependent idea to be used in constructing approximate models *as long as it is pragmatically useful*. It is supported by no physical law. The U is obviously not homog at all scales and when you have unlimited expansion leading to widely scattered matter among vast tracts of void then you are on track to automatically violate homog at very large scale.
New concept: the Lambda-dominated era. :^)

 

[Quantizer]

No, because there is no such "final state". More precisely, if the universe will expand forever, then its entropy will also increase forever; it will never reach a maximum because there is no maximum, i.e., there is no upper bound to how large it can get.

However, beyond the Black Hole era, post Hawking Radiation, there should be near nothing to decay, and there is nothing but near emptiness, how can Entropy increase unbounded, if there is nothing to propagate further disorder, surely Entropy must reach a maximum, and does this happen as the temperature asymptotically approaches 0K

 

[ChrisVer]

No, because there is no such "final state". More precisely, if the universe will expand forever, then its entropy will also increase forever; it will never reach a maximum because there is no maximum, i.e., there is no upper bound to how large it can get.

Why would the entropy increase in an adiabatic expanding universe? I think the only time in our universe the entropy increased was during the inflation...

 

[Quantizer]

Entropy is increasing due to 2nd Law of Thermodynamics towards Thermodynamic Equilibrium of Maximum Entropy ...

 

[ChrisVer]

thanks- i was wrong

 

[PeterDonis]

beyond the Black Hole era, post Hawking Radiation, there should be near nothing to decay, and there is nothing but near emptiness, how can Entropy increase unbounded

Because the universe is still expanding, and that expansion adds gravitational degrees of freedom. If the universe expands forever, it continues to add degrees of freedom forever. The whole idea of a "maximum entropy" implicitly assumes that there is a maximum possible number of degrees of freedom; if the number of degrees of freedom can increase without bound, so can entropy.

 

[PeterDonis]

I decided that they just go ahead and let the universe violate homogeneity when it gets a huge tract of empty space which is effectively deSitter.

As I read the paper you linked to, it looks to me like the argument is based on the fact that whether you view de Sitter spacetime as "expanding" or "contracting" depends on how you slice the spacetime into space and time. One and the same de Sitter spacetime can have a slicing that is "expanding" *and* a slicing that is "contracting". Which slicing is "natural" for a given region of the spacetime depends on what the matter and energy in that region are doing.

In our region of spacetime, the matter and energy are expanding, so the expanding slicing is natural; but before what we call the Big Bang, the matter and energy were contracting, so the contracting slicing was natural. They then invoke the "bounce" idea from Loop Quantum Gravity to explain how the matter and energy changed their state of motion once they got compressed enough.

As far as homogeneity goes, I think this model *needs* it in order to make sense, because the whole idea of using different slicings on de Sitter spacetime requires the spacetime to be maximally symmetric, which de Sitter spacetime is. Any violation of homogeneity makes it less symmetric, and correspondingly makes the idea of "switching slicings on the fly" less viable. At least, that's how it looks to me.

 

[Quantizer]

Because the universe is still expanding, and that expansion adds gravitational degrees of freedom. If the universe expands forever, it continues to add degrees of freedom forever. The whole idea of a "maximum entropy" implicitly assumes that there is a maximum possible number of degrees of freedom; if the number of degrees of freedom can increase without bound, so can entropy.

Good answer, can there exist conditions, a specific scenario whereby dark energy or equivalent repulsive forces causing expansion to become zero in the very far future post Hawking Radiation Era, such that there is no increase in degrees of freedom in any variable, only then can we achieve Maximum Entropy.

Furthermore are quantum processes still possible due to uncertainty principle, when there is such a state of Maximum Entropy, to seed a future Big Bang to appear out of nothing at Maximum entropy

 

[PeterDonis]

can there exist conditions, a specific scenario whereby dark energy or equivalent repulsive forces causing expansion to become zero in the very far future post Hawking Radiation Era, such that there is no increase in degrees of freedom in any variable

Not due to dark energy or any "equivalent repulsive forces", no. Those can only produce an expansion that accelerates forever.

 

[Quantizer]

Not due to dark energy or any "equivalent repulsive forces", no. Those can only produce an expansion that accelerates forever.

The reason why I ask is in relation to recent posts on this thread ...
What physical processes can cause a DeSitter Contraction to kick in an already expanding DeSitter Phase very far in the future of the Universe, thanks

 

[PeterDonis]

What physical processes can cause a DeSitter Contraction to kick in an already expanding DeSitter Phase very far in the future of the Universe, thanks

I'm not sure how the paper marcus linked to answers that question; they only seem to talk about the "bounce" part (contraction to expansion).

In a "pure" de Sitter spacetime, as I said in a previous post, "contraction" vs. "expansion" is just a choice of coordinate chart; nothing physical actually has to change. But of course, in a "pure" de Sitter spacetime, there is no ordinary matter or energy; the spacetime is vacuum other than the cosmological constant. So for a particular region to "switch" from expansion to contraction in the actual universe, where ordinary matter and energy are present, yes, something physical should have to change, and I don't see anything in the paper that really addresses that.