There has been some discussion about the problem of entropy in a cosmos that is infinite in time and yet closed in space. I think this is true, and so therefore, anybody proposing a cosmoc infinite in time would also have to propose one infinite in space. In an open system, entropy doesn't apply. I know this is a bit abstract, but there are two questions I have.

First, how would entropy work in an open system? Would the system be constantly becoming closer to entropy, without every reaching it, or would it be meaningless even to speak of entropy?

The second is a bit more concrete. It seems to me that the cosmological redshift would be a problem in such a cosmos. I can think of three solutions:
(1) the redshift is not a doppler redshift.
(2) the redshift is a doppler redshift, but is only a local phenonomenon (I think that Eric Lerner adopted this position).
(3) the redshift is a doppler redshift, but has something to do with an expansion or contraction of space itself.

The question I have in this case concerns the third option. Would it be possible, in an infinitely sized and timed cosmoc, to have a doppler redshift based on a change in space itself? On one hand, it seems contradictory -- how can everything be expanding in an infinitely large universe?

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"Open systems" can be treated within equilibrium thermodynamics.
Do a search for canonical and grand-canonical distribution within statistical mechanics.


"Open system" means that the system is in contact with another system.
So it can exchange entropy with that other system.


Why?
Before proposing solutions, you need to make clear what the problem is.

As I said, you have to explain to make sure there is a problem first.
However, on cosmological scales, one has to use General Relativity, and I don't know whether or how thermodynamics is treated within that framework.



EDIT to fix tags.

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

In my model of Rotating Universe is another possibility.
In the infinite space and time is Energy, which was in a finite time concentrated and transformed into a mass of the Observable Universe. This matter of the Observable Universe may expand and entropy increase according to flatness of the geometry and supply of the energy from outside. Increase of the entropy is seen as Doppler shift.

I guess my understanding was not exactly correct. What would you call a system that is infinite in both space and time? Is it open or closed? I understand well that in a closed system, entropy means that everything will eventually become equalized, but I'm not certain what would happen in a real infinite system.

I'm not sure if I quite understand. I guess if I have to answer this, it would be something like, "a thought experiment." Or another, more , an infinite cosmos would seem more logical to me to one that is not infinite. Of course I realize that reality doesn't necessarily follow what we think it should. But it's the same with Santa Claus. My own personal feeling is that he doesn't exist, for my own logical reasons. But I'm perfectly willing to recognize his existence, if there is no other choice.

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Usually, the term open system is reserved to systems that exchange energy and/or matter with other systems.
This does not seem to happen with our Universe.

An infinite Universe which does not interact with another system, would be a closed system.
The entropy should reach a maximum, but I do not expect this within a finite amount of time.
A state of equilibrium, corresponding to maximum entropy, would be asymptotic (that is, reached only in the limit for time -> infinite).

My point was that maybe there is no problem with entropy of the Universe.
If you think there is a problem, you need to tells us exactly how this problem arises and what makes it a problem.
Only when we know the terms of the problem, can we discuss the possible solutions.
I did not address your solutions because I could not see a problem: I simply thought that considering the Universe as open system was incorrect, and hence the problem you were trying to solve was non-existent.

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

Ok, I understand, and maybe I can put it in simpler terms.

I'm inclined to believe the universe is infinite rather than finite. Would such a cosmos present a problem in terms of entropy?

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*cough**cough*

As far as I understand, it is not problem (a pity, maybe, but not a problem).

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

Actually, this was another question I wanted to get some feedback on. It doesn't seem easy to me to explain how the cosmological redshift could exist in an infinite universe.

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I am not an expert in cosmology, but I don't think that expansion of space is compatible with an Universe infinite in size and in time.

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

Entropy in an infinite spatial/time universe would be at its maximum. There would be no macroscopic/microscopic diferences of state in any area of the universe and no differences in energy to drive any further change. That universe would have 'wound down.'

:-?

Is it usually taken that an infinite spatial universe is also infinite temporally?
Researching...

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On a level that makes sense. But then I wondered, "wound down" from what? I think then that the cosmos would have had to start out in a wound down state. If it was ever in a non-wound down state, then I don't think it would not be able to wind down.

I don't know, but I can't imagine it any other way. It would seem illogical for one to be infinite but the other to be finite. Having an infinite space with fine time makes one wonder, what happens to the unused space? By contrast, a finite space and infinite time would lead to heat death, I think.

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I asked partly because I'm not absolutely certain, but it appears, to the best of my limited capability to understand, that Narlikar and Hoyle were proposing a universe that was unlimited in size and time, and yet where matter was being created. I can't say it's easy to understand. :-?

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Hi Jeans
I wrote in my post above about created matter in a unlimited by space and time Universe.

Hang on: matter creation?
In this case, I would not consider the Universe strictly a closed system.
You could model the Universe as an open system in contact with another system (where the matter comes from).
This other system would then provide the entropy for the Universe.

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

Reasoning about infinity is tricky to do consistently, and being un-comfortable with an idea is not the same thing as that idea being illogical. It is kind of a tangent, but I'm reminded of a puzzle posed by Martin Gardner:

The Hotel Infinity has an infinite number of rooms. Each room is numbered: 1, 2, 3, etc. A guest arrives late one night. The desk clerk greets the guest, but says "I'm sorry sir, but all our rooms are full." It is a dark and stormy night, the guest is tired, and doesn't want to look for another hotel, so he tells the clerk: "Look, move the person in room 1 into room 2, move the person in room 2 into room 3, move the person in room 3 into room 4, ..., and so on. Now you have a vacanct room." The clerk agrees and so is able to accomodate the guest.

After making the arrangments and returning to the desk the clerk is horrified to find an infinite number of new guests! "No problem" the new guests point out, "Just move the person in room 1 to room 2, move the person in room 2 to room 4, the person in room 3 to room 6, and so on". After this shuffle all of the odd rooms are free, and since there are an infinite number of odd numbers all of the new guests can be housed.

Would it help you could to think of the natural numbers (1, 2, 3, ...) as an example of an entity with a finite origin but infinite extent?

I just want to point out that the terms "open" and "closed" are used with different meanings in cosmology and thermodynamics.

In cosmology, the terms closed, flat, and open are used to refer to spatial cross-sections that have positive, zero, or negative curvature respectively. Closed spaces have a finite volume, flat and open spaces have infinite volume.

In thermodynamics, the terms open and closed refer to systems that can or cannot exchange energy and momentum with other systems respectively.

There is no reason why a universe cannot be both closed thermodynamically and either open or flat spatially. I hope this clears up some confusion.

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Yes, that's correct. Continuous creation was needed because the original steady state model was in permanent inflationary expansion, and Hoyle, Bondi and Gold (and presumably Narlikar) subscribed to the "perfect cosmological principle", which stated that the universe's average properties were unchanging in space and time. An expanding universe without continuous creation would break the perfect cosmological principle (obviously, the average matter density would tend to decrease). Hence the point thermodynamical violation represented by the big bang's initial singularity was replaced with continous, uniform violation. This can also prevent heat death, because you have an indefinite source of low entropy energy to draw upon.

The model was eventually abandoned after some of the best entertainment available anywhere in published science*. The official successor to the steady state model is a lot more complicated, and as I understand it, oscillates rather than expands continuously.

You might also encounter variants on "static state" cosmologies, where no expansion takes place, and yet the universe is infinitely old (i.e. where the perfect cosmological principle is still held to apply). That model really does have an entropy problem; you can't resort to continous creation because then the average density of the universe would increase (even ignoring gravitational effects), and break the perfect cosmological principle. But without it, you're stuck with an infinitely old closed system, without an external source of low entropy energy. We should be dead in this model.

I've heard that puzzle described as Hilbert's Hotel; I assumed David Hilbert was the first to describe it?

* There are some fantastic arguments in the literature between early big bang supporters and the steady state cosmologists.

Here is where the problem of closed versus open gets confusing to me. Even if the cosmos is closed, in the thermodynamic sense, what if it is infinite in space? Doesn't that mean that there would be an infinite amount of energy? Which would mean that entropy could never wind things down. What I'm a bit unsure of, because of the infinity, is whether entropy would work, making things ever closer to complete entropy but never reaching it, or whether the size being infinite would prevent entropy from even making a dent at all.

Also, with regard to the creation of matter, there is also the possibility I guess of recycling, where matter created somewhere is compensated by a destruction somewhere else.

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In an infinite universe with finite energy and matter, entropy would work. And if there was infinite energy, then the entire infinite universe would be packed with energy.

I might also like to add that current research indicates that the universe is actually finite.

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Jens is talking about universe that is spatially infinite, so even if we would have, for example, only one photon per cubic gigalightyear, we would still have infinite number of photons (= infinite energy) because volume of the universe would be infinite.

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I found an article in New Scientist from 2003, though, titled "tantalizing evidence hints that universe is finite." The author said, "many astronomers suspect that the universe is infinite." Also, there was a mathematician quoted as saying the universe may be finite, but there were two astronomers quoted as saying they didn't find it convincing. So it seems at least from this that there is still uncertainty on this issue.

http://www.newscientist.com/article.ns?id=dn4250

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I know there is uncertainty, which is why I used indicates rather than proves or says.

Of course that might be a distinction that only I use.

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"We can't test an elixer of immortality! It'd take forever!"

What you have there is the "dodecahedron universe" notion that managed to make a brief splash in the popular press a couple of years ago. Basically, the investigators presented evidence that the universe has a strange topology, wrapping in on itself so that it could be fairly small (as far as universes go). The evidence was refuted almost as soon as it was published, and this particular notion is now effectively dead. The search for unusual topologies continues; but it's a really long shot.

Ned Wright has a good concise write up in his News of the Universe archive. Look for "A twelve-sided Universe? - Probably not".

Another approach is to look at the curvature of the universe. Neglecting topological complications, whether the universe is finite or not depends on whether curvature is positive or negative -- assuming homogeneity, which is another big assumption. Basically, positive curvature means a universe roughly analogous to a finite hypersphere; and negative curvature means a universe roughly analogous to an infinite hyperboloid; and zero means a "flat" universe roughly analogous to what we'd normally think of as unbounded space in which parallel lines remain at the same separation indefinitely.

A first rate description is at this Cosmology 101 lecture by James Schombert.

The curvature is so close to flat that measurement can barely discriminate between positive and negative curvature models. But recent observations do indicate a slight positive curvature, which suggests a finite but enormously large universe. This turns up in, for example, astro-ph/0501171, in which curvature is considered even though finiteness is not mentioned. Look for Ω_k &lt; 0; which confusingly means positive curvature.

Strange topologies in which different regions of space connect in weird ways would still allow a finite universe with positive curvature; but negative curvature would be a strong indication of finiteness without any need for strange topologies.

If distant regions of the universe far beyond horizons of visibility have significantly different curvature properties, then all bets are off again. This is by no means a settled question.

I plumb for finite; but there is a fair amount of meta-physics bound up in any expression of definite opinion. Some scientists have philosophical preferences for finite; and others for infinite; and so far the universe is being coy on the matter.

Cheers -- Sylas

I knew I was missing something.
Thanks.

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

Thanks for all the tips for searching for more. This is something that seems puzzling to me; the fact that the curvature is so close to 1. From what I understand, it would quickly run away from 1 in one direction or the other, so the fact that it is so close to 1 means that it must have started extremely close to 1. So my inclination is to believe there must be some reason why it is so close. Though I have no idea what that might be. :-?

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Very insightful question. This is indeed a major puzzle in cosmology; and one of the proposed solutions is inflation. A large vacuum energy will rapidly drive curvature towards zero. Somehow then the associated field decays, and we are left with an almost flat universe with subcritical density.

The major and very surprising discovery of recent years is that there is still a non-trivial vacuum energy term; nothing like what would have been needed to drive the original inflation, but enough that expansion is apparently accelerating. Effectively, we are pretty close to inflation right now; but the doubling time for scale factor is in many billion of years rather than tiny fractions of a second proposed for the inflationary epoch of the very early universe.

Cheers -- Sylas

Hi Sylas
I search what causes the expansion of the Universe. I suggest one idea that it could be due to decay of the matter.
The matter might be just compressed space according to oscilation frequency.

If neutrino is a balance for electron in beta decay it may play a role in space warping. In my philosophy of space a photon of energy shrinks (contracts) and expands the space according to its frequency. A particle with rest mass has an average volume between this warping.
During beta decay the electron goes away with its gravity contracting the space. A particle left ( proton) has less gravity then before (neutron) hence changed its space curvature. This emission of the neutrino may be manifests by an expansion of the space itself. .

This neutrinos may have as pressure of the space a repulsive force. It is not antigravity but just pressure of the expanding space. In Cosmic Voids may be more and more neutrinos, so this pressure act on galaxy clusters forming them in filaments that we see. This space pressure as Dark Energy in Cosmic Void may be like Dark Matter force around galaxy.
Larger Cosmic Void may contain (longer distance) more neutrinos. It causes acceleration of the expansion.

It is strange idea but something must causes this expansion.

It isn't; no chance.

The physics of expansion follows fairly directly from general relativity, and it's got nothing to do with decay of matter. The rate at which expansion develops depends on energy density; and the energy can have various forms. The two major forms at present are (as far as we can tell) matter, and vacuum energy. "Decay of matter" would correspond to conversion from matter energy to radiation energy. Radiation energy was significant in the early universe, but not now; in fact the signature of expansion is precisely the opposite of what radiation energy would give. The observations fit a strong vacuum energy component, in which the energy density remains roughly constant as space expands. Matter density drops off as the cube of the scale of the universe, and radiation drops off as the fourth power of the scale factor. Radiation energy dominance would have the opposite effect to what appears to be going on at present.

Cheers -- Sylas

The idea with neutrino is a speculation only. OK.

If the space expands by itself it was compressed then before and space must have its structure if it expands. Nothing can not expand. What compresses the space ? Does it mean the energy is a compressed space ?

I can't say I understand this 100%; the problem is the "associated field," which is probably not a really clear concept for laypeople.

The one thing I would wonder about inflation is: is it something that happens to be there, or something that must be there? If it's the former, I would be pretty skeptical of the whole idea. If theoretically, there is a need for something that would keep the curvature near 1 (for example, an inflation that constantly drives curvature toward 1 while other things drive it away) then it would seem logical. But then, I'd want to understand why this must arises.

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