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1. The Second Law (of thermodynamics) requires that entropy in the Universe increase with time.
2. The entropy of the Universe at the Big Bang must have been very much less than its current entropy.
3. Any local decrease in entropy must be more than balanced by increase on a cosmic scale.
4. If the expanding Universe is constantly gaining entropy, it would seem logical to expect that contraction would lead to lower entropy.
5. Contraction under gravity leads to increased entropy, resulting from velocity changes and the associated rise in temperature of the contracting group.
6. If the expansion of the Universe were reversed, the resulting contraction would be gravitational, so entropy would have to increase.
7. If the universe is cyclic, then the entropy of each cycle must be higher than that of the preceding cycles.
8. Is there a limit to the level of entropy that can be attained?
9. If there is a limit, and if the cosmos, i.e. the totality of cyclic universes, is infinite; why was this limit not reached infinitely long ago?
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Some one must have something to say, even if it's only "Rubbish!"
Where's Orac when you need him?
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It seems there's no reason to believe that your point '4.' is true, Bill. The process of contraction would not be a re-run of the expansion in reverse order. The arrow of time would still point from past to future: http://library.thinkquest.org/06aug/02088/hawking.htm"...as Don Page and Raymond Laflamme, Hawking's colleague and student, respectively, pointed out, no law of physics, quantum mechanics, or relativity said that the universe would have to contract in reverse-time and that entropy would have to decrease. Hawking backtracked and realized they were right..." I can't find the references right now, but I believe your take on the cyclic universe hypothesis is in agreement with current thinking; i.e. entropy would increase with each cycle. Not sure about that though...but if true, the final curtain would be when entropy reached maximum - no 'work' could be done by such energy as remained (so-called 'heat death')
Last edited by redewenur; 01/23/12 03:30 PM.
"Time is what prevents everything from happening at once" - John Wheeler
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Thanks for the comment, Rede.
If you take points 4 - 6 in succession the reasoning becomes: Although “A” might seem logical at first sight, “B” must in fact be the case.
How about the "logic" of the whole sequence?
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Sorry about the late edit on the previous post.
It strikes me as logical enough. But then I'm looking at it with a layman's eyes. Recent views of cosmologists would be interesting, if only I could find some.
"Time is what prevents everything from happening at once" - John Wheeler
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I, too, am looking at it with a layman's eyes, as must be painflly obvious to any cosmologist. However, it does still seem to leave the question as to why "so-called 'heat death'" was not reached infinitely long ago.
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"9. If there is a limit, and if the cosmos, i.e. the totality of cyclic universes, is infinite; why was this limit not reached infinitely long ago?" I'm tempted to say "Who knows?" . But one can imagine many possibilities, such as our hypothetical cyclic universe is one of an infinite number of cyclic universes, each spawned in like manner in an eternal vacuum. It might also be that the 'heat death' state at the end of one set of cycles becomes the spawning site for new Big Bangs...and so on..erm..ad infinitum.
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But one can imagine many possibilities, such as our hypothetical cyclic universe is one of an infinite number of cyclic universes, each spawned in like manner in an eternal vacuum. This sounds like a possible answer, but it has two pitfalls: 1. It treats infinity as though it were an infinite series of finite periods, which doesn't really make sense. 2. If infinity could be treated in this way, an infinite number of finite periods would already have passed, so there would be no more to come. How can you have more than an infinite number?
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Rede, that was an interesting link.
It ends with: "When the universe begins to contract and the cosmological arrow reverses direction, there will be no solid direction for the thermodynamic arrow to point in, since entropy could not increase much more."
How does one square that with the fact that such contraction would constitute gravitational collapse, which should cause entropy to increase?
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But one can imagine many possibilities, such as our hypothetical cyclic universe is one of an infinite number of cyclic universes, each spawned in like manner in an eternal vacuum. This sounds like a possible answer, but it has two pitfalls: 1. It treats infinity as though it were an infinite series of finite periods, which doesn't really make sense. 2. If infinity could be treated in this way, an infinite number of finite periods would already have passed, so there would be no more to come. How can you have more than an infinite number? We've been here before, Bill. As you probably know, I disagree on both points. Re 1. Our universe may exist within a time dimension that's without beginning and without end, yet each tick of the clock, each event, measures a finite period. Re 2. Infinity can be added to, subtracted from, multiplied or divided, and what remains is still infinity.
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Rede, that was an interesting link.
It ends with: "When the universe begins to contract and the cosmological arrow reverses direction, there will be no solid direction for the thermodynamic arrow to point in, since entropy could not increase much more."
How does one square that with the fact that such contraction would constitute gravitational collapse, which should cause entropy to increase? I think the answer is in the preceding sentence: "However, by the time the rate of expansion of the universe falls below critical speed and the universe's own matter begins to pull in on itself, all the stars will have burnt out, galaxies will have collapsed, and protons and neutrons will have decayed into radiation and photons; basically, the ultimate state of disorder (or very close to ultimate). When the universe begins to contract and the cosmological arrow reverses direction, there will be no solid direction for the thermodynamic arrow to point in, since entropy could not increase much more." It seems the author is telling us that gravitational collapse would make little difference in those conditions.
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Is any activity possible without entropy change?
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Not in your physical world but in quantum mechanics all the time :-) => http://en.wikipedia.org/wiki/Quantum_entanglement This associates the reversibility of a process with its resulting entropy change, i.e. a process is reversible if, and only if, it leaves the entropy of the system invariant. This provides a connection between quantum information theory and thermodynamics. Rényi entropy also can be used as a measure of entanglement.
Good old QM simply refuses to obey the laws as usual. Now go back to the original theory and factor QM law in and you should see there is a wee little problem.
Last edited by Orac; 01/24/12 06:48 PM.
I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.
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Not in your physical world but in quantum mechanics all the time Does QM not underlie the physical world? The Wiki article gets a bit too technical for me. I'm not at all sure I see the connection between quantum information theory and thermodynamics here.
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Perhaps I will be able to get my head round it if we take one step at a time.
"The Second Law (of thermodynamics) requires that entropy in the Universe increase with time."
Does QM agree with this?
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Hmmm this is going to get hard at a layman level Perhaps start here => http://www.sciencedaily.com/releases/2011/06/110601134300.htmThe key point Perfect classical knowledge of a system means the observer perceives it to have zero entropy. This corresponds to the memory of the observer and that of the system being perfectly correlated, as much as allowed in classical physics. Entanglement gives the observer „more than complete knowledge" because quantum correlations are stronger than classical correlations. This leads to an entropy less than zero. Until now, theoretical physicists had used this negative entropy in calculations without understanding what it might mean in thermodynamic terms or experimentally.
No heat, even a cooling effect In the case of perfect classical knowledge of a computer memory (zero entropy), deletion of the data requires in theory no energy at all. The researchers prove that "more than complete knowledge" from quantum entanglement with the memory (negative entropy) leads to deletion of the data being accompanied by removal of heat from the computer and its release as usable energy. This is the physical meaning of negative entropy. Renner emphasizes, however, "This doesn't mean that we can develop a perpetual motion machine." The data can only be deleted once, so there is no possibility to continue to generate energy. The process also destroys the entanglement, and it would take an input of energy to reset the system to its starting state. The equations are consistent with what's known as the second law of thermodynamics: the idea that the entropy of the universe can never decrease. Vedral says "We're working on the edge of the second law. If you go any further, you will break it."
Knowing you by now Bill you will have some questions but be warned we don't have all the answers the jury is still out on all this. .
I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.
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I was thinking about how to simplify Quantum mechanics and entropy for you Bill S and I was jogged to this which may help although I dislike this particular formalization for very technical grounds it is probably more understandable http://en.wikipedia.org/wiki/Quantum_thermodynamics
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Thanks Orac & Rede; that will give me something to work on when time permits.
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You are absolutely right, Rede, we have been here before. I begin to feel as though I am the only person in the world who has this problem with infinity, and it won’t go away. I just hope I can get some “resolution” before everyone runs out of patience. Perhaps its too late already! When I started this thread I really didn’t mean it to turn into yet another round of the eternal discussion. Our universe may exist within a time dimension that's without beginning and without end, yet each tick of the clock, each event, measures a finite period. Try to take this mental image beyond that of a limitless procession of seconds. It is easy to think we can imagine such a procession going on to infinity in both directions, but that is because we can imagine a vast series of seconds, then vaguely wave a hand in either direction and say: “it goes on to infinity”. Can time be infinite? The easy answer is “yes”, there is an infinite number of seconds in the past and in the future. That’s fine if you don’t think too much about the implications. Mathematically, it may work well, but physically, what is an infinite number of seconds? If an infinite number has already passed, can there really be another infinite number waiting to pass? What we are actually doing is treating infinity as though it were a very large number. Infinity can be added to, subtracted from, multiplied or divided, and what remains is still infinity. Mathematically that seems to work, but your statement could be paraphrased as: “addition, subtraction, multiplication and division have absolutely no effect on infinity”. In other words, infinity is outside the remit of mathematics, unless it is a mathematical infinity, which may not be the same as a physical infinity. I can imagine people saying, with some exasperation, he’s getting into philosophy here, this has nothing to do with science. However, if our Universe (or cosmos) is infinite, and if we are ever to understand it, then science has to look at infinity, and its no good hiding behind comfortable mathematical interpretations. Amen!
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