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?

Some one must have something to say, even if it's only "Rubbish!"

Where's Orac when you need him?

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')

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?

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.

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.

"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.

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?

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?

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.

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.

Is any activity possible without entropy change?

Not in your physical world but in quantum mechanics all the time :-)

=> http://en.wikipedia.org/wiki/Quantum_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.

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.

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?

Hmmm this is going to get hard at a layman level

Perhaps start here => http://www.sciencedaily.com/releases/2011/06/110601134300.htm

The key point




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 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

Bill, you might enjoy this video as much as I did:

Sean M Carroll on Origin of the Universe & the Arrow of Time
http://www.youtube.com/watch?v=rEr-t17m2Fo

This might be of interest too. Note the highlighting of the predictive power of mathematical physics, and his closing comments at 51:30):

Neil Turok: What Caused The Big Bang?
http://www.youtube.com/watch?v=M9iJMWJdyw8&feature=player_detailpage

Thanks Orac & Rede; that will give me something to work on when time permits.

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.



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.



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!

I'm going to have a go at those links and try to get myself back to entropy; promise!

The answer is yes, there can.
We're not treating infinity as a very large number. We're saying that time may stretch endlessly into the past. At least, I am. Aren't you? You seem to doubt that the universe can be eternal, on the grounds that we are experiencing the passage of further time now.

On the contrary, I am saying that the cosmos (universe) must be eternal, and what we perceive as the passage of time is a psychological device that allows us to make sense of the limited perspective we have on reality.

I almost said “yes”, then I gave it some thought, and in fact I have to say “no”.

The time that we experience, we are assured, was created at the Big Bang and is a characteristic of our Universe. Obviously, this does not necessarily preclude the possibility that time existed before the BB, but, as far as I am aware, there is no evidence that time has always existed.

Do we have any reason, other than that it is difficult to understand, to believe that eternity is not an unchanging “now”?

As is so often the case, it seems we are stumbling over semantics.

"While in the popular mind, eternity (or foreverness) often simply means existence for a limitless amount of time, many have used it to refer to a timeless existence altogether outside time. By contrast, infinite temporal existence is then called sempiternity. Something eternal exists outside time; by contrast, something sempiternal exists throughout an infinite time. Sempiternity is also known as everlastingness." Wikipedia

- I raised that point yonks ago in one of your threads, from which I acquired the mistaken impression that you were using the pupular definition of eternity, i.e. sempiternity.


Assured by whom, Bill? All I can find from eminent cosmologists and particle physicists in recent years, is a lack of such assurance. S. Hawking's contention that time must have been created at the Big Bang is now known to have been based on false premises.

Still, so long as the ideas remain speculative, we can hold whatever provisional beliefs we feel at home with. and kick them around till the cows come home.

btw, if we are done discussing cosmic entropy, and are resuming philosophical speculations on infinity, we ought to continue that in an NQS thread, don't you think?

I rather hope we have not finished discussing entropy. You may have noticed that I am easily side-tracked where infinity is concerned, but entropy is what I’m struggling with.



OK, I admit my comment was a bit outmoded, but I did at least add that this did not necessarily preclude the possibility that time existed before the BB. There’s something to be said for a bit of butt covering.

In order to avoid (repeated) semantic pitfalls, I should say that I consider “sempiternity” is to eternity as mathematical infinity is to infinity. Useful as each term may be in its own context, they should not be used as though they were synonymous.

Back to entropy!



I have probably not understood this, but it seems to be saying that SM regards entropy as “ultimate disorder”, while QM sees it as “perfect order”.

Could be I need putting right on that before trying to go any further.

I'm not sure this is on topic for this thread, but I'm posting it here rather than start a new one for something so closely related.

The following quote is from Wiki.

“Dirac hypothesized that what we think of as the "vacuum" is actually the state in which all the negative-energy states are filled, and none of the positive-energy states. Therefore, if we want to introduce a single electron we would have to put it in a positive-energy state, as all the negative-energy states are occupied.”

Does this imply that the vacuum cannot be infinite?

From a QM perspective information can not be created nor destroyed so a vacuum is most certainly finite, I am not sure what Dirac thought we have moved along way since his era.

Take an infinite number conceptually we understand it the biggest number that can exist and it has no real value. However when we take infinity into a practical world say even on a computer or calculator it has to take a finite form based on the decimal places that can be represented on the device.

I keep explaining to you infinity is an illussion like a rainbow based solely on perception. A rainbow is real you can see it but it is also an illussion ... observations are not necessarily reliable something Einstein hated.

Orac, I empathise with your frustration in dealing with someone who must seem unable to grasp a relatively straightforward concept. I accept that the rainbow is almost as illusory as the crock of gold at its base. I accept that for all practical purposes infinity is an illusion. I also accept that those who find infinity encroaching on their work have to devise a way to make it practical. I realise that without the “shut up and calculate brigade” in QM our technological progress would stagnate, and that the same sort of concept has to be applied to infinity.

However, having said all that, I suspect that QM could tell us more about reality than we need to know to build computers and the like. I also suspect that there must be more to infinity than illusion. If there were not, we would not be here to have this discussion.

You answered your own question to a degree ... on one hand you accept that a rainbow is an illussion yet for some reason you feel certain that infinity is not.

Can I ask why?

Take human experience.

- Originally the universe was a flat earth
- In the 1500's we progressed to earth centre of universe and sun and moon circling it.
- Progressively we realized there was more bodies and our universe grew.
- By 1900's and Einstein we had progressed to the known universe as you would refer to it.

QM is simply telling us the universe is even bigger and more complex than that, if by the universe you mean the term to encompass all known things.

Is that the end of the line? ... it might not be we can not know at this point in time there may be something beyond that.

My problem with your conjecture is we can not even clearly define the universe and you worry about is it infinite or not ... to me thats a bit strange.

Historically, I think you have fallen into the “Dark Ages” trap here. The idea that educated Europeans believed the Earth was flat until Columbus accidentally bumped into America is; like the idea of the Dark Ages; an invention of French and Italian Humanists who seemed to feel that there was not enough about the Church in the Middle Ages that they could criticise, and had to think up some extra bits. However, that’s an aside.



You will recall that the way in which I use “Universe”, “universe” and “cosmos” is intended to avoid confusion as to what I might “mean the term to encompass”.

All I am saying is that if the cosmos were not eternal (infinite), there would still be nothing now.



We don’t actually need to define the universe in order to conclude that something must always have existed, and this conclusion necessitates an infinity that does not lend itself to renormalization.

Outside science? Perhaps, but is it further out than strings, multiple universes and a multitude of extra dimensions?

Just a thought on illusion. Why choose the rainbow, especially? Anything presumed from it's appearance to be something other than it actually is, is an illusion, the rainbow being no more nor less so. The whole of what we perceive to be reality may be regarded as illusion, since we can perceive it only in a limited way by limited means, and are therefore limited to erroneous mental representations. In attempting to understand reality, it seems to me that infinity is comprehensible whereas the back of my hand, ultimately, is not.
I second that motion.

Thanks Rede; but I notice you avoided mention of the second half of the sentence.

Why might infinity be different from the rest of reality?

There is an article for you to read Bill S it is fairly technical but should be understandable.

It explains why gravity can't be entropy which cuts right to the basis of your argument.

http://motls.blogspot.com.au/2010/01/erik-verlinde-why-gravity-cant-be.html

Thanks for the link, Orac. You are right, it is fairly technical.

I think I managed to grasp enough of it to follow the general argument. All I have to do now is go back to my OP to see if I can remember what I was trying to figure out at the time, and see how this article impacts on that.

General rule 1 for objects: "objects" only look "discrete" when we describe them in a superficial manner, without looking into their structure. The discrete social security number or drivers licence is only a good description of a person for those who are not interested about anything else connected with the person.


General rule 2 for objects: No two discrete objects can ever be identical. The closer you look at an object the more fuzzy the object becomes and subtle differences appear even between two seemingly identical objects. Take this down to the ultimate two identical atoms which can not be seperated in any way will spontaneously decay at different times. This implies whatever any discrete object is built out of has imperfections or fluctuations.


Entropy is a description of the relative order of discrete objects. Now look again at rules 1 and 2. How could entropy be anything other than a general description of discrete objects in much the same way as temperature is a measure of the speed of vibration of particles. Knowing the temperature of something does not tell you anything about how the temperature came about and similarly knowing the entropy of something tells you nothing deeper.

One of the problems with this thread is that infinity keeps causing a distraction; I can't think how that happens.

Earlier I quoted from a linked article and asked a question which I think I need answered in order to progress.





I have probably not understood this, but it seems to be saying that SM regards entropy as “ultimate disorder”, while QM sees it as “perfect order”.

Could be I need putting right on that before trying to go any further.

Again a frame of reference issue ... I will sort of dumb it down to ridiculous to make the point

QM everything slops around in and out of existance so if you have something doing that it's pretty normal (low QM entropy), if you have something solid and organized then it's pretty non QM'ish (high QM entropy).


Classic physics says something that is solid and ordered is pretty normal (low entropy) something that is randomly jumping around is unordered and not normal (high entropy).

So classic physics say things go from low to high entropy as stated by the classic law of thermodynamics.

QM would sort of say you observed or applied some force to lock the solid object into being solid it really wants to be the floppy random thing and eventually it will do so by decaying if nothing else happens.

So yes they are opposites because classic physics wants things to be solid, discrete and should exist forever, QM says everything is floppy and fuzzy and even locking something into an observed state it will eventually decay back into the fuzzy floppy state.

Rough and ready but it sort of explains the different backgrounds.

Perfect! Thanks, that's just what I needed.

Going back to an earlier link,
http://motls.blogspot.com.au/2010/01/erik-verlinde-why-gravity-cant-be.html



Is that because the discrepancy would cause decoherence, if so, why?