What about 2nd law of thermodynamics in Cyclic Universe Model?

[Duda Jarek]

Not everyone likes the idea of universe ​​created from a point singularity, so recently grows in popularity cyclic model - that our universe will finally collapse, use obtained momentum to bounce (so-called Big Bounce) and become the new Big Bang.

One might criticize that we "know" that universe expansion is accelerating. But it is believed to be pushed away by "dark energy", so accordingly to energy conservation, this strength should decrease with R^3 ... while attracting gravity weakens like 1/R^2 and so should finally win - leading to collapse.

 

But it seems there is a problem with the second law of thermodynamics here - on one hand entropy is said to be always increasing into the future, on the other Big Bangs should intuitively 'reset the situation' - start new entropy growth from minimum.

I wanted to collect the possible approaches to this problem and discuss them - here is a schematic picture of the basic ones (to be expanded):

 

 

The age of thermal death means that there are nearly no changes, because practically everything is in thermodynamical equilibrium, most of stars have extinguished.

 

1) The second law is sacred - succeeding Big Bangs have larger and larger entropy,

2) It is possible to break 2nd law, but only during the Great Bounce,

3) It is possible to break 2nd law in singularities like black holes - the universe may be already in thermal death, while the entropy slowly "evaporate" with black holes (I think I've heard such concept in Penrose lecture in Cracow),

4) The second law of thermodynamics is not fundamental, but effective one - physics is fundamentally time/CPT symmetric. So Big Bounce is not only single Big Bang, but from time/CPT symmetry perspective, there is also second BB-like beginning of universe reason-result chain in reverse time direction. The opposite evolutions would finally meet in the extremely long central thermal death age, which would probably destroy any low-entropic artifacts.

 

Personally,

I see 1) as a total nonsense - thermal death is near possible entropy maximum (like lg(N)).

Also 3) doesn't seem reasonable - hypothetical Hawking radiation is kind of thermal radiation - definitely not ordering energy (decreasing entropy), but rather equilibrating degrees of freedom - leading to thermalization of universe.

2) sounds worth considering - physics doesn't like discontinuities, but Big Bounce is kind of special - crushes everything, resetting the system.

And 4) is the most reasonable, but requires accepting that thermodynamical time arrow is not fundamental principle, but statistical effect of e.g. low entropic BB-like situation: where/when everything is localized in small region. To see that 2nd law can work in both time directions, there is nice thought experiment: http://www.scienceforums.net/topic/62327-thermodynamical-thought-experiment-with-nonorientable-spacetime/

 

Assuming our universe will eventually collapse, which thermodynamical scenario seems most reasonable? Why?

Perhaps above list requires expansion?

Did universe started in a point, or maybe something ends - something begins (like tonight)?

Edited December 31, 2011 by Duda Jarek

[Sorcerer]

Ok I won't vote but if ur hypothesising a big crunch, at the equilibrium(center) entropy starts to reverse. You can test this on any closed system in the lab - although u need to increase entropy outside the system to create such an effect.

 

Current observations suggest the universe will expand at and ever increasing rate and entropy will approach infinity. Although any entropy is enough for life to "feed" off it may just have to do it at an ever decreasing rate (but what is time to and organism but observational), that is if this type of universe is conducive to any type of "life" (jim but not as we know it).

 

See my post, on "the default state of the universe is inflation"

 

Ok I did vote to #2 even though current observations don't see it as possible.

 

Btw it's reasonable, not reasonably.

[Duda Jarek]

Yes, I've mentioned that currently universe expansion seems to accelerate, but is there a reason to believe that it will be maintained forever?

Gravity says that it should decelerate, but there is something pushing it away - so called dark energy ... but energy conservation says it should weakens with expansion - faster than gravity. Untrue?

 

I completely agree that we observe only entropy growth ... but thermodynamics is effective theory, while more fundamental are time/CPT symmetric.

The only solution to this conflict I can see, is that time arrow is not fundamental property of physics, but a property of the concrete solution we live in - in vicinity to low entropic Big Bang state - in which everything was well localized in small region and which has started our natural reason-result chains: star, earth creation, evolution, our lives...

To see that 2nd law can work in both time directions, see e.g. thought experiment theoretically allowed by GRT: http://www.scienceforums.net/topic/62327-thermodynamical-thought-experiment-with-nonorientable-spacetime/

[Sorcerer]

IMO entropy is only relative to the observer within the system. Entropy always increases. BUT can u define minimum entropy or infinite entropy? Well rhetorical, but no because the laws of physics break down at these points. SO even if what we observe is entropy increasing, it is just a point on an infinite timeline that is everything, perhaps the only period in which we can exist to observe it, perhaps not.

 

oh btw I shouldve voted, #1 but u didnt explain it in words properly and I didn't look at ur graph untill now. And #1 is the closest I would depict it graphically, but not nearly close all the same.

 

"1) The second law is sacred - succeeding Big Bangs have larger and larger entropy"

 

There isn't a suceeding big bang implied here, unless u take my idea (inflation as default) into account. This is basically stating ur first option and twisting it. But yes I see the increase in entropy leading to more and more overlapping systems (hubble volumes) with increased entropy.

 

Oh I will read http://www.sciencefo...able-spacetime/ when I'm sober, I got to thought experiment and did a raspberry.

Edited December 31, 2011 by Sorcerer

[michel123456]

Duda I went back to your other thread in which you posted a link to this thought provocative paper from Mark J Hadley Department of Physics, University of Warwick, Coventry CV4 7AL, UK

Inadvertently I quoted it in the other thread, I'll do it again here.

 

The best part from it IMHO is

It would appear that the existence or otherwise of a time reversing region is dependent upon the observer.

 

Everything is relative! Even the arrow of time, why not, indeed?

 

The whole problem of the faith of the universe arises when we consider the observations we get from the outside world as absolute. Maybe there is no absolute expanding Universe, but we are observing an expanding universe relative to us. Relative must be the key.

I can imagine some E.T. made of anti-matter and asking himself why the arrow of time is going this way and not the other and why entropy is always pointing in this direction, all of which are so well mirrored to him that the result is exactly the same: to him, we are the ones made of anti-matter, we are the weird ones because everything is relative.

Edited December 31, 2011 by michel123456

[Duda Jarek]

sorcerer,

Entropy can indeed relate to subjective information of an observer, but it also describes the ordering of system.

For example imagine a box with two partly separated pars, in which there is some number of objects - we see that e.g. n of them are in left part, while m of them are in the right part - while shaking the box, natural entropy should increase:

h(n/(n+m)) where h(p):=-p lg(p)-(1-p)lg(1-p)

Entropy is indeed about probability - if there is only one objective scenario (probability is completely localized), entropy is zero ... but changing the picture into more effective one: from choosing which part given object chose, into choosing how many objects choose left part - makes that there appears entropy describing ordering of the system.

 

While instead of dividing into two, we make a grid and finally take infinitesimal limit, we get phenomenological thermodynamics, like in diffusion equation.

Even knowing the exact atom configuration, for each point we can calculate the number of atoms in a small ball around - getting density function - probability analogue allowing to define entropy.

 

About entropy as our information, here is example showing that it can decrease with time (by attaching in the future):

We know that given person just couldn't miss given meeting (almost certainly will be there in that moment) ... accordingly to our knowledge, 15 minutes before the meeting probability distribution of his possible positions will be more spread (larger entropy) and so on entropy will grow while going back in time...

... but after the meeting time, such entropy will grow again - this time in the proper direction.

Big Bounce is kind of such a meeting - was well localized, so had relatively small entropy, so created entropy gradient and our natural reason-result chain ...

 

About choosing scenario 1 ... but entropy is usually bounded from above: among probability distributions among N objects, maximal entropy is lg(N) ... so do you think the entropy would tend with succeeding BB to infinity, or maybe asymptotically tend to some finite value?

 

michel,

Not everything is relative, for example our mugs can break only toward our future ... but they were created in our past.

The question is if e.g. your aliens could provide with mugs made in our future - they should also have tendency to increase entropy(break), but this time it could be made only toward our past.

[Sorcerer]

if there is only one objective scenario (probability is completely localized), entropy is zero

 

ok I will read ur post more thoroughly when I am sober, however I could not resist now but pick out this point.

 

You just confirmed ur first poll result without wanting to. The big bang is a point with zero entropy.

 

Edit (and still drunk) - Ok I'll admit u added the conditional "if", so maybe not confirmed.

 

However to further ur analogy, peices of broken mugs can make something too, peices of peices can make something too. Heat death just means a slower transfer of energy.

 

If the universe is expanding at an increasing rate and entropy is increasing, where does it end?

 

Only when the hubble volume of a single quanta is all that is left.

 

Why is that quanta not then an infinite point of density in space? Edit easier way to say that is : why doesn't a single quanta within is own hubble volume have zero entropy?

Edited December 31, 2011 by Sorcerer

[Duda Jarek]

Big Bang in inflation theory could start with mathematical point which can be interpreted as having zero entropy ... but I thought Big Bounce would have rather some nonzero minimal radius and nonzero minimal entropy ... ?

But even if it would be exactly zero, I don't understand why you think it should imply the first poll result?

 

Heat death is not a well define state - it doesn't mean complete thermal equilibrium, but only approximate - like most of stars could not only became e.g. brown stars, but then they could still cool down to temperature near the surroundings (like current 2.7K) ... but thermodynamics should also make them evaporate to equilibrate the matter density - but gravity doesn't allow for that ... (gravity in opposite to electromagnetism is kind of opposing entropy growth - not spread uniformly, but rather gather everything in a single collapse ...)

Heat death is not exactly slower transfer of energy as you write - in thermal equilibrium there is still a lot of energy transfer, but the same amount in both directions.

Better description is that there are no gradients of different thermodynamical values, like average energy (temperature) or density of different substances (like osmotic pressure in our cells).

 

ps. Penrose claims that there is even seen experimental evidence of something before Big Bang: http://physicsworld.com/cws/article/news/44388

This article supports what I have written about what I think I've heard on Penrose lecture - scenario 3) :

"Central to Penrose's theory is the idea that in the very distant future the universe will in one sense become very similar to how it was at the Big Bang. He says that at these points the shape, or geometry, of the universe was and will be very smooth, in contrast to its current very jagged form. This continuity of shape, he maintains, will allow a transition from the end of the current aeon, when the universe will have expanded to become infinitely large, to the start of the next, when it once again becomes infinitesimally small and explodes outwards from the next big bang. Crucially, he says, the entropy at this transition stage will be extremely low, because black holes, which destroy all information that they suck in, evaporate as the universe expands and in so doing remove entropy from the universe. "

Edited December 31, 2011 by Duda Jarek