Entropy of Static and Perpetually Old Universe

[modest]

You have ignored every question and every statement of my last post only to repeat the statements they corrected.

 

I consider the issue closed, and will leave you with Hawking's description,

 

In the 19th century, however, evidence began to accumulate that the earth, and the rest of the universe, were in fact changing with time. On the one hand, geologists realized that the formation of the rocks, and the fossils in them, would have taken hundreds or thousands of millions of years. This was far longer than the age of the Earth, according to the Creationists. On the other hand, the German physicist, Boltzmann, discovered the so-called Second Law of Thermodynamics. It states that the total amount of disorder in the universe (which is measured by a quantity called entropy), always increases with time. This, like the argument about human progress, suggests that the universe can have been going only for a finite time. Otherwise, the universe would by now have degenerated into a state of complete disorder, in which everything would be at the same temperature.

http://www.ralentz.com/old/astro/hawking-1.html

 

I firmly believe that the validity of this argument has no bearing on your acceptance of it making it pointless to discuss further.

 

~modest

[quantumtopology]

You have ignored every question and every statement of my last post only to repeat the statements they corrected.

 

I consider the issue closed,

 

I was gonna suggest to create a new thread about this, we are sort of highjacking the redshift thread, and I' be delighted to discuss these interesting themes with you there.

 

I honestly haven't ignored your questions any more that you have ignored mine, I'd say we are simply debating.

If you wanna end the discussion with an authority statement, of course you are free to do it, but I think that might be seen maybe as if you considered there is only one way to look at the physical questions (your own) and therefore as if you were avoiding a normal debate in fear of not being able to sustain your view.

By the way, even Hawking is acapable of changing his mind in questions as important as the entropy of black holes, the theme of much of his long career, he recently did (2004). He is still young in spirit and willing to challenge the mainstream as in his recent comments on his doubts about the possibility that the LHC might find the Higgs boson.

 

In any case, some final remarks, don't you find odd that such scientists as Einstein that knew about thermodynamics much more than you and I together, never considered entropic objections to his eternal (and spatially finite¡¡) universe? Even more the physicsts of his time neve used that objection either, it was as you know on the ground of instability that his model was rejected at first and later by the expanding hypothesis.

Also in a much humbler sale of course, the static model proposed by CC in 2005, I believe, but I'm sure if this is not correct you'll be able to tell me, has not been objected in terms of thermodynamics.

I take it as a compliment that the only serious objection your raising lately is the entropic one.

In short maybe , just maybe the reason behind this is that nobody is so confident about the behaviour of the second law of thermodynamics when using the universe as the chosen system to reject a model only based on that.

It's different in the case of the first law, in this case there is consensus, thus the problem of the SST and his creation of matter.

 

Think about this paradox: If the thermal equilibrium is really a possibility in the evolution of the universe, then the 2nd law: Change in S>0 is no longer a valid law since i thermal equilibrium entropy can't increase.

 

 

Regards

Qtop

 

PS: please consider the idea of the new thread, if you really cannot continue debating interesting ideas is OK too.

[modest]

PS: please consider the idea of the new thread, if you really cannot continue debating interesting ideas is OK too.

 

I am not trying to debate you. I've given you a very straightforward objection based on a fundamental law of physics. Noted physicists have given the same line of reasoning. Your response—that I don't understand entropy or infinity, or that Hawking has changed his mind about things in the past—are points I have no interest in debating.

 

In any case, some final remarks, don't you find odd that such scientists as Einstein that knew about thermodynamics much more than you and I together, never considered entropic objections to his eternal (and spatially finite¡¡) universe? Even more the physicsts of his time neve used that objection either, it was as you know on the ground of instability that his model was rejected at first and later by the expanding hypothesis.

 

Tolman in 1931:

On Thermodynamic Equilibrium in a Static Einstein Universe

...since [math]\phi_0e^{3\mu / 2}[/math] is evidently the entropy associated with unit coordinate range, the result has the simple physical interpretation that the only possible changes in the state of an Einstein universe must be such as not to decrease the entropy content associated with each range of coordinates.

§ 5. Conditions for Thermodynamic Equilibrium in a Static Einstein Universe.

In accordance with the result of the foregoing section, the condition of thermodynamic equilibrium will evidently require that the quantity [math]\phi_0e^{3\mu / 2}[/math], which cannot decrease with the time, shall be a maximum at each point x, y, z. And noting equation (10) which defines [math]\mu[/math], we can express this somewhat more conveniently by the requirement that [math]\phi_0e^{3g / 2}[/math] shall be a maximum.

 

Think about this paradox: If the thermal equilibrium is really a possibility in the evolution of the universe, then the 2nd law: Change in S>0 is no longer a valid law since i thermal equilibrium entropy can't increase.

 

The second law is dS/dt ≥ 0, not dS/dt > 0. If S is at a maximum then no precess can increase S meaning no useful work can be done.

 

~modest

[Vox]

 

Would you like to try and help build it? You have lots of knowledge about this stuff. The worst that can happen is that ends up being wrong, but we can cope with that, can't we? .

 

Regards

Qtop

 

So "juicy" remark that I could not resist to add my comment.

 

Why we consider event / life as "intend to arrive" ? Normal approach seems to be that we need to set a goal and get rid of this moment as soon as possible and heading to the "goal" which is naturally somewhere else than right now..Analogue: While dancing we do not intend to arrive to certain spot in dance floor when music stops..whole point is to dance and ejoy while it lasts.. it is the journey not the ends which matters.. never mind being "right or wrong" in life, that is relative if anything is

 

We all arrive ,when we die, enjoy the journey while you can

[quantumtopology]

The second law is dS/dt ≥ 0, not dS/dt > 0. If S is at a maximum then no precess can increase S meaning no useful work can be done.

 

You are right, I made up a false paradox, actually I am aware that the second law is dS> or=0, but notice that you've been sayin all the time that entropy must always increase in time, so I followed that line of thought.

What the second law does not actually say is that every system must reach a maximum, but that statistically tends toward a maximum, so that this theoretical maximum can be thoght of as a moving target for an infinite universe, whether static or expanding as people like Lineweaver explains: http://www.mso.anu.edu.au/~charley/papers/LineweaverChap_6.pdf

So given the fact I have not been able to explain the perfect cosmology principle, even without resorting to it, my point was that it is not straightforward at all that the whole universe, and even less if it's infinite, can be treated as a normal thermodynamical system like an adiabatic box or a steam engine, and this seems to be reasonable and has been acknowledged before by mainstream science.

Even if one decides to consider the universe as a regular isolated system, it is far from clear that it must reach a maximum given the peculiar features of the universe as a system..

These seemto me like reasonable considerations that lead me (and others) to think that the entropic objection as presented here should not be used to discard a static universe hypothesis.

But it is an opinable matter of course.

 

Regards

Qtop

[modest]

You are right, I made up a false paradox, actually I am aware that the second law is dS> or=0, but notice that you've been sayin all the time that entropy must always increase in time, so I followed that line of thought.

What the second law does not actually say is that every system must reach a maximum, but that statistically tends toward a maximum, so that this theoretical maximum can be thoght of as a moving target for an infinite universe, whether static or expanding as people like Lineweaver explains: http://www.mso.anu.edu.au/~charley/papers/LineweaverChap_6.pdf

 

I think that article is about a maximum rate of entropy (per time) generated by a system, not the maximum entropy that the system can reach.

 

So given the fact I have not been able to explain the perfect cosmology principle, even without resorting to it, my point was that it is not straightforward at all that the whole universe, and even less if it's infinite, can be treated as a normal thermodynamical system like an adiabatic box or a steam engine, and this seems to be reasonable and has been acknowledged before by mainstream science.

 

I keep saying "you don't have to consider the entropy of the whole universe..." and you keep responding "yeah, but I don't think we can consider the entropy of the whole universe". In a static and homogeneous universe you will have no net energy or entropy crossing boundaries. Any arbitrary area should reach a maximum of entropy.

 

~modest

[quantumtopology]

Hi, Modest

 

I think that article is about a maximum rate of entropy (per time) generated by a system, not the maximum entropy that the system can reach.

I didn't choose the most appropriate reference to back my statement, that's for sure. Still I think it is in any statistical thermodynamics text, if you think is wrong, please let me know, perhaps I misunderstood.

 

I keep saying "you don't have to consider the entropy of the whole universe..." and you keep responding "yeah, but I don't think we can consider the entropy of the whole universe". In a static and homogeneous universe you will have no net energy or entropy crossing boundaries. Any arbitrary area should reach a maximum of entropy.

That is because I disagree with that description of static infinite universe. Maybe I am not quite understanding something. Let's see if we can work this out and get to some agreement.

If we consider an arbitrary finite area of the universe as a thermodynamc system, you say we must think of it as isolated,(at sufficiently large scale of course) as not having net heat, energy or matter , no net entropy crossing its imaginary boundary because the universe is homogenous (not only a non-expanding but a expanding universe is homogenou so your assertion would be valid for both), and since the system is isolated it should reach a maximum and so all the finite areas of the universe should reach a maximum entropy.

If I have this wrong please, explain it to me better.

 

What I say is that, in my opinion, this hypothesis might be correct in a finite universe (and I'd say it would have to be static too), but it can not be applied to an infinite universe:

 

The first caveat of the hypothesis in an infinite universe is that it can not be divided up in finite areas, is not mathematically feasible unless you accept the operation infinite/infinite.

 

Second caveat is ,physically in an infinite universe you always have another outer layer where entropy can go and then another....there is always (eternally) a bigger surrounding (n+1) where the entropy can go, remember there is always time and space availble for entropy to increase in. You would have an infinite cold sink, so to speak, for every finite space you might wanna consider.

 

Third caveat, if you reject the first cavet, you would still not have all the finite areas reach maximum entropy, they would just infinitely tend to the maximum as the possibility of an n+1 area to let the entropy increase would exist for an infinite time.

 

The notion of infinite time and space universe is tricky enough to at least be cautious as to whether the concept of maximum entropy can be applied to it , regardless if considered as a system on the whole or considering the entropy of finite areas.

 

Even in an infinite expanding universe there are now serious doubts that its future will be thermal death as the wiki page on entropy pointed out :"entropy gap", being the main reason that as it expands it logically tends to infinity.

 

These are some of the arguments that lead me to think that an static universe is not forbidden by entropic considerations. But of couse is just my opinion, others will think otherwise, but my main claim is that in the literature there is no consensus about this, and that is why I object your assertion that it is perfectly clear from thermodynamic considerations that a non-expanding universe is forbidden.

 

Regards

Qtop

[modest]

That is because I disagree with that description of static infinite universe. Maybe I am not quite understanding something. Let's see if we can work this out and get to some agreement.

If we consider an arbitrary finite area of the universe as a thermodynamc system, you say we must think of it as isolated,(at sufficiently large scale of course) as not having net heat, energy or matter , no net entropy crossing its imaginary boundary because the universe is homogenous (not only a non-expanding but a expanding universe is homogenou so your assertion would be valid for both), and since the system is isolated it should reach a maximum and so all the finite areas of the universe should reach a maximum entropy.

If I have this wrong please, explain it to me better.

 

You've got it.

 

The first caveat of the hypothesis in an infinite universe is that it can not be divided up in finite areas, is not mathematically feasible unless you accept the operation infinite/infinite.

 

You need make only the following assumptions:

• The universe is infinite (you have already asserted this)
  
• I live in a part of this universe (again, undeniable)
  
• My part is the same as any other (this assumption is 'homogeneity' and you have already asserted it)
  

Nowhere did I divide up an infinite universe into an infinite number of parts. There is no need. Put simply: if the universe is homogeneous then entropy is homogeneous.

 

Second caveat is ,physically in an infinite universe you always have another outer layer where entropy can go and then another....there is always (eternally) a bigger surrounding (n+1) where the entropy can go, remember there is always time and space availble for entropy to increase in. You would have an infinite cold sink, so to speak, for every finite space you might wanna consider.

 

If the universe were not homogeneous then you'd be free to say that we border an infinite area of space hotter than our area and also border an infinite area of space colder than our area. It would then be possible for entropy to remain perpetually low and constant. You'd have to give up homogeneity for the above quoted paragraph to be true. Scientists in the late 1800's and early 1900's did just that in order to avoid the entropy problem.

 

Third caveat, if you reject the first cavet, you would still not have all the finite areas reach maximum entropy, they would just infinitely tend to the maximum as the possibility of an n+1 area to let the entropy increase would exist for an infinite time.

 

The universe is too far from equilibrium. The probability that useful work can be done has not approached zero. An assortment of astrophysical processes do useful work all the time. They are many orders of magnitude hotter than their surroundings. This is not a universe that has evolved for anything like the amount of time you contemplate.

 

These are some of the arguments that lead me to think that an static universe is not forbidden by entropic considerations.

 

I don't think a static universe is forbidden by thermodynamics. Your assumptions (static, homogeneous, perpetually old) however, are inconsistent with thermodynamics and observation.

 

~modest

[quantumtopology]

Nowhere did I divide up an infinite universe into an infinite number of parts. There is no need. Put simply: if the universe is homogeneous then entropy is homogeneous.

 

If the universe were not homogeneous then you'd be free to say that we border an infinite area of space hotter than our area and also border an infinite area of space colder than our area. It would then be possible for entropy to remain perpetually low and constant. You'd have to give up homogeneity for the above quoted paragraph to be true. Scientists in the late 1800's and early 1900's did just that in order to avoid the entropy problem.

 

The universe is too far from equilibrium. The probability that useful work can be done has not approached zero. An assortment of astrophysical processes do useful work all the time. They are many orders of magnitude hotter than their surroundings. This is not a universe that has evolved for anything like the amount of time you contemplate.

 

 

I don't think a static universe is forbidden by thermodynamics. Your assumptions (static, homogeneous, perpetually old) however, are inconsistent with thermodynamics and observation.

 

I think we've reached the heart of your objection, homogeneity.

 

But I think it is not only useful but necesary to think of homogeneity as a statistical property, certainly it does not have to be exactly homogenous in all the universe at once, the universe is statistically homogenous, wich in an infinite universe would mean there is room for net flux of entropy among the different areas.

We know ultimately, thermodynamics is a statistical theory and entropy has a statistical nature that doesn't allow to treat the "homogenous" compartments in the way you want to do it.

 

Entropy is not exactly homogenous then, it only statistically tend to be, this allows random flux of energy, matter and entropy , that in an infinite universe would have infinite magnitude too.

 

Therefore my assumptions (static, infinite, with perfect cosmology principle universe ) seem to be perfectly consistent with both observation and thermodynmics.

Unless you have some other explanation.

 

Regards

Qtop

[modest]

But I think it is not only useful but necesary to think of homogeneity as a statistical property, certainly it does not have to be exactly homogenous in all the universe at once, the universe is statistically homogenous, wich in an infinite universe would mean there is room for net flux of entropy among the different areas.

 

Statistical variations don't allow for a net flow.

 

You could, however, say that our local universe has recently undergone a statistical variation breathing new life into a long-dead system. It wouldn't be too far from Guth's ultimate free lunch. Or, as they say "our Universe is simply one of those things which happen from time to time."

 

You'd have to elaborate on exactly what you mean. If our local universe has always had low entropy, always sat on a temperature gradient, always looked about like it does now, then there can be no homogeneity—statistical or otherwise.

 

~modest

[quantumtopology]

Statistical variations don't allow for a net flow.

I would agree with this statement if if we were talking about a finite universe, but what I am trying to express if that if the universe is infinite this is , at the very least, not obvious.

 

But as I think of it, it occurs to me that maybe there is some basic incompatibility betwen the property of homogeneity and infiniteness. Maybe for an infinite universe all we could say is that it tends to homogeneity.

 

QUOTE=modest;301067]You'd have to elaborate on exactly what you mean. If our local universe has always had low entropy, always sat on a temperature gradient, always looked about like it does now, then there can be no homogeneity—statistical or otherwise.

As I'm saying, If absolute homogeneity is not compatible with infinitenes, I'd have to give up the premise of total homogeneity for my hypothesis. This ( the non-absolute homogeneity at large scales) is totally in agreement with the last observations of clusters in large scale observational astronomy. For instance: http://arxiv.org/pdf/astro-ph/0411204

 

 

You could, however, say that our local universe has recently undergone a statistical variation breathing new life into a long-dead system. It wouldn't be too far from Guth's ultimate free lunch. Or, as they say "our Universe is simply one of those things which happen from time to time."

 

I don't like these kind of "Deus ex machina" solutions used to salvage the LCDM model, I don't even like them in movies but in real life such low probability events as inflation or the Big Bang itself IMO just don't happen.

I remember when Guth first came up with inflation at the beginning of the 80's, how wild and specultively ad hoc it seemed for most. Honestly never thought back then that such "free lunch" ideas were gonna become mainstream in a few years.

 

Regards

Qtop

[Turtle]

...

modest

You could, however, say that our local universe has recently undergone a statistical variation breathing new life into a long-dead system. It wouldn't be too far from Guth's ultimate free lunch. Or, as they say "our Universe is simply one of those things which happen from time to time."

I don't like these kind of "Deus ex machina" solutions used to salvage the LCDM model, I don't even like them in movies but in real life such low probability events as inflation or the Big Bang itself IMO just don't happen.

I remember when Guth first came up with inflation at the beginning of the 80's, how wild and specultively ad hoc it seemed for most. Honestly never thought back then that such "free lunch" ideas were gonna become mainstream in a few years.

 

Regards

Qtop

 

nobody likes paying for a free lunch. :confused:

 

http://www.nytimes.com/2007/04/22/books/chapters/0422-1st-tale.html

...What we call here a Black Swan (and capitalize it) is an event with the following three attributes.

 

First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.

 

I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explain almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives. Ever since we left the Pleistocene, some ten millennia ago, the effect of these Black Swans has been increasing. It started accelerating during the industrial revolution, as the world started getting more complicated, while ordinary events, the ones we study and discuss and try to predict from reading the newspapers, have become increasingly inconsequential. ...

 

an avian overview from wiki: :( Black swan theory - Wikipedia, the free encyclopedia

[quantumtopology]

nobody likes paying for a free lunch. :confused:

an avian overview from wiki: :( Black swan theory - Wikipedia, the free encyclopedia

 

Hi Turtle

 

I think there are significant differences between ad hoc explanations that serve as fudge factors and the events that the Black swan theory tries to explain, for instance the third attribute mentioned in the quote is not met, or is actually the other way around, in the sense that this hypothesized explanations of the universe are logically built backwards from the observed present, so that we concoct and retrospectively predict first, and then assume that what we retrospectively predict happened no matter how unlikely. It is like the negative of a Black Swan, where we first find an unexpected event that surprises us due to human nature's "bad memory" and then we rationalize it and explain it in retrospect.

 

But I see where you find the similarity, Turtle. it's a rather tricky distinction

 

Regards

QTop

[Turtle]

Hi Turtle

 

I think there are significant differences between ad hoc explanations that serve as fudge factors and the events that the Black swan theory tries to explain, for instance the third attribute mentioned in the quote is not met, or is actually the other way around, in the sense that this hypothesized explanations of the universe are logically built backwards from the observed present, so that we concoct and retrospectively predict first, and then assume that what we retrospectively predict happened no matter how unlikely. It is like the negative of a Black Swan, where we first find an unexpected event that surprises us due to human nature's "bad memory" and then we rationalize it and explain it in retrospect.

 

But I see where you find the similarity, Turtle. it's a rather tricky distinction

 

Regards

QTop

 

i was responding primarily to this comment you made:

...in real life such low probability events as inflation or the Big Bang itself IMO just don't happen. ...

 

this from my understanding is what black swan theory addresses. as i have broached this topic earlier in another vein/thread, i'll leave off where i did there with no further comment until or unless i actually read taleb's book. thnx for taking note. :(

[quantumtopology]

i was responding primarily to this comment you made:

Quote:

Originally Posted by quant

...in real life such low probability events as inflation or the Big Bang itself IMO just don't happen. ...

this from my understanding is what black swan theory addresses.

 

Yes you are right, just notice that the calculated probabilities of the quoted events are many orders of magnitude below the unlikeliness usually considered in Black swan theory, which is more related to psychologically neglected, apparently low probability events ("outside the realm of regular expectations").

 

Regards

Qtop

[HydrogenBond]

To increase the entropy of the universe, we need to input energy. Entropy is not an isolated effect but needs energy input to increase. For the 2nd law to be satisfied, requires a continuous source of energy for the entropy. When we go higher to lower energy the difference helps to satisfy the energy for entropy. The two laws are connected with energy needing to be available to increase entropy.

 

The question becomes, which comes first the chicken (energy) or the egg (entropy)? Can entropy increase first, without energy, creating an energy deficit, which then requires the release of energy somewhere to maintain the energy balance? Or does energy come first, making the energy needed to increase the entropy?

 

Let us use first assumption. If we red shift energy, since we are going from red wavelength to say the microwave wavelength (for example) the energy value of each energy quanta have lowered. Does this energy difference per quanta provide available energy for entropy? If we put the egg first, does an entropy increase create an energy deficit, thereby causing the need for energy to lower, which shows up as red shift?

[modest]

Statistical variations don't allow for a net flow.

I would agree with this statement if if we were talking about a finite universe, but what I am trying to express if that if the universe is infinite this is , at the very least, not obvious.

 

I think you keep getting hung up on the idea of infinity. If space is static and our area of space has always had low entropy (for a perpetually long amount of time) then it will have always been importing useful energy from one area of bordering space and always exporting entropy to another area of bordering space.

 

That is the antithesis of homogeneity, and it makes no difference if the universe is spatially infinite.

 

By the way, it is with a sense of irony that you have now objected to my objection for the following two reasons:

 

• You cannot consider the past to be infinitely long.

• Space is infinitely large.

 

...

modest

You could, however, say that our local universe has recently undergone a statistical variation breathing new life into a long-dead system. It wouldn't be too far from Guth's ultimate free lunch. Or, as they say "our Universe is simply one of those things which happen from time to time."

I don't like these kind of "Deus ex machina" solutions used to salvage the LCDM model...

 

nobody likes paying for a free lunch. :confused:

 

http://www.nytimes.com/2007/04/22/books/chapters/0422-1st-tale.html

...What we call here a Black Swan (and capitalize it) is an event with the following three attributes....

 

Yes :( The idea that the whole visible universe is a black swain is kind of thought provoking too.

 

~modest