Entropy of Static and Perpetually Old Universe

[modest]

Moderation Note: The following 19 posts have been moved from Redshift z in favor of having their own topic of discussion in this thread.

 

 

Curved spacetime explains redshift (whether it is curved hyperbolically or spherically).

 

Right. Curved time gives a scale factor. We keep conflating space and spacetime.

 

The age of stars is not proof of expansion, or that the universe itself is young (say 13.7 Gyr old).

 

Low mass stars can be trillions of years old. The oldest dated stars and the oldest dated globular clusters are 1% of that age. It needs to be explained. If there was no big bang and the universe is not expanding then why aren't stars a hundred and more times older than they appear? Why isn't entropy at a maximum? Why isn't every celestial object at the same temperature? Why isn't iron the most abundant element?

 

These are real problems of an infinitely-aged universe that hyperbolic space doesn't solve. I'm not pointing them out to prove, or even support, expansion. I'm pointing them out because they are real problems for your proposed idea, and any non-dynamic solution.

 

Not would it be proof to argue the age of the earth based on the age of trees.

 

If we knew trees could acquire a trillion years of rings, but we found them no older than the earth (5 billion years) then anyone saying that the earth is at least a trillion years old would have a problem needing to be explained.

 

General relativity is all you need to explain redshift with hyperbolic space.

 

GR makes exact predictions.

 

Models will predict the redshift / distance relation not laws of physics.

 

Models follow laws of physics.

 

Curved spacetime is explained by the mass-energy content, which is nonzero and nonnegative. GR predicts that a universe with mass cannot be Euclidean.

 

Space can be euclidean in a GR universe that has mass.

 

The de Sitter universe predicts redshift with hyperbolic space. There are others too.

 

De Sitter's universe has a recession speed proportional to distance. A static metric with redshift means that distant galaxies are redshifted with recession due to Doppler shift. In other words, things move through static space. A dynamic metric with redshift means that distant galaxies are redshifted with expansion due to a scale factor. In other words, things stay where they are in space while space expands.

 

In both cases the physics interpretation is the same. Everything is getting further away from everything else. De Sitter used a static metric, but as Klein, Eddington, and others showed, the things in a de Sitter universe are not static. They scatter. They do exactly what an FLRW universe with de Sitter parameters says they should.

 

Actually, the 1998 prediction by Hoyle and Burbidge (The Origin of Helium and the Other Light Elements) is consistent with observations.

 

Hoyle makes clear in that paper that a physical mechanism must be "able to thermalize the radiation that is initially released through hydrogen burning as ultraviolet photons from hot stars in starburst situations in galaxies". That physical mechanism is expansion.

 

The things that you are proposing as solutions are inconsistent with a non-dynamic universe.

 

The only requirement is that stars have been burning hydrogen for 100 Gyrs. That is the timescale needed for stars to produce the abundance of helium observed according to Hoyle and Burbidge. The abundance of deuterium is nicely explained in the same work. As is too the CMB blackbody spectrum.

 

Again, the cause of CMBR in Hoyle's QSSU requires expansion. It is redshifted from ultraviolet to microwave via the expansion of space.

 

It would be a pity to rule out a potential scenario before it's fully developed.

 

That's fine, but in reality the problem is not that we are ruling out the unknown model which has made no predictions. The problem is that the model is unknown and has made no predictions.

 

~modest

[quantumtopology]

Hi, Modest

 

Occam's razor would prefer the theory that explains the most data with the fewest assumptions.

Exactly, even if "explain" is a tricky word and could lead to endless philosophical debate about its real meaning in every context.

Expansion explains redshift, CMB, the abundance of light elements, the lack of old stars, etc. Hyperbolic space explains (at best) redshift alone.

The Hyperbolic space also explain and predicts CMBR, the properties of EM radiation in a hyperbolic geometry lead to the prediction of an isotropic and homogenous radiation identified with the space of horospheres, radiation represented by horospherical wavefronts homogeneously fills the entire hyperbolic universe. Therefore, assuming a hyperbolic universe, just from its geometrical relations applied to EM waves, we must have an isotropic and homogenous radiation filling the universe.

If the universe was filled only with radiation, this CMB would be totally homogenous but since there exists matter, that fact is reflected in the form of fluctuations or anisotropies.

Curiously enough the fact that the horospherical surfaces are euclidean fits with the measurements of the CMBR that give a flat geometry.

Abundance of light elements has been addressed by Hoyle as something perfectly logic in a universe with eternal time. And people such as Lerner have criticized frequently that the expansion model might explain anything about light elements abundance, but certainly I don't have enough knowledge to treat this matter. And it is not related directly, I would suppose, with hyperbolic geometry.

 

Stars age, and galaxies age has been used against the expansion model but again is not something strictly related to redshift mechanisms.

 

 

To explain redshift with hyperbolic space you would need new physics. The current laws of physics do not predict a distance / redshift relationship due to hyperbolic space.

You might be right, but I firmly believe that hyperbolicity can be explained with relativity. (I'll try to address this in another post). The current laws of physics are centered in the Euclidean geometry that isperfectly valid for distances at least as large as our Local Group.

However, relativity in my opinion predicts the kind of distance / redshift relationship due to hyperbolic space that the hyperbolic hypothesis proposes.

The new physics would, for example, explain why space is hyperbolic (what causes it) and how curved it is.

We might need new physics to explain the last cause of this, you are right.

 

Both models? I don't know of any cosmological model explaining redshift with hyperbolic space.

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? .

I have worked out the line element from the original Einstein field equations without lambda, but I need help to make sure I have not made any big mistakes. Also I need to find time to learn the latex format to post it.

 

The way the scientific method works, a model would make predictions which could be compared to observation. For example, big bang cosmology predicts that 24% of baryonic matter should be helium. If there were no Big Bang then elements would exist in abundances predicted by Burbidge and Hoyle in the '60s. There would be almost no helium nor deuterium.

In this way, the scientific method corroborates explanations of redshift which include a big bang and rule out explanations which do not.

Yes but mos of your examples were ad hoc "postdictions" rather than predictions, witty ways to make observation fit a theory.

What Burbidge and Hoyle predicted in the 60s about abundance of elements in a universe without Big Bang might very well totally flawed, and I believe they have modified their views afterwards.

Anyway their model (SST) had expansion and redshift was explained by that expansion.

 

 

Regards

Qtop

[quantumtopology]

Low mass stars can be trillions of years old. The oldest dated stars and the oldest dated globular clusters are 1% of that age. It needs to be explained. If there was no big bang and the universe is not expanding then why aren't stars a hundred and more times older than they appear? Why isn't entropy at a maximum? Why isn't every celestial object at the same temperature? Why isn't iron the most abundant element?

 

These are real problems of an infinitely-aged universe that hyperbolic space doesn't solve. I'm not pointing them out to prove, or even support, expansion. I'm pointing them out because they are real problems for your proposed idea, and any non-dynamic solution.

 

If we knew trees could acquire a trillion years of rings, but we found them no older than the earth (5 billion years) then anyone saying that the earth is at least a trillion years old would have a problem needing to be explained.

 

There might be some confusion going on here, I only ask you to try and keep an open mind here: a universe that follows the perfect cosmological principle, that is, homogenous and isotropic in both space and time, can be perfectly Dynamic in the scale of time we are talking about.

This reminds me of the supposed flaw people novice in cosmology find when first encounter the cosmological principle when applied to space, they say :" How can anybody claim the universe is isotropic and homogenous, I can see nothing like that, there are big aggregates of matter, there are planets , stars, politicians... all kinds of certainly not homogenous staff and that looks different depending on the direction you look".

And then you have to explain them that the principle works if you look at a Big enough picture of the universe.

So the same thing happens with the time part of the perfect cosmological principle, you have to consider huge amounts of time to see it. On much smaller scales of time, of course the universe is dynamic, stars evolve, they are born and they die, they have a time scale evolution that although enormous compared with humans time scale is not even close to the scale where the perfect cosmological principle is noticeable.

So, if you realize this there is no proble at all with the age of stars in a hyperbolic space, however, there is a serious problem with galactic age in the BB model. There are observations of galaxies near the 13.3( I'm counting only from the time of last scattering) Bly limit that appear as old as nearby ones,what is more important perhaps, it is observed that the distribution of galactic ages at distances around 8-12 bly(IIRC, I have to look for the references) is similar to the age distribution close to our galaxy. That speaks more in favour of a universe with perfect cosmological principle that one with a finite time beginning.

 

Most of physics laws are time-reversible,which is the obligate consequence in a perfect cosmologic principle universe.

No expansion doesn't mean a non dynamic universe at all.

 

Regards

Qtop

[modest]

There might be some confusion going on here, I only ask you to try and keep an open mind here:

 

Pointing out something that is true does not require a closed mind.

 

a universe that follows the perfect cosmological principle, that is, homogenous and isotropic in both space and time, can be perfectly Dynamic in the scale of time we are talking about.

This reminds me of the supposed flaw people novice in cosmology find when first encounter the cosmological principle when applied to space, they say :" How can anybody claim the universe is isotropic and homogenous, I can see nothing like that, there are big aggregates of matter, there are planets , stars, politicians... all kinds of certainly not homogenous staff and that looks different depending on the direction you look".

And then you have to explain them that the principle works if you look at a Big enough picture of the universe.

So the same thing happens with the time part of the perfect cosmological principle, you have to consider huge amounts of time to see it. On much smaller scales of time, of course the universe is dynamic, stars evolve, they are born and they die, they have a time scale evolution that although enormous compared with humans time scale is not even close to the scale where the perfect cosmological principle is noticeable.

 

There is a confusion.

 

I used the word "non-dynamic" in order to avoid the word "static". We have been using the word static a lot and it has been used referring to 1) a static metric and 2) a static universe. The former does not imply the latter which has caused some communication problems.

To avoid this I used the word "non-dynamic" to mean a universe where the distance to distant objects neither increases nor decreases over time.

 

There would be no reason to assume that such a universe is not infinitely-aged. Any process which takes time would have had an arbitrarily large amount of time to occur.

 

So, if you realize this there is no proble at all with the age of stars in a hyperbolic space, however, there is a serious problem with galactic age in the BB model. There are observations of galaxies near the 13.3( I'm counting only from the time of last scattering) Bly limit that appear as old as nearby ones,what is more important perhaps, it is observed that the distribution of galactic ages at distances around 8-12 bly(IIRC, I have to look for the references) is similar to the age distribution close to our galaxy. That speaks more in favour of a universe with perfect cosmological principle that one with a finite time beginning.

 

Most of physics laws are time-reversible,which is the obligate consequence in a perfect cosmologic principle universe.

No expansion doesn't mean a non dynamic universe at all.

 

Regards

Qtop

 

Time is anisotropic, so I don't know what you mean by "perfect cosmological principle". Some of the specific points you make are refuted by some of the quotes below.

 

Entropy increases with time. For example, two bodies in an isolated system with different temperatures will, over time, reach an equilibrium of temperature. This represents an increase in entropy which happens in the forward time direction. If the universe is infinitely aged (and it is a closed system) then entropy would be at a maximum. This means every object in the cosmos would have the same temperature. Stars, planets, comets, etc—all would have the same temp.

 

This is a problem that simply must be addressed with any model that does not have a beginning. For example, Hoyle's steady state universe has no beginning so he addresses the problem in 1948 as soon as he creates the model by abdicating the first law of thermodynamics (he makes the universe an open system):

A further interesting feature is that the total “entropy” within the observable universe does not increase with time. Although entropy increases in a localized region, the total entropy remains approximately constant because local condensations carry entropy out of the observable universe. Thus thermodynamics has only localized application.

1948MNRAS.108..372H Page 372

 

Likewise, infinitely cyclic cosmology has no beginning and if properties of the universe are carried from one cycle to the next an entropy problem exists,

 

In the 1930s, theoretical physicists, most notably Albert Einstein, considered the possibility of a cyclic model for the universe as an (everlasting) alternative to the model of an expanding universe. However, work by Richard C. Tolman in 1934 showed that these early attempts failed because of the entropy problem that, in statistical mechanics, entropy only increases because of the Second law of thermodynamics.[1]

Cyclic model - Wikipedia, the free encyclopedia

 

I'm *not* bringing these things up because I don't have an open mind. The fact is—a static universe where redshift is caused by hyperbolic space must face these problems either solving each ad hoc or with a model consistent with evidence.

 

 

In the same way that meteors that fall to earth can be dated to about 4.5 billion years, spectroscopy-based radioactive dating can show the age of stars. If the Milky Way has been here for trillions of years then one would need to explain why the oldest stars are about 10^10 years.

 

As wiki says:

 

After some controversy, the age of Universe as estimated from the Hubble expansion and the CMB is now in good agreement with (i.e., slightly larger than) the ages of the oldest stars, both as measured by applying the theory of stellar evolution to globular clusters and through radiometric dating of individual Population II stars.

Big Bang - Wikipedia, the free encyclopedia

 

More in direct conflict would be:

 

Observations of distant galaxies reveal that as the distance from the Earth increases, the density of galaxies rises and their "metal" content (relative proportion of chemical elements heavier than lithium) declines

Cosmological principle - Wikipedia, the free encyclopedia

 

The hypothesis of cosmological history is also supported by the fact that many more fragmentary, interacting and unusually shaped galaxies are found at high red shifts (earlier time) than in the local universe (recent time), suggesting evolution in galaxy structure as well.

Cosmological principle - Wikipedia, the free encyclopedia

 

The simplest explanation is usually correct.

 

Everything in the observable universe used to be closer together. During the 20th century cosmology became a matured physical and experimental science. To reject the whole foundation of modern cosmology requires something more than an open mind.

 

~modest

[quantumtopology]

Pointing out something that is true does not require a closed mind.

 

 

 

There is a confusion.

 

I used the word "non-dynamic" in order to avoid the word "static". We have been using the word static a lot and it has been used referring to 1) a static metric and 2) a static universe. The former does not imply the latter which has caused some communication problems.

To avoid this I used the word "non-dynamic" to mean a universe where the distance to distant objects neither increases nor decreases over time.

 

There would be no reason to assume that such a universe is not infinitely-aged. Any process which takes time would have had an arbitrarily large amount of time to occur.

 

 

 

Time is anisotropic, so I don't know what you mean by "perfect cosmological principle". Some of the specific points you make are refuted by some of the quotes below.

 

Entropy increases with time. For example, two bodies in an isolated system with different temperatures will, over time, reach an equilibrium of temperature. This represents an increase in entropy which happens in the forward time direction. If the universe is infinitely aged (and it is a closed system) then entropy would be at a maximum. This means every object in the cosmos would have the same temperature. Stars, planets, comets, etc—all would have the same temp.

 

This is a problem that simply must be addressed with any model that does not have a beginning. For example, Hoyle's steady state universe has no beginning so he addresses the problem in 1948 as soon as he creates the model by abdicating the first law of thermodynamics (he makes the universe an open system):

1948MNRAS.108..372H Page 372

 

Likewise, infinitely cyclic cosmology has no beginning and if properties of the universe are carried from one cycle to the next an entropy problem exists,

 

Cyclic model - Wikipedia, the free encyclopedia

 

I'm *not* bringing these things up because I don't have an open mind. The fact is—a static universe where redshift is caused by hyperbolic space must face these problems either solving each ad hoc or with a model consistent with evidence.

 

 

In the same way that meteors that fall to earth can be dated to about 4.5 billion years, spectroscopy-based radioactive dating can show the age of stars. If the Milky Way has been here for trillions of years then one would need to explain why the oldest stars are about 10^10 years.

 

As wiki says:

 

Big Bang - Wikipedia, the free encyclopedia

 

More in direct conflict would be:

 

Cosmological principle - Wikipedia, the free encyclopedia

 

Cosmological principle - Wikipedia, the free encyclopedia

 

The simplest explanation is usually correct.

 

Everything in the observable universe used to be closer together. During the 20th century cosmology became a matured physical and experimental science. To reject the whole foundation of modern cosmology requires something more than an open mind.

 

~modest

You completely missed my point here, is like if we were talking different languages, perhaps we shoul switch to spanish

 

I never implied that you had a closed mind, I don't know how you could have reached that conclusion, we ave talked about many things and never told you you were close-minded.

 

When I used the phrase "keep an open mind" I meant that in general, not to you personally ,it is always a good advice to try to understand something without prejudiced, nothing to do with anything you might have said earlier, honestly I couldn't imagine such an innocent advice could be taken as ofensive.

But actually perhaps you should try to read again my explanation, it is not that hard to understand,.

The perfect cosmological principle is the same principle normally used but that includes not only space but also time, if you have doubts about it ask what speifically don't understand about it.

Time is isotropic according to this principle, but if you had read with care my post you woul have understood that indeed in our normal time scales is anisotropic, just like space is anisotropic in our size scales.

 

Glad you bring up thermodynamics and entropy because it has a lot to do with my explanation of time as homogenous and isotropic, basically what Hoyle says serves in this case, entropy is a local prperty.

I am addressing these issues , I can't do it all at once, be patient.

 

Who has said the milky way has been around for trillions of years? Read again my explanation please, I said that stars and gallactic systems can have their own life timescales, it is as if you asked , how come we don't live trillions of years if the universe is eternal? .

 

About the metalicity of stars I have an interesting reference, have a look.

http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.2683v4.pdf

 

Finally you said:

"Everything in the observable universe used to be closer together."

That is what the expansion model asserts, what is new about this? I am trying to build a plausible alternative.

" During the 20th century cosmology became a matured physical and experimental science."

Another trivial truth disconnected with the discussion at hand.

" To reject the whole foundation of modern cosmology requires something more than an open mind."

I can only think after reading this that you must have had a bad day or else that you are not discussing in good will.

Where have I said that I want to reject anything, you are badly wrong here, amigo.

I'm using the freedom of thought allowed in this forum to investigate alternative hypothesis. If you see something wrong with that you just have to suggest it and I'll disappear without reproachs.

 

 

Regards

QTop

[modest]

I'll try to keep my reply short and I apologize in advance for failing to do so :hihi:

 

You completely missed my point here, is like if we were talking different languages, perhaps we shoul switch to spanish ;)

 

:D ...

 

When I used the phrase "keep an open mind" I meant that in general, not to you personally ,it is always a good advice to try to understand something without prejudiced, nothing to do with anything you might have said earlier, honestly I couldn't imagine such an innocent advice could be taken as ofensive.

 

No, I certainly didn't take offense. "Pointing out something that is true does not require a closed mind" was just me trying too hard at clever wordplay.

 

But actually perhaps you should try to read again my explanation, it is not that hard to understand,.

The perfect cosmological principle is the same principle normally used but that includes not only space but also time, if you have doubts about it ask what speifically don't understand about it.

Time is isotropic according to this principle, but if you had read with care my post you woul have understood that indeed in our normal time scales is anisotropic, just like space is anisotropic in our size scales.

 

I understand what you're saying. I disagree with it.

 

Isotropic means "the same in all directions". To say that space is isotropic means that you can put an experiment in an isolated box and the results of the experiment must be the same regardless of the direction the box is facing. The results are invariant under rotational translation.

 

My objection specifically involves entropy and the second law of thermodynamics. The second law has an arrow of time. It is not invariant under a time-reversal translation,

T-symmetry

 

T Symmetry is the symmetry of physical laws under a time reversal transformation:

[math] T: t \mapsto -t[/math]

Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.

T-symmetry

Time, in this sense, is anisotropic. Whether it is over short or excessively long time scales should not matter because the second law would be valid over any period of time.

 

I'm trying to keep this post short, so I'll just say that if the hypothesis of a hyperbolic universe is static and isolated with no 'beginning' then I believe you would have an entropy problem whereby entropy would have reached a maximum because, as the second law states, "The total entropy of any isolated thermodynamic system always increases over time, approaching a maximum value".

 

Glad you bring up thermodynamics and entropy because it has a lot to do with my explanation of time as homogenous and isotropic, basically what Hoyle says serves in this case, entropy is a local prperty.

I am addressing these issues , I can't do it all at once, be patient.

 

Hoyle avoids an entropy problem even though his universe has no beginning because new matter is constantly being created with his C-field and old matter is constantly leaving the visible universe as expansion carries it across the cosmological horizon. It is because his universe is expanding that he is able to solves the entropy problem. I don't see this working for a static space.

 

Who has said the milky way has been around for trillions of years?

 

If the universe is static then I would expect looking back a few billion years you would have to find the mass of the milky way here. Conservation of energy would require it. Looking back a few more billion years I think we'd again have to find the same mass. If we keep looking back further and further I don't know at what point we would say or why we would say it is no longer here.

 

If that mass were in the form of stars then why are those stars not here now for us to date?

 

Read again my explanation please, I said that stars and gallactic systems can have their own life timescales, it is as if you asked , how come we don't live trillions of years if the universe is eternal? .

 

We know from stellar models that low-mass stars can have lifetimes of trillions of years. We know people don't have lifetimes that long.

 

About the metalicity of stars I have an interesting reference, have a look.

http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.2683v4.pdf

 

Yes, I’ve said before on Hypography a few times that iron-rich QSO’s and high-mass, metal-rich galaxies at high redshift are possibly discordant and are the best refutation of Lambda-CDM. I think those observations are the best route of investigation toward solving dark matter and dark energy.

 

My point, however, is the same. Whether this QSO you link is currently ~14 billion years old or not, my point would be that it is not perpetually old. It is iron-rich, but it is not depleted of fusionable elements. In other words, it is not 80 or 120 billion years old. No stars are dated that old and that doesn't makes sense to me if the universe is static and at least that old.

 

Finally you said:

"Everything in the observable universe used to be closer together."

That is what the expansion model asserts, what is new about this? I am trying to build a plausible alternative.

 

I have enjoyed spending time considering an alternative explanation for redshift—looking for solutions, pointing out problems, and supporting the traditional explanation. This is nothing new. It's a long thread :) Everything has been repeated at least once ;)

 

What I would find interesting as an alternative to a Friedmann cosmology would be freely coasting cosmology. As I'm sure I've said before on Hypo, I find it fascinating how well it agrees with observation given such a simple assumption (that the scale factor at time t is proportional to t).

 

As it relates to redshift, the age of the universe at z is greater than it would be in Lambda-CDM, particularly at high redshift. Because [math]a(t) \propto t[/math] the current age would be [math]t_0 = H_0^{-1}[/math] which is about 15 billion years. There would be more time for small scale structure formation without the need for dark matter at z > 6. And, it agrees perfectly with SNe-1a observations.

 

Unfortunately, it does not agree with GR :(

 

During the 20th century cosmology became a matured physical and experimental science. To reject the whole foundation of modern cosmology requires something more than an open mind."

I can only think after reading this that you must have had a bad day or else that you are not discussing in good will.

I did not mean that you have a closed mind, or that all you have is an open mind, or however else badly it could have been taken. I was just again doing a poor job of being clever with words.

 

What I was meaning to say was that this alternative explanation of redshift to be consistent with evidence would be a paradigm shift. Modern cosmology would demand you have a good theory capable of good predictions to make that shift. In fact, it would (most likely) require a new theory of gravity in order for the model to be consistent with

1. null forces (i.e. flat potential) and hyperbolic space
   
2. local post-Newtonian tests
   
3. a lot of observational evidence.
   

This would be, to put it mildly, quite difficult.

 

The reason I say this is not to be discouraging or to suggest it is a worthless thing to try. On the contrary, I think looking for alternatives in this way is not only fun, I think it is necessary for science. The reason, rather, is to counter this idea that Occam's razor can chose between expansion and hyperbolic space because they make equivalent predictions,

• "According to extrapolations of the equivalence principle (to cosmology) both interpretations are consistent with observations."
  
• "The thing is astronomical observations probably won't solve the problem since both models are very hard if not impossible to distinguish with the current and near future technology."
  

I disagree with those statements. Right now, expansion is part of a complete model that makes predictions that have been confirmed. The model is an exact solution of a very powerful and well-tested theory of physics.

 

On the other hand, hyperbolic redshift is just not any of those things. With no predictions and no theoretical backing (e.g. why is space curved hyperbolically? how can we predict how much it is curved? etc.) I think we have a ways to go.

 

~modest

[quantumtopology]

My objection specifically involves entropy and the second law of thermodynamics. The second law has an arrow of time. It is not invariant under a time-reversal translation,

 

Time, in this sense, is anisotropic. Whether it is over short or excessively long time scales should not matter because the second law would be valid over any period of time.

 

I'm trying to keep this post short, so I'll just say that if the hypothesis of a hyperbolic universe is static and isolated with no 'beginning' then I believe you would have an entropy problem whereby entropy would have reached a maximum because, as the second law states, "The total entropy of any isolated thermodynamic system always increases over time, approaching a maximum value".

 

Ironically, entropy is one of the most serious problems that the standard model faces. The odds against the extraordinarily low entropy of the Big Bang singularity are tremendous.

 

But I think it is all somewhat more subtle, even though in popularization of science the concepts of entropy and the arrow or direction of time have been mixed up, a rigorous treatment of entropy shows that this is not the case.

In his seminal work "Investigations on the Foundations of Thermodynamics", Constantin Carathéodory axiomatized thermodynamics, and showed that one could not prove that entropy increased with time, all one could say was that in isolated systems entropy moved in the same direction, that was observer dependent, in other words, this direction of increase was chosen by the observer as the direction of time.

So entropy direction of increase, being defined by the observer is a local property.

So if the direction is observer-dependent , there is no need of a gobal direction, in large scales of time it can be isotropic.

 

If the universe is static then I would expect looking back a few billion years you would have to find the mass of the milky way here. Conservation of energy would require it. Looking back a few more billion years I think we'd again have to find the same mass. If we keep looking back further and further I don't know at what point we would say or why we would say it is no longer here.

 

If that mass were in the form of stars then why are those stars not here now for us to date?

Energy must be globally conserved, but not in the exact same form, we know that enery-mass can be transformed. I cannot understand your objection here.

 

 

We know from stellar models that low-mass stars can have lifetimes of trillions of years.

Would you back with some source that assertion?

In any case, one thing is that theoretically stars could last that long(I don't even know if we are able to determine that kind of age) and a different one is that every star should last that long actually. As I said a non-expanding eternal universe can have a strong dynamics in astronomical scales. I know there are galaxies with stimated ages well above the age of the universe according to the standard model.

 

 

On the other hand, hyperbolic redshift is just not any of those things. With no predictions and no theoretical backing (e.g. why is space curved hyperbolically? how can we predict how much it is curved? etc.)

You can't compare a structure with 75 years and thousands of cosmologists working on it with a hypothesis that is being developed as we talk. That is not fair.

By the way, could you tell me what you consider the most important predictions of the BBT?

 

I think we have a ways to go.

Indeed

 

Regards

Qtop

[modest]

We know from stellar models that low-mass stars can have lifetimes of trillions of years.

Would you back with some source that assertion?

 

Stellar Lifetimes

Although more massive stars have more fuel to burn and might be expected to last longer, they also must radiate a proportionately greater amount with increased mass. Thus, the most massive stars may remain on the main sequence for only a few million years, while stars with less than a tenth of a solar mass may last for over a trillion years

Main sequence - Wikipedia, the free encyclopedia

 

By the way, could you tell me what you consider the most important predictions of the BBT?

 

No single most important prediction.

 

~modest

[quantumtopology]

Stellar Lifetimes

Main sequence - Wikipedia, the free encyclopedia

Thanks for the link.

You are totally right that low mass stars like red dwarfs that are superabundant in our galaxy,(proxima centauri for instance is one of them, right there close to us), can remain in the main sequence for many trillion years, the bad news is these stars can not have their age estimated , they could be millions or trillions years old, we don't have a way to tell as long as they keep on the main sequence.

The sad fact is, it is very hard to pin down the age of a star in general, there are exceptions of course, and the dating is very model-dependent, so this is another observation that so far,unless some surprise comes up, is not suited to discern between a expanding model and hyperbolic space model.

 

No single most important prediction.

There aren't so many: CMBR and and light elements abundance are the two usually being considered, although I would consider only CMBR as a genuine prediction.

Only problem is the CMBR is predicted by other models without expansion too.

 

Regards

QTop

[modest]

Thanks for the link.

You are totally right that low mass stars like red dwarfs that are superabundant in our galaxy,(proxima centauri for instance is one of them, right there close to us), can remain in the main sequence for many trillion years, the bad news is these stars can not have their age estimated , they could be millions or trillions years old, we don't have a way to tell as long as they keep on the main sequence.

The sad fact is, it is very hard to pin down the age of a star in general, there are exceptions of course, and the dating is very model-dependent, so this is another observation that so far,unless some surprise comes up, is not suited to discern between a expanding model and hyperbolic space model.

 

You may or may not be seeing how the entropy problem is related to the age-of-stars problem. If the universe is static and infinitely-aged then there should be no fusion going on at all. Star birth is not an endless process. Eventually it will shut down. The most-abundant element will be iron and entropy will be at a maximum. By definition, nothing useful will be happening in our quite-old universe. Our universe isn't there. Stars aren't that old. By pure logic and the laws of physics: our universe is not static and 'perpetually' old.

 

There aren't so many

 

The hyperbolic redshift idea has made no predictions.

 

CMBR and and light elements abundance are the two usually being considered, although I would consider only CMBR as a genuine prediction.

 

You would be wrong. CMB and the abundance of light elements were both predicted before several aspects of those predictions were confirmed.

 

Only problem is the CMBR is predicted by other models without expansion too.

 

I've asked you previously to show me a static model predicting CMB that has not been falsified and I don't think I got an answer. If you're carrying on this belief then please let us know what model this is you keep talking about.

 

Steady state has been falsified and is not static.

Quasi-steady state is not static.

 

There are other confirmed predictions of BBT that you do not give. There are very strong ones like variation of temp of the CMB with redshift. A static model could not possibly have predicted that.

 

There are predictions of evolution that a static model cannot make. The radio source count evolves with redshift. These are confirmed predictions. That means they were predicted before they were observed. The CMB peak-anisotropy size was predicted before being observed. The light element abundance and CMB were predicted before they were observed.

 

Other models have been consistent with one or more of these aspects, but only after the observation has been made do they fit the model to the data ad hoc.

 

It is not for nothing that BBT is such a strongly-held cosmological staple.

 

~modest

[quantumtopology]

You may or may not be seeing how the entropy problem is related to the age-of-stars problem.

You may or may not be seeing that I have addressed this in my last posts.

 

If the universe is static and infinitely-aged then there should be no fusion going on at all. Star birth is not an endless process. Eventually it will shut down.

Why??! You keep making asserions without logic and without even attempting to explain it in astrophysical terms,or cite the source of your assumptions, perhaps astrophysics is not your strong point, I admit that am trying hard to raise my level on this subject.

 

The most-abundant element will be iron and entropy will be at a maximum. By definition, nothing useful will be happening in our quite-old universe. Our universe isn't there.

Empty assertions again, and misunderstanding the perfect cosmological principle and entropy, as I told you maximum entropy could only be defined in a local system, You can not consider an infinite universe as an isolated system as there will always be an outside of that system, at least that is what my thermodynamics book says (Attard 2002): "The fundamental object treated by thermodynamics is the isolated system, which is one that is closed and insulated from its surroundings so that it does not interact with them." , an infinite universe can't reach equilibrium because it can't be considered a system in the thermodynamical sense.

Not only that, but as I explained, the direction of entropy is determined by the observer, if you consider the universe as a system you cannot observe nor determine the direction of maximisation of entropy, the scale of time you need to consider the whole universe is infinite too, thus at scales that tend to infinity time loses the arrow of time, is isotropic.

 

Stars aren't that old.

You know better than the regular astrophysicist, I guess.

 

By pure logic and the laws of physics: our universe is not static and 'perpetually' old.

What logic? what laws? Be specific.

 

The hyperbolic redshift idea has made no predictions.

Well, if we were living before 1964 it could predict the CMBR, too bad we're late. As of now it predicts there are no such things as Dark matterand Dark energy, that space is not flat at large scales, it explains why we haven't found white dwarfs without metals, an observation that contradicts predictions of the standard model.

 

I've asked you previously to show me a static model predicting CMB that has not been falsified and I don't think I got an answer. If you're carrying on this belief then please let us know what model this is you keep talking about.

 

Look at post 596 and falsify it, but first plase read something about Non-Euclidean geometry, specially about horospherical spaces.

 

Certainly I wouldn't say I belief in any model more than in another, for me is not a question of belief, rather of common sense. To me is quite shocking the almost religious determination with wich the standard model is defended, that defensive attitude is not scientific in my opinion, it shows insecurity or even worse fanatism. One should not fall in love wih a theory, it leads you to minimize its problems. Others yet have a sickly tendency to follow the mass, and play on the defensive merely on authority terms. If everybody thinks something is true it must be true.

 

There are predictions of evolution that a static model cannot make. The radio source count evolves with redshift.

Radio source count? what is that? Specify, please

 

Other models have been consistent with one or more of these aspects, but only after the observation has been made do they fit the model to the data ad hoc.

That is what the standard model has been accused of many times, yes.

 

It is not for nothing that BBT is such a strongly-held cosmological staple.

Who could argue with this statement? I would only add that one of the motives could be that people is not encouraged to look for alternatives even when the model faces problems that would lead to inmediately dismiss any aspiring alternative.with scorn and mockery.

 

Qtop

[modest]

If the universe is static and infinitely-aged then there should be no fusion going on at all. Star birth is not an endless process. Eventually it will shut down.

Why??!

 

Because stars are not perpetual motion machines. Such a thing is forbidden by the second law of thermodynamics.

 

The most-abundant element will be iron and entropy will be at a maximum. By definition, nothing useful will be happening in our quite-old universe. Our universe isn't there.

Empty assertions again, and misunderstanding the perfect cosmological principle and entropy, as I told you maximum entropy could only be defined in a local system

 

Entropy should be at a maximum over any finite part of a static and perpetually old universe. Consider that it is static. You will have no useful energy crossing boundaries.

 

Not only that, but as I explained, the direction of entropy is determined by the observer, if you consider the universe as a system you cannot observe nor determine the direction of maximisation of entropy

 

The direction of maximum entropy is by definition the future as the second law creates an arrow of time.

 

Stars aren't that old.

You know better than the regular astrophysicist, I guess.

 

What I am saying is standard astrophysics.

 

By pure logic and the laws of physics: our universe is not static and 'perpetually' old.

What logic? what laws? Be specific.

 

If entropy is at a maximum then no useful work can be done. Such will be said in any text explaining the second law. Consider putting a heat engine between a heat source and cold sink of the same temp. It can do no work. If our universe is perpetually old, isolated, and static then it stands to reason that entropy is at a maximum. Hence: no useful work can be done. This is not the case in our universe therefore the universe is not perpetually old, static, and isolated.

 

Hoyle understood this problem as would any first year physics student. His steady state model explicitly avoids the problem because the system is not closed. He introduces new matter into his universe thus violating the first law of thermodynamics and considers old matter as lost to any finite portion of his universe because his model is expanding and old matter is lost behind a cosmological horizon.

 

Your idea of static hyperbolic redshift simply doesn't fix the problem, and lashing out at me for pointing out the problem is not helping to solve it. You cannot introduce new matter to your universe because it is not expanding—it would quickly fill to an infinite density.

 

The only possible solution I could see to this problem would be to introduce new matter via some unknown process (exactly as Hoyle did) and at the same time remove old matter via some unknown (non-expansion) process. But, this would be awfully ad hoc and an explicit violation of the first law—it'd be almost impossible to consider realistically.

 

I've asked you previously to show me a static model predicting CMB that has not been falsified and I don't think I got an answer. If you're carrying on this belief then please let us know what model this is you keep talking about.

Look at post 596 and falsify it, but first plase read something about Non-Euclidean geometry, specially about horospherical spaces.

 

I don't see a cosmological model there.

 

One should not fall in love wih a theory

 

This type of hyperbole is not useful.

 

There are predictions of evolution that a static model cannot make. The radio source count evolves with redshift.

Radio source count? what is that? Specify, please

 

A radio source is something that emits radio waves that you see in the sky. A 'count' is the number of something in a given area of space. The count could also be per flux. Active galactic nuclei are such an example:

 

More interesting is the study of the evolution of the AGN population. Most luminous classes of AGN (radio-loud and radio-quiet) seem to have been much more numerous in the early universe. This suggests (1) that massive black holes formed early on and (2) that the conditions for the formation of luminous AGN were more readily available in the early universe — for example, that there was a much higher availability of cold gas near the centre of galaxies than there is now. It also implies, of course, that many objects that were once luminous quasars are now much less luminous, or entirely quiescent. The evolution of the low-luminosity AGN population is much less well constrained because of the difficulty of detecting and observing these objects at high redshifts.

Active galactic nucleus - Wikipedia, the free encyclopedia

 

You see, the AGN population has evolved over time.

It is not for nothing that BBT is such a strongly-held cosmological staple.

Who could argue with this statement? I would only add that one of the motives could be that people is not encouraged to look for alternatives even when the model faces problems that would lead to inmediately dismiss any aspiring alternative.with scorn and mockery.

 

You appear uninformed as to the way science works. It is every physicists dream to create a model which would make some predictions which the standard model does not make only for those predictions to be confirmed. This is the whole goal. This is why physicists have worked on loop quantum gravity and brane theory. This is why particle physicists built a 4 billion dollar particle accelerator under Geneva. They are trying to break the standard model of particle physics.

 

I believe you would do well to read about entropy and the second law of thermodynamics as well as falsificationism and the scientific method.

 

~modest

[quantumtopology]

Just for the record, I am not lashing out at you, it's just too bad you can't cope with disagreement and you take it in a personal way. Have you ever conceived the possibility of being wrong about something? I guess not.

 

Just a couple of things, do you consider an infinite universe as an isolated system? if not what kind of thermodynamical system do you consider it?

Have you reflected on the fact that the 2nd law of thermodynamics might not be suited to deal with the universe as a whole? People far more knowledgeable in these matters than you and me have done just that.

From the wikipedia:

QUOTE

"Entropy and cosmology

Since a finite universe is an isolated system then, by the Second Law of Thermodynamics, its total entropy is constantly increasing. It has been speculated, since the 19th century, that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source....

The role of entropy in cosmology remains a controversial subject. Recent work has cast some doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly, moving the universe further from the heat death with time, not closer. This results in an "entropy gap" pushing the system further away from the posited heat death equilibrium.[49] Other complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult." END QUOTE

 

And finally I never said a static universe could not evolve in time, can't figure out what your quote about AGN and radio source counts has to do with anything we've been talking about, is this some kind of "straw man" argument?

 

Regards

QTop

[modest]

Just a couple of things, do you consider an infinite universe as an isolated system? if not what kind of thermodynamical system do you consider it?

 

Like I said in my last post, if the universe is static then you can treat any finite portion of an infinite universe as an isolated thermodynamic system. Useful energy will not cross boundaries in a net positive way. So, we are not saying that an infinitely-sized universe is an isolated system (although I personally wouldn't have a problem saying that), but rather that each finite portion of your static infinite universe can be treated as such.

 

Have you reflected on the fact that the 2nd law of thermodynamics might not be suited to deal with the universe as a whole?

 

The second law of thermodynamics demands that any spontaneous process increase the entropy of "the whole universe".

 

People far more knowledgeable in these matters than you and me have done just that.

From the wikipedia:

 

...The role of entropy in cosmology remains a controversial subject. Recent work has cast some doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly, moving the universe further from the heat death with time, not closer.....

 

Such a refutation of the application of the second law would apply only to an expanding universe. It appears to be a weak argument, but I'd have to check the source "God: The Failed Hypothesis" to be sure, and I don't have the book. Notice that the very same wiki page says:

 

Unless an external event intervenes (thus breaking the definition of a closed system), the room is destined to remain in the same condition for all eternity. Therefore, following the same reasoning but considering the whole universe as our "room", we reach a similar conclusion: that, at a certain point in the distant future, the whole universe will be a uniform, isothermic and inert body of matter, in which there will be no available energy to do work.

Entropy - Wikipedia, the free encyclopedia

 

This is a well-known problem with static and perpetually-old models.

 

And finally I never said a static universe could not evolve in time

 

Actually, that's what isotropic time means—systems do not evolve with time.

 

can't figure out what your quote about AGN and radio source counts has to do with anything we've been talking about, is this some kind of "straw man" argument?

 

I gave it as a confirmed prediction of BBT. You listed two, and I give you others. Do you recall this?

 

~modest

[quantumtopology]

Like I said in my last post, if the universe is static then you can treat any finite portion of an infinite universe as an isolated thermodynamic system. Useful energy will not cross boundaries in a net positive way. So, we are not saying that an infinitely-sized universe is an isolated system (although I personally wouldn't have a problem saying that), but rather that each finite portion of your static infinite universe can be treated as such.

Each finite portion is certainly not in the same thermodynamic state, so this argument is feeble, among other things to get each point to be in the same state would violate the limits to information transport: the speed of the light limit. And as I said many times every finite portion is allowed to evolve differently in finite period of time.

The second law is hardly applicable to infinite time, that is also stated in the thermodynamics wiki page.

 

 

Such a refutation of the application of the second law would apply only to an expanding universe. It appears to be a weak argument, but I'd have to check the source "God: The Failed Hypothesis" to be sure, and I don't have the book. Notice that the very same wiki page says:

 

Entropy - Wikipedia, the free encyclopedia

Here we disagree, you seem comfortable with the idea of treating the universe as a "room". But that looks like speculation to me.

Wiki quote:

"In thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration. Anything under consideration is called a system. A hypothetical boundary separates the system from the rest of the universe, which is referred to as the environment, surroundings, or reservoir"

 

This is the working definition of thermodynamic system, it seems like extending it to the whole universe would involve some speculative or loose use of this definition and a departure from how Clausius and Carnot originally used it.

 

Actually, that's what isotropic time means—systems do not evolve with time.

No, that is not exactly what it means, it means time looks the same in any direction, as I said that would be the case taking scales of time longer than we can imagine, for shorter periods evolution is perfectly allowed, or just because space is homogenous we shouldn't observe planets or galaxies?

 

 

I gave it as a confirmed prediction of BBT. You listed two, and I give you others. Do you recall this?

That is a prediction of any model that allows evolution then.

 

QTop

[modest]

Each finite portion is certainly not in the same thermodynamic state, so this argument is feeble among other things to get each point to be in the same state would violate the limits to information transport: the speed of the light limit. And as I said many times every finite portion is allowed to evolve differently in finite period of time.

 

In a static and perpetually old universe there has been enough time for any part to communicate with any other part regardless of a maximum speed of communication, but your point, even though it is mistaken, is not a refutation of what I was saying.

 

Are you assuming that our local part of the universe is importing useful energy and exporting entropy to the other parts of the universe?

 

If so, then can the same be said for all parts of the universe?

 

If not, then why is our local part of the universe not at a maximum of entropy?

 

The second law is hardly applicable to infinite time, that is also stated in the thermodynamics wiki page.

 

It is not necessary to object to your model because it is of infinite age. It is enough to call it 'perpetually old' and give specific examples of systems which are too far from equilibrium to have had some arbitrarily large amount of time to evolve.

 

Here we disagree, you seem comfortable with the idea of treating the universe as a "room". But that looks like speculation to me.

 

As I have explained, it is not necessary to consider the total entropy of an infinite universe. Any arbitrary part (for example, our part) can be considered isolated so long as we do not consider it exceedingly special.

 

No, that is not exactly what it means, it means time looks the same in any direction

 

If the AGN population increases as you look to the past and decreases as you look to the future then time does not look the same in both directions.

 

as I said that would be the case taking scales of time longer than we can imagine

 

But, there is no need to consider time scales longer than we can imagine. It is easy enough to look at our local galaxy cluster and come quickly to the conclusion that it has been evolving for a relatively short period of time (no more than a few billion years). Any more evolution than that creates significant problems where the predictions do not match observation.

 

for shorter periods evolution is perfectly allowed, or just because space is homogenous we shouldn't observe planets or galaxies?

 

If it is homogeneous and perpetually old then the planets, stars, and other objects should all be isothermic. They are not.

 

~modest

[quantumtopology]

The finite portions are certainly not isolated systems from the rest of the universe, so your argument just don't work here. Try again.

 

You seem to have a hard time understanding the concept of infinity and that isolated systems are idealizations , useful approximations to local systems, not to the whole universe

 

The word "old" loses its meaning in an infinite universe, You might as well call it "perpetually young", it makes no difference. An infinite universe is "perpetually" in all imaginable ages.

 

So your argument is misleading once more, or at the very least not at all the stumbling block for a static universe that you wanna make it appear.

 

haven't you realized yet that the direction of increase of entropy is determined by the observer of the system?, you can't observe the whole universe and be part of it at the same time.

 

Regards

Qtop