Talk about entropy and cyclical cosmology from spacetime thread

[Michael Mooney]

Moderation Note: The following 10 posts were moved from What is "spacetime" really? where they were off topic and deserving of their own thread.

 

The Cosmos is, by definition, a closed system, as it is "all that is".

Entropy is NOT the sum total of all matter and energy as implied by MM.

Entropy is a measure of order/disorder of that matter and energy.

If a Cosmos had all its matter and energy at one point, then entropy would be maximum.

If a Cosmos had all its matter and energy equally spread out everywhere, with no gradients, then entropy would be minimum.

 

First, you have it backwards.

From The Free Dictionary on Entropy:

"1. Symbol S For a closed thermodynamic system, a quantitative measure of the amount of thermal energy not available to do work.

2. A measure of the disorder or randomness in a closed system.

3. A measure of the loss of information in a transmitted message.

4. The tendency for all matter and energy in the universe to evolve toward a state of inert uniformity.

5. Inevitable and steady deterioration of a system or society.

 

So, if the universe just kept expanding and dissipating matter/energy, " toward a state of inert uniformity"... it would just "run down"... the state of maximum entropy.

 

If, on the other hand, there is enough mass in the universe (the "missing matter/energy" is found) all of it will be "caught in the universal gravitational net" (at the extreme of its expansive phase) and brought back for another in a perpetual series of bangs and crunches.

 

Actually I know very well what entropy is and I never implied that "Entropy is... the sum total of all matter and energy"

The sum total of all matter and energy in the universe is never increased or diminished. It is presently in the process of expanding *toward* maximum entropy, but if there is enough mass for *critical cosmic mass* for gravitational reversal, it will all come back and start over again... with *no loss.*

 

Michael

[maddog]

The Cosmos is, by definition, a closed system, as it is "all that is".

Entropy is NOT the sum total of all matter and energy as implied by MM.

Entropy is a measure of order/disorder of that matter and energy.

If a Cosmos had all its matter and energy at one point, then entropy would be maximum.

If a Cosmos had all its matter and energy equally spread out everywhere, with no gradients, then entropy would be minimum.

First, you have it backwards.

From The Free Dictionary on Entropy:

1. Symbol S For a closed thermodynamic system, a quantitative measure of the amount of thermal energy not available to do work.

2. A measure of the disorder or randomness in a closed system.

3. A measure of the loss of information in a transmitted message.

4. The tendency for all matter and energy in the universe to evolve toward a state of inert uniformity.

5. Inevitable and steady deterioration of a system or society.

Pyrotex,

 

This has to be one for the History books, yet here is where I agree with Michael, Entropy

is measured against a Closed System. Thus it would be fine to consider the Entropy

of the Universe (as long as it was "Closed"). With a lot of models today considering

other geometries than closed, proper boundary condition may need be laid out (that I

have seen not).

 

maddog

[modest]

Pyrotex,

 

This has to be one for the History books, yet here is where I agree with Michael, Entropy

is measured against a Closed System. Thus it would be fine to consider the Entropy

of the Universe (as long as it was "Closed"). With a lot of models today considering

other geometries than closed, proper boundary condition may need be laid out (that I

have seen not).

 

maddog

 

I have to agree with Pyrotex and it's a very well-known problem with models of an eternal (as in no beginning) cosmos. Entropy can only increase and the entropy of the visible universe is not at a maximum. Hoyle's steady state model solves this problem by allowing new hydrogen to spontaneously be generated as the universe expands, but this in turn breaks the first law of thermodynamics (conservation of energy). Anyone claiming there is no beginning to the matter in the universe is ultimately faced with an entropy problem.

 

I don't think allowing the universe to be open can solve this problem.

 

~modest

[Michael Mooney]

Me:

I have consistently argued that more simple "dark matter"* is being found all the time with better detectors, so that6 the "missing matter problem" against reversal/implosion may not be a "problem much longer. (*Ordinary matter not emitting or reflecting light.)

And then, as in the quote above... whatever "dark energy" and "dark matter" might be (??) could add to the equation for viable critical cosmic mass.

 

Modest:

 

I'm afraid this is a subject you can't really gloss over with a few loose phrases. Dark energy (i.e. the cosmological constant / Lambda) which the wiki article mentions is an entirely different thing from dark matter. Rather than being an enigmatic concept which fixes your broken philosophy, it is an energy density attributed to empty space. As such, I'm sure you would reject it ardently if you knew anything about it.

 

Modest,

You continue *as always* to misrepresent what I write.

I didn't "gloss over" "dark energy" and "dark matter." I don't understand what they (theoretically) are... or even *if* they "are," as clearly indicated in my parenthetical (??.)

 

One** of the classic objection to a cyclic cosmos is the "missing matter problem" which is becoming less of a "problem" all the time as more matter is being detected, as I clearly stated above.... with or without the help of "mystery matter/energy" in its latest theoretical incarnation as "dark matter/energy."

 

Another is the "entropy" objection, which I have again addressed just above in reply to Pyrotex.

 

Yet another objection (to the classical "Bang/Crunch" theory) is the dynamic of the "Bang" itself... which I have addresssed in brief several times on this thread as the "multiple bangs and crunches cosmic juggling act" as a series of up-scaled supernovae-like bangs sending out cosmic matter like "supernova remnants" even as more matter is collapsing inward.

 

I think it was Pyrotex who observed that this thread is a bungled up mess, and I volunteered that your consistent mangling of my meaning is a primary cause.... and I cited the most recent example at the time.

Again I ask you to get off my case, as you show no comprehension of my meaning intended in any given post, as above.

Michael

[maddog]

I have to agree with Pyrotex and it's a very well-known problem with models of an eternal (as in no beginning) cosmos. Entropy can only increase and the entropy of the visible universe is not at a maximum. Hoyle's steady state model solves this problem by allowing new hydrogen to spontaneously be generated as the universe expands, but this in turn breaks the first law of thermodynamics (conservation of energy). Anyone claiming there is no beginning to the matter in the universe is ultimately faced with an entropy problem.

 

I don't think allowing the universe to be open can solve this problem.

 

~modest

Modest,

 

I was only pointing out the issue with Entropy and Boundary Conditions. Yes for matter and

the Universe as we know it to be, Entropy always increases (for the most part).

 

I do remember a Biophysicist friend when I was in college and he was having Entropy

issues with any System he created where living things were included (Terrarium for

example). He found Entropy deviated from the predicted path for inanimate matter.

His professors had said his error was inappropriately applying his Boundary Conditions.

Of course that is slightly getting off topic. ;)

:)

 

maddog

[modest]

Of course that is slightly getting off topic. ;)

:)

 

I agree. I myself am guilty of pulling this thread off topic lately. As I think this thread has been a good source of discussion and I think it deserves our respect in keeping it on topic, I will move any subsequent posts which focus on anything not related to "What is "spacetime" really?" elsewhere.

 

Michael, I'm sure you'll want to respond to some of the cosmology stuff I wrote above, and I'm sure that's fine. But, hopefully we can put a quick end to discussion of entropy and cyclic universe models and whatnot in this thread.

 

~modest

[modest]

entropy... is not valid for cosmos as a whole... in which no energy/matter is ultimately lost.

Can you even 'wrap your head around" this difference?

 

Can you please provide a scientific reference supporting this claim? Doing so is a requirement of the Hypography site rules.

 

By my understanding the laws of thermodynamics work on the universe as a whole most especially because "no energy is ultimately lost" (it is a closed system). As the second law of thermodynamics is applied to the universe we find the universe will eventually reach a state commonly referred to as "heat death".

 

The heat death is a possible final state of the universe, in which it has "run down" to a state of no thermodynamic free energy to sustain motion or life. In physical terms, it has reached maximum entropy. The hypothesis of a universal heat death stems from the 1850s ideas of William Thomson, 1st Baron Kelvin who extrapolated the theory of heat views of mechanical energy loss in nature, as embodied in the first two laws of thermodynamics, to universal operation.

 

Heat death of the universe - Wikipedia, the free encyclopedia

 

~modest

[watcher]

michael,

entropy is unassailable.

in time the universe would simply spaced out

our universe is like an echo that fades away in a one way trip to oblivion.

but don't lose heart, your cyclic model is still feasible in a multi dimensional universe model. where rebirth of new universe happens and assures that existence in general would not cease.

ironically you are against multidimensionality of it.

so you see your ideas of space and time is not even compatible with your endless cycle cosmology.

[lawcat]

Can you please provide a scientific reference supporting this claim? Doing so is a requirement of the Hypography site rules.

 

By my understanding the laws of thermodynamics work on the universe as a whole most especially because "no energy is ultimately lost" (it is a closed system). As the second law of thermodynamics is applied to the universe we find the universe will eventually reach a state commonly referred to as "heat death".

 

 

 

~modest

 

True. Entropy is "unuseful" energy within environment. It is defined as a heat transfer relationship between two objects -- entropy = heat (kJ/kg)/ temperature (Kelvin).

For example, if 3000 Kj/kg of heat flow from planet A to planet B, and planet A has temperature T=300K, then entorpy of planet A is 3000kJ/kg/300K = 10 kJ/kgK (planet A has lost some useful energy).

 

If universe has mass and no-mass, then theoretically all mass energy can be converted to heat in no-mass. Then, mass would have maximum entropy, and no real useful energy.

 

I don't believe this can happen, for I believe that mas can be reconstituted, and created from space and time.

[Michael Mooney]

Can you please provide a scientific reference supporting this claim? Doing so is a requirement of the Hypography site rules.

 

By my understanding the laws of thermodynamics work on the universe as a whole most especially because "no energy is ultimately lost" (it is a closed system). As the second law of thermodynamics is applied to the universe we find the universe will eventually reach a state commonly referred to as "heat death".

 

~modest

 

I will provide the logical contex for the claim, then document sources for the classic "Bang/Crunch" cosmology if required.

 

Context: The universal law of conservation of matter and energy (and plasma as a transitional state) states that nothing is ever created or destroyed but only changes form.

 

The Merriam Webster Online Dictionary defines entropy, as applied to the universe as a whole as follows:

2 a: the degradation of the matter and energy in the universe to an ultimate state of inert uniformity b: a process of degradation or running down or a trend to disorder

 

The "universal gravitational net" part of the classic "Bang Crunch" cosmology states that if the "missing matter" is found (and that is happening... which will revive the supposedly debunked "bang/crunch") then all matter/energy/plasma in the universe will be ultimately pulled back into a Big Crunch in prep for the next Big Bang.

It is important to notice that nothing is lost in this model, and tho the model was supposed to have been debunked, the "found matter" to make "critical cosmic mass" for this gravitational reversal possible may well herald a revival of "my favorite cosmology" as above (and shared several times in this thread.)

 

Further contex... a reply to NomDePlume on the entropy issue:

 

This (the universal law of conservation of matter/energy) means that there is no loss of anything, cosmically speaking. So the second law of thermodynamics, so clearly valid for "isolated systems" in which there is "space" outside the system for, say heat to escape into... making the isolated system "lose steam" ... entropy... is not valid for cosmos as a whole... in which no energy/matter is ultimately lost.

 

So... entropy as above defined *will not happen* if the missing matter is found to bring it all back together for another in a perpetual series of bangs and crunches.

There would be no energy loss ultimately, and no " ultimate state of inert uniformity...(the)... process of degradation or running down or a trend to disorder.

The outer extreme of the expansion phase would, perhaps *approach* maximum entropy, but like the ultimate melodrama, the "gravitational net" powered by the required "critical cosmic density" would save the universe from such max entropy and bring it all back for the next "re-birth."

 

I agree that if the challenge against the bang/crunch model continues to insist that it is debunked by "expanding space" that a new thread will be required to continue the debate.

 

Still, such a debate must ultimately come back to what it is that "expands" if space retains its original meaning as emptiness... which it does in my vocabulary. (And if it disappears if the stuff in it disappears, what *was* it anyway?...)

 

Then (in such a thread) I will engage the *dogma* that "stuff" does not expand, explosion-wise out into infinite, empty space.

 

Michael

[Michael Mooney]

Modest:

Can you please provide a scientific reference supporting this claim? Doing so is a requirement of the Hypography site rules.

 

i got yet another bleeping "infraction" for not immediatly citing a "scientific reference" for my "claim" that entropy does not apply to a "Bang/Crunchg" model where absolutely all of it comes back to 'crunch' and then immedialy "bang" again.

I promised to cite such a "bang/crunch" reference if my explanation in the next post did not suffice.

It apparently didn't.

Now, Im traveling and on an strange computer without access to a notepad or back-up browser that i know of... so, anyway I Googled and got an engaging snipet from a 2004 inquiry/response on this subject from (I think) one of Hawking's inner circle.

 

I know it is just another cafe conversation, and I will get serious soon (at my own computer) on :scientific references .

(Thinking logically does not count as science on this forum of librarians!) but here is the snipet I got so far:

 

Behalf Of Owen Densmore

Sent: Wednesday, May 26, 2004 10:31 AM

To: The Friday Morning Applied Complexity Coffee Group

Subject: [FRIAM] Big Bang, Big Crunch: Decrease in Entropy?

 

 

During a conversation yesterday with Stephen, (Hawking?... MM) it occurred to me that

the second law would be violated at the turning point to the big

crunch, right?

 

I.e. if the universe begins to shrink back to a singularity (well, not

quite if you think the string theory picture is right), wouldn't order

increase in that era?

 

MM: Yes, a whole new round of order would begin in the next bang cycle after *all of it* (even the "heat") is brought back into the primordial "ball of all there is"... crunches, and then rebounds... in one of at least two theoretical ways.

 

"Nothing at all lost" on cosmic scale 'violates' the second law of thermodynamics (with total impunity from the universal Law :naughty: because it was conceived for "local systems" which *do* lose energy into the surrounding environment. this does not apply to a Bang/Crunch cosmos... and IT is not yet "dead" just because relativity theorists can not see "the big picture!"

 

Gotta go.

Michael

[watcher]

MM: Yes, a whole new round of order would begin in the next bang cycle after *all of it* (even the "heat") is brought back into the primordial "ball of all there is"... crunches, and then rebounds... in one of at least two theoretical ways.

 

the expansion of the universe will lose steam and decelerates to a halt and then the residual gravitational pull of matter will pull everything back together.

 

is this the general idea?

gravity acts like an elastic string that stretched out when dark energy repulse everything and snap back when the expanding force dissipated.

[Michael Mooney]

Here is a thread from "Physics Forums" website which has discussed this topic in some depth on "Entropy in a Big crunch."

Entropy in a Big Crunch

 

I suggest anyone interested check it out. As for the "scientific references" Modest demanded,

I'm on it and will bring back what I find. But it's not like we can cite an experiment that gives conclusive evidence. It is cosmological theory here.

Michael

PS:

Here is another from same forum on "Entropy of a collapsing universe"

http://www.physicspost.com/physicsforums/topic.asp-ARCHIVE=&TOPIC_ID=7731.htm

 

(I really don't think we need to re-invent the subject in this thread!)

 

Another from WikiAnswers.com (but a sign in is required):

http://wiki.answers.com/Q/What_is_the_entropy_difference_between_the_Big_Bang_and_the_hypothetical_Big_Crunch

[Michael Mooney]

This from "Frequently Asked Questions in Cosmology"

"Does entropy prevent a Big Crunch?"

 

Frequently Asked Questions in Cosmology

 

(This is not an endorsement. Just another "answer" to the topic question.)

Michael

[Michael Mooney]

MM:

Yes, a whole new round of order would begin in the next bang cycle after *all of it* (even the "heat") is brought back into the primordial "ball of all there is"... crunches, and then rebounds... in one of at least two theoretical ways.

Watcher:

the expansion of the universe will lose steam and decelerates to a halt and then the residual gravitational pull of matter will pull everything back together.

 

is this the general idea?

gravity acts like an elastic string that stretched out when dark energy repulse everything and snap back when the expanding force dissipated.

 

Yes. The debate has two major fronts.

#1: Is there enough matter in the cosmos to reach the critical mass required for such a gravitational reversal of the expansion phase?

More ordinary matter which is hard to detect* is being found all the time, which may eventually solve the "missing matter" problem.

(* Matter not "visible" because it is not emitting or reflecting light... and "far far away" and/or obscured by other matter between it and us.)

I don't know what "dark matter" and "dark energy" are in their more mysterious forms, or If they exist at all outside the minds of the theorists who have named them.

 

#2: Entropy. See links above and my previous posts on it.

The law of conservation of energy/matter seems to me to contradict the second law of thermodynamics on cosmic scale, speaking of "all there is" going out, reversing, and coming back via enough gravity to bring it all back.

Michael

[modest]

#1: Is there enough matter in the cosmos to reach the critical mass required for such a gravitational reversal of the expansion phase?

This is a great question. Astronomers have been working on answering it since Lemaitre and Friedmann first developed expanding relativistic cosmology in the 1920’s.

 

As Michael alludes, the question of whether the universe will continue to expand forever or will eventually stop expanding and recollapse depends on how much mass there is in the universe per area. Mass per area is density so this is a question of the universe’s mass density or, more properly, “energy density”—since gravity responds to more than just mass but all forms of energy. The energy density needed to eventually stop the universe from expanding is called the critical density. If the current energy density of the universe is equal to or greater than the current critical density then cosmologists expect the universe will eventually halt expansion and recollapse into a big crunch

 

So, there are really two questions.

1. What value is the critical density? In other words: how much mass per area will make the universe eventually stop expanding?
   
2. Is the actual measured energy density greater or less than the critical density. In other words: what is the universe actually going to do?
   

Standard cosmology uses the FLRW metric along with the ΛCDM model parameters and it would be easy to answer the first question with FLRW and the second with ΛCDM, and that was most recently done in this post. But, that's kind of like cheating and stealing the answers. Besides which, there is a more satisfying way to answer these questions which doesn’t rely on model-specific relativistic cosmology, but rather uses simple concepts of classical physics. In deference to Michael Mooney, the method I’m about to use doesn’t rely on expanding spacetime, relativity, or textbook authority. :)

 

To calculate the critical density above which the universe should eventually collapse we consider a sphere situated in the universe

The sphere does *not* represent the whole universe, but just an arbitrarily designated portion. We are situated at the center considering a point on the edge. The sphere expands with the universe so that the distance to the point changes with time. The distance (which is the radius of the sphere) is D(t) and the point has a velocity of dD/dt. We can easily consider the volume of the sphere:

[math]Vol = \frac{4}{3} \pi D(t)^3[/math]

 

We can consider the universe filled homogeneously with expanding matter. The matter at the edge of the sphere expands with an equal velocity as the sphere. Matter closer to the center (and inside the sphere) has less velocity than the point at the edge and matter farther than the edge has a greater velocity than the point at the edge which is under consideration. We can therefore say the mass of the sphere does not change with time. As it expands the matter in the sphere is always the same. The density, however, changes with time. As the sphere expands the volume increases as the mass stays the same. We call density rho(t):

[math]\rho(t)[/math]

Recognizing mass is density times volume:

[math]m = \rho(t) \cdot Vol[/math]

[math]m = \rho(t) \frac{4}{3} \pi D(t)^3[/math]

This gives enough info to calculate the escape velocity, [imath]V_E[/imath], for the point under consideration. The mass in the sphere can be treated like a point mass similar to a planet. The mass outside makes a hollow sphere and there is no gravitational force (no gradient in the gravitational potential) in a hollow sphere. The mass outside can therefore be safely ignored when considering the escape velocity. The escape velocity is the speed beyond which the point will not slow down, stop, and fall backwards toward the center which establishes the critical density. Escape velocity is:

[math]E_V = \sqrt{ \frac{2GM}{D(t)}}[/math]

The actual velocity of the point will be Hubble’s constant times distance. We substitute this for excape velocity and also substitute the mass we found above:

[math]H_0 \cdot D = \sqrt{ \frac{2 G \rho \frac{4}{3} \pi D^3}{D}}[/math]

Solving for density ([imath]\rho[/imath]) we find the expression for critical density:

[math]\rho_c = \frac{3 H_0^2}{8 \pi G}[/math]

We can check that our expression is correct by seeing what the Friedmann equations give:

An expression for the critical density is found by assuming Λ to be zero (as it is for all basic Friedmann universes) and setting the normalised spatial curvature, k, equal to zero. When the substitutions are applied to the first of the Friedmann equations we find:

[math]\rho_c = \frac{3 H^2}{8 \pi G}[/math]

 

Friedmann equations - Wikipedia, the free encyclopedia

We have it right. To find the numerical value of the critical density we only need to know Hubble's constant and the Gravitational constant. These are both easily tested experimentally and well-known values, so we can solve our expression being very confident in our result:

[math]\rho_c=\frac{3H^2}{8 \pi G} = \frac{(3)(2.3 \times 10^{-18})^2}{(8)(3.14)(6.67 \times 10^{-11})} \approx 10^{-26} \ Kg/m^3[/math]

we get approximately [imath]10^{-26} \ Kg/m^3[/imath] or [imath]10^{-29} \ g/cm^3[/imath] which is about 5 atoms per cubic meter. If the density of the universe is on average greater than that (and the cosmological constant is zero or less than zero) then we've got a big crunch in our future.

 

The answer to the second question... "Is the actual measured energy density greater or less than the critical density". If we cheat here and steal the answers :) Looking at: What is the Universe Made Of? we see the mass density of the universe is only about 25% of the critical density (about 1 atom per cubic meter). So, the best evidence at the moment is that the universe does not have enough energy density to stop its expansion and it will expand forever.

 

More ordinary matter which is hard to detect* is being found all the time, which may eventually solve the "missing matter" problem.

(* Matter not "visible" because it is not emitting or reflecting light... and "far far away" and/or obscured by other matter between it and us.)

Yup. The concordance model (ΛCDM model) has 4% of the critical density coming from visible baryonic matter. Most of the mass of the universe comes from dark matter which ΛCDM has making up 22% of the critical density. This would mean there is 5.5 times as much dark matter as normal visible matter.

 

The presence and quantity of dark matter is found through its gravitational effects. Judging by how fast galaxies rotate and how they interact with one another it is possible to estimate the mass in the galaxies and galaxy clusters. The rate of expansion of the universe itself can indicate the amount of mass.

 

~modest

[Michael Mooney]

Modest:

"2: Is the actual measured energy density greater or less than the critical density. In other words: what is the universe actually going to do?"

 

The answer to the second question... "Is the actual measured energy density greater or less than the critical density". If we cheat here and steal the answers Looking at: What is the Universe Made Of? we see the mass density of the universe is only about 25% of the critical density (about 1 atom per cubic meter). So, the best evidence at the moment is that the universe does not have enough energy density to stop its expansion and it will expand forever.

 

Just a parting shot here. This is par for the course for Modest.

 

If more baryonic (ordinary) matter is being detected all the time, (and there is!) then there is no final report on "the actual measured energy (/matter) density" compared to the critical density required. So the question, " what is the universe actually going to do?" is quite premature based on present measures... finding more energy/matter the more we look with better tools and detection techniques.

 

Even elements dispersed as single atoms way out near the cosmic event horizon count as part of that "critical mass", as does much mass which is "outta sight" as I mentioned above.

But here we have Modest proclaiming that "we see the mass density of the universe is only about 25% of the critical density..." and then concluding: "So, the best evidence at the moment is that the universe does not have enough energy density to stop its expansion and it will expand forever.

 

"At the moment"??.... but... but... we keep finding more.....

 

Oh well... he has his math, after all...

 

Michael