Big Bang & Entropy: Proof & Theories Explained

[Cantor]

I am reading Cycles of Time by Penrose, page 71-72. Could someone explain if the universe started out with at a state of extraordinarily tiny entropy or a state of maximum entropy and what proof or theories do we have to justify this choice. I find the explanation in the book confusing.

Thank you.

 

[kevinferreira]

He says that the big bang was a state of tiny entropy because if we accept the law of 'ever increasing entropy', i.e. 2nd law of thermodynamics (which Penrose explains in every detail), then going backwards in time mist take us to states of ever decreasing entropy. Going way back to the big bang, we see it must have a very low entropy.

 

[bapowell]

Just to add -- the extraordinary low entropy initial state of the universe is one of the prevailing mysteries of modern cosmology. Sean Carroll, for one, has been doing much writing on this topic and its connection to the arrow of time: http://preposterousuniverse.com/eternitytohere/faq.html

 

[Chronos]

You may find this paper of interest - Inflation as a Solution to the Early Universe Entropy Problem?, http://arxiv.org/abs/1212.1087

 

[Naty1]

Here's are review excerpts of the book I found on Amazon books...

Penrose doesn't believe the inflation theory, which is that space expanded incredibly rapidly right after the Big Bang. He says his conformal cyclic cosmology theory explains the things that inflation was invented to explain: it explains correlations in temperature in the cosmic microwave background between areas that are separated by large angles, and the scale invariance in the temperature fluctuations. The CCC theory also requires Weyl curvature to be zero at the Big Bang. This apparently explains why we don't see magnetic monopoles, another thing that inflation is invoked to explain, although Penrose doesn't discuss this in his book.
The CCC theory seems much more appealing than the inflation theory. It's more parsimonious, not requiring extra fields or an incredibly rapid expansion of spacetime. The universe would have expanded at the normal rate, only over a very very long time before the Big Bang.
The big hole in Penrose's theory is that our universe can only lose track of the scale of space and time if rest mass disappears. Rest mass gives a scale to spacetime. So it's necessary that all particles should eventually decay into massless particles like photons, or lose their rest-mass some other way. He hasn't come up with any good explanation for how this would happen. His best attempt at a theoretical framework for the decay of rest mass is:
"A standard procedure for addressing the idea of an 'elementary particle' is to look for what are termed the 'irreducible representations of the Poincare' group'. Any elementary particle is supposed to be described according to such an irreducible representation. The Poincare' group is the mathematical structure describing the symmetries of the Minkowski space M, and this procedure is a natural one in the context of special relativity and quantum mechanics. The Poincare' group possesses two quantities referred to as Casimir operators, these being rest-mass and intrinsic spin, and accordingly the rest-mass and spin are deemed to be 'good quantum numbers', which remain constant so long as the particle is a stable one and does not interact with anything. However, this role of M appears to be less fundamental when there is a positive cosmological constant L (Greek letter Lambda in the book) present in physical laws (as L=0 for M), and it would seem that, when we are concerned with matters related to cosmology, it should be the symmetry group of de Sitter space-time D, rather than of M, that should ultimately be our concern. However, it turns out that rest-mass is not exactly a Casimir operator of the de Sitter group (there being a small additional term involving L), so that its ultimate status is more questionable in this case, and a very slow decay of rest mass seems to me to be not out of the question."
I don't know how convincing this is. Does rest mass need to be a Casimir operator of the spacetime, to be a good quantum number, so that it's conserved for a particle as long as it exists? Apparently nobody's worked out what becomes of quantum mechanics and the Standard Model of particle physics in de Sitter spacetime. Until they do, and rest mass really does turn out to fade away in the expanding universe, Penrose's theory will limp badly.

 

[chill_factor]

you may think, why is the entropy of the matter immediately after the big bang so low, even though it is spread out very evenly?

let me offer a small opinion as to why. can we agree to the 2 following facts?

the matter after the big bang is not a black hole.
the entirety of matter after the big bang is a gravitating system.

For a classical gas kinetic energy <K> = 3/2*kT. In contrary to conventional notation, due to T being occupied by the temperature, K will instead be used for the kinetic energy.

A self gravitating system obeys the virial theorem because the kinetic and potential energies, and the momenta, of all particles, are bounded. <K> = -1/2 <U> where <U> is the time average of the potential energy. The proof is long so let's take an example instead: the 2 body central force problem.

U = -GmM/R (gravitational potential)
F_{g} = -GmM/R^{2} (gravitational force)
F_{c} = mv^{2}/R (centrifugal force)

at equilibrium and in appropriate coordinates the net force is zero.

GmM/R^{2} = mv^{2}/R
rearrange to get (1/2)mv^{2} = (1/2) GmM/R

oh look we have K = -(1/2)U. If it works for 2 particles, maybe it works for N particles.

So K = -(1/2)U, U = -2K. total energy E = K + U = K - 2K = -K.
K = (3/2)kT. So E = -(3/2)kT

In other words, total energy = -number*temperature, and as temperature increases, E is decreasing.

What is gravitational potential energy of a sphere of gas?

http://scienceworld.wolfram.com/physics/SphereGravitationalPotentialEnergy.html

U = -3GM^{2}/R.

So E = -number*1/R -> T = number/R. As R decreases T increases. As T increases, E decreases.

This means that self gravitating systems want to decrease their energy by decreasing their size (measured by radius R) and increasing temperature. The uniform state after the big bang is therefore a state with extremely low entropy and favored to evolve towards higher entropy states. Indeed, energy would be minimized if R approached zero.

 

[Cantor]

Thank you all for the responses.

So if the Big Bang was in a state of tiny entropy, why when looking at the CMB radiation we notice there is thermal equilibrium? Wouldn't this imply maximum entropy even during the beginning of the Big Bang also. (I could be misunderstanding the idea of course graining and thermal equilibrium. Still a novice at this)

 

[Naty1]

the matter after the big bang is not a black hole.
the entirety of matter after the big bang is a gravitating system.

This is backwards from the Penrose Conformal Cyclic Cosmology : The entirety of energy after the big bang is repulsive gravity according to him.

There are different ideas what might be the causes...a recent one I posted was a research paper attributing it to TORSION of space-time...

...why when looking at the CMB we notice there is thermal equilibrium?

I think you mean uniformity...rather than equilibrium ...except for small perturbations the CMBR is UNIFORM. The CMBR is NOT in thermal equilibrium and never has been. For example it started out close to 3,000 degrees K and is now about about 2.73 degrees K .

Penrose attributes the extraordinary low initial entropy to that of gravity...other elements as I recall he does not claim to be in low entropy...

As I posted previously:

...The big hole in Penrose's theory is that our universe can only lose track of the scale of space and time if rest mass disappears. Rest mass gives a scale to spacetime. So it's necessary that all particles should eventually decay into massless particles like photons, or lose their rest-mass some other way. He hasn't come up with any good explanation for how this would happen.

High entropy with gravity means clumping mass...likes planets,stars,etc...w/o mass I am guessing Penrose thinks gravitational entropy would be low...

yes! found this note I made from his video:

At end of our expansion we come to masslessness and as black holes evaporate and as information is lost, we return to a low entropy state…

More here:

https://www.physicsforums.com/showthread.php?t=427567&highlight=cycles+time+roger+penrose&page=2
Cycles of time--Penrose says his cyclic cosmology obeys thermodynamics

/////
Cycles of Time [great slides,diagrams, although a bit 'handwavy'
http://www.slideshare.net/scexxn/cycles-of-time-16403194

 

[Naty1]

Cantor: I have this description in my notes about CCC, did not record the source:

In the past, Penrose has investigated cyclic cosmology models because he has noticed another shortcoming of the much more widely accepted inflationary theory: it cannot explain why there was such low entropy at the beginning of the universe. The low entropy state (or high degree of order) was essential for making complex matter possible. The cyclic cosmology idea is that, when a universe expands to its full extent, black holes will evaporate and all the information they contain will somehow vanish, removing entropy from the universe. At this point, a new aeon with a low entropy state will begin.

My notes from the above slides:

As time goes on cosmological acceleration is increasing…that expansion means a colder and colder and emptier universe. Back holes are colder, but expansion will eventually cause universe to be colder and black holes will disappear via Hawking radiation…black holes disappear in a ‘pop’ [magnitude of an artillery explosion] and release entropy and DO swallow information….so our notion of entropy changes….must redefine definition entropy….. [explanation not clear].. second law still works, but definition changes due to swallowing information by black holes…very end is low entropy state…..similar to big bang….

Mass finally fades away is Penrose’s theory…..sort of an anti Higgs mechanism….

Marcus posted this in another discussion:

I heard Penrose give this argument in March 2006 to an audience of math and physics people at the MSRI. He was charming and had great slides but the argument was handwaving and not convincing. You cannot use entropy in a rigorous math argument unless you can define it and he was not able to define the global entropy through the course of the LQC bounce. So he used vague suggestive language and did not claim certainty.

In addition there is good reason to believe entropy cannot be well defined without defining an observer...and the number of degrees of freedom also have major impact on defining entropy...further Penrose has changed his mind about black hole information loss.. Penrose has returned believing it IS lost...if the information were NOT lost, as black holes spew forth their contents [ 99% of the information of the universe] it would be recovered at the end of this aeon...hardly a low entropy state
so beware... there are MANY subtleties in all this...

FYI: For those with Penrose's book ROAD TO REALITY, he does discuss these ideas..