Okay, let's talk about the Penrose Conformal Cyclic Cosmology
Roger Penrose is a candidate for greatest living cosmologist. We need to take what he says seriously. What motivates the CCC cosmology? Penrose is an advocate of the "past hypothesis". A good source that describes its motivation is Sean Carroll's book: amazon.com
@seanmcarroll is up there in consideration for greatest living cosmologist too, in my opinion. Of course this could be a selection bias since I tend to believe the past hypothesis as well!
Two sources from Penrose I suggest: amazon.com
amazon.com
Two sources from Penrose I suggest: amazon.com
amazon.com
The Road to Reality contains all the math you need to understand to do calculations in modern cosmology! 700 pages of it! Penrose really likes to prove things. About page 700 he gets into the reason why he ultimately proposed his CCC theory.
The other Penrose source was written in 2016, and thus contains a popular level description of CCC. But let's not go there yet. What is the past hypothesis and what motivates it? This question deals with the apparent fantastically low entropy condition of the Big Bang.
The 2nd Law of Thermodynamic is a statistical law. It speaks to likelihoods rather than absolutes. Carroll gives several examples in his book one of which I tweeted the other day in my (apparent) fine-tuning examples. A closed box with a gas in various states. (See my media)
Carroll & Penrose also speak to entropy states that include gravity. In a negligible gravity state (like the gas in a small box), uniformity in volume distribution is the one of highest entropy. When you include gravity, however, the opposite obtains.
Gravitational entropy maximizes when matter clumps. So here are two mysteries. First, entropy is described by defining coarse grained states that are collections of all the microstates a system can have. For example, if all the molecules in small box are bunched in a corner.
If that seems intuitive unlikely, you are on the right track. The coarse grained state called "uniform distribution" has many more ways of occurring when you sum up combinations of microstates. In fact, "uniform distribution" is the state of maximum entropy.
Now, imagine all the different ways of arranging the molecules. This constitutes a "phase space". Under evolution, the state of the system will trace out a history through different states in the phase space. As Carroll points out, this description of evolution . . .
. . .does a pretty good job of predicting the future. Histories will reliably go from low to high entropy. If at the maximum state, it will tend to stay in thermal equilibrium. The problem comes in that we can attempt to 'predict' the past as well and it gives us the same answer!
Carroll uses the example of a half melted ice cube in a glass of water. We remember a full ice cube going into room temperature water. Yet our phase space statistical history prediction (starting with the half melted ice cube) tells us the past is . . .
. . . the same as the future, nothing but room temperature water! Hence the creation of the 'past hypothesis' that there really was a low entropy condition in the past that evolved to our present state. This idea is somewhat controversial!
Gravity throws another monkey wrench into the discussion. As we look to the past, and, for convenience, we believe the General Theory of Relativity (GTR) prediction of a singularity in our past, we should see something like a black hole singularity - maximized entropy.
But our astronomical evidence looking back further and further in time toward the Big Bang tells us the entropy appears lower and lower as we look to the past. How did this happen? Cue Roger Penrose and his 'Weyl curvature hypothesis'. Penrose proposes that the initial . . .
. . . singularity must have been very smooth (in GTR this is zeroing out the Weyl tensor). This very special initial condition allows us to have our 'past hypothesis' but leaves us without an explanation for how such a thing could obtain.
Now Roger Penrose is not a theist as far as I know. He does mention in his writings that he would prefer a physical solution rather than allowing that 'God did it'. Hence the Conformal Cyclic Cosmology.
The CCC makes use of a technique in GTR called 'analytic continuation'. This technique is used to analyze times in a Friedmann-Lemaitre-Robertson-Walker (Big Bang) model near the Big Bang. He argues this allows one to push times back 'before the big bang'.
Now, in an FLRW model the Big Bang is a past boundary where (normally) spacetime ends. There is a mathematically similar entity at the 'end of time' as well. If the model predicts the universe will last forever the boundary still exists. It is merely at 'future infinity'.
So what Penrose wants to do is imagine there was an era that was temporally earlier than ours. This previous 'aeon' as Penrose refers to it, is a universe essentially identical to ours. He then uses the technique of analytic continuation from the boundary at 'future infinity'
. . . to imagine going 'past infinity' and connecting with our universe. Now, the immediate problem is that going 'past infinity' seems nonsensical. Penrose agrees. So he needs for the future of an FLRW model to have a finite future. Here is what he proposes.
Penrose wants to say that time 'just is' the existence of clocks. He then makes an argument that all particles in the universe except for zero mass bosons can theoretically serve as clocks. So he proposes that they must cease to exist via some mechanism.
Now, Penrose is very open about the problems in his model. This is one of them. Some Grand Unified Theories will predict that protons should decay (we are still waiting for proof), but his idea necessitates that electrons must decay.
There isn't any motivation for suggesting this other than that Penrose needs it to happen for CCC. All our existing evidence points toward the reliability of the Standard Model of Particle Physics, and stable electrons.
There are two other problems with this that are more esoteric. One has to do with thermal fluctuations that produce new electrons, and the other has to do with tracing a timeline from aeon to aeon.
Our current cosmological evidence has us heading toward something called an asymptotically De Sitter state (AsDs). Penrose agrees with this assessment. This is a very simple future where the universe is empty, and expanding under the influence of a cosmological constant.
Now, our universe has matter and energy in it. So it is not a pure De Sitter vacuum. But, as one evolves toward the future, it mathematically approaches that state. So what can we say about it? Well, one problem is that a De Sitter state is a lot like a box filled with a gas.
We talked earlier about tracing out histories through phase space that included all the possible states of the system. This applies to the universe. As the universe wanders through its possible states it will occasionally have entropy lowering events called thermal fluctuations.
The smaller the entropy excursion, the more likely it is. Creating random electrons should be very likely. So there is a process that competes with Penrose's imagined physics that wants electrons to decay by creating new electrons.
Which side wins? Well, considering that the universe may be spatially infinite in extent it seems fantastic to imagine that all electrons everywhere will cease to exist. But put that aside for now. It is not enough to posit that electrons decay. They must decay so fast . . .
. . . that an infinite universe can become truly empty.
Here is the second problem Suppose the universe could empty out. Recall this is Penrose's solution to bringing 'future infinity' to a finite future. But by doing so, he proposes that time itself disappears. Here is the problem. If time disappears, then . . .
. . . before-after relations disappear as well. He appears to have posited a new boundary that cannot be 'after' the 'previous' aeon or 'before' the 'current' one. There isn't a smooth timeline. The other aeon cannot be said to precede ours. Now there is a technical basis for . .
. . . arguing for causal, rather than temporal, priority given Penrose diagrams and analytic continuation. But this will not serve Penrose. He needs temporal relations. If the other aeon exists, it is not 'before' ours. But that is the only reason for positing it.
The last topic to talk about is entropy in the far future. Penrose opposes most cosmologists on this topic in two ways. He needs the entropy of the far future to lower itself so as to allow for the low Big Bang state we observe in our own FLRW universe. How can this happen?
Now, as Sean Carroll points out, a De Sitter space is a maximal entropy condition; not a minimum one! See, for example, page 310 of 'From Eternity to Here'. He is talking about pure De Sitter, (which would apply to AsDs as well).
Now, Carroll also points out here and in his academic writings that defining entropy of the universe in these conditions is a topic still open for debate. Penrose is making use of this room. But the dominant position is that De Sitter (empty space with CC) is maximal entropy . .
. . . that is, exactly the opposite of what CCC needs. Independently, Penrose argues that all the entropy tied up in black holes will also simply disappear. He doesn't describe how this is possible except to raise the issue of whether informations is lost in black holes.
If unitarity is preserved (Carroll will argue it is), then the 'degrees of freedom' of everything that went into the black hole in the first place is preserved.
How can the information disappear? Well, in the far future, black holes radiate all their energy and disappear into radiation. Most cosmologists think this is a unitary process that uses the 2nd law of thermo and will increase entropy. Penrose posits that somehow, that isn't so.
For the largest black holes, this happens on a time scale of something like 10^100 years. This time scale plays into the argument made earlier of De Sitter producing new electrons. Now, one should mention that Carroll has a proposal that once AsDs becomes mathematically . . .
. . . identical to De Sitter, thermal fluctuations may stop. This doesn't affect the CCC issue, but it does figure in the Boltzmann brain discussion which we will eventually delve into.
So, there you are. CCC is Penrose's attempt to explain the ridiculously low entropy 'at' the Big Bang. It needs 'five consecutive miracles' to succeed. IMHO, its many problems are fatal. But if one's prior view of the likelihood that God could exist is a hard zero, there you go.
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