This essay examines physicist Roger Penrose's extremely wild and imaginative theory for explaining the ridiculously improbable order of the Big Bang without invoking an intelligent cause. Penrose describes the tremendous problem of explaining the unlikely Big Bang as follows:
In order to produce a universe resembling the one in which we live, the Creator would have to aim for an absurdly tiny volume of the phase space of possible universes – about 1/10^10^123 of the entire volume…This is an extraordinary figure. One could not possibly even write the number down in full…
When Penrose speaks about the Creator, he means it metaphorically, as he doesn’t believe in God. This essay shows how Penrose’s theory - Conformal Cyclic Cosmology - attempts to explain the improbable order of the Big Bang without an intelligent creator, and ultimately justifies why we think the argument for an intelligent cause still stands.
Highlights of this essay:
Below is an essay version of the ideas presented in Episode 16 of Season 2 of the Physics to God podcast. You can hear the audio version above.
Introduction
Recall from series 1 essay 9, Roger Penrose calculated the odds of our universe’s highly improbable initial conditions occurring by chance alone as 1 out of 10^10^123. Other than the multiverse, there are two scientific theories that attempt to explain this unlikely beginning without an intelligent cause.
Last time, we discussed Paul Steinhardt’s Bouncing Cosmology, and this time we’ll discuss Penrose’s Conformal Cyclic Cosmology, often called CCC. Penrose first presented CCC in his 2010 book, Cycles of Time.
It’s worth noting at the outset that CCC only attempts to explain the low entropy initial conditions of the big bang but doesn’t even attempt to address the fine tuning of the constants of nature or the design of the qualitative laws.
We won’t pretend that this essay will be easy. It will probably be the most difficult essay in this series, which is one reason we saved it for last. But, rest assured, we’ll try to simplify it as much as possible so you can get a basic idea of how it works. But we’re warning you - certain parts of this essay may be hard to follow. We apologize. No matter what, you’ll see once again just how imaginative you have to be to explain the highly improbable big bang without an intelligent cause.
Conformal Cyclic Cosmology
Penrose’s theory proposes that the universe goes through an infinite number of cycles, or aeons, with no beginning or end. In each cycle, the universe begins in a very small and dense state like the big bang, and then expands until it becomes extremely large and spread out. Then, without a contraction phase (and we realize this will sound like a contradiction) the very large universe transitions to the very small beginning of the next cycle, kicking off a new expansion phase, thus forming an infinite chain of succession.
The main idea is that according to CCC, throughout every stage of each cycle, the universe always expands and never contracts. Nevertheless, and this is the hard part, the very large end of one cycle somehow transitions into the very small beginning of the next.
In his book Fashion, Faith, and Fantasy (2016) - page 381 - Penrose explains his basic approach to an ever-expanding universe as follows:
The idea is that our current picture of an ever-expanding universe, from its Big Bang origin (but without any inflationary phase) to its exponentially expanding infinite future is but one aeon in an infinite succession of such aeons, where the F [final state] of each matches conformally smoothly with the B [beginning state] of the next.
We’ll explain what “conformally smooth” means in a second. Before that, let’s discuss the two obvious problems Penrose must deal with in positing an ever-expanding universe while simultaneously identifying the end of one cycle with the beginning of the next. First, at the end of one cycle, the universe is infinitely big, while at the beginning of the next cycle, the universe is infinitely small. How can such a transition be justified without a period of contraction?
Second, because the second law of thermodynamics says that entropy always increases, the end of one cycle is characterized by high entropy. Yet, the beginning of the next cycle’s big bang is a state of low entropy. So how can they be identical?
We’ll try to keep this as simple as possible and leave the entropy question for later. For now, let’s address the question of how CCC can identify the infinitely big with the infinitely small.
To solve this problem, Penrose proposes a very creative solution. He suggests that despite all appearances, there’s a surprising mathematical identity between the infinitely big and the infinitely small. He argues that under certain conditions we’ll discuss in a minute, the laws of physics are conformally invariant. Conformal invariance means that if we change the distances between objects in the universe but maintain the same angular separation between them, then both situations can be described with the same mathematical equations.
Let’s try to explain that a bit more clearly. Conformal invariance is just a way of saying that there are physical situations where different distances aren’t physically discernable from each other. In such situations, the distance between things doesn’t matter - the only thing that matters is the angles between them. For example, imagine taking a picture and changing the sizes of things but keeping the angles the same, meaning that things at right angles stay at right angles, things at 45-degree angles stay at 45-degree angles, and so on. As long as all the angles remain the same, there’s a type of identification of the infinitely big with the infinitely small. It’s hard to give a clearer picture in words.
The basic notion of conformal invariance is depicted in certain paintings by M.C. Escher, such as Circle Limit III. Check it out to get a better idea of what we’re talking about. A picture is worth a thousand words.
The bottom line is that Penrose works out a situation where, at least mathematically, it’s reasonable to treat the infinitely big and the infinitely small as identical to one another. He therefore proposes that, even without a contraction phase, the infinitely big end of one cycle can in some sense transition to the infinitely small beginning of the next cycle.
The Universe Loses Track of Time…
After establishing that the final state of one aeon can be treated as mathematically identical to the beginning of the next aeon, Penrose takes the next step and posits that at the end of every aeon, the universe restarts from the beginning. Hence, CCC posits an infinite series of aeons with the universe restarting in the same state each time.
You may be wondering: How exactly does the universe restart? Why doesn’t the universe just keep expanding? What makes it end and then restart?
The answer is that along with the identification between the infinitely big and infinitely small, CCC also posits that, in the universe’s far-distant future, time itself will lose all meaning and the universe will start over again from the beginning.
You may argue this is getting worse. Now, we need to explain what that means. Specifically, how does time lose all meaning?
We know it sounds nonsensical. To understand this abstract idea, it’s important to introduce how modern physics views the notion of time. According to the theory of relativity, there’s no reality to an abstract clock ticking away absolute time. Rather, for time to have any meaning at all, it must be measured by a physical system (appropriately called a physical clock).
This is one of the unintuitive points of Einstein’s theory of relativity. While it’s not necessary to understand why this is true, you need to know that if it’s impossible to measure time, then, according to modern physics, there’s no such thing as time. Of course, you don’t need to build an actual clock to measure time. Physicists use the term ‘clock’ for any regular measure of change, such as the sun’s daily motion, a vibrating atom, or even a heartbeat.
With this in mind, Penrose argues that in the far-distant future, for a reason we’ll explain shortly, it will be impossible for a clock to exist. If so, according to the theory of relativity, there will no longer be any meaning to the concept of time, and then one can suggest that the universe restarts from the beginning. In Cycles of Time (pg. 150), Penrose explains this point as follows:
Photons and gravitons are both massless, so it seems not unreasonable to adopt a philosophy, relevant to the very most distant future, that since, in a very late stage in the universe’s history it would in principle be impossible to build a clock out of such material, then the universe itself, in the remote future, would somehow ‘lose track of the scale of time’...
Let’s now explain why it will eventually become impossible to build a clock and what this has anything to do with photons and gravitons being massless.
There are two types of particles, particles like electrons that have mass (or, technically speaking, rest-mass), and particles like photons that are massless. A physical clock must have mass, which is another way of saying that it’s impossible to make a physical clock out of only massless particles. Therefore, in order for the future universe to lose track of time and thereby restart, Penrose speculates that in the far-distant future, all mass will disappear. He explains this as follows (on page 146):
To put this another way, it would appear that rest-mass is a necessary ingredient for the building of a clock, so if eventually there is little around that has any rest-mass, the capacity for making measurements of the passage of time would be lost (as is the capacity for making distance measurements, since distances also depend on time measurements).
Penrose is adding the crucial point that once you don’t have a clock to measure time, you also won’t have a ruler to measure space - so the disappearance of mass causes the universe to lose track of both time and space.
One more point: according to quantum mechanics, even the existence of a single particle with mass - what’s called a massive particle - can function to imbue time, and consequently space, with meaning. As Penrose explains (on page 93):
There is a clear sense in which any individual (stable) massive particle plays a role as a virtually perfect clock.
The bottom line is that if there were any mass in the far-distant future, you’d be able to use it to build a clock and then use that clock to make a ruler and measure distances. On the other hand, if all mass completely disappears in the distant future, then it begins to make some sense, at least to Penrose, that time loses all meaning and the really big universe starts again as a really small universe.
We know that the idea of the universe starting again sounds crazy - Penrose himself kind of acknowledges that. But for now, let’s just accept the supposition that if all mass disappears, then time and space would lose all meaning and everything would just start again in a new big bang.
Disappearance of Mass
Even if we accept that point, it only works if all mass disappears. However, current physics maintains that at least some particles in the far distant future of the universe will inevitably have mass. Those particles should function as physical clocks, thereby preventing the universe from losing track of time and restarting! So how can CCC just posit that all mass will eventually disappear?
Penrose attempts to overcome this major problem by suggesting that all massive particles will eventually turn into massless particles.
By the way, in case you’re wondering about the law of conservation of mass, it’s worth mentioning that there’s no fundamental law in physics that mass is conserved. Einstein’s famous equation, E=mc^2, says that mass is just one form of energy, and it’s really energy that’s conserved, not mass. So, on its own, the transformation of massive particles into massless particles doesn’t violate any law of physics.
Penrose suggests two ways a particle can lose its mass. Which of these two ways actually applies to a given particle in the far distant future will depend upon whether it has fallen into a black hole or is instead isolated from all other particles.
Let’s deal with these two scenarios one at a time. Let’s start with the easier case and explain how, according to CCC, particles in a black hole eventually lose their mass.
According to CCC, over a very long time, the universe will continue to expand, and its temperature will drop. As the background temperature of the universe drops below a black hole’s temperature, a well-accepted process known as Hawking radiation will cause all black holes to evaporate and disappear (via the radiation of photons which are particles of light). Through this process, all the mass originally contained in black holes will eventually be converted into massless photons.
That’s the first way. Let’s now deal with the second and more difficult scenario of isolated particles. Since the measured expansion of the universe is great enough to allow some particles to escape the gravitational attraction of black holes, there will necessarily remain isolated massive particles as well. Dealing with these particles is one of the more significant challenges CCC faces.
When dealing with these isolated massive particles, we have to consider two different cases: those with charge and those without charge. Uncharged massive particles can, at least in theory, decay into uncharged massless particles like photons. While this has never been observed, it could theoretically happen without violating any fundamental conservation principle. Again, there’s no fundamental law in physics that mass is conserved, only that energy and charge are conserved, and the transformation of an uncharged massive particle into an uncharged massless particle would conserve both energy and charge.
However, massive charged particles present an even bigger problem. They can’t just lose their mass and keep their charge because charged massless particles don’t exist. And, they can’t lose both their charge and their mass because of the fundamental principle of charge conservation. Therefore, particles with both mass and charge pose a really big problem for CCC.
To address this serious problem (page 154), Penrose explains:
The one remaining possibility that occurs to me, and which actually strikes me as something to be considered seriously, not merely the least of all evils, is that the notion of rest-mass is not the absolute constant that we imagine it to be. The idea is that over the reaches of eternity, the surviving massive particles…would find that their very rest-masses would very, very gradually fade away, attaining the values zero in the eventual limit. Again, there's absolutely no observational evidence, as of now, for such a violation of ordering notions concerning rest-mass, but in this case the theoretical backing of the conventional ideas is far less substantial than for charge conservation.
Let’s try to explain that simply. The big question is what to do about a charged massive particle, like an electron. It can’t just turn into an uncharged massless particle, like a photon, because that would violate the principle of charge conservation, and we know based on strong theoretical considerations that charge is always conserved. So the only remaining option is to say that an electron’s mass completely fades away while retaining its charge so that it naturally turns into a charged massless particle.
We’ll try to summarize the main idea in plain English. Penrose speculates that some unknown mechanism causes the mass of all isolated particles, both charged and uncharged, to slowly fade out over time. While there’s zero evidence for the claim that mass simply disappears, this plays a critical role in CCC because without it, mass would continue to exist forever and the universe would never lose track of time.
Of course, as far as physicists can measure, the masses of the fundamental particles are always constant. All observations and experiments done to date have shown that the masses have not changed at all since the time of the big bang. This is of course why the masses of the fundamental particles are called constants of nature! If Penrose’s conjecture is true, then the rate of the fade-out time must be very, very slow, such that 14 billion years is still not long enough for us to detect it. Of course, that’s a good thing for us because if it faded out too quickly, it would be impossible for galaxies, planets, and life to ever form.
Hawking Radiation and Entropy Transcendence
Let’s now revisit the second problem we mentioned earlier identifying the universe at the end of one cycle with the beginning of the next. The second law of thermodynamics states that the entropy of a closed system, which is a measure of its disorder, always increases with time. For example, if you randomly shuffle an ordered deck of cards, it will slowly become disordered.
Therefore, even if the big bang at the beginning of an aeon is in a low entropy state, the end should be in a higher entropy state. If so, the end of one aeon and the beginning of the next would appear to be completely different! Consequently, even if the universe did lose track of time and restart, it should restart in a higher and higher entropy state each and every time. If so, nothing would be gained in terms of explaining our universe’s low entropy initial conditions without an intelligent cause.
To answer this problem, Penrose claims that the process of black hole evaporation through Hawking radiation not only causes particles to lose their mass but also causes the overall entropy of the universe to decrease. In Fashion, Faith, and Fantasy (page 386), Penrose explains:
We see from this that, according to CCC, there is no violation of the second law - and a good deal of the behaviour of black holes and their evaporation may, indeed, be considered to be driven by the second law. However, because of the loss of degrees of freedom within a black hole, the second law is, in a sense, transcended. By the time all the black holes have completely evaporated away in an aeon (after some 10^100 years since its big bang), the entropy definition that would initially be employed as appropriate would have become inappropriate after that period of time, and a new definition, providing a far smaller entropy value, would have become relevant some while before the crossover into the next aeon.
This is a hard point. While we’ll get a bit technical shortly and discuss degrees of freedom and information loss, the main idea is as follows. Penrose argues that reducing the overall entropy of the universe through Hawking radiation doesn’t directly violate the second law of thermodynamics. Instead, through the process of black hole evaporation, entropy is reduced and the second law is somehow “transcended”.
Now to get a bit technical. Penrose’s claim is contingent on choosing one of two possible solutions to what is known as the black hole information paradox. The paradox, first propounded around 1975 by Stephen Hawking and Jacob Bekenstein, is based on an apparent contradiction between general relativity and quantum mechanics. According to general relativity, the physical information that was contained in the degrees of freedom of a particle should permanently disappear once it falls into a black hole, and the photons emitted through Hawking radiation should contain no information about the particles that fell into the hole. However, according to quantum mechanics, the photons that are emitted from the surface of a black hole through Hawking radiation should preserve the information of the original matter that comprises the black hole. To solve this paradox, one of the theories must be altered.
Penrose’s claim that entropy is reduced in the distant future only works if general relativity is correct and Hawking radiation destroys information. At first, Stephen Hawking accepted this conclusion and maintained that quantum mechanics needed to be altered. However, many quantum physicists argued with Hawking and maintained that quantum mechanics is correct and that information is conserved.
According to Leonard Susskind, one of the main physicists opposing Hawking’s original view, most physicists now believe that quantum mechanics is correct and that information is not destroyed but is rather encoded in the radiated photons, and therefore entropy is not reduced. In fact, in 2004 Hawking himself changed his position and paid out a bet he had made about the issue. However, Penrose believes that Hawking’s original position is correct - that information is destroyed and entropy is reduced.
The bottom line is that the idea that black hole evaporation reduces entropy, a conclusion that’s crucial for CCC, is contingent upon Penrose being correct and most other physicists being wrong about how to resolve the black hole information paradox. While this is a controversial issue, we’re in no position to adjudicate between Penrose and other physicists. We’re just mentioning this as one further issue that CCC must maintain, against the opinion of most physicists.
Evaluating Conformal Cyclic Cosmology
Now that we’re done presenting Penrose’s theory of Conformal Cyclic Cosmology, let’s tie this essay together and evaluate whether CCC can successfully explain our universe’s low entropy initial conditions without an intelligent cause. Before doing so, we want to reemphasize that CCC has nothing to say about the indication of an intelligent cause from fine tuning of the constants or the design of the laws. Like Steinardt’s Bouncing Cosmology, CCC only addresses our universe’s highly ordered initial conditions.
In assessing CCC, let’s first discuss its advantage over multiverse theories. Because it’s not a theory of infinite random chaos, CCC is capable of making a scientific prediction without introducing an ad hoc measure.
It predicts certain patterns in the cosmic background radiation of our universe that are influenced by the universe’s hypothesized prior cycle. There is currently much debate between Penrose and other physicists as to whether CCC’s predictions have been verified or not. As far as we can tell, almost no one besides Penrose thinks it has been. Nevertheless, we’re not in a position to decide this issue, and we leave it to the interested listener to investigate it further.
Let’s now review all the necessary claims that CCC must make in order to explain our universe’s low entropy initial conditions without an intelligent cause:
There’s a mathematical identity, based on conformal invariance, between the infinitely big end of one aeon and the infinitely small beginning of the next aeon. Penrose must maintain that this identity between the infinitely big and the infinitely small is more than just a mathematical trick but actually has physical significance.
The mass of both charged and uncharged isolated particles must slowly fade out and disappear in the universe’s far-distant future. Penrose himself admits, “there's absolutely no observational evidence” for this assumption.
In some unexplained way, when all mass in the infinitely big universe disappears and the universe loses track of time, it must somehow restart again with an infinitely small beginning. Needless to say, this isn’t an obvious point. At least to us, the far more intuitive conclusion to draw is that the end of time would just mark the end of the universe, as opposed to a seemingly magical restarting of a new cycle of time.
Penrose must be correct that black hole evaporation destroys information and that the second law of thermodynamics is transcended such that the entropy at the end of one cycle becomes as low as at the beginning of the next cycle. This proposed destruction of information is disputed by most other physicists.
Despite the fact that CCC isn't accepted by other physicists, Penrose is universally recognized as a genius even among top physicists. So while we’re unable to conclusively show that CCC is wrong, we hope that this essay has at least given you a sense of the highly imaginative type of theory that’s needed to explain away our highly ordered initial conditions without an intelligent cause.
All in all, while CCC is a valiant attempt to scientifically explain our universe’s low entropy initial conditions without an intelligent cause or a multiverse, it’s a highly imaginative theory that posits a tremendous amount with very little evidence. For this reason, we think that the incredibly unlikely initial conditions of the big bang remain a valid argument for an intelligent cause, as the far simpler, more straightforward, explanation for our universe’s initial state is that the same intelligent cause that fine tuned the constants and designed the laws of nature also arranged the proper initial state that would eventuate in our complex, structured, and ordered universe.
Before closing, let’s revisit Penrose’s quote that kicked off this essay. He said as follows:
In order to produce a universe resembling the one in which we live, the Creator would have to aim for an absurdly tiny volume of the phase space of possible universes – about 1/10^10^123 of the entire volume…
As we already mentioned, Penrose, like many other scientists, doesn’t believe in God and was speaking metaphorically. However, after hearing the extremely contrived and imaginative explanations for our universe’s highly ordered initial conditions, it seems clear that Penrose should have meant his statement literally. In order to produce a universe resembling the one in which we live, the Creator did aim for an absurdly tiny volume of the phase space of possible universes.
So you may be wondering, why isn’t Penrose convinced? Furthermore, after this entire series, you might also be wondering: How is it that so many really smart people believe in such wild and speculative theories like an infinite multiverse, Cosmological Natural Selection, or Bouncing Cosmology? Why won’t these brilliant scientists acknowledge that fine tuning, design, and order indicate an intelligent cause?
In our opinion, one of the main reasons all these scientists reject the idea of an intelligent cause of the universe is because they immediately identify the idea of an intelligent cause with the childish notion of god they were exposed to in their youth, and they therefore automatically reject it.
Of course, they also have numerous serious questions about God. What caused God? Who fine tuned the fine tuner? What does God even mean? And more.
That’s why even after our first two series, our argument is still incomplete. To be fully convincing, we must present a clear, logical, coherent, and intuitive idea about God that can answer all these questions. And that’s exactly what we’ll do in our next series.
But before moving to Series 3, we’ll conclude this series by summarizing Series 2’s argument against the multiverse and addressing assorted questions.
Comments