In this episode, we complete our final argument and convincingly show that the low entropy initial conditions at the big bang point directly to an intelligent cause for the order in our universe - what we’ll call an intelligent orderer. In doing so, we’ll encounter an amazing, mind-bogglingly gargantuan number. Once we explain how massive this number actually is, you’ll see how massively unlikely it is that our universe emerged by chance alone.
OPEN
Elie
Aaron, last time we kind of stopped in the middle of the argument. We showed how the universe must have had an improbable beginning, but because it was getting a little long and complicated, we never really clinched the argument by bringing it around to God.
Aaron
That’s true, Elie. Today we'll complete last episode’s argument and convincingly show that the low entropy initial conditions at the big bang point directly to an intelligent cause for the order in our universe - what we’ll call an intelligent orderer.
Elie
In doing so, we’ll encounter an amazing, mind-bogglingly gargantuan number. This number is so big that we’ll have to take a moment to simply explain how to think about it and to help you appreciate just how enormous this number actually is.
Aaron
And once you see how massive this number is, you’ll also see just how massively unlikely it is that our universe emerged by chance alone. I’m Rabbi Aaron Zimmer.
Elie
And I’m Rabbi Dr Elie Feder. Welcome to Physics to God!
Introduction
Aaron
Let’s quickly review the main line of reasoning from last time. We presented the apparent contradiction between the second law of thermodynamics and statistical reasoning. While statistical considerations imply that the most likely past state of the universe was less ordered and had higher entropy, nevertheless, the second law and all our observations tell us the universe was more ordered in the past and had lower entropy.
Elie
Scientists’ solution to this problem came from the realization that the apparent contradiction was based on the assumption that the universe had randomly determined initial conditions. This unsupported assumption caused statistical reasoning to contradict the second law.
To resolve this contradiction, scientists realized that the universe must have begun in a very ordered state with very low entropy. As a result of starting that way, all subsequent states end up having higher entropy based purely on statistical considerations. The fact that past states are always of lower entropy is in perfect accord with our observations, statistical reasoning, and the second law, as long as we add the fact that the universe began with very low entropy initial conditions.
Aaron
Of course, this solution raises new questions. Given the set of all theoretically possible initial states for our universe, how ordered were the initial conditions? Meaning to say, just how improbable would it have been to attain our extremely ordered initial conditions by chance alone? And finally, if chance isn’t a good explanation (spoiler alert: it isn’t), what is the reason for the low entropy initial conditions?
An Explanation of Phase Space
Elie
To help address these questions, we’ll introduce something called phase space. While this may sound complicated or unfamiliar at first, it will actually help us think about things more visually. And, it will help us understand the language that physicists use to describe this topic. Now, when Aaron describes it, it will definitely make things sound more complicated. But don’t worry. I’ll give an analogy to help you understand it.
Aaron
It’s not that bad, Elie. The best way to calculate just how unlikely the initial state of our universe was, is to consider all the different states in which the universe could ever potentially exist. To do this, scientists use the concept of “phase space”. Phase space is not an actual space somewhere, rather, it’s an abstract way of representing all possible states of a system.
Each point in phase space represents a different overall state of the system. Since every particle in a system has its own location and velocity, the exact state of a system can only be completely described by specifying every single particle’s location and velocity. For example, if we keep the universe exactly the same but move a specific particle ten meters to the left or increase its velocity by 10 m/s, we’ll get a different state of the universe than before. This new state will be represented by a different point in phase space.
Elie
Let me interrupt Aaron to provide an analogy that will help you understand what in the world he’s talking about. Imagine there are two students in a class who each take a test that is graded from 0 to 100. To keep track of both of their grades, you make a chart where the horizontal axis is numbered 1 to 100 and tells you one student’s grade and the vertical axis the other’s. This chart can be seen as the phase space for these students’ test results.
Each single point on this chart tells you two pieces of information about the results of the test: both of their grades. It turns out that there are 100 x 100 or 10,000 possible combinations of grades and therefore 10,000 possible points on the chart.
If one of the students is given a ten point bonus, then that will move us to a new point on the chart which is ten units away from the original point. This would be analogous to moving one particle ten meters to the right.
While it might not seem like we need a fancy chart to keep track of two students’ grades, if there were trillions of students, the chart would be a simple way of representing the information about all their grades in one single point. Of course, this would demand a multi-dimensional chart which is obviously more complicated and impossible to visualize. For the sake of the analogy, however, we’ll only use two students. This will allow us to think about a chart with a two dimensional area instead of a higher dimensional volume, but it’s all the same idea.
Aaron
To help classify various states, we can group together different points in phase space based on their common emergent properties. One example of this would be to group together all the different states of the universe that contain stars. Based upon such groupings, if a certain emergent property has only a few arrangements that bring it about, then it would occupy a small volume of phase space. If, on the other hand, there are many ways of bringing about that emergent property, then it would occupy a large volume of phase space.
If you remember from last episode, the entropy of a system measures how many different arrangements produce a particular emergent property. Applying that idea to phase space, the entropy measures the volume of phase space occupied by states having a particular emergent property. (For those who want to be technical, the entropy is proportional to the logarithm of the volume of phase space.) By calculating the volumes of phase space for states with different emergent properties, we can compute the probability of systems being in various states.
Elie
Going back to our analogy, we can group together all points which represent both students failing or getting under 65. This can be represented by the set of all points in the lower left hand region of our chart. There are actually 65 x 65 or 4,225 such points in this region. Similarly, we can group together all points representing both students getting above 90. This can be represented by the set of all points in the upper right hand corner of our chart. There are actually 10 x 10 or 100 such points in this region.
For whatever grouping we choose, we can calculate the size of the region it occupies. By comparing the area of each respective region to the area of the chart as a whole, we can compute the probability of both students failing, or both getting above 90. This is analogous to the way that the volume of phase space is used to compute probabilities of different emergent properties of a system.
Aaron
Now, let’s apply these ideas to the universe as a whole. To calculate the probability of the universe starting off the way it did at the big bang, we need to calculate the entropy of its initial state. To do that, all we need to do is consider the volume of phase space it occupies and compare it to the total volume of phase space.
Elie
Going back to the analogy, let’s imagine you were to randomly throw a dart at our chart. The probability of the dart hitting any region is dependent on the size of that region. It’s more likely that the randomly thrown dart would hit a big region which corresponds to a high entropy state (like them both failing), and it’s less likely that it would hit a small region which corresponds to a low entropy state (like them both getting above 90).
Likewise, to measure the likelihood of our initial conditions coming about by pure chance, we must compute the probability of a randomly thrown dart hitting the region of the chart corresponding to our universe’s initial conditions.
I know this might have sounded complicated, even with the analogy, but it’s going to get clearer as we go along. Let’s now get some idea how phase space helps us determine just how unlikely our initial conditions were.
The Creator's Challenge in Ordering the Initial Condition of the Universe
Aaron
The well-accepted, rather ingenious, method for calculating the entropy of the initial conditions was first pioneered by physicist Roger Penrose. In his 1989 book,The Emperor’s New Mind, Penrose explained the problem and how trying to solve it led to analyzing the entropy of black holes.
Elie
I just want to mention one point before reading the quotes in which Penrose uses the term ‘Creator’. We don’t mean to give the impression that he agrees with us that an intelligent Creator is the cause of the order in our universe. While the special initial conditions naturally invite describing them in terms of a Creator, it seems that Penrose himself is speaking metaphorically. As we’ll mention shortly, he proposes a different possible explanation for the low entropy initial conditions.
Aaron
Here’s Penrose describing his process of calculating the entropy of the initial conditions:
Try to imagine the phase space of the entire universe! Each point in this phase space represents a different possible way that the universe might have started off. We are to picture the Creator, armed with a ‘pin’ -- which is to be placed at some point in the phase space. Each different positioning of the pin provides a different universe. Now the accuracy that is needed for the Creator's aim depends upon the entropy of the universe that is thereby created. It would be relatively ‘easy’ to produce a high entropy universe, since then there would be a large volume of the phase space available for the pin to hit… But in order to start off the universe in a state of low entropy - so that there will indeed be a second law of thermodynamics - the Creator must aim for a much tinier volume of the phase space. How tiny would this region be, in order that a universe closely resembling the one in which we actually live would be the result? In order to answer this question, we must first turn to a very remarkable formula, due to Jacob Bekenstein (1972) and Stephen Hawking (1975), which tells us what the entropy of a black hole must be.
Elie
That sounded really interesting, Aaron, until he got to the black hole part. Then it started getting complicated. Do we really need to get involved in that?
Aaron
We can’t skip black holes entirely, Elie. Part of Penrose’s genius was to discover the best method for rigorously calculating the entropy of the initial state of our universe. He did this by building on the discoveries of Bekenstein and Hawking in the 1970’s which showed that of all possible physical systems, black holes have, far and away, the highest entropy. Knowing this, we can figure out what the maximum entropy state of the universe could potentially have been, and compare it to what the initial conditions actually were.
Elie
I understand, Aaron, but we’re trying to keep things simple. Therefore, as fascinating as they are, we don’t need to go into what black holes are or how scientists calculate their entropy. All we need to know is that nothing has higher entropy than a black hole, and therefore it’s the most likely arrangement for our universe.
Aaron
Fair enough, Elie. Penrose calculated the maximum total entropy that the universe would have if it were all black holes. He then showed how that number absolutely dwarfs the entropy of any other possible state of the universe, thereby arriving at the probability that our universe started off in a low entropy state. He concluded 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, in the ordinary denary notation: it would be ‘1’ followed by 10^123 successive ‘0’s! Even if we were to write a ‘0’ on each separate proton and on each separate neutron in the entire universe -- and we could throw in all the other particles as well for good measure -- we would fall far short of writing down the figure needed. The precision needed to set the universe on its course is seen to be in no way inferior to all that extraordinary precision that we have already become accustomed to in the superb dynamical equations (Newton's, Maxwell's, Einstein’s) which govern the behavior of things from moment to moment.
Elie
Penrose’s calculations rigorously demonstrate just how extremely ordered the initial state of the universe had to be for our universe to naturally emerge by chance alone. This initial arrangement was highly specialized, in the sense that any significant variation in the initial conditions would have resulted in a disordered universe (filled with black holes) instead of the ordered universe that we witness today.
If the universe did not start off in this special, highly unlikely state, then even if we had all the same qualitative laws of physics and all the same fine tuned constants of nature, we would never get a beautiful, ordered, and complex universe. The probability of obtaining such a state by random chance is staggeringly low.
Just how big is Penrose's Number?
Aaron
Let’s digress for a moment to convey the enormity of Penrose’s number - that is 10^10^123. It’s not like it sounds. It sounds like the very large number 10 to the 123rd power - that’s 1 with 123 zeros. A very big number in its own right. But it’s not that. It’s much much much larger than that. It’s 10 to the power of 10^123. This is what’s called a double exponent. To appreciate this number, we have to get some sense of the power of double exponents.
Elie
We’ll do this by comparing them to single exponents. We all know that 10 to the second power is 10 x 10 which is 100. Now let’s consider the double exponent 10^10^2nd power - this is so much bigger than 100 - it’s 10 to the 100 power, that's a 1 followed by 100 zeros. That’s more than a trillion trillion trillion trillion trillion trillion trillion trillion. That’s much bigger than 10^2nd or 100. And that’s only 10^10^2nd. Now consider 10^10^3rd. Well, 10^3rd is only 10x10x10 which is 1000, but 10^10^3rd power is 10 to the thousandth power - that’s a 1 followed by 1000 zeros. That’s trillion trillion trillion….83 trillions. That’s already a bigger number than all the numbers we’ve encountered in the fine tuning literature. And we’re just getting started.
Jumping up a bit, 10^6th power is a million. But 10^10^6 would be 1 followed by a million zeros - that’s a trillion trillion trillion…It would take you about a full day - 24 hours - of saying trillion to get to this number. Once you get to 10^10^30, you’ll have to say trillion from the beginning of the universe until now to get that big. And that’s still nowhere close to Penrose’s number of 10^10^123 - the amount of zeros on that number is 10^123. For number enthusiasts, this number puts googolplex to shame. And Penrose computed that the probability of getting our initial conditions by chance alone is 1 out of that crazy number.
Intelligent Orderer
Aaron
Since the state of maximum entropy is by definition the most probable state for a system to be in, if the universe’s initial state was randomly determined, we would predict that it would be in its most probable state. But it isn’t! It’s nowhere close to its most probable state! Why not? It can’t be chance! Based on Penrose’s calculation, we see that it’s untenable to maintain that such an improbably ordered arrangement randomly occurred in just the right way to naturally unfold into our complex universe - that would be a crazy 1 out of 10^10^123 coincidence.
Elie
So, let’s return to our question: If the initial conditions weren’t set randomly, what did cause them? Why did our universe begin in a state of such extraordinarily low entropy?
Aaron
Well, let’s notice that the low entropy initial conditions of our universe are responsible for our complex, ordered, structured universe which is full of atoms, molecules, planets, stars, galaxies and life. If the universe would have instead started with the most likely, high entropy initial conditions, then we would simply have a universe of black holes.
It’s not that black holes aren’t interesting - they’re truly fascinating and wondrous objects, but it’s just much more interesting to have a complex universe with atoms, molecules, planets, stars, galaxies, life, and black holes, as opposed only black holes. It’s much more interesting to have a universe full of wisdom and science where in addition to just physics there is chemistry, biology, astronomy, without even mentioning the humanities. As such, we can see that the initial conditions are not just some random arbitrary state. Rather, they are the special conditions that are capable of ultimately developing into our amazing complex universe.
Elie
Now, since the very definition of intelligence is the ability to choose one meaningful possibility from the set of all possibilities for the purpose of getting a whole which is greater than the sum of its parts, we can infer that the special ordering of the initial conditions points directly to an intelligent cause of our universe. In other words, we can infer that an intelligent orderer - God - selected the low entropy initial conditions at the big bang for the purpose of bringing about our complex ordered universe.
Aaron
In the same manner as we argued that the fine tuning of the constants and the design of the qualitative laws of nature each independently point to an intelligent agent, we now see that the low entropy initial conditions of our universe provide a third independent line of evidence that our universe has an intelligent cause.
How Multiverse Solves the Low Entropy Initial Conditions
Elie
Now let’s briefly discuss scientists’ alternative explanations for the low entropy initial conditions which don’t involve an intelligent cause. First up is of course the most popular explanation - the multiverse. Multiverse scientists say that if there are an infinite number of universes, each with randomly set initial conditions, then by chance alone there will be a universe with incredibly unlikely, low entropy initial conditions. And since it’s only possible to have intelligent observers in that lucky universe, it’s no surprise that we find our universe with such low entropy initial conditions. We’ll discuss the validity of this approach and the significant challenges it encounters in more depth in the miniseries on the multiverse.
Aaron
There are two other, highly speculative scientific approaches, which are not multiverse theories, yet try to solve this problem without an intelligent agent. One is Conformal Cyclic Cosmology by Roger Penrose, who speculates that in trillions and trillions of years in the future, all the mass in the universe will fade away and the universe will, in his words, “lose track of time.” Once it does that, he speculates that the universe will start again with a new big bang in a low entropy state because the entropy that comes from gravity will be eliminated in the great reset. This process cycles infinitely from one aeon to the next and is suggested by Penrose to be the cause of our universe with its low entropy initial conditions. There’s a lot more to this theory and we’ll discuss it in the multiverse miniseries.
Elie
Don’t worry if you don’t understand this theory or the next one, right now. For the sake of intellectual honesty, we’re just giving a brief overview of the competing explanations even though we won’t discuss them in depth just yet.
Aaron
Lastly, another theory called Bouncing Cosmology by physicist Paul Steinhardt speculates that every trillion or so years, there’s a collision of two string theory membranes that exist in higher dimensions of space - extra spatial dimensions that are too tiny to be observed. When the membranes collide they bounce, causing a big bang and a new beginning. This cycle of collisions and bounces repeats infinitely. According to his theory, while entropy always increases, the entropy density remains low, thereby explaining our low entropy initial conditions. We’ll discuss this theory too in the multiverse miniseries.
Why the Proof of God from the Initial Conditions Does Not Fall Prey to the Same Issues as God of the Gaps
Elie
Let’s now discuss why the argument from the low entropy initial conditions doesn't fall prey to each of the three characteristic problems of “God of the gaps” reasoning. We’ll address these three problems one at a time, just like we did regarding the fine tuning argument.
Aaron
Remember, God of the Gaps reasoning is a line of thinking that’s employed to plug a hole in our current understanding of the universe by always just saying "God did it".
Elie
The first problem with a God of the Gaps argument is that it doesn’t emerge from any direct inference to God but only from a lack of knowledge. This type of fallacious argument is merely an argument from ignorance. When a reasonable person is ignorant and has a gap in their knowledge, they don't just posit God but simply admit that they don’t know. They wisely acknowledge that when they gain more knowledge, maybe they'll be able to pursue a deeper understanding of the phenomenon at hand.
Aaron
However, our argument isn’t based on ignorance. We’re not just saying “since no one knows what determined the initial conditions of the universe, it must have been God”.
Rather, everything we’re saying is based on scientific knowledge and proper philosophical reasoning. First, there’s the scientific knowledge of the second law of thermodynamics that necessitates low entropy initial conditions at the beginning of the universe. Then, based on knowledge of black hole entropy, Penrose rigorously calculated that it would be ridiculously improbable to get our initial conditions by chance alone. It’s also scientifically known that the incredibly low entropy beginning was necessary for our universe to contain atoms, molecules, planets, stars, galaxies, and life as opposed to being only black holes.
Therefore, we inferred that an intelligent cause selected the initial conditions for the purpose of bringing about our complex universe. This entire argument is based upon scientific knowledge and proper philosophical inferences, and is clearly not a God-of-the-gaps argument from ignorance.
Elie
The second problem with God of the Gaps reasoning is that a particular gap within the details of a robust scientific theory is likely due to our insufficient knowledge, and is no indication of the failure of science or the hand of God. Positing divine intervention to fill such gaps in our knowledge is poor methodology, and hinders the advancement of science. It’s far more reasonable to say that the overall theory is sound and that we’re only lacking knowledge of certain details - the gaps.
Aaron
It’s clear that this problem also doesn’t apply here. The second law of thermodynamics, entropy, and the initial conditions of the universe are not mere gaps or details, but are fundamental elements of the universe and physics. As physicist Arthur Eddington said with regard to the second law and entropy: “The law that entropy always increases holds, I think, the supreme position among the laws of Nature.”
Likewise, the issue of explaining the initial conditions at the big bang is not a mere detail; it is an essential issue which goes to the core of physics and the very foundations of the universe. The resolution of these fundamental issues, not mere gaps in knowledge, point directly to an intelligent cause.
Elie
The third problem is that any "theory of the gaps" posits something - whether it is God, luck, or anything else - as a solution to every gap in knowledge. However, any answer that can be used to explain anything at all, in truth explains nothing at all, because no matter what the universe would look like, that could be called an “explanation”. But that’s not really explaining anything!
Aaron
Once again, we can see that this problem doesn’t apply. This is because the theory that an intelligent cause selected the initial conditions of the universe for a purpose only explains a universe with tremendous order, not a purposeless universe of randomness and disorder. For example, if the universe was exclusively filled with black holes, but no atoms, molecules, planets, stars, galaxies or life, it would be unreasonable to say that an intelligent agent chose the initial conditions for a purpose. Random luck would be a much better explanation in that case. We can see from this point that the theory of an intelligent cause does not explain every possible universe. In fact, we would only be justified in inferring an intelligent cause from a tiny miniscule fraction of all possible universes.
Elie
Putting it all together, we see that this argument isn't subject to any of the three flaws of God of the gaps reasoning.
OUTRO
Aaron
Elie, we’ve finally finished the three independent arguments for an intelligent cause. In the next episode, which will be the final one of this miniseries, we’re going to summarize and clarify our three arguments. We’ll also tie up any loose ends we still have from this miniseries, as well as discuss what still needs to be done.
Elie
Wait a second Aaron. Before moving on, I’d like to raise a problem that may be bothering some of our listeners. We’ve presented three arguments from three distinct features of modern physics which each independently indicate that our universe resulted from an intelligent cause. We even saw Penrose analogize the selection of our amazingly improbable initial conditions to a Creator placing a pin into a small region of phase space.
Nevertheless, Penrose and most physicists don't agree with us and don’t see any of these arguments as compelling evidence for an intelligent cause of our universe. Granted that we aren’t arguing with scientists on the science, but only on the philosophical conclusion to draw from the agreed-upon science. Nevertheless, someone may be wondering why are we drawing a different conclusion from so many great scientists? In other words, if the arguments are really as clear as we’re making them sound, then why don’t all scientists agree with our conclusion?
Aaron
That’s a great question, Elie. We’ll address that question too in the next and final episode of this series. We’ll indicate why scientists reach a different conclusion than us, and thereby justify the need for the two remaining miniseries - one on multiverse and the other on God. So stay tuned. I’m Rabbi Aaron Zimmer.
Elie
And I’m Rabbi Dr. Elie Feder, and this is Physics to God!
