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How the Discovery of Fine Tuning Provides a Clue to Solve the Mystery of the Constants

In this episode, we explain fine tuning, the major clue that physicists have discovered to help solve the mystery of the constants. The idea of fine tuning is that the constants of nature are not just arbitrary numbers, but there's something special about their values. Only numbers within a certain range of values will yield a universe with atoms, molecules, planets, stars, galaxies, etc.



Aaron, why don't we do it a little differently this time? 


Sure. Elie. What do you mean?


Why don't I start the episode with something that is really simple. I'll show you how to get our listeners attention without sounding too technical or scary.


Okay. Fine, Elie. We'll see how it goes.


Don't worry about it. I got this. When discussing some special features of our universe, including the fundamental constants, - you know, those strange numbers we've been discussing - the famous physicist, Stephen Hawking said the following: 

Most of the fundamental constants in our theories appear fine tuned, in the sense that if they were altered by only modest amounts, the universe would be qualitatively different, and in many cases unsuitable for the development of life. The laws of nature form a system that is extremely fine tuned, and very little in physical law can be altered without destroying the possibility of the development of life as we know it.


That was pretty simple Elie. But we still have a lot of explaining to do. My name is Rabbi Aaron Zimmer. And, today we're going to talk about fine tuning, the all important clue which leads to the solution of the mystery of the constants.


And my name is Rabbi Dr. Elie Feder. And, today I will help explain, in simple terms, what exactly fine tuning is and why its discovery changed everything about how we look at the constants of nature. Welcome to Physics to God.

Discovery of Fine Tuning

Last time, we talked about the mystery of the constants, what Richard Feynman called one of the greatest mysteries in all of physics. If you recall, the laws of physics have certain fixed quantities called the constants of nature. Physicists, in their pursuit of a theory of everything, want to understand and explain these strange numbers. Are they fundamental? Or do they have a cause? Where do they come from and what explains their seemingly arbitrary values?


Today, we're going to explain fine tuning, the major clue physicists have discovered which opens the way to understanding these constants. If you recall, the mystery of the constants was that these numbers seem completely arbitrary and random with no seeming reason of why they have the values that they have. From the perspective of physics, these numbers could have been anything, they could have taken on any value from one to a million - and anything in between. 

The idea of fine tuning is to realize that these numbers are, in fact, special. They're not just arbitrary random numbers. But there's something special and very important about these numbers, the values that they have. And that is that they exist within a certain range. And it's only within a certain range of values that these constants of physics will yield a universe that has atoms and molecules, planets, stars, galaxies. 

So, from the framework of physics the values don't seem to matter. You end up with a universe, from the perspective of physics, if you change the numbers, that looks exactly the same - a bunch of fundamental particles bouncing around with just different quantities. But you couldn't really tell the difference - it looks exactly the same from the perspective of physics. But there would be no chemistry, because there'd be no atoms and molecules, there'd be no stars, there'd be no astronomy, you'd have no life, there'd be no biology if you change these constants out of a certain range. 

And that's what we mean by fine tuning, which we're going to discuss a lot in this episode, that there's a specific range of values, a fairly narrow range for most of these constants. And it's only because these values fall within this narrow range that we have a universe that has atoms and molecules, stars and planets, and life.


You can think of the constants as being controlled by little dials which set their values. So for every constant, you can imagine a dial which could be changed, and depending on where the dial is set, that will determine the value of the constant. Fine tuning showed that these dials have to be set to very specific values, or within a very small range of values, in order for the fundamental laws of physics to generate all the order and structure in our universe, in order to generate atoms and molecules and stars and planets and galaxies and life. And the fine tuning is a reference to the fact that these dials are all set perfectly, they're tuned finely to be able to bring about the outcome of the universe which we see.


Now, of course, there's no such thing as these little dials. Elie's just giving you an analogy to help you understand what it means. Really, we just have these numbers. And the idea of them being any different is a theoretical exercise that we can do once we have a knowledge of physics, to understand if these numbers were different, what would happen to the universe.


Of course, of course.


For some historical perspective on the discovery of fine tuning, it was first proposed in 1974 by Brandon Carter, when he argued that the particular values of many of the constants are fine tuned and special. The idea was much more thoroughly analyzed in Barrow and Tippler's landmark book, The Anthropic Cosmological Principle in 1986. However, it wasn't until 1998, when cosmologists measured the incredibly fine tuned value of the cosmological constant, which we'll discuss more as we go on, that this major breakthrough in our understanding of the constants became a widely known and accepted fact.


Because the details of fine tuning are very complicated, I convinced Aaron that I should give an analogy for fine tuning before he explained a few complicated examples of fine tuning in physics. The analogy goes back to our ethical system. 

In our ethical system, if you recall, we had a number of laws that we tried to unify by the principle, "Do unto your neighbor as you would want unto yourself." Some of the laws involved quantities. For example, we had a minimum requirement to give charity, perhaps a minimum of 18.4 or 5%. And our question was, what's the source, how do we explain this minimum requirement? Another one would be, for example, a maximum amount of interest that we would be allowed to charge? And again, the question is, how do we explain these numbers? 

Let us suppose that economists, through very rigorous studies, were able to observe a relationship between the specific values of these quantities and the resultant stability, productivity, peacefulness of the society which is governed by these ethical laws. For example, let's say they discovered, again through rigorous calculations, that if the charity requirement is too high, let's say the charity requirement was above 20%, then no one would work, productivity would suffer, people would feel if you're forcing me to give so much charity, then I might as well just not work, I might as well receive charity myself, and it would hinder the development of society. 

On the other hand, again, this is all hypothetical, but let's say these economists would study the charity requirement and determine that if it were too low, it for let's say, below 18%, then the poor people would starve. There would be class warfare, society would fall apart. The idea is that if economists were able to determine that this charity requirement had to be within the range of 18 to 20% in order to ensure that our society will be stable, productive, peaceful, that would be a discovery that the minimum requirements for charity are actually fine tuned, that that quantity is a number which corresponds or correlates to the resultant stability, productivity, peacefulness of the society that emerged from these laws. 

While this is an example of fine tuning in the area of economics of our ethical system, it's not really realistic to have such a discovery of fine tuning in the area of economics. The degree of rigor and precision and calculations are not really that advanced to be able to come to these numbers, that it has to be within 18 to 20%. We can't model the future of a society in such a rigorous way. 

However, when it comes to physics, physicists have the ability to model our universe very, very precisely, and to see what would happen if we change the values of these constants of nature. So Aaron's going to show you how physicists have realized that if the values of the constants were different, than our universe would be a very different place. 

And I want to give you a word of caution before Aaron gets started. The examples he's going to give, some of the details are very complicated. And perhaps some of you will have a hard time following the details, but not to worry. The idea is, keep your eye on the ball, keep the focus of what fine tuning is. If you want to think to the example of the society and the ethical system, that's okay. But I think it's valuable for those listeners who will be able to understand some of the details and each on his own level. Again, I just don't want you to get scared away by some of the difficulties or some of the details, but try to get an idea of the overall picture, and each person should be able to follow it on their own level.

The Fine Tuning of the Mass of the Electron


Okay, so let me start with the example of the masses of the particles. So there's many different ways you can show how the different fundamental particles, their masses have to be within specific ranges. We're just going to talk about one of them today, the mass of the electron, which we've been discussing, and we're going to speak about one specific direction of it. We don't want to confuse too much here. 

So there's two things to understand first, before we get into discussing the fine tuning of the mass of the electron. The first is how physicists think about atoms. An atom is made up of basically three particles: there is the electron, which is the outer part of the atom, and that orbits the nucleus of the atom which is made up of protons and neutrons. A proton has a positive electric charge, an electron has a negative electric charge, and a neutron is neutral, no electric charge. Okay, that's the basic picture of atom. It's gonna be helpful for this example and the next one, of an electron orbiting a nucleus which is made up of protons and neutrons. 

The second thing when we speak about masses of fundamental particles - the easiest way to think about them is relative to each other - how big is a proton or a neutron compared to an electron, and then we could speak purely in terms of numbers. And it comes out like this - that protons and neutrons are much heavier than electrons. Because electrons are so light, their mass, how much they weigh, is so small, and protons and neutrons are almost the same size as each other. When you speak about them, compared to an electron, every proton is 1836 times as big as electron. And every neutron is 1838 times as big as an electron, almost exactly the same as each other. And that difference between the two of them, that one proton is 1836, and the neutron is 1838 times as heavy as an electron, is really important. 

And the reason is like this, because particles can combine with each other and make other types of particles. And, in theory, because an electron has a negative charge and a proton has positive charge, they could combine. And if an electron and proton were to combine, they would make a neutral particle, and they can, in theory, make a neutron. And the only reason that that doesn't happen is because there's not enough energy, not enough mass - mass and energy are the same thing - between an electron and a proton combined, because an electron isn't big enough. 

And if an electron were a little bit bigger, it's really tiny, but if were two and a half times bigger than it is, an electron and a proton could combine to make a neutron. And if that happened, there would be no atoms anymore, you wouldn't have protons and neutrons surrounded by electrons, you would just have neutrons. And there wouldn't be atoms and molecules and everything else in the universe that comes from the combination of atoms. In their book, Barrow and Tippler described the disastrous situation that would result if this were the case, that electrons were a little bit bigger. And they said this: 

This would lead to a world in which stars and planets could not exist. These structures, if formed, would decay into neutrons by proton-electron annihilation (meaning, protons and electrons would combine and you end up with only neutrons). If that were to happen, no atoms would ever have formed, and we would not be here to know it.


That was nice and complicated, Aaron. Remember, we're trying to keep it simple. So basically Aaron is saying that if electron's mass were much bigger, or a little bit bigger, there wouldn't be stable atoms, stars, or planets. Let's move on to the next example. Try to keep it simpler. Please!

The Fine Tuning of the Fine Structure Constant


Okay. Okay, the next one is the fine structure constant, which we've mentioned the past two episodes. As we discussed, the value of the fine structure constant, which is one divided by 137 point something, is responsible for the strength of the electric force between charged particles like protons. So again, the nucleus of atoms is made up of a bunch of protons and neutrons. Now, if the fine structure constant were bigger, than the electrical force between protons - because all protons have positive charge - would be stronger. And the atom wouldn't be able to stick together, because the positive charges of the protons, they would repel each other too strongly, they wouldn't be able to stick together through the strong force - that's a different force we're not going to discuss, of the neutrons and protons which keeps them glued together - and the electrical force would rip them apart and the entire atom would fly apart, if the fine structure constant were a little bit bigger and the force between the protons were stronger. 

If that were the case, you wouldn't have any stable atoms again. And if no atoms, no molecules, planets, stars, all the different things that come along with not having stable atoms. Physicist, Leonard Susskind describes some of the many significant consequences that would occur if the fine structure constant had a different value:

What if the fine structure constant were bigger, say about one? This would create several disasters, one of which would endanger the nucleus. Why is the fine structure constant small? No one knows. But if it were bigger, there would be no one to ask the question. - The Cosmic Landscape, pg.175


That was better Aaron, but still pretty complicated. The bottom line is that if the fine structure constant had a value that was too far off of one out of 137, atoms wouldn't be stable because the protons at the core of an atom wouldn't be able to stay together. 

Just to emphasize, regarding both of these examples, if these values were different, there would be nothing wrong with fundamental physics itself, just the quantities would be different. The problem with different numbers is that they would prevent these fundamental particles from merging together to form any larger complex structures, like atoms, molecules, life, and so on. Aaron, let's move on to the last example.

The Fine Tuning of the Cosmological Constant


Okay, the last example is the cosmological constant, which is one of the most impressive examples of fine tuning. The cosmological constant is the constant that comes up in general relativity. All the other constants we've been discussing have really come from quantum mechanics. This is the one constant of general relativity, which governs space-time and the evolution of the entire universe. 

Now, the cosmological constant can be anything. Theoretically, there's no limits to whether it's a positive number, a negative number, big, small, or even zero. If the cosmological constant is positive, that causes the universe to expand. If you have a negative cosmological constant, it causes the universe to contract. 

Physicists realized, even before the cosmological constant was measured in 1998, just through theoretical considerations they knew that the cosmological constant could take on any value. But they knew that almost any value besides zero would lead to a universe incapable of producing galaxies, stars, or life. If the cosmological constant was not zero, but it was a positive number that was bigger than 10 to the minus 120 - 10 to the minus 120 is an incredibly small number. It's 0.000... 119 zeros, and let's say a 1. That's a really tiny number. So if it was a positive number, bigger than that, then the universe would be expanding too quickly and galaxies would never have been able to form. 

And likewise, if it was a negative number, but you know, a big negative number or even a tiny one, but not super tiny, where it's a negative number bigger than 10 to the minus 120, then the universe would have collapsed right in on itself in the very beginning. And again, you don't have any galaxies, because everything just collapses down to a black hole. 

So they knew that the cosmological constant couldn't be bigger than this tiny number 10 to the minus 120. But it's such a small number. They figured that it must be, it's exactly zero. And that was what we were discussing last time, the mystery of the constants. The mystery the constants is when you have these really strange numbers, how do you get these numbers? But they figured it must be the cosmological constant is exactly 0. Zero is a number that you can give a qualitative argument why it should be zero, and people tried to give different arguments why it should be zero. And that's something that, in theory, they tried to argue. They didn't know exactly why it was, but it was reasonable to speculate that you could come up with a qualitative reason why the cosmological constant was exactly zero. 

But in 1998, through measuring distance supernovae, cosmologists measured the cosmological constant to be about three times 10 to the minus 122. Again, that's a decimal point, followed by 121 zeros and then a three. If it only had 119 zeros, we wouldn't be here right now. The discovery of the incredibly small, yet nonzero value for the cosmological constant served as the major impetus for many scientists to take the clue of fine tuning seriously. 


To sum it up, if the cosmological constant was even a bit bigger or smaller than its observed value, the universe as we know it would either expand too fast for any galaxies to form, or collapse in on itself before any galaxies had a chance to form. 

Scientific Consensus on Fine Tuning

Now that we've seen a few examples of fine tuning, and we got the basic idea of what it is, we're done with the hard part. You might be wondering, how universal is the acceptance of fine tuning? Does everyone agree to it? Or is it a subject of debate between theistic and atheistic leaning physicists? Well, it's almost unanimous. Both atheists and theist physicists agree that fine tuning is real, and demands an explanation. 

In the opening of this episode, I read a quote from Stephen Hawking - who was an atheist - that discussed fine tuning. Let me read two more quotes from prominent physicists to give you a small sampling of the broad consensus about fine tuning, and also to bring out some subtle aspects of fine tuning. Here's a quote from Leonard Susskind, who's an atheist.

The laws of physics are almost always deadly. In a sense, the laws of nature are like East Coast weather - tremendously variable, almost always awful, but on rare occasions, perfectly lovely. Our own universe is an extraordinary place that appears to be fantastically well designed for our own existence. This specialness is not something that we can attribute to lucky accidents, which is far too unlikely. The apparent coincidences cry out for an explanation.


Let me try to explain Susskind's statement that luck can't explain something that's too unlikely. The reason is that these numbers, they're just too big. Assuming there's only one universe and you have one cosmological constant, the odds of getting something that small and precise, just by chance alone,  remember these numbers are ridiculously fine tuned, the cosmological constant is 10 to the minus 122, it's such a small number. When you have to figure out whether you can get something through luck, you have to balance the unlikelihood of that occurrence against the number of opportunities for that to happen. The odds of getting even one of these constants, not to mention all of the constants, by luck alone, to have them all be in the right range, it's simply not reasonable to attribute that to luck if there's only one universe.


Some of you might be skeptical about saying something is too much to be a coincidence. After all, we all know that coincidences do occur, things which are one in a million happen. After all, there are millions of things which happen. And often times things which appear to be something significant are, after all, just coincidences. So let me take an example and try to explain why it is that things which are one in a million do occur, and why that line of reasoning does not apply to fine tuning, not in this degree of fine tuning. 

Let's take an example. Imagine you go to New York City, and you're walking through Penn Station, and you happen to see your friend, Joe. And you say, "Whoa, Joe, that's an amazing coincidence that I happened to bump into you, what are the odds that I would see Joe this day in Penn Station? That’s gotta be one in a million!" 

If someone told me that, I personally would be skeptical, and I would think something like this: You happen to know many people, maybe hundreds or 1000 people just like Joe. And in Penn Station, there are thousands of people that you happen to come across. So while it's true, the odds of meeting the one Joe on a random place is one in a million, the amount of interactions you have, there are so many people that you know, and so many people in Penn Station, that it might even be more likely to meet someone that you know, then to meet nobody that you know. Meaning, nobody you know might even be a bigger coincidence. And again, it's one in a million to meet Joe. But there are so many different possible people you could have met, and so many people that you did see that it's actually kind of likely, and it's not much of a coincidence at all. 

However, if we change the example a little bit, assume you didn't know anybody except Joe, he was your only friend, your only acquaintance. And also assume you weren't walking in Penn Station, but you're walking in the middle of the Sahara Desert and you're just walking along in the Sahara Desert, and you bump into Joe, the one guy that you know. You say, "Wow, that's crazy!” Is luck, coincidence, a good explanation for that? I don't think so. The odds of that occurring has got to be one in a million million million. And that being the case, you certainly would say, "That's strange. Why do I and Joe happen to both be walking in the Sahara Desert at this time?" and you'd look for a better explanation. 

Even that is a very, very small coincidence, compared to the coincidence of all these numbers being fine tuned. We have to appreciate just how big these numbers are. But the cosmological constant, 10 to the 120th power, is a massive number. The amount of particles in our universe is estimated to be somewhere like 10 to the 85th power. This is an extra 35 zeros. This number, the odds are ridiculous. And that's what Susskind meant when he said this specialness is not something that we can attribute to lucky accidents, which is far too unlikely. The apparent coincidences cry out for an explanation.


One more point about the unlikelihood of these numbers is, if you realize that fine tuning is a type of knowledge about the relationship between these constants and the universe. The less physicists knew about these relationships, meaning the less physics knew before they discovered all of modern physics, the more arbitrary the numbers seemed. But as physicists gained tremendous amounts of knowledge over the past few decades, the more knowledge they gained, the more they came to realize just how fine tuned the constants are. It has become clear to everyone that luck is no longer a reasonable explanation. As knowledge increases about these constants and about the physical universe, the degree of fine tuning keeps increasing and increasing, because fine tuning is a type of knowledge.


While there are many quotes from the greatest scientists of our generation about fine tuning, let's see one last quote from astrophysicist, Luke Barnes, an expert on fine tuning. Barnes says as follows: 

There are a great many scientists, of varying religious persuasions, who accept that the universe is fine tuned for life. For example, Barrow, Carr, Carter, Davies, Dawkins, Deutsch, Ellis, Green, Guth, Harrison, Hawking, Linde, Paige, Penrose, Polkinghorne, Reese, Sandage, Smolin, Susskind, Tegmark, Tippler, Vilenkin, Weinberg, Wheeler, Wilczek. They differ, of course, on what conclusion we should draw from this fact.


That's an impressive list of scientists. Now there's one more final, important point we want to make. You may have noticed that all these quotes keep saying that fine tuning is necessary for life and intelligent observers. And while that's technically true, the evidence really shows something more basic than that. 

Fine tuning is necessary for all the complex things in our universe, which also happen to be the prerequisites for intelligent life. But there's nothing about fine tuning which specifically makes life special, above and beyond things like stars and atoms. The minimally true inference we are entitled to draw from the discovery of fine tuning is that the laws of nature are fine tuned to allow all the various components of the universe to exist, such as atoms, molecules, planets, stars, galaxies, life, and intelligent life. 

The reason that all the scientists focus on how fine tuning is necessary for intelligent observers is because they believe the correct conclusion to draw from fine tuning is that there exists a multiverse, which is an infinite number of unobservable universes where everything possible happens, including the hypothesis that each universe has a different value for every one of the constants. We'll discuss the multiverse in much greater depth in a separate mini-series dedicated exclusively to it. And when we do, you'll understand why multiverse theory must claim that the values are necessary for intelligent life in particular, not merely atoms, molecules, planets, stars, and so on. 

What we're showing here today is that everything in the universe, not just intelligent life, atoms, you wouldn't have any atoms, you wouldn't have any molecules, you wouldn't have any stars. Everything - all the different complex structures in the universe would be impossible, would not exist, if all these constants were not fine tuned.



An infinite number of universes where everything possible happens! While this might sound like science fiction to some, many of the top physicists in the world believe in it. Is the problem of fine tuning so serious that it justifies positing something as wild as that? 


It really is, Elie. Fine tuning is not a small problem. Next time, we're going to explain the underlying conceptual problem fine tuning presents to the current model of scientific thinking that forces scientists to posit something as revolutionary as the multiverse, which is such a massive paradigm shift in how they think about everything.


You know, I have to ask you, Aaron, what about God? 


Oh, come on, Elie. You can pretty much see how God is going to come in at this point, can't you? Either way, after we justify the need for a new paradigm to explain fine tuning, we'll develop the theory of an intelligent cause and argue that it's the most natural and intuitive conclusion to draw from fine tuning. All in due time. So stay tuned for more on Physics to God. I'm Rabbi Aaron Zimmer.


And I'm Rabbi Dr. Elie Feder, and this is Physics to God.

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