Pod Insights Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas 331 | Solo: Fine-Tuning, God, and the Multiverse About this episode Certain features of our universe seem unnatural to us. These include "constants of nature" such as the cosmological constant and the mass of the Higgs boson, as well as features of the initial conditions like the curvature of space and the initial entropy. But they can't truly be "unnatural" -- they are literally features of Nature itself. Some have turned to the anthropic principle and the multiverse, while others look to theism for an explanation. I talk here about my views on the various attitudes one might take toward these apparent fine-tunings, and why it is important to think about them.
Blog post with transcript: https://www.preposterousuniverse.com/podcast/2025/10/06/331-solo-fine-tuning-god-and-the-multiverse/
Support Mindscape on Patreon https://www.patreon.com/seanmcarroll.
Some readings of relevance:
Livio and Rees, Fine-Tuning, Complexity, and Life in the Multiverse https://arxiv.org/pdf/1801.06944 Carroll, In What Sense Is the Early Universe Fine-Tuned? https://arxiv.org/abs/1406.3057 Barnes, A Reasonable Little Question: A Formulation of the Fine-Tuning Argument https://quod.lib.umich.edu/e/ergo/12405314.0006.042/--reasonable-little-question-a-formulation-of-the-fine-tuning?rgn=main;view=fulltext Goff, Our Improbable Existence Is No Evidence for a Multiverse https://www.scientificamerican.com/article/our-improbable-existence-is-no-evidence-for-a-multiverse/ Neal, Puzzles of Anthropic Reasoning Resolved Using Full Non-indexical Conditioning https://arxiv.org/abs/math/0608592
Transcript 21,071 words · 16 speakers
Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.
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0:56 Sean Carroll? Hello, everyone. Welcome to the Mindscape Podcast. I'm your host, Sean Carroll. Those of you who've been around here for a while know that here at Johns Hopkins, I'm teaching this semester two different courses. Both are a lot of fun in very different ways. One is quantum mechanics, the standard quantum mechanics course for all physics undergraduates. And the other is one called Philosophy of Cosmology. That's an upper-level lecture course in the philosophy department, obviously, and it's for a general audience. So there's some philosophy majors there, but there's a whole bunch of different people. So a wide variety of levels of expertise are there. The quantum mechanics course is fairly standard.
1:38 Sean Carroll? Like I said, I'm actually doing threads on Blue Sky where I try. I think I've been successful so far. Every day after the lecture, I give a couple of little sentences about what was in that lecture. And if you follow the thread on the quantum mechanics course, you'll get a feeling for how very, very different quantum mechanics is for the working physicist than it is for the popular discussions of quantum mechanics. I love the popular discussions of quantum mechanics. I'm part of them myself, but they rarely involve how to deal with operators that have degenerate eigenvalues and therefore their eigenvectors do not form a unique basis. Oh, my goodness, what do you do with that? No one ever talks about that in the popular level books.
2:23 Sean Carroll? So you learn a little bit about that in the thread where I cover everything I'm doing. The other course, the Philosophy of Cosmology course, though, that's almost me talking for myself in some sense. I think that the topics we're covering, we're focusing on three big questions. One is the multiverse and the anthropic principle. One is entropy and the arrow of time. And the other one is the foundations of quantum mechanics, especially the many worlds approach to it. These can be interesting to just about anyone, you know, these big topics. But they're also questions with very big unanswered issues floating around, issues that I'm interested in myself from a research level. And therefore, you know, I get to think through how I think about these things,
3:08 Sean Carroll? often with questions that I don't have strong opinions about what the answers are. I'm trying to learn, sharing that lack of complete confidence with the class. Maybe they could help me out. Maybe I can learn something from them. That's always possible. And in particular, there's one issue that it occurred to me would make for a good solo podcast. Actually, there's a whole bunch. I could, you know, do a series of solo podcasts, basically covering the whole Philosophy of Cosmology class. But, you know, I like to hear other people also. So I thought I would talk about this one. It's an old chestnut. It is by no means as a topic new and fascinating, nor have there been any recent breakthroughs in it. But in many of these Philosophy of Cosmology questions,
3:50 Sean Carroll? I'm just not that impressed with the level of conventional discourse about these hard questions. The questions are hard. Quantum mechanics, I think, is the one area where people really, really thought hard about it. I disagree with a lot of things that people say. But it's certainly a high level of discussion. Entropy and the arrow of time, there are levels of discussion that are very high, but it's not absolutely universal. But the multiverse anthropic thing is a place where there's a whole bunch of things, both on the philosophy side and on the physics side, the cosmology side, if you like, where I think we could just do better. It's not just that I disagree.
4:33 Sean Carroll? I'm like, come on, you gotta think harder about this stuff. In particular, this issue of fine tuning, that is what I want to talk about today. Fine tuning is roughly speaking, when you look at the world and you characterize the world in the form of some numbers, right? Some physical parameters for constants of nature, but also some numbers that specify the initial conditions of the universe. And you notice, if something is fine tuned, one way or the other, it's surprising. It's not what you would have expected. And therefore, you wonder whether or not there's some deeper reason why this number, this constant of nature, this feature of the initial conditions, is what it is. Now, just by putting it that way, you can tell, this is a little fuzzy, right? This is a little vague.
5:18 Sean Carroll? Like, what do you mean? Unexpected, surprising. Who gave you what the expectations were? And that's what things we're going to have to talk about. But it's a substantive conversation, and for better or for worse, two of the leading ways of thinking about fine tuning are either, like we said, the multiverse and the anthropic principle, or the existence of God. The argument from design, the idea that the parameters are what they are because some higher being made them that way. And, you know, I actually don't have strong opinions about what is the right explanation for fine tuning. I do have a strong opinion that it's not the existence of God, but well, we can talk about that, but there are serious discussions of it.
5:59 Sean Carroll? I think that the idea that God is the answer for the fine tunings we observe in the universe is 100% a respectable idea to think about, and we should think about it. I personally come to the conclusion that it's not a very good answer, but we have to establish that. We shouldn't dismiss it out of hand. My point, though, is that on both the side of the multiverse and the side of theism or the existence of God, there's many people who kind of get emotional. They kind of lose their ability to sort of think dispassionately about these very, very difficult issues, and they get insulted very quickly if you don't agree with them, or they disparage the intelligence or the good faith of the people who are disagreeing with
6:42 Sean Carroll? them, which is a trap I don't want to fall into. So I want to think- About these things, and I'm not going to be giving you the final answers. I think it's important to think through all of these things carefully and, you know, include the possible existence of God as a scientific hypothesis that we can think about, to include the multiverse as a scientific hypothesis we can think about, to include other possible explanations. Again, dispassionately, fairly thinking them all through. That's what we're going to try to do in this little kind of easy and fun solo podcast. I'll say just before we start in that you are always encouraged to support the Mindscape
7:23 Sean Carroll? podcast on Patreon. You can go to patreon.com/shawnmcarroll and toss in a dollar or whatever for every episode of Mindscape. We have plenty of Patreon supporters, so it's very, very much appreciated that we're getting the support that we are. I will say, though, the whole podcast landscape is changing kind of wildly now with AI and with people trying to sell their series and be sponsored and be created by big companies rather than individuals. So it's good that there is Patreon. Let's put it that way. I'm very, very happy that I get the support from Patreon. It is very important to the continued success
8:05 Sean Carroll? of Mindscape. But I just also, it gives me a warm feeling to think that so many people appreciate it that much. And we have a nice little community, and I try to give back to the supporters some little goodies in return. And with that thought, let's go.
8:35 Sean Carroll? We might as well start right there at the beginning with the question of what is fine tuning supposed to be? We already alluded in the intro to the fact that it's kind of a fuzzy notion. And in fact, if you get on the internet and Google around and whatever and look for different definitions of it, the definitions will not be the same. And Some of that is just because people are trying to be careful and they're careful in different ways. Some of it is because they truly do mean different things by fine tuning. And there's many things they mean. Let's focus on two of them. One is the idea that the parameters, the numbers, the physical quantities that go into describing our universe. So typically, the laws of physics numbers, right?
9:20 Sean Carroll? The strength of a given force of nature, or the mass of a certain particle, or when you get into the weeds, something like the expectation value of the Higgs field in empty space, right? These are all numbers. And there's some math you have to do, but it's not very hard math. And you realize that you could easily have imagined these numbers being very different. In other words, in the space of all possible worlds that are somehow physically reasonable, whatever that means, the numbers that you're seeing are located within a very, very narrow band, typically near zero. In other words, the simplest version of fine tuning is just that some parameter of physics
10:05 Sean Carroll? is unnaturally small. It could have been, in some units that you'll have to specify somehow, it could have been one, and it's 10 to the minus 20, or 10 to the minus 100, or something like that. And that's what fine tuning is, a lot to a lot of physicists in particular. Sometimes, that's phrased as saying that fine tuning is a matter of sensitivity. In other words, if you changed the parameters substantially, the results would be very different. What do you mean by the results? You mean, well, the higher level emergent phenomena that you would get. You know, if you change the mass of the electron, chemistry would be very different, things like that. But I don't think it's really just sensitivity, because it's sort of sensitivity plus unnaturalness.
10:49 Sean Carroll? Like, not only, I think that the usual emphasis of fine tuning is not only that the numbers that you're looking at are ones whose values have important effects on higher level emergent phenomena, it's that, and, they actually, in the real world, are in this narrow window that is special somehow, that allows something to happen. It's the unnaturalness of the value. Plus, the sensitivity of different sort of large-scale phenomena to the value that makes something fine-tuned. But unnaturalness itself raises some questions. Like, after all, it's the universe. It is nature.
11:32 Sean Carroll? Nature, by definition, can't be unnatural. When we say that a parameter of nature appears unnatural to us, and I'm going to give some examples soon enough to put some meat on these bones. But when we say that a parameter appears unnatural, that's a statement at least as much about us as it is about the universe, right? It appears unnatural to us. And that's okay. That's perfectly okay. And we're going to discuss the extent to which this is a problem at all. Like, one attitude towards fine-tuning is this is a you problem, not the universe's problem. This is because you have the wrong conception of what is natural and unnatural for the universe to be in. But that doesn't mean you should go inventing wildly new theories of the universe.
12:15 Sean Carroll? Maybe you just need to accept that the numbers are what they are. That's possible. But there's another sense of the phrase "fine-tuning" that is sometimes what people mean. And it's very similar to just the simple unnaturalness idea. So I wanted to highlight it just because some people come into the conversation with this in mind, which is the idea that not only are parameters unnatural in some way, but they're unnatural in just the right way to allow life to exist. In other words, there's parameters of nature where if the numbers were very different, then chemistry would be impossible, biology would be impossible, life would be impossible. Clearly, in our universe, those things are possible.
12:59 Sean Carroll? So this aspect of fine-tuning is not just that the numbers are small in some unknown probability distribution. It's they're exactly what they need to be for a certain reason, which is very special, namely, the existence of life. Clearly, the ones who want to point in the direction of either an anthropic explanation or a theistic explanation are going to emphasize these aspects. Aspects, because these are going to be, as we'll discuss, those kinds of mechanisms, either an anthropic principle explanation or a theistic explanation, point at making the parameters what they need to be to allow for the existence of life, and that all fits together very well. But I'm just letting you know that physicists don't always even care about that.
13:44 Sean Carroll? You know, as long as some number is way smaller than we might have naturally expected it to be, whether or not it has anything to do with the existence of life, we might still call it fine tuned, okay? Anyway, that sounds maybe a little vague, so I do want to put some meat on the bones by giving you examples. And the examples are intentionally a wildly diverse lot, okay? There's some examples of fine tuning out there in physics and cosmology that are kind of crowd favorites. They're always trotted out, and you might have heard them before. There's others examples that are very true puzzles, but are less likely that you've heard them. There are some examples where we know the answer, so we don't usually count it as a fine tuning.
14:28 Sean Carroll? But by the criteria of, oh, there was a small number in the dimensionless quantities of physics, then yeah, it really should count. And I emphasize the word dimensionless here. What does that mean? When we have quantities in physics, like the mass of the electron, we measure it in some units, right? We measure mass in units of kilograms or something like that. Typically, particle physicists have this habit where we use what we call natural units. That's where we set Planck's constant h bar equal to 1, and also the speed of light c equal to 1. In general relativity land, sometimes people set Newton's constant equal to 1, but particle physicists don't do that, and I'm not going to do that either.
15:12 Sean Carroll? So if you set h bar and c equal to 1, well, just setting c equal to 1 all by itself means that energy and mass have the same units, right? Because E equals mc squared. So in a world where c equals 1, the speed of light is set in units to be equal to 1, E equals m. E and m are the same kind of thing. They use the same units, and therefore we can use energy units and mass units. Interchangeably, you just have to multiply by the right factor of C squared or divide by the right factor of C squared to go back and forth. I say all this, which is completely uninteresting to you, because the units in which physicists usually think about the masses of elementary particles are something called electron volts, which are actually units of energy.
15:56 Sean Carroll? And they're units of energy which are defined in a completely goofy way, like the energy it takes to move an electron across one volt of electrostatic potential. That has absolutely no intuitive feeling for anybody. So here's a way to think about it. A proton is roughly a billion electron volts, okay? That's what's going on. An electron is roughly half a million electron volts, okay? So we say one G E V, which is one giga electron volt for the proton, and half an M E V, capital M E V is a million electron volts for the electron. You're not going to remember any of these. They're not on the test. This is the other thing that teaching these courses puts you in the mode of making sure your listeners know
16:41 Sean Carroll? what's going to be on the test and what's not going to be on the test. Nothing about the masses of particles or units or anything like that is going to be on the test. I'm just letting you know, this is how physicists think, okay? So the mass of the electron can't be fine tuned in a very real sense, because it is a dimensionful quantity. Like, you can't say the mass of the electron is a big number or a small number compared to one. That dramatically depends on what units you use, right? So physicists have this idea that the things that could possibly be fine tuned, the things that you should worry about, being numbers much, much less than one, being numbers very, very different than one,
17:25 Sean Carroll? and therefore somehow unnatural, are dimensionless numbers, are numbers that don't have any units attached to them at all. So you might say, well, what are the interesting dimensionless numbers? Sometimes you just are handed an interesting dimensionless number, like the fine structure constant. The famous constant alpha of electromagnetism has a dimensionless value of approximately 1 over 137. And that is, to physicists, that's close enough to 1. It's actually less than 1%, right? But in this world that we're talking about, 1 over 137 is small, but it's not crazy small, right? I mean, there might be 4 pi's and things like that that you're neglecting and what you compare to what else.
18:10 Sean Carroll? So if you want a fine tuning, you want something that is really less than 10 to the minus 10, at the very least, right? Then you can say like, okay, yeah, that's real. If you have something that's 10 to the minus 2, that doesn't really bother you. We're happy that the fine structure constant is small because it makes it easy to do calculations in quantum electrodynamics, but we're not worried about it being too small. So that is a non-fintuned, dimensionless constant of nature. But even if you have dimension-full quantities, that is to say quantities that are measured in some units, like mass, or time, or length, or whatever, you can always just divide it by a different quantity that has mass, or time, or length, or whatever. And very often, since we're doing fundamental physics,
18:54 Sean Carroll? the natural thing to divide by are Planck units. You've all heard about Planck units invented by Max Planck, the famous father of quantum mechanics. And it was interesting, as soon as he noticed, Planck, back in 1900, as soon as he noticed that he had to invent a new unit, a new constant of nature in order to describe this phenomenon of quantum mechanics, one of the first things he did was, you know, with my new constant of nature, I can now define universally agreed upon length, mass, time, energy, temperature, all those things. And he literally said, like, now we can talk to aliens. Because now we can tell the aliens how tall we are
19:39 Sean Carroll? and how long we live, because we can just use Planck units. I don't think he called them Planck units. But those are units which are more or less given by the constants of nature, which is always very nice. However, those units are very, very far away from everyday life. The Planck length, the length that we get by combining the units of h bar for quantum mechanics, G Newton's constant for gravity, and C, the speed of light, we combine them in the right form to get a length, just by canceling the units appropriately, and we get about 10 to the minus 33 centimeters. That is a very, very short length for the Planck length. Likewise, the Planck mass is something like 10 to the minus 5 grams.
20:22 Sean Carroll? That actually is pretty macroscopic, like it's small. It's certainly smaller than anything you would come across in your everyday life, but it's imaginable. Like, you could imagine holding a little dust grain that was exactly the Planck mass. The thing that makes it actually very, very big by human standards is that when we think about quantum gravity or particle physics and stuff like that, we want to put all of that mass into a single particle, or a single collision between two particles, or something like that. And that's an enormous amount of density of energy. Like, the mass of the proton, which is a billion electron volts, is roughly 10 to the minus 15, no, 10 to the minus 17 times the Planck mass, right? That's very, very far away.
21:07 Sean Carroll? So, that's something which is, you know, the Planck mass in energy in particle physics units is huge compared to our everyday way of thinking about things. Okay.
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22:17 Sean Carroll? All that is to say, I'm trying to like lay the groundwork to get to the fun stuff here. Don't worry about it. All that is to say, when we talk about numbers in physics being unnaturally fine tuned, we have to be sure to talk about dimensionless numbers. When the thing we have in mind naturally has units of something, we want to divide it by something else with units of that thing. Sometimes, very, very often in fact, it is natural to use the Planck units as the measuring stick. We're going to measure things with these spectaplanck units. In fact, there is a whole justification for doing this that I'm not going to get into. If you have read "Quanta and Fields," my most recent book in the Biggest Ideas series, I go on a lot about effective field theory.
23:02 Sean Carroll? And it's really within the context of effective field theory where you're summing up a whole bunch of influences that are happening at short wavelengths and high energies into their effects on lower energy, longer wavelength phenomena, that you really get this idea that certain parameters of nature, especially masses of particles, should naturally be big, should naturally be driven up because of all of these hidden effects at high energies to very high values themselves. And so there is some justification for using this very high scale of the Planck scale as our measuring stick. If you don't want to use it, that's okay.
23:45 Sean Carroll? You can pick some other scales and if you're anywhere close to being reasonable, you'll still get fine tuning problems coming out of it. But this is something that, you know, because we do have these problems, we don't always know what the solution to them is, you're welcome to worry about these problems in a very realistic way. Just understand, I mean, you're welcome to worry about it, but you should understand why the physicists pick the things they do. So dimensionless numbers would be things like the mass of the electron divided by the Planck mass, or the mass of the proton divided by the Planck mass. In other words, the masses of these particles in Planck units. Those are things that we can ask, are they fine tuned or not? Okay. So going through some famous and less famous examples.
24:28 Sean Carroll? One is the spatial curvature of the overall universe. Remember, I said we're not talking just about numbers built into the laws of nature. We're also talking about the initial conditions of the universe. Casually and informally, because physicists don't know the final theory of everything, in the usual way of thinking about physics, the entire history of a system depends on two things. Number one, the dynamical laws that say how the system evolves from time to time. And number two, the initial conditions. So for the universe as a whole, we imagine that there were some initial conditions set at or near the Big Bang. We have to be a little bit fuzzy about that, because the Big Bang probably didn't occur as an actual moment of time.
25:11 Sean Carroll? There's probably some quantum gravity substitute for it. But not long after whatever happened, happened, there is a more or less sensible classical universe that we can talk about, and that's what we mean by conditions near the Big Bang. And the spatial curvature of the universe today is related to the initial conditions. You just understand what the initial conditions are. You understand the stuff that is in the universe that helps explain how it expands and evolves over time, and you can predict the spatial curvature today. What do we mean by spatial curvature? Well, in cosmology, you know that the universe is pretty uniform over large scales. There's plenty of conditions that you can imagine, like if you're next to a black hole, conditions are not uniform.
25:56 Sean Carroll? The black hole is over there, and empty space is on the other side, right? But in the very, very specific context of the universe as a whole, on very, very large scales, the matter distribution, as far as we can observe, looks pretty uniform to us. So in that very, very specific context, you've heard that in general relativity, spacetime is curved, right? So in the context of cosmology, where the distribution of matter is uniform, the curvature of spacetime takes on a very natural decomposition. It's the sum of two different contributions. One is the curvature of just space.
26:37 Sean Carroll? So you have three dimensional space evolving with time, expanding, as a matter of fact, in the universe that we live in, and that three dimensional space has curvature. And the curvature could, in principle, be wildly different from place to place, and in fact, it is, but the fact that things are smooth and uniform on very large scales means that there is a single number, which is the same throughout the observable universe, which is the overall curvature of space itself, okay? And that's different than the sort of all the different components of the Riemann tensor of spacetime curvature that you could have in general. We're not talking about in general, we're talking about the very, very specific example of a uniform space in an expanding universe, okay?
27:22 Sean Carroll? So one contribution to the curvature of spacetime is the curvature of space, and that's just a single number. The other contribution is the expansion rate, the rate at which space is changing over time. And the famous Friedman equation of cosmology relates the expansion rate to the energy density, the amount of stuff in the universe, and to the spatial curvature. So there is something called the flatness problem in cosmology, which I don't know exactly who invented it first, but it was certainly highlighted by Robert Dickey and Jim Peebles back in the 1970s, and it was one of the motivations for Alan Guth in the late 70s, when he invented the theory of cosmological inflation, as we will see.
28:06 Sean Carroll? And the point of the curvature problem, the flatness problem, the flatness problem is that the curvature is very small. Small curvature means flat. The universe is flatter than it should be, okay? That's one way of putting it. Now, what do you mean by what it should be? How do you know what it should be? The usual way that the flatness problem is presented is to say the following: without inflation, if you didn't believe in inflationary cosmology, and I'll talk a little bit about what inflation says in a bit, but in conventional cosmology, where the universe is full of matter and radiation, basically, and space could or might not be curved, that's an initial
28:45 Sean Carroll? condition that you put into your model, in that theory, if you have some amount of curvature, some amount of matter, and some amount of radiation... The effective energy density in matter and radiation dilute away faster than the effect of spatial curvature. Spatial curvature lingers around longer, and if they were approximately equal at early times, then at later times, the curvature is relatively huge and the matter and radiation are relatively negligible. That is not at all what we see in the actual universe. In fact, we see negligible curvature, and we see a decent amount of matter and a certain amount of radiation.
29:28 Sean Carroll? So in order for that to be true, if you thought about it in terms of initial conditions, the early contribution of spatial curvature to the universe had to be less than the contribution from matter and radiation by something like a factor of 10 to the minus 25. That's a very, very rough number, because it depends on exactly when you start your calculation of what's going on in the early universe, but the beauty of this whole discourse is that nobody cares what the exact number is. The point is, if you are randomly picking universes from a hat, and you got a number that was 10 to the minus 25, that could have been 1, or it could have been minus 1, you're weirded out a little bit. You think like, "Oh, I don't know.
30:13 Sean Carroll? That seems like it would not have been what I would have guessed would have come out." And that is the flatness problem. Why was the universe so spatially flat at early times? That's fine-tuning problem number one, is the flatness problem. Fine-tuning problem number two is the cosmological constant problem. You must have heard that our universe is accelerating. We attribute that acceleration to the presence of dark energy in empty space. And the simplest candidate for dark energy is Einstein's cosmological constant, which he started thinking about back in 1917, which is equivalent, precisely equivalent, precisely the same as energy density of the vacuum, energy density in empty space itself. It turns out that in the context of general relativity, where you have an unambiguous relationship
30:57 Sean Carroll? between energy sources and the curvature of spacetime, spacetime itself can be an energy source. Empty space can contain energy. And this is basically what Einstein came up with in 1917. He came up with it for bad reasons, but his conclusion is still true. Empty space could have energy. And you go out and measure it. I mean, maybe it's zero. Maybe you were guessing it was zero all along. But in fact, in modern particle physics, a better guess would be the Planck scale. Or since it's an energy density, energy density is, you know, energy per volume. That is to say, energy per length cubed. So you might say, I'm going to guess the cosmological constant should be one Planck
31:42 Sean Carroll? energy per Planck volume. Okay? Now, you're welcome to disagree with that guess. Go ahead and disagree with that. But it's a natural guess. Had it been right, no one would have complained. It is not right. In fact, the observed value of the dark energy, if we attribute it to the cosmological constant, divided by what we just said was the natural guess for the vacuum energy, is a famous number of about 10 to the minus 120. That's an incredibly absurdly tiny number. Famously, the worst prediction in all of physics. Not really a prediction, of course. It was just a guess, just a natural value. But so very, very far off that we think like, there's got to be a reason for that. Right? Like, it can't just be it happened that way. We couldn't have just got lucky. Right?
32:27 Sean Carroll? That's a fine tuning. A fine tuning between the natural value for the vacuum energy, which does, after all, involve both quantum mechanics and gravity, and the Planck scale, which you might have thought, sorry, the Planck scale is the natural value versus the observed value that we get from astronomical data. So that was fine tuning number two. Fine tuning number three is what we call the hierarchy problem of particle physics. So the hierarchy problem, we just call it the hierarchy problem, but there's lots of different hierarchy problems. The big one, the famous one, is a difference of two energy scales. One scale is the energy scale characterizing the weak interactions of particle physics.
33:07 Sean Carroll? You can think about this in different ways. You can think about it as the mass of the Higgs boson. The Higgs boson gets a non-zero expectation value in empty space, and this is what makes the weak interactions special. What makes the W and Z bosons heavy, and therefore the weak force weak. But it also gives masses to all the other particles. So, once the Higgs gets a value in empty space, that value of the Higgs is a number, expressible in terms of its units are actually energy units, the same as the units of the mass of the Higgs boson. So, it is true and natural that the mass of the Higgs and the expectation value of the Higgs should be close to each other. That turns out to be correct. That is not a fine tuning.
33:51 Sean Carroll? But they're close to each other. They're very far away from the Planck scale, okay? The ratio of the expectation value of the Higgs boson to the Planck mass is something like 10 to the minus 16, right? Another big number. As long as we're 10 to the minus 10 or smaller, we're going to count that. When I say big number, I mean big discrepancy. We're going to count that as a big discrepancy, 10 to the minus 16. And the hierarchy problem is an interesting one, because with the cosmological constant, you know, it does involve quantum mechanics and gravity and all these things. And you figure like, maybe there's just something I'm missing. The hierarchy problem is pretty down to earth. It's kind of within the wheelhouse of what we expect to be able to understand. It's just particle physics, really.
34:36 Sean Carroll? We're comparing the Higgs scale to the gravity scale, because it's a convenient benchmark. But really, just in a more general sense, the weak interaction scale is very tiny compared to anything we might have expected it to be. Even if you just ignored gravity and imagined grand unification or something like that. The Higgs scale is very different than that. And it shouldn't be. It should be nearly the same one. And we have good effective field theory reasons to expect that. So that's the hierarchy problem. That's number three. So we've gone through the spatial curvature, the cosmological constant, and the Higgs expectation value. Number four is the proton mass. Now, this one's going to get me in trouble.
35:17 Sean Carroll? Because particle physicists don't consider the proton mass to be fine tuned. But if you just plug in the numbers and go by the definition we gave you, the mass of the proton divided by the Planck scale is about 10 to the minus 17, 10 to the minus 18, depending on where you put the two pi's in there. Again, it doesn't matter, it's much less than 10 to the minus 10, okay? So, the mass of the proton, much lighter than the Planck scale, that is an example of a fine tuning. The reason why, I'm gonna give away the answer here. The reason why we don't list it among the many fine tunings that we know about is because we have an answer to this one. This one makes perfect sense. We're not surprised by this one, ex post facto. But if you're just looking for small numbers, it would absolutely count. So let's put it on the list.
36:00 Sean Carroll? Number five, and this one is a little bit different than the other ones. The ratio of the neutron mass to the proton mass. So, or I could just say like, the neutron mass. But the neutron mass being small in Planck units is not surprising, once you've already told me the proton mass is small in Planck units. They're basically the same thing. Protons and neutrons are very, very similar to particle physicists. And so it's not surprising at all that the neutron and the proton have roughly equal masses. But the mass, but the difference here is that, they are roughly equal. The mass of the neutron is about 1.0014 times the mass of the proton. So that's not a small, that's not a small number compared to 1, that's very, very close to 1.
36:45 Sean Carroll? The small number, if you want, if you wanted to force yourself to make the small number, would be the mass of the neutron minus the mass of the proton, divided by the mass of the proton. That would be .0014, right? What's weird about that one? I mean, it's, you know, given that the neutron and proton are kind of similar creatures, maybe we shouldn't be surprised they have similar masses. Here is where the question of life comes in to the game. The question of life already came in, as we'll talk about in a second. All these other parameters do in principle affect the possibility of life existing. But here's one that you might not have thought was fine tuned until you started thinking about how desperately important this number is for life as we know it.
37:28 Sean Carroll? The mass of the neutron divided by the mass of the proton. The neutron is a little bit heavier than the proton. That's the motto that we get from measuring their values. What that means is heavier particles tend to decay into lighter particles, right? One way of thinking about that is a collection of light particles has higher entropy than a single heavier particle, so they like to decay. And so the neutron decays into the proton. And indeed it does. If you let a neutron out there all by itself, it will at some point decay into a proton, an electron, and then what we call an anti neutrino. But you go through the calculations. You can actually calculate exactly how this happens. You get the right answer.
38:09 Sean Carroll? This goes back to Enrico Fermi and his theory of, Fermi's theory of beta decay, as it's known, the decay of the neutron. So we understand this very, very well. And what happens is the neutron is gonna decay because it can. All of its conserved quantities are still conserved in this decay, and all of the masses of the particles it decays into add up to less than the mass of a single neutron. So in the neutron decay process, neutron converts into proton, electron, and neutrino. The extra energy that got disappeared turns into kinetic energy. The mass of the electron plus proton plus neutrino is less than the mass of the neutron,
38:52 Sean Carroll? and the change in mass goes into energy equals mc squared. It's converting the kinetic energies of the other particles. But because the difference in mass of the neutron and the proton is so small, there's not a lot of room for that to happen. The way quantum mechanics works is basically every single way a process can happen adds up to the total is a contribution, and you just add up all the contributions. In this case, the different contributions are basically just different ways to share the energy, to share the kinetic energy, between the proton, electron, and neutrino. But because there's so little energy to share, there's not that many ways to do it. And that means that the decay is small.
39:34 Sean Carroll? The mass of the, the lifetime of the neutron is something like 10 minutes, which by particle physics standards is hilariously long.
39:43 Sean Carroll? The lifetime of the Higgs boson, which is only 100 times more massive than the neutron, is 10 to the minus 21 seconds. That's a decent particle physics time scale, okay? The neutron lives a very, very long time. But it still does decay, and both those facts matter. If the neutron were much heavier, and by much heavier, I don't mean like, you know, a billion times heavier, I mean if the neutron were twice as massive as the proton, it would decay right away. It would decay very, very quickly. And furthermore, you notice that there are neutrons in the world, right? There are neutrons out there. There's a bunch of neutrons in your body right now. Probably most of the mass of your body is actually neutrons. I actually don't know that for sure, so don't quote me on that.
40:27 Sean Carroll? But of order the same mass in your body comes from neutrons and protons. And how is that possible if neutrons decay away? The answer is that even though a free neutron by itself will decay away, neutrons can be bound into atomic nuclei. Neutrons bound with protons have, there's a negative energy in that binding, and you could have a situation where, let's say, in a single helium nucleus, where you have two neutrons and two protons, even though the mass of the neutron is bigger than the mass of the proton, because of the negative binding energy in the helium nucleus, the mass of a helium nucleus is less than the mass of four protons.
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41:40 Sean Carroll? So the helium nucleus is perfectly stable. It's not going to go anywhere. The neutron can be stable as long as it is in a stable nucleus. If the mass of the neutron were twice the mass of the proton, it would be so unstable that you would not be able to make nuclei. You would not be able to make stable nuclei. You would only have protons as stable nuclei, which means that the only element in the universe would be hydrogen. It is thought that you cannot make living creatures out of nothing but hydrogen. The only molecules you can make are basically H2. There's no organic chemistry if you only have H2 in the world, double hydrogen atoms.
42:22 Sean Carroll? So, of course, we don't really know the precise set of conditions under which living beings can be constructed, but certainly by the methods that we know, you can't make life if the neutron is twice as heavy as the proton. What if the neutron were a little bit lighter than the proton? That was close to it, but a little bit below? Also, no chance of getting life. In that case, it's the proton that is now unstable. If a proton is heavier than neutron, the proton will decay into the neutron. And then you just get a world full of neutrons. There's no electrons hanging around. They've all been converted. Electrons plus protons have been converted into neutrons plus neutrinos.
43:06 Sean Carroll? And once again, there's no chemistry, right? Now, rather than having a universe with nothing but hydrogen, you have a universe with nothing but neutrons. You don't even have atoms, much less chemistry. So once again, it seems like it's very difficult to get life out of the laws of physics if the neutron has a lower mass than the proton. So the neutron-proton mass difference is not a case where a number is anomalously small, less than 10 to the minus 10. It's a case where a number is special in the sense that it's just right to allow for the existence of life, apparently, as far as we know. So that counts as a fine-tuning that we might want to keep our eyes on when we're trying to explain why fine-tunings occur in the universe.
43:50 Sean Carroll? The next example is actually my favorite, and you've heard me talk about it before, which is the entropy of the early universe. This is, once again, a matter not of the constants of nature, but rather the initial conditions of the universe, the configuration the universe was in at early times. And I've talked about this multiple times on other occasions, but the upshot is that there is a scale by which we can judge the entropy of the universe, which is sort of what its maximum entropy could be. Roger Penrose figured this out back in the 70s, just by asking the simple question after Stephen Hawking figured out the entropy of a black hole.
44:32 Sean Carroll? Penrose asked himself, "Well, okay, if we took all of the known matter and energy in the universe, put it into a single black hole, what would its entropy be?" And the answer is enormously bigger than what the entropy is. And the early universe, where we started, right after the Big Bang, has even a much lower entropy than that. The entropy of the early universe divided by what its entropy could have been, its maximum entropy, is something like 10 to the minus 122. It depends on the details, once again. A factor of 10 or 4 pi among friends isn't going to bother us. 10 to the minus 122 is a very, very tiny number. This is reflecting the fact that the conditions in the early universe were very special.
45:15 Sean Carroll? Which is, if you don't believe they're special, notice that the early universe doesn't stay like the early universe. The early universe rapidly expands and cools and turns into the universe like we have now. And if you give it a few more quadrillion years, it will empty out, right? It will empty out, stars will burn out. That's the natural state for the universe to be in. All the matter and radiation flung to the four corners of spacetime, and everything looks almost empty, right? The early universe looks the opposite of that. It's a very, very unusual configuration, where it's super-duper dense. And not only is it dense, it's super-duper smooth. That's very, very strange to us. If the universe were to collapse into a big crunch, there's no known reason.
46:00 Sean Carroll? Why it would smooth itself out along the way, we would expect it to get lumpier and lumpier indeed. As it collapsed, that would be the natural high entropy thing to happen. But that's not what we see in the early universe. It's smooth and dense at the same time. That's very weird. That's a reflection of the fact that its entropy is very, very tiny. So that's a fine tuning, not of a constant, but rather of the initial conditions of the universe. I know this is a lot of fine tunings, but that's the whole, kind of the whole point. We're, we have two more to go. And we should be struck by the fact that there's a whole bunch of ways. In which the universe really isn't what you might guess in a natural way. Okay.
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47:36 Sean Carroll? Seventh example of fine tuning is something called the strong CP problem. Which those of you who are really fans of particle physics or cosmology will have heard about, but many others might not have. CP here stands for charge parity, which are two.
47:55 Sean Carroll? Transformations you can do in particle physics. The charge transformation basically says, let's convert all particles into antiparticles. The parity transformation basically says, let's switch right-handed with left-handed. Let's take a mirror image of whatever configuration of physical stuff we have. And it was an interesting and Nobel Prize worthy set of events back in the 50s, 60s, where we realized that these transformations were not actually symmetries of the universe. Parity was violated, and then we realized that even the combination of charge and parity is violated, and that was very surprising. But then, once we did realize that, we realized that there's no reason for these transformations
48:40 Sean Carroll? to be symmetries. It could matter what the orientation of your axes were, for example, in a particle physics experiment. Then we started asking, well, okay, should we violate them? Can we write down terms, again, from an effective field theory perspective, for example? Can we write down things in the standard model of particle physics that would violate CP? The answer is yes, and there are terms that do violate CP, and they're small in the weak interactions. There's also a term you can write down in the strong interactions that violates CP, and it's not there. That is to say, if this term were there with a natural value, it would be very, very noticeable.
49:25 Sean Carroll? People have calculated how we would detect it. If you want to know the details, it's the electric dipole moment of the neutron that is proportional to this parameter called theta QCD. QCD is quantum chromodynamics, the strong interactions. So there's this parameter we know how to write down, that we could put into the dynamics of the standard model. If we did, it would show up, it would be detectable, and we've looked for it, and it's not there. In fact, you can put a limit on how big it is. It's, guess what, about 10 to the minus 10, or less. We haven't detected it. It could be 10 to the minus 100, for all we know. 10 to the minus 10 of its natural value. Okay? So that's the strong CB. Problem.
50:06 Sean Carroll? And again, we're still not quite sure what the answer to that one is. And I'll give you one final one. This is the eighth example of a fine tuning, although it's a slightly different example because we don't actually know if it exists or not. This is the mass of the dark energy field. Okay, so what is we talking about here? I just said that we know that there's dark energy, or there's something anyway, making the universe accelerate. And we call it dark energy. Maybe it's the cosmological constant, but maybe it's not. I had mentioned on the podcast, there's been little hints in recent years that maybe the dark energy is not simply the cosmological constant. Maybe it is changing over time and changing very gradually, otherwise we would have discovered a long time ago. Okay.
50:50 Sean Carroll? And this is something that I thought about a lot back in my days as an enthusiastic young cosmologist. And it's hard to make the idea work. It's a natural idea. Yeah, a lot of the motivation for thinking about whether or not dark energy can be variable, can be dynamical, rather than just constant, is kind of an expression of humility, you know? Back when I was your age, when we were thinking about the vacuum energy, but hadn't yet discovered it, right? The cosmological constant. We knew the cosmological constant was too small compared to its natural value. We knew that it was 10 to the minus 120 or less times its natural value. And there was this school of thought that said, look, in the space of all possible theories
51:34 Sean Carroll? that we haven't thought of yet, I don't know what explains why the cosmological constant is small, but it's easier for me to imagine a theory that sets the cosmological constant to exactly zero, even though I don't have that theory yet, than it is to imagine a theory that sets the cosmological constant to 10 to the minus 120, its natural value. I don't know how to do that, exactly the value that we haven't yet observed yet. But that's what it is. That's what it turned out to be. We were wrong, okay? So we were wrong. And when I say we, I include me literally, not just figuratively. It's not the royal we. I was there and I was wrong about this. The cosmological constant is, or apparently looks like, 10 to the minus 120, its natural value.
52:19 Sean Carroll? So maybe it's not the cosmological constant that we're observing. Maybe the cosmological constant really is zero. Maybe we were right in some weird way, that there is some mechanism that we haven't yet invented that sets the vacuum energy equal to zero. And what we're seeing in the acceleration of the universe is some field that has an almost constant energy, but not quite, okay? Here's the problem with that idea. We would call this dynamical dark energy, or quintessence, sometimes it's called. The problem is, the same is the problem with the hierarchy problem and the weak interactions. The Higgs boson field is a field that pervades all of space.
53:02 Sean Carroll? And its mass is small compared to the Planck mass, right? Its mass is 10 to the minus 16, something like that, the Planck mass. And we say, that's a small number. Masses in particle physics, under the rules of effective quantum field theory, tend to be big, tend to be driven up to very large numbers, okay? And so the hierarchy problem is just that there's a factor of 10 to the minus 16 between the Higgs mass and the Planck mass. If you have a dark energy field that is making the universe accelerate, it needs to be changing very slowly. Otherwise, we would have noticed a long time ago. If it were changing rapidly on cosmological scales, that would have been easy to detect.
53:46 Sean Carroll? It wouldn't even have acted like dark energy. The whole thing that dark energy needs to do is to change slowly, so that its energy density is approximately constant and it can make the universe accelerate. So if it's an ordinary, not weirdly atypical field, filling all of space, that has some kind of mass, we talk about the mass of a field, what we really mean when we say that is the mass of the particle you would make by jiggling that field. That's what we mean when we talk about the mass of the Higgs field or something like that. It's the mass of the particle you would make. In the case of dark energy, you're not actually making any particles. You're not jiggling it and doing any particle physics experiments. But we can still mathematically talk about the mass parameter that characterizes the
54:30 Sean Carroll? field that we can generally quite easily relate to its rate of change. Okay, the mass is basically how much push the field is getting from its potential energy, which in turn is related to its rate of change. Anyway, at the end of the day, the mass of the dark energy is about, needs to be, in order to fit the data, something like 10 to the minus 33 electron volts, which is lower than the Planck mass by a factor of 10 to the minus 60, not 16. So the Higgs boson, we already said, was anomalously low mass. Its mass is 10 to the minus 16, the Planck mass. The dark energy needs to have a mass of 10 to the minus 60 times the Planck mass in
55:15 Sean Carroll? order to fit the data. Oh my goodness. And of course, I have a vested interest in this. One of my better papers that I've written as a physicist was pointing this out, pointing out that this was very unnatural, pointing out there's a whole nother set of unnaturalnesses involved with dynamical dark energy, because that dynamical dark energy can also interact with photons and with electrons and with neutrons and things like that. And it apparently doesn't. So there's a whole bunch of new parameters you have to invent and then fine tune all of them. So I wrote a little paper explaining that that's a problem and also suggesting a way out and also suggesting an experimental test of the way out. And that test would potentially lead us to cosmological blyrefringence, rotation of
56:00 Sean Carroll? the polarization angle of light from the cosmic microwave background or other distant sources. And that's something we're looking for, and there's even little hints we might have found it. So my fingers are crossed that we do find it and then forget about this cosmological constant stuff, I'm going to be a dynamical dark energy guy. But we haven't found it yet. It's still a little bit, still a little bit up in the air. So cautious optimism, but you have to wait for more data to come in.
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57:22 Sean Carroll? Okay. Anyway, that took longer than I expected. That's usually what happens because I, you know, I get into it. I get enthusiastic. I warm to my subject. We have eight different fine tunings on the table that I specifically and intentionally chose to be very different from each other in character. The spatial curvature is much smaller than it might have been. The cosmological constant is much smaller than it might have been. The mass of the Higgs boson, or equally well, the scale of electroweak symmetry breaking is much smaller than it might have been. The proton mass is much smaller than it might have been. The neutron-proton mass ratio is close to 1, but a little bit above, but not too much above or too much below, which seems a little fine tuned. The entropy of the early universe is very tiny.
58:07 Sean Carroll? The violation of CP in the strong interactions is very tiny, and the mass of the dark energy, if it's there, would be very tiny. So. Why am I giving you all these very, very different examples of purported fine tunings? Just because I think that the discourse about fine tuning tends to kind of wander all over the place sometimes, and part of that is that different fine tunings come in different forms. So, as I mentioned, as we were going through that, most of these fine tunings involve small numbers. But not all of them do. The neutron to proton mass ratio is a number that is very close to 1, just like it's supposed to be. It's the specific close to 1 value that is fine tuned, but not the fact that it's a
58:51 Sean Carroll? very tiny number compared to 1. So there's one way of being fine tuned, which is just to be small, and there's another way that says it's just a weird value that seems to be purposeful, intentional, special, whatever you want to call it. Some of these fine tunings, either we know the answer to them, we know why they're like that, or we have a really, really good theory for why they might be like that. Remember I told you that the mass of the proton is never listed as something that's finely tuned? That's because we know where it comes from. We know that the mass of the proton depends on the symmetry... symmetry breaking is not the right way to put it, even though it would count. The scale at which the strong interactions become strong.
59:36 Sean Carroll? There's an energy scale at which, below which, the strong interactions are strong, but the strong interactions have this interesting property called asymptotic freedom. As you go to higher and higher energies, interestingly, the strong interactions become weaker and weaker. They don't become that strong anymore, and there's a crossover threshold point where the strong interactions go from effectively being strong to effectively being weak. That interaction point, the energy at which that happens, is roughly the mass of the proton, and that makes 100% sense. That's what it should be. It's roughly the mass of the neutron, roughly the mass of most strongly interacting particles. So the question is, this energy scale, which is called the QCD scale, again, QCD is
1:00:20 Sean Carroll? quantum chromodynamics, why is it so different from the Planck scale? But we know that one. It wasn't actually that different from the Planck scale and dimensionalist units. But then it turns out that there's a relationship between the high-energy scale where we imagine our minds, maybe correctly, maybe not. We imagine that, you know, God sets the parameters of the universe at high energies. And then they flow down to low energies using what is called renormalization. But for something like QCD, they flow very, very slowly. So if you start with a number that is not much different than 1 at very, very high energies, and move it down to lower energies to ask where does it cross over from being less than
1:01:03 Sean Carroll? 1 to being greater than 1, so the strong interactions go from being weak to being strong, you very, very naturally get a big, big difference, a big, big hierarchy between the high-energy scale and the QCD scale. So I know I'm skipping over a lot of deep and esoteric physics here. All I want to let you know is, the reason why people don't worry about the mass of the proton being fine-tuned, even though it's 10 to the minus 18th of the Planck mass, is we know exactly a good theory that explains that one, okay? Compare that to the case of the spatial curvature, right? The flatness problem. The flatness problem only became famous once we learned the solution to it, or at least
1:01:46 Sean Carroll? a very good solution to it, which is inflationary cosmology. The flatness problem was popularized in Alan Guth's paper about inflation, where he said, "I have solved this problem that you didn't know was a problem." And indeed, no one quoted it as a problem until he solved it. And the solution of inflation is, imagine there is some field that we don't, haven't detected directly in the laboratory, maybe never will, but it's a field that has the property that it's kind of like we imagine the dark energy field to be today, except it wasn't dominating the mass of the universe recently, it was dominating the mass, the energy of the universe near the Big Bang. So basically, what you're imagining with inflation is, there's a period...
1:02:27 Sean Carroll? Of super-high-density quasi-dark energy, super-rapid expansion. Inflation pushes the universe apart at an incredibly high rate, and in doing so, it smoothes out the universe. It also flattens it. It decreases the ratio of the spatial curvature to the energy density of the universe. It's the opposite of what happens if you live in a universe with just matter and ordinary radiation. With matter and radiation, the relative effects of spatial curvature grow with time. With this quasi-inflationary dark energy, the relative effects of curvature shrink over time. And then, the thing is, at the end of inflation, all this energy that was trapped in this
1:03:11 Sean Carroll? quasi-dark energy field gets converted by ordinary particle physics process, in a process known as reheating, into matter and radiation. But it does not get converted into spatial curvature. There's no way for that to happen. So roughly speaking, the inflaton field, as we call it, which is, again, purely hypothetical at the moment, it dominates the energy density of the universe, it flattens the universe out, and then it converts into matter and radiation in a universe which is very, very close to spatially flat, just as we observe it to be right now. So inflation provides a dynamical explanation for why the curvature of the universe is so small.
1:03:52 Sean Carroll? Now, a footnote there, I wrote a paper with Haywood Tam years ago, a decade ago or more, which pointed out, or tried to make the argument, semi-successfully, I mean, we were right, but people haven't listened to us yet, that the flatness of the universe was never fine-tuned to begin with. The flatness of the universe is a perfect case of where you really actually do need to think more carefully about what you should have expected the number to be. You know, I gave you the flatness problem as saying the curvature, spatial curvature of the universe had to be incredibly tiny at early times for it to be sufficiently tiny today, not to be noticeable. That's 100% true.
1:04:36 Sean Carroll? But then the other half of the argument in the flatness problem is, "And it had no right to be so tiny at early times." I'm not going to go into details about this because it's not the main focus of what we're talking about today, but I argue, and Haywood and I argue, that if you do the math correctly, almost all universes are exactly spatially flat. It's very, very difficult to randomly pick a universe out of the set of all universes and get one with substantial spatial curvature. There isn't really a flatness problem in my mind. It's very natural for almost smooth universes to be essentially spatially flat. That's just an example that I'm giving you as a possible set of ways of thinking about these fine-tuning problems.
1:05:21 Sean Carroll? Maybe they're just not there if you think better about what the probability distribution for these parameters is. Okay, anyway, do we have other good theories? Yeah, you know, there's also this Higgs boson thing, the weak interaction thing, right? For the cosmological constant, we essentially have zero good dynamical theories that explain why it is small. I say that as someone who has written papers putting forward theories. I just don't think they're very good. Sometimes you have good theories, sometimes you have less good theories. For the Higgs boson, it's a tough one. You know, the weak interaction strength, the electroweak scale, the thing that sets what we call the hierarchy problem of particle physics.
1:06:03 Sean Carroll? It is very possible to come up with good dynamical theories that naturally explain the existence of a hierarchy between the Planck scale and the electroweak scale. Indeed, an enormous amount of effort over the past 30 or 40 years has gone into doing exactly that. Indeed, the famous hopes for supersymmetry being discovered at the Large Hadron Collider were based on the idea that supersymmetry could help explain the hierarchy between the electroweak scale and the Planck scale. And if it did, it would predict a whole bunch of new particles to be discovered near the Higgs boson in mass.
1:06:45 Sean Carroll? There were other possibilities involving extra dimensions of space and things like that that also could plausibly explain the hierarchy problem and also predicted new particles near that energy scale.
1:06:58 Sean Carroll? We turned on the LHC, the Large Hadron Collider, at CERN in Geneva. We spent $10 billion building it. Part of the motivation for building the LHC was to search for the Higgs boson itself, but a big part of the motivation was to solve the hierarchy problem, was to solve the fine-tuning problem given to us by the difference in energy scales between the electroweak theory and the Planck scale, because almost all of the favorite solutions predicted new particles there to be discovered. We have discovered none of them. Now, look, maybe we'll discover one tomorrow. That is possible. Maybe we just haven't found it yet. That's conceivable. But, you know, we absolutely could have found it the day after turning on the LHC, back in like 2008 or whatever it was.
1:07:43 Sean Carroll? As soon as we turned on the LHC the first time, it blew up. And we took a while to fix it again, but by 2008 it was really running. So, that's another cautionary tale as far as physics and fine-tuning is concerned. We had a fine-tuning where there were a handful of different theories that could have reasonably explained it. They all made certain kinds of predictions, and none of them apparently is right, as far as we can tell. That, again, that might go away. The LHC doesn't have infinite reach. It only reaches a little bit beyond where the Higgs boson is. So, I would say we have a dynamical theory with issues in the case of the electroweak scale.
1:08:22 Sean Carroll? And then, you know, there's just a different sort of sense of some of these problems, because some of them are relevant to the existence of life, like the neutron and proton masses. The cosmological constant is relevant to the existence of life. If the cosmological constant, the vacuum energy, were really, really, really big, it would explode the universe apart at such an enormous rate that you couldn't make atoms, much less stars or galaxies or living beings or anything like that. If the cosmological constant were huge in magnitude and negative in value, it would cause the universe to recollaps really, really rapidly, and that would not give you enough time for life to develop. So, something like the cosmological constant, the vacuum energy, the energy inherent in
1:09:07 Sean Carroll? space itself, turns out to be sneakily relevant to the existence of life. Whereas other things, like the strong CP problem, the value of the parameter that violates the CP transformation symmetry in the strong interactions, that has nothing to do with life. It wouldn't matter at all if it were its natural value. So there are dynamical theories that help explain it. The axion particle is a particle you might have heard of. It's a very popular candidate to be the dark matter. But the reason why the axion was initially proposed was as a dynamical explanation for why there is no CP violation in the strong interactions.
1:09:48 Sean Carroll? A dynamical explanation for that particular apparent fine tuning. So if that turns out to be right, we don't know whether axions exist or not. One of the reasons they're so popular, they're popular as a particle physics idea because they help explain that strong CP problem. And then later it was realized they could also be the dark matter. And then later it was realized that the other popular dark matter candidate, the weakly interacting massive particles, could have already been discovered and haven't been yet, so they've become less popular. So the axion is getting a resurgence in popularity as a possible explanation for the dark matter. If that turns out to be true, then what looks right now to us like a fine tuning
1:10:32 Sean Carroll? will be explained dynamically. The axion is essentially a field that rolls in a potential. You know, the usual picture you have of a ball rolling in a hill. And you can explain very, very naturally why the bottom of the hill is a place where the effective violation of CP is minimized in the strong interactions. It's very, very close to zero. Basically, the axion takes whatever violation of CP you thought you had and it cancels it out almost exactly. And so that will be very, very natural and good for all sorts of reasons. We just haven't quite detected it yet. So you see, it's a wide variety of things going on, right? I mean, it's not...
1:11:12 Sean Carroll? At all crazy or misguided to talk about fine tunings in particle physics and cosmology. They are there. When I say the fine tunings are there, I don't mean God did it. I don't mean they're necessarily there because life exists. I just mean there are more than one numbers in the fundamental constants of nature that have values that seem very wrong to us. And that is something that should be addressed by fundamental physics, by thinking about it in some way. And again, the ways for the, the answers for the different fine tunings might come from different directions. That would be perfectly okay. Or there might be one giant theory that explains them all. I think it's actually much more likely that they come from different directions
1:11:57 Sean Carroll? because these problems are so different from each other than there's one giant theory. But you know, we keep an open mind. So now finally, I get to talk about what I wanted to talk about a little bit, which is, and it won't take too long, don't worry, what the answers could possibly be, okay? What are the possible attitudes we can have towards these different fine tunings? And I can, I think that there's basically four different attitudes one can have. I don't want to call them solutions because people can debate whether some of these attitudes actually even count as solutions or explanations. But they're attitudes people can and do have. Some of the attitudes are literally theoretical constructions. So they wouldn't normally be called attitudes.
1:12:39 Sean Carroll? But okay, we have to call them something, scenarios, if you want to call them that. One scenario is for each of these fine tunings, there is a dynamical theory that explains why this apparently small number has the value it does. Let's get into that in a little bit more detail in a second, but let me go through the different scenarios. So one scenario is the existence of a dynamical theory, like inflation, for example. The second scenario is there's a multiverse. This is not the quantum mechanical many worlds that we've talked about lots of times here on the podcast. In quantum mechanical many worlds, if I measure the spin of an electron, it's spin up and spin down, then there's one world in which it's spin up and one world in which it's spin down.
1:13:22 Sean Carroll? But the fundamental parameters of physics are the same in those two worlds. This is not moving me in the direction of explaining any fine tunings anywhere, okay? In the cosmological multiverse, it's a very different story. People noticed soon after inflation was proposed that in most models of inflation, and I'm not quite sure what the word "most" means there, but in lots of models of inflation, inflation keeps going forever. It ends in some places and keeps going in other places. And where it keeps going, it can sort of end differently in different places. This is called eternal inflation. And you marry this to something called the string theory landscape. The string theory landscape actually came along much later,
1:14:07 Sean Carroll? but the idea that something like the string theory landscape was already there in the 1980s, this is basically the idea that when inflation does end, when it turns into matter and radiation, the local laws of physics in the region where it ends can be very different in one region of the universe than somewhere else. By the local laws of physics, I mean the parameters, exactly what we're talking about. The vacuum energy, the mass of the quarks and the leptons, the strength of the constants of nature, like the fine structure constant, even things like what forces of nature there are. You know, we have the famous SU3 cross SU2 cross U1 standard model of particle physics, but maybe in another region of space, very, very far away,
1:14:52 Sean Carroll? the forces of nature are things that are completely different than those, or at least a little bit different. Even the number of dimensions of space. In these models, you know, we have a world where there are three dimensions of space all around us. And string theorists believe there's at least six dimensions that are hidden from us, curled up in very tiny balls. Maybe somewhere else, there are six dimensions of space that everyone sees and three dimensions are curled up into little tiny balls. So this cosmological multiverse...
1:15:22 Sean Carroll? Two aspects of it that are really important. One is, conditions are very different, literally in different regions of space. It's really not a multiverse at all, okay? It's just, things are so far away, much further away than we could ever get to, moving slower in the speed of light, that for all intents and purposes, we're labeling different regions of space with different local laws of physics as different universes, different pocket universes, Alan Guth calls them, okay? And the other is, it's not a theory, in the sense that you don't start by saying, "Well, what if there's a multiverse?", okay? The theory is eternal inflation plus string theory, or some substitute for string theory
1:16:03 Sean Carroll? that gives you some landscape of different possible local laws of physics, which people can invent and have invented that. The multiverse is a prediction of such models. It is not a theory by itself. The theory is inflation plus the landscape. And both of those theories, inflation plus the landscape, were invented for other reasons. They were not invented to get you a multiverse. In that sense, it is very, very analogous to the many worlds of quantum mechanics. In quantum mechanics, we didn't get many worlds out because we wanted to. Hugh Everett didn't say, "Can I sit down and come up with a theory that invents a multiverse?" He noticed that his multiverse was predicted by the Schrödinger equation.
1:16:46 Sean Carroll? Likewise, the cosmological multiverse is predicted by eternal inflation plus a landscape. Its relevance to fine-tuning happens if the fine-tunings are relevant for the existence of life. If you have a cosmological multiverse, you can say, "Well, some places in the multiverse, life couldn't exist, and they have certain constants of nature. Some other places, life can exist, they have different constants. Of course, we're gonna find ourselves in the regions that can have life." And I'll talk about that in a little bit more detail in a second. That's the anthropic principle at work. The third scenario is theism. God did it, the argument from design. And again, I take this argument seriously.
1:17:29 Sean Carroll? I'm not convinced by it, for reasons that will become clear, but it plays by the rules, this argument. I think it's completely wrong to think that this argument is just non-scientific. I think that the people who are gonna say that it's non-scientific do so because they don't like the conclusion that it's trying to reach. I don't agree with the conclusion it's trying to reach, but I disagree for scientific reasons, and I can try to explain what those are. But the argument from design as an explanation for fine-tuning should be pretty straightforwardly obvious. To the extent that some of these apparently fine-tuned parameters of physics and cosmology are indeed necessary for our existence here, it's not completely crazy to suggest they
1:18:13 Sean Carroll? were set that way by somebody, by an agent, by an intelligence with intentionality and with purpose and with the goal of creating a universe in which creatures could exist, right? That's just the argument from design, and I think that it's not dismissible, even though I am ultimately not persuaded by it. And then the fourth scenario is, we just got lucky. There is no explanation. I think that even though some of these numbers are kind of wild, 10 to the minus 120 and things like that, it's absolutely allowed to just say, there's no explanation for these things.
1:18:53 Sean Carroll? None of these is a disagreement between theory and experiment, because we don't have a well-tested theory, or even a very respectable theory, that predicts the numbers we're talking about. All it is, is a disagreement between observation and our guesses. And so, one very plausible attitude is, your guesses were wrong, deal with it. Our job is to measure these things, not to worry that they weren't the values that we would have guessed had we measured them. And I'm not making this up. There are people who absolutely have these attitudes, and I think that it is a plausible attitude, just like the argument from design. I am not persuaded by this attitude, but I don't think it's disreputable to think that, so we should give it its due. So.
1:19:39 Sean Carroll? With those four scenarios on our plates, the existence of a dynamical theory explaining the fine tuning, a multiverse plus anthropic explanation, a theistic argument from design explanation, or we just got lucky, shut up and measure rather than shut up and calculate. Let's think about these different possibilities in comparison to each other. Let's think about them a little bit more carefully. So let's think about the possibility that there are dynamical theories that explain some of these fine tunings. You know, I think this is the one that everyone agrees is very respectable, right? Like when you see a number and it's very, very small, if you can come up with a theory that provides an explanatory framework
1:20:24 Sean Carroll? that says, you know what? You shouldn't have been surprised by that in the first place. Everyone's happy. This is why people like inflation so much, right? We don't have direct evidence that inflation is right. We have indirect evidence that it's right. It's pretty compelling in some ways. There's some sort of theoretical shortcomings of it that I've talked about before. But it really makes things nice and easy. You know, again, when I was a grad student in the 80s and 90s, astronomers didn't like inflation. Why didn't they like inflation? Because as far as they could tell, inflation made one prediction, namely, the universe was spatially flat. You can convert that prediction, the universe is spatially flat, into a prediction for the energy density of the universe.
1:21:08 Sean Carroll? And they measured the energy density of the universe. They had gone out and counted the stars and measured the dark matter and all that. And they didn't get the right answer. They only got like about 30% of the way there. So as far as astronomers were concerned, you made one prediction, it was wrong. I'm not going to give you a lot of credit for that. But of course, by the end of the 90s and the early 2000s, we realized that the other 70% of the universe was dark energy. And indeed, that one prediction inflation had made comes spot on. And so that's actually pretty good. And now astronomers all believe that inflation is right. That's kind of the gold standard. Even though I personally am still a little bit less willing to declare inflation completely successful, this is what you're looking for. You're trying to invent some dynamical theory
1:21:53 Sean Carroll? that makes these things explained in a very natural way. The problem is, they're hard to find, right? Inflation works pretty well. Like I said, the theory that we have for the mass of the proton and QCD and the running of the coupling constants, that works perfectly well. That's wonderful. But what about like the entropy of the early universe, right? I mention this because I care about it. I have tried very hard to explain the entropy of the early universe. And as I try to say very honestly, I think that my explanation, the one that Jennifer Chen and I put forward 20 years ago, is on the one hand, still the best explanation on the market, on the other hand, still not great as an explanation. I
1:22:35 Sean Carroll? mean, it might be the right explanation. I absolutely believe it has a chance of being correct, but there's an enormous amount of ill-understood physics that goes into it. And so it's not like it's so good that people should think that it's the right answer yet. I mean, maybe we'll get there someday. The point is just that even though you try very hard to do it, coming up with explanations for these things is difficult. As I said before, no one has come up with a good dynamical theory that explains the value of the cosmological constant, even though it's been a super interesting problem for 50 years now. And so we should look for those dynamical theories, but we can't be guaranteed to find them. So
1:23:15 Sean Carroll? we should also be open to other possibilities. So let's contemplate the anthropic explanation, the multiverse explanation. The one example that should always be contemplated when you're thinking about the multiverse and the anthropic principle is Steven Weinberg's prediction of the cosmological constant. So to set the stage, it is 1987. So it's more than a decade before we actually gathered evidence in favor of the cosmological constant, but we already knew about the cosmological constant problem. Okay, so we knew that given the current constraints that existed at the time, the cosmological constant couldn't be bigger than 10 to the
1:23:59 Sean Carroll? minus 120 its natural value. That's the cosmological constant problem. And as I mentioned, almost everyone thought, even though we don't know what the answer is, eventually we'll find the answer and it'll be zero. There'll be some symmetry, some dynamical mechanism that we don't know about yet that will set it equal to zero. There's another reason, which I could have included among the fine tunings, but it's a little messier, so I didn't. There was another reason why people thought that the cosmological constant was probably zero, not just this idea of the space of all possible theories. Given the limits, the observational limits we had in the 1980s for the cosmological constant, if it were noticeable, if we were able to detect it, there would be what is called the coincidence problem.
1:24:44 Sean Carroll? It would be that the cosmological, the vacuum energy, the energy density in vacuum, the cosmological constant, is of the same order of magnitude in size as the matter density of the universe. And the weird thing about that coincidence between the matter density and the vacuum energy density is that one of them, the matter density, changes rapidly as the universe expands, while the other one, the vacuum energy density, remains constant. So the statement, "The vacuum energy and the matter density are of the same order of magnitude in size," is a temporary statement. In fact, in a real sense, it only describes a relatively short period in the history of the universe.
1:25:28 Sean Carroll? And in order for the cosmological constant to be detectably large, it's true that we live in that period. That's the coincidence. Why would we be so lucky to live in the period where the vacuum energy is exactly that size? Okay, so that was the sort of mind state that people were thinking about in the late 1980s. And Steven Weinberg, you know, he knew about inflationary cosmology and the possibility of a multiverse, and he had thought about the cosmological constant himself for other reasons. So he decided to be a little bit more systematic than average in thinking about what you should predict the cosmological constant to be if there is a multiverse. He didn't have any specific model of the multiverse
1:26:13 Sean Carroll? or the string theory landscape or anything like that. He just imagined that there were different regions of space, and in different regions of space, or different somethings, different universes, one way or the other, the cosmological constant was different. Okay, that's all he imagined. He did need to be a little bit more specific than that. He needed to give a probability distribution, or a sort of a frequency, a relative number of universes where the cosmological constant was one value versus another. But he made the following clever argument. He said, "Look..." The allowed range that we know the cosmological constant is in is incredibly tiny compared to its natural range, right?
1:26:52 Sean Carroll? It's plus or minus 10 to the 120, or 10 to the minus 120, times its natural range. So if you think about the, some true distribution of universes, with the true distribution of cosmological constants, there's some curve, right? Some probability density of being in one universe versus another. And you're sampling that curve over an incredibly tiny window, 10 to the minus 120 of its distance from left to right. And so, he knew that if you sample a curve that is relatively smooth over a very, very, very tiny interval, that curve will look like a constant. It will just look flat, unless it's like really wildly varying at every point,
1:27:36 Sean Carroll? which seemed unlikely, it seemed unmotivated anyway. So Weinberg said, "Look, within the allowed window, I am perfectly allowed, justified, in assuming there is a constant probability distribution, a flat, uniform probability distribution, a measure, if you want to call it that, on the set of possible cosmological constants." And then, he knew enough astronomy to say the following thing. "I can calculate," I mean, I can't, Sean Carroll, but I, Stephen Weinberg, can calculate the number of galaxies that will form in a universe with a given value of the cosmological constant. He could do it back of the envelope, pencil and paper. He and some collaborators actually did better computer simulations afterward.
1:28:21 Sean Carroll? But even just using pencil and paper, he could say, "If the cosmological constant gets bigger and bigger, it gets harder and harder to make a galaxy. The galaxies are trying to pull themselves together, the cosmological constant is trying to push them apart." So there's a competition, and when you get a larger and larger cosmological constant, you get fewer and fewer galaxies, okay? You see where this is going? You get the largest number of galaxies when the cosmological constant is smallest. And so he said, I can use these data to make a prediction with one extra assumption. The extra assumption, which deserves a whole podcast on its own, I'm not going to go into it right now, is that you and I are randomly chosen from the set of all of these possible observers.
1:29:06 Sean Carroll? So there's some observers in universes with zero cosmological constant. There's some observers in the universe where the cosmological constant is 10 to the minus 121 times its current value. There's universes where it is what we think it is now, 10 to the minus 120. There are fewer observers in universes where it's 10 to the minus 119. That's a slightly bigger value of the cosmological constant, which pushes galaxies apart, makes it harder to form stars and therefore form observers. So basically, he used the number of galaxies as a proxy for the number of observers. He assumed we are typical in that distribution and he made a prediction. What is the likely value of the cosmological constant? The answer is zero for the likely value overall.
1:29:51 Sean Carroll? But then you can ask, okay, what's the typical deviation from zero, right? A small positive number is allowed, a small negative number is allowed. And what he found, given all the many, many huge uncertainties in what he's doing, is that the ratio of the cosmological constant to the matter density in a typical observer's universe should be between 0 and 10. The cosmological constant should, on the one hand, not be very big compared to the matter density. But on the other hand, there's no anthropic reason for it to be very small compared to the matter density either. And this is 1987, he's saying this. So he makes a really provocative point using this anthropic reasoning in 1987.
1:30:36 Sean Carroll? He says, if this is the reason why the cosmological constant is small, we should probably be able to observe it someday. That was a very radical thing to say in 1987. And guess what? He was exactly right. I mean, the observed ratio of the cosmological constant to matter is about 3. If you pick a random number between minus 10 and 10 and you get 3, you are not surprised by that. That's not a fine tuning. That's a perfectly legitimate thing for it to be.
1:31:04 Sean Carroll? This is on the one hand amazing that he got it right and it's also provocative. It makes you think. It's certainly not a reason to declare victory. Okay, you can't just say, well, this is the right answer. We know it now. There's a lot of assumptions that went into Weinberg's argument that I think are questionable. What is that probability distribution? Are we typical observers and so forth? Are there other things that you should also be scanning over as people say? Like, what if you just had bigger density fluctuations in the early universe? Then you could make more.
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1:32:32 Sean Carroll? Alexi's, are you saying your theory predicts the largest possible density fluctuations? Because that doesn't seem to be true. So there's a lot of work to be done, a lot of provocation out there. Still, 10 years before the observation, he made the prediction he was right. In science, you always get points for that. So it's at least one example where an attempt at reasoning anthropically, in other words, reasoning by saying, there's a lot of different values in different parts of the universe. We are typical observers. What should we predict? That kind of reasoning worked. And I want to emphasize that the anthropic principle sometimes gets a bad rap for being
1:33:13 Sean Carroll? kind of tautological, like people think of it as saying, "Life exists only when life can exist." I mean, that would be tautological, right? But this is more than that, clearly. I hope that it's clear that this is more than that. This is not just saying we exist where we can exist. This is saying we should reason as if we are typical observers in some ensemble, and that allows us to make quantitative predictions for things that have different values within that ensemble. That's not tautological at all. That's actually quite powerful. It only makes sense, it only works, if the multiverse exists, okay? And that has its own problems for all sorts of reasons.
1:33:55 Sean Carroll? Also, just to say, you know, there's people who don't like the multiverse idea because they don't believe you can calculate anything. Like Weinberg did calculate something, but there's kind of an infinity divided by infinity problem that he glossed over a little bit. If you truly have an infinitely big universe, then the number of people who observe a cosmological constant like us is infinite, and the number of people who observe a cosmological constant 10 times bigger is also infinite, or 100 times bigger is also infinite. Is it really legit to say that it's more probable that we observe what we observe? You're taking infinity by infinity, and you might think, "Well, maybe I can be careful and regularize and take a limit."
1:34:40 Sean Carroll? Guess what? People have tried to do that, it doesn't really work. It's what is called the cosmological measure problem. This is one of the things we talked about in the class, in my Philosophy of Cosmology class. It turns out to be really difficult to wrangle these infinities and their ratio down to a finite number. Not that it can't be done, but there are people out there who despair of ever being able to do it, and they therefore think that the multiverse is just not predictive at all. Maybe they're right, or maybe we're just not being clever about it quite yet enough. Okay, let's switch gears to the very different idea of theism, or the argument from design. You know, this goes back to William Paley, back, I don't know, 1800s, I think? Just before Darwin. He was making this idea, he was a theologian, who said, "Look, if
1:35:25 Sean Carroll? you're walking down the beach, and you stumble across a rock, you go, 'Ah, there's a rock,' and you go on your way. It's not like a big deal. You see rocks on the beach all the time. But if you stumbled across a wristwatch lying there on the beach, you wouldn't think to yourself that the random motions of the surf, and the sand, and the wind, and the Earth's natural ways of being, had randomly put together a wristwatch. You would think, rather, that someone had built it, and then someone had lost it there, on the beach. Why? Because the wristwatch is an exquisitely designed mechanism. Every piece inside the wristwatch fits together, in a certain way, for a certain purpose. And that is the sign,
1:36:08 Sean Carroll? in Paley's view, that it was the outcome of a designed process, not a random process. And of course, what he was having in mind was biology. What he was thinking was, biological organisms are also exquisitely organized machines. Clearly, this is evidence for the existence of a creator who designed them. And Charles Darwin, more or less, came up with a better explanation, not too long afterwards, so that lost a little bit of power. But maybe, you can use the same logic for the universe, as a whole. People like Robin Collins, who is a contemporary theologian, have done things like this. So Collins made the case, "Look, what if we eventually do get on a rocket, and travel to Mars? And
1:36:52 Sean Carroll? when we go to Mars, we find, not just what we already know is there, but also, a habitat, like an artificial-looking habitat, like, you know, a dome, that has air in it, and there's a source of water, and there's food, and things like that, and that is exactly right for human beings to step into." Would you think that that was just something that randomly arose due to the Martian version of geology and plate tectonics and things like that? No, you would think that someone had put it there. Either human beings had gone secretly before that, or aliens did it for us, or some supernatural force did it, but you wouldn't think that it had just happened. And in Collins's view, again, the universe is like that.
1:37:34 Sean Carroll? The universe is a hospitable habitat for humanity that needed to be designed in order for life to be possible. So the idea of all of these arguments, you know, they sort of change with time as our scientific understanding improves, but the idea, one way of thinking about it is to be a good Bayesian, right? You know what it means to be a good Bayesian. You have a different set of propositions, and you assign prior probabilities or prior credences to these propositions, and then you update your priors on the basis of new data. So in this case, the propositions are theism, that is to say that there exists a godlike
1:38:16 Sean Carroll? supernatural being that cares about us and shapes things for our benefit, or naturalism, the idea there's just a natural world, obeying the laws of physics, nothing more. And the point is of the fine-tuning argument for the existence of God, that these observed fine-tunings in nature, in physics and cosmology, have the feature that if they weren't there, some of them anyway, life would be impossible. If the cosmological constant were its natural value, life would be impossible. If the neutron were much, much heavier than the proton, life would be impossible. If the entropy of the early universe was maximal, that is to say, if the universe was just in thermal equilibrium all the time, life would be impossible.
1:39:02 Sean Carroll? So what they claim is that these fine tunings are evidence that naturalism is getting the wrong answer. If your prior for naturalism was of similar order of magnitude to your prior for theism, so the argument goes, you should update it on the fact that life exists. And the probability that life exists under theism is of order one. Our notion of what God is includes the fact that God wanted us to be here. The fine tunings are evidence that the likelihood of life existing under naturalism in the set of all possible worlds where all these physical parameters could have taken on different values is infinitesimally small.
1:39:46 Sean Carroll? So when you update your priors using Bayes' theorem, if the priors are similar, the likelihood that life exists under theism is so much bigger than under naturalism that you end up concluding that theism is true. That's the argument from design. Okay. I'm obviously skimming over some details just because you've heard things like it before. The details matter to the experts, for sure. But I don't believe it. So, and it's my podcast, so I'm gonna tell you why I don't believe it. I think there's a lot of issues here. Some of the issues that are more obvious issues are not actually the most important ones. The most obvious issue is, do you really think you know what the probability of life existing is under naturalism? That is to say, how well do we really know that if the constants of nature were different,
1:40:31 Sean Carroll? life would be impossible? I, on the one hand, I try to be humble about our knowledge. I do think that life could be possible under a wide variety of circumstances that we don't actually know about. Let's put it this way, if someone just handed you the standard model of particle physics without any knowledge of the macroscopic world and said, "Is life possible under these laws of physics?", you would have a difficult time showing that life would be possible. So it's possible that under very different values of the parameters, life is still possible. But nevertheless, I take the gist of the argument, the strength of it, the thrust of it, because some of these fine tunings are Both very big and very blunt.
1:41:15 Sean Carroll? You know, the cosmological constant, if it were 10 to the 10 times its current value, I cannot imagine a way that life would be able to exist, much less 10 to the 120 times its current value. So I think it's okay. I'm gonna give him that. I'm gonna grant the theologians and theists out there that the probability of life given theism in this perspective is greater than the probability of life given naturalism. The reason why I don't accept that conclusion all the way is of course the multiverse, is of course the anthropic argument. If you think about the probability of life given naturalism as the probability of life given a single universe cosmology
1:41:58 Sean Carroll? times your prior for a single universe cosmology, plus the probability of life given a multiverse cosmology times your prior for a multiverse, as long as the multiverse has some substantial prior probability to it, the probability of life given that we're in a multiverse is very, very large. Right? Somewhere in the multiverse, you're bound to have parameters of nature that allow for the existence of life. So that's why people who are using the fine tuning argument to argue for the existence of God are so dead set against the multiverse. They can only sort of get their argument off the ground if you think the multiverse doesn't work for one reason or another. Just to give you one example of someone who doesn't think it works, who wants to get the theistic answer,
1:42:43 Sean Carroll? former Mindscape guest Philip Goff has been writing about the fine tuning argument for the existence of God and for the anthropic multiverse argument. He makes an interesting and I think ultimately not very convincing argument, but I'll give you a brief idea of what it is. He says that the anthropic argument is an example of the inverse gambler's fallacy. What is that? So the gambler's fallacy is when you have some random process going on and there's some result you're hoping to get and you've gotten it even less than you should have by sheer random chance. So let's say you're rolling two dice and you want double sixes and you should get that one out of 36 times. But you've rolled 100 times in a row and you've gotten it not at all.
1:43:26 Sean Carroll? Okay, so that's less likely than you would have predicted. The gambler's fallacy is, I'm due.
1:43:33 Sean Carroll? Because it hasn't happened yet, it's probably more likely than average to happen next time. That's a fallacy. If you actually have a good random number generator or random stochastic process, it's still a 1 in 36 chance every time, even if you haven't had it. That's the gambler's fallacy. The inverse gambler's fallacy is this weird thing. It's kind of unconvincing. I don't know why anyone would fall for it, but the idea would be if someone walks into a room, I'm not exactly sure what the setup's supposed to be, so you walk into a room, you see someone rolling dice, and they roll double sixes the first time, okay? The inverse gambler's fallacy says, "Well, that was really unlikely that you would have rolled double sixes in just one roll, therefore, I conclude you've been rolling for a long
1:44:17 Sean Carroll? time. There were a lot of rolls prior to this, because that's the only way to make it likely there would have been double sixes on the roll that I saw." This is clearly a fallacy. I think I agree. This is such a bad fallacy, I can't imagine anyone getting it. Just because you see an unlikely number doesn't mean you happen to see the last example of a large series of trials of that process, okay? One way or the other, you only saw one of them. Now, you kind of see the analogy with the anthropic principle. Philip is saying, "Look, we see one trial, we see the universe we're in. It seems unlikely to us, and therefore, the multiverse people are saying, 'Therefore, there must be a multiverse.'"
1:45:02 Sean Carroll? But that's just the inverse gambler's fallacy. I think it's just not a good analogy. I think that that's not what the multiverse people are saying, because it's different seeing someone roll double sixes than seeing life existing. The question you're asking in the cosmological example is different than the question you're asking in the dice example. In the dice example, you've seen one roll, and it happened to be double sixes, and you're saying, "What does that tell me about other rolls?" The answer is nothing. In the cosmology example, you're seeing that life exists and you don't know how many universes there are out there, but you know that somewhere in the ensemble of universes, life exists.
1:45:46 Sean Carroll? So the question you're asking now is not, "How likely is it?" Or, "What can I conclude from the fact that in my universe, life exists?" You're saying that as grand cosmological scenarios go, if I'm comparing a cosmological scenario with a multiverse, in which in different parts of the universe, different cosmological parameters take different values everywhere, versus a cosmological scenario with just one universe and one randomly selected set of constants of nature, which one is it likely for life to exist anywhere? That's the difference and why it's not the gambler's fallacy, because you are, by the nature of being a living being,
1:46:27 Sean Carroll? post-selected to be only in the part of the universe you're looking where life exists. That's not the case in the dice example. There was no principle of physics that said, "When you walked into the room, you were definitely going to see the example where its double sixes." In the universe, you're definitely going to find yourself in the case, in the part where life can exist. So if your universe is amenable to the existence of life, that theory fits the data better. So goes the anthropic reasoning. So I don't think that that argument really works, the inverse gambler's fallacy argument, but you kind of see the philosophical to and fro that is necessary to think about this. I think that it's actually, it was funny, because Philip will say, and other people will say,
1:47:11 Sean Carroll? that the fine-tuning argument does give you evidence for the existence of God. He will buy into the general design argument. But that would be, if the inverse gambler's fallacy argument worked at all, just as bad for the theistic argument. I mean, one way or the other, you can't reason from this one particular thing that we've observed. I do think that Philip's argument is right next to an important argument, which I actually don't know how to think about, which is the issue of old evidence in Bayesian reasoning. This is an issue that was brought up by philosopher Clark Glymore all the way back in the 1980s. He said the following, "Look, what if you, you know,
1:47:54 Sean Carroll? you're trying to be a good Bayesian, which means you have some priors, collect some new data, update your priors on the basis of a likelihood function. So that's how it's supposed to work. What if you had the data all along? What if you always knew the data?" The example he had in mind was actually Albert Einstein inventing relativity and knowing the procession of mercury. Clark Glymore claimed that Einstein couldn't really count the procession of mercury as a successful prediction of general relativity because he already knew it was true. And people have gone back and forth about whether or not that counts. I think it doesn't count. I think that people correctly say that Einstein might have known that the procession of mercury was off, but he didn't know that his new theory predicted the right one. That calculation that he did counts as new information
1:48:39 Sean Carroll? that is perfectly fair for you to update your priors with. But the basic issue of old evidence is still there, and it is especially important for anthropic reasoning. There is no evidence older than the fact that we exist. You know, we wouldn't be having this conversation if we didn't exist. And I think this is sort of spiritually, if you'll forgive the word, what Philip Goff is getting at, that it is not quite fair, maybe, to use our existence as evidence of anything at all. Because we literally couldn't be having this conversation without that. It's a precondition, not a surprising experimental result. At least, maybe, like, that's an argument
1:49:23 Sean Carroll? that I could at least take seriously. I'm not, I don't think it's true. I don't think that what I just said is correct, the right way of thinking about it. I think there's better ways of thinking about it, but it's on the table there as something to think about. Let me, uh, I don't have that much time left, sorry. I've scheduled myself badly here, so I actually had to wind up a little bit. So let me get to what I think is actually the more important worry about the argument for design, um, from, yeah, argument from design. The argument from design is stated as an argument about the probability of life existing under theism versus naturalism. But the fine tunings that are purportedly necessary for life to exist aren't necessary
1:50:08 Sean Carroll? for life to exist under theism. That is to say, these fine tunings with the cosmological constant, the mass of the neutron or whatever, what do they really allow to exist? What they allow to exist are physical configurations of matter that come into the form of complex information gathering adaptive systems, right? You can make atoms and chemistry and molecules and cells and biological organisms all without violating the laws of physics. That's what the fine tunings allow for. But guess what? You only need to have physical configurations that are complex adaptive information gathering
1:50:51 Sean Carroll? systems under naturalism. You don't need that under theism. The fine tunings are not evidence that souls are possible because the value of the cosmological constant is so small. God could have made life, no matter what the constants of nature were. If you, any of you saw, you know, we had Daniels as podcast guests. They were the writer-directors of Everything Everywhere All at Once. And there's a funny scene where there's two people talking to each other and both people are portrayed as boulders on a beach wearing googly eyes. In the world where God exists, that's totally plausible. He's God. He can do anything. He's not bound by the laws of physics.
1:51:33 Sean Carroll? He could attach individual souls or essences or minds to any configuration of stuff he wanted. It doesn't have to be complicated, able to gather information, adapt or any of those things. So secretly, the fact that the constants of nature are so amenable to precisely the kind of complex systems that would be lifelike without any supernatural help is actually evidence for naturalism, not for theism. Especially when you take into consideration all of the other ways. I think that if you're going to play this game at all, you have to be good Bayesian about it, okay? And that means not only updating your priors,
1:52:15 Sean Carroll? but updating your priors with all of the evidence that you collect. And here is where it gets very, very tricky. You're trying to say, what kind of universe would you expect, given theism, given the existence of God? And you're absolutely welcome to say, well, I don't know. I don't know God's intentions. That's fine, if that's your attitude, 100% fine. But don't tell me that the argument from design works, because the argument from design relies on knowing God's intentions and deriving that the probability of life existing under theism is large, okay? But if you do know God's intentions, then why is God making all these galaxies? Why is God doing things so extravagantly?
1:53:00 Sean Carroll? Why is so much of the universe inhospitable to life, right? And you might say, well, no, no, God would have done it that way. Okay, but guess what? You had a chance to say that before we discovered that there were other galaxies and other planets and things like that, and nobody did. Before the existence of modern astronomy, the conventional way of thinking about cosmology was the Earth was all there was, right? That was the apparent prediction that theism was giving you, not the universe that we see. So I think if you're a good Bayesian and you take into account all of the data we have about the universe, it doesn't look like one God would have created. So because of that, and because of the fact that God could have done life even without all of these fine tunings,
1:53:46 Sean Carroll? I don't think the argument from design really works. So the last one then is, we just got lucky, right? And I know people, some of my favorite, smartest physicists and cosmologists have a very explicit attitude that our job is not to predict these numbers. Our job is to measure these numbers. And we have no right to have any expectation for these numbers, like the cosmological constants, to be big, small, blue, yellow, green, or anything like that, okay? And that's it, there's nothing to be learned. We move on with our lives. I think that's wrong also. I think that's a wrong-headed attitude. But I think, I get why they do that, because sometimes these fine tunings are portrayed, like I said, as disagreements between theory and experiment.
1:54:31 Sean Carroll? And we don't have a theory that predicts them, so it's not quite right to think of them in that way. What they are is surprising. And I think that the surprisingly-ness to us human beings isn't nothing. It's not to be discounted. And the reason why it's not to be discounted is, we don't know the final true theory of the universe, right? We are not done yet with science and physics and cosmology. We don't have our theories of everything. We're still trying to work our way toward them. And the importance of fine tunings, in my mind, is that they might be clues to finding the correct further future theories of everything, the theories we don't have yet.
1:55:14 Sean Carroll? But let's put it this way, forget about big numbers and small numbers. What if we had measured the mass of the muon, which is exactly like an electron but heavier, right? It's the heavier cousin of the electron. It's about 200 times heavier than an electron. What if we had measured the mass of both the electron and the muon? And in this different possible world we're imagining, the ratio of the mass of the muon to the mass of the electron had been exactly pi. It was 3.14159, I don't know, to 10 decimal places, okay? For no good reason. We just measured it. We measured the mass of the muon, measured mass of the electron, divided them by each other, the answer was pi to 10 decimal places. What are you gonna say?
1:55:58 Sean Carroll? Are you gonna say, "Oh, we just got lucky, that's nice. Makes it easier to have the particle data book table where we list the mass of the muon, it's just pi times the mass of the electron." Maybe, or maybe you would say to yourself, you know, I bet there's an explanation for that. I bet that there is a formula in a theory that we don't have yet that predicts mass of the muon is pi times mass of the electron. Now, that's not what we have. We have these tiny numbers, not these funky metrical quantities. But the point is that these apparent fine tunings, to me, are special places in the set of all possible future theories, the set of all possible worlds, if you like, the
1:56:41 Sean Carroll? set of all possible physical realities. There's a subset of all the possible ones that have these explanatory relations in them that say, oh, here's why spatial curvature is small, here's why the cosmological constant is small, et cetera. And if you find those, and they're really there, that teaches you something incredibly valuable that might be important for other reasons. You know, inflation was motivated first, actually, by there were certain grand unified theories that overpredicted the abundance of magnetic monopoles in the universe. And then Guth was extra motivated when he learned about the horizon and flatness problems, and that was great motivation, trying to explain these fine tunings.
1:57:25 Sean Carroll? But eventually, it was realized that inflation actually offered something in addition. It offered a predictive theory of the perturbations, the density fluctuations that come out of the early universe and that we see today in the cosmic microwave background and in large-scale structure. So by taking a fine tuning seriously, by looking for a theory that provided an explanatory reason for that fine tuning, and by pushing that forward into regions you hadn't thought about before, you learn something new about the universe. That's why I think that fine tunings are important to pay attention to. I'm not saying it can't be possible that we just got lucky.
1:58:07 Sean Carroll? It might be that for some of these values, it's just how it is. And, you know, they, in the set of all possible worlds, they could have been different, and life wouldn't exist in those worlds, and too bad for them. Whether or not there is a multiverse, maybe we're just lucky that the reality of the cosmos allows the existence of life even without a variety of different... Environments in different places. But we don't know that. And we might be missing a big clue about what the correct theory of the world is if we don't try to explain these fine tunings. The explanation might be new dynamical theory. It might be the anthropic principle and the multiverse. It might even be the existence of a supernatural designer, or for that matter, a college-level
1:58:51 Sean Carroll? computer programmer in a higher reality who's running a simulation. And we live in that simulation. You know, the design argument works just as well for simulation as it does for the existence of God. So I think all of these are worth thinking about carefully. As I said, I didn't try to pick on too many people. I picked on Philip a little bit. Sorry, Philip. No hard feelings, but I didn't try to pick on too many specific people. But I do think that this whole field of fine tuning and anthropic reasoning and old evidence and Bayesian updating, I think there's a lot of work to be done to turn our philosophical musings into something more rigorous and useful. And it might even help us predict things in the future for the next generation of experiments.
1:59:36 Sean Carroll? That's the best we can hope to do. Thanks for listening. I'll talk to you next time. Bye bye.
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