What is the fine structure constant? Where does it come from? Why is it so important? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPTION (AUTO-GENERATED)

Have you ever heard of numerology? It's the study of numbers, or rather important numbers, or rather, numbers that appear to be important and seem to be connected to other things that also happen to be important, Like deciding that there is some important lesson to be learned from the digits in your birthday or the number of steps you took today or the license plate of the car that backed into you or all of the above. Uh, the license plate was 605723 and you're you're 60 years old. You were. You were born on the 23rd and you had you had 57 miles left before you ran out of gas. This is important. This is a connection. I mean, naturally, this all gets a little bit silly pretty quickly because we are surrounded by numbers everywhere, and we are surrounded by connections everywhere. Some of those connections are meaningful, and some of those connections are just coincidence, so you can turn anything into a number.

I can look at the title of a book, and I can assign a number to each letter and then add them up. Or or maybe multiply them together? Or is it divide the first half by the second? Anyway, it doesn't matter, or I can count the number of steps I take. Uh, the the amount of water droplets I use in a shower the the amount of how many slices of cheese I had with my breakfast. That's right. My breakfast. Don't judge me. We're surrounded by numbers, and we're surrounded by potential ways to connect those numbers. And so numerology is an attempt, Uh, not a very rigorous attempt to try to find meaningful connections and interactions between all those numbers to try to explain the existence of the numbers that we find in our lives and try to use those numbers to explain other important things in our lives. So what if I told you that very serious scientists the true nerds sometimes get obsessed with numerology?

It's because of one specific number. The most random, unexpected UN asked for number in all of physics that turns out to be perhaps the most important number in physics. The magic number is drum roll, please. 137. Yeah, that's it. 137 137. The number 137 Explain that number and you can explain the universe. Maybe we'll we'll get to that. OK, well, well. 100 and 37 of what? 100 and 37 kg. 100 and 37 astronomical units. 100 37 heartbeats. 100 37 square inches. Don't none of those. It's 100 and 37 patreon to subscribers. That's patreon dot com slash PM, sir. That's right. If you can explain the number of patreon subscribers that I have, then you might just explain the universe. No, it's 100 37. This number that very serious scientists get all numerological about this number that appears in many of our equations of physics, this number that we did not predict we cannot account for, and we didn't know it until we saw it has no units.

That's special, because there are a bunch of important numbers constants that that appear in physics, chemistry, biology, avogadro's number, the plank constant the speed of light. But but these are all dimension full numbers. These numbers have units associated with them. These are numbers that tell you how much of a certain thing. But if you change the unit system. You Could you change the actual value of the number like the speed of light? You know, the speed of light is some speed. 300 million m per second. But I can change units. What is a meter? What is a second? The actual value of the speed of light. The actual number that I type in depends on what my definition of a meter is and what my definition of a second is. I could just as easily call the speed of light like 47 or 6.2 or one times 10 to the negative 500.

It doesn't matter because I can just find units and change around the number. But not this number, not 137. It doesn't have units. It doesn't matter how long a meter is. It doesn't matter how long a second is and doesn't matter how many times a caesium atom cycles through itself. It doesn't matter. No matter the unit system. No matter how I make measurements, no matter how I decide to standardize the measurements and observations in the universe, I will always arrive at 137 as the value for something we call the fine structure constant. Well, um, well, actually, it's It's one over the fine structure and constant the actual fine structure. Constant is is one divided one by 137. Which is another reason why you shouldn't get too wrapped up in numerology because there's always different ways to write numbers. But it's still that value that 1/137.

It's a number, and it doesn't matter how you approach the universe. You'll always arrive at that same number. In fact, if we were to meet an alien civilization and we were able, we finally got the chance to talk. We sat down in a room together and say, OK, let's hash out. Let's compare notes on our understanding of reality. You show me yours, I'll show you mine. We're gonna have a lot of trouble talking about things like the speed of light or the distances to nearest stars or the lifetime of the universe, because those are all dimensions. So we got back up. We can't say like, well, according to us, the universe is 13.77 billion years old. What's your answer? And they say Well, it's it's it's 47. Grab knots. What? What does that mean? Well, OK, so a year is the the amount of time and it gets No. But we can go to that table and we can sit down across from the aliens and say, Hey, fine structure, Constant 1/137.

0, and and this is what we mean by 137. You know, we we we would have to define our our number system. That's not nearly a big deal. And they would translate into that their their own number system. Uh, how they do decimals represent, represent numbers and they say, Oh, yeah, us, too. It's It's 1/137. We'd agree on it with no reference to anything else in the universe if I wanted to find the speed of light and and give the number for it. I have to reference something I have to say. Well, well, first, you gotta measure how long it takes for the Earth to orbit the sun. But I can just say, Oh, fine structure Constant 1/137. I don't have to reference anything else it. It stands apart from the universe. It stands apart from our standards and definitions of the universe. It is a bare raw number that appears in physics, and it has no explanation. But first, the name Let's let's clear up the name, uh, you know, the bore model of the atom, you know, developed by Neil's bore. There is a pre quantum idea of how the atom worked, if somehow the bore model the atom with with the nucleus in the center and then the electrons whizzing around, as in this like mini solar system.

Somehow that became the international symbol for physics, especially, and sometimes even science, even though it's wrong. But But anyway, I don't know how that happened anyway. The Bore model, uh, is a very, very simplified, pre quantum mechanical model of how atoms work and electrons happen. Uh, one of the things that the Bore model can get you is the appearance of spectral lines of of the emission and and absorption of very specific wavelengths of light. Because you jump, the electrons jump from one level to another, they can absorb a very specific wavelength, and they'll jump to that very specific energy level, or they'll drop from one energy level to another, and then they will emit some radiation with that exact same energy and that exact same the wavelength needed for that energy basic board. Model it. It helps you at least get a start and understanding spectral lines the the emission of very, very specific wavelengths of light from atoms. But once you start getting into a proper quantum treatment and especially starting to incorporate notions of spin electron spin and the interaction of spin with the nucleus and how this might affect, uh, the kind of radiation you see that there isn't just a one line, one emission line, one very specific frequency of light or wavelength of light emitted by an atom that there are really two.

they're just very, very, very close together. But that tiny little difference between the two is due to quantum mechanics and and quantum field theory and understanding of all sorts of cool stuff. We call this a fine splitting of a spectral line. Also, we call it a fine structure of a spectral line, and the fine structure constant was first discovered when looking at the quantum nature of electrons inside of atoms and how that affected the splitting of spectral lines. And so that's how we get the name, the fine structure. Constant tells you how much splitting you get. It it tells you how strong that splitting is. No way to have that backwards. It how much splitting you measure in the spectral lines tells you the value of the fine structure constant. Like you sit here, you say, OK, OK, OK. I see that splitting happens of these spectral lines from atoms, and I can understand how this splitting happens by applying a little bit of quantum mechanics to my understanding of the atom.

I can predict the amount of splitting, or at least I can predict that splitting happens, and the amount of splitting the the strength of the splitting the width of the splitting, however you want to describe it is, well, it's a number. It's a random concept. It could be anything. Could be 15 could be 6,223,542,143. It could be pi, Uh, but nothing in my quantum mechanical theory tells me what the number should be So instead I have to go out and measure it. And then that will tell me what the constant is somehow the the voice of an early 20th century physicist. So we don't predict the value of the fine structure constant. Instead, we have our theories and our models that tell us, uh, how the atomic world works. And then this constant appears. You see that you need some number to account for this. That number is the fine structure constant. But then there's nothing in the theory itself that tells you what the value of that number should be. So instead you have to go out and make some measurements and then backtrack to plug in the gap.

And when the fine structure constant was first discovered, it was like, OK, whatever constants appear everywhere in nature, that's not anything new for a constant, uh, a number that appears in your calculations that you have to go out and measure like like like take hooks, law, right. You you press on a spring or you pull on a spring and you meet some resistance, and the resistance is proportional. To do this of the spring, uh, to how strong of a spring it is, and you don't know it ahead of time. The theory doesn't tell you that. Instead, you just have to go and measure this particular string with this particular stiffness. And then you can get all the other calculations and you can go on to do the rest of your physics. So, like what? S. But then the fine structure Constant started showing up in other places, and it started getting all sorts of interesting interpretations, like there it. It turned out there was more than one way to generate this fine structure Constant. It didn't just appear in the equations of of atomic spectral line splitting it.

It was showing up in other things. Things like, uh, we'll take two electrons, put them a certain distance apart, measure the energy needed to overcome their natural repulsion at that distance. Then take the energy of a photon with a wavelength. Two pi times that distance, and the ratio of those two energies is the fine structure constant. Or take. Take that bore model with a little orbiting electron around a nucleus and take the velocity of the electron in the lowest energy orbital, the closest it can get to the atomic nucleus, measure its velocity and divide by the speed of light. You get the fine structure constant. Uh uh. Take the electrons energy in that lowest level and divide by the rest. Mass energy of the electron. That's the square of the fine structure. Constant the fine structure. Constant started to show up in more than one place as we were developing quantum mechanics in the early 20th century, and it came up every time we started looking at the interaction of electrons and radiation, like the classic emission of radiation from an atom, when an electron jumps energy levels or comparing speeds of electrons to the speed of radiation or the energy contained between two electrons and and the same amount of energy in a same size photon.

Any time we were comparing contrasting, combining charged particles with electromagnetic radiation, the fine structure constant kept popping up again and again and again, and we came to realize that the fine structure constant isn't just a constant that is hyper specific, specific to a model of the splitting of spectral lines of radiation coming off of atoms. So it's much more broad than that. It's much more general. It's a measure of the strength of the interaction between charged particles and radiation. It tells us the fine structure. Constant tells us how easily electrons talk to radiation or charge particles in general, Talk to radiation. Talk to electromagnetic radiation. It could be anything. The the strength of that coupling, that strength of that interaction could literally be anything, just like the strength of gravity could be anything. There's a constant that appears in our gravitational equations, called Newton's G, and it has a specific value.

It tells us the the fundamental strength of gravity, the fine structure. Constant tells us the fundamental strength of the relationship, the interaction between charge particles and electromagnetic radiation. You can even define it. You can write down a formula for it in terms of other constants and parameters of nature. It's usually represented by the Greek letter Alpha. You can write as one divided by four pi, divided by the electric constant or the permittivity of free space times the fundamental charge squared, divided by the reduced planks, constant times, the speed of lights. And right there you see the fine structure constant. The way this is defined is a relationship between the charge the elementary charge, say the charge of the electron and the speed of light right there. It's a connection between charge particles and electromagnetic rea. It tells us how strong these are relative to each other. It tells us if I have a certain amount of charge, how easily it will talk to radiation and vice versa.

But unlike those other numbers, like the speed of light planks constant the fundamental charge. The fine structure. Constant doesn't have units. It's just 1/137. And in fact, at first, when we were first measuring this, we thought the fine structure constant was exactly 1/137 which is where all the numerology came in and because it didn't have units like the speed of light has units. G has units. All these things have units. So the number itself doesn't matter because you can just change the units and get a different number. But with a fine structure constant, you can change your units all day long, folks. You can switch from feet to meters from seconds to hours. Kilograms pounds. It doesn't matter. You can change your units all day long, and the fine structure constant will simply be 1/137. So it seems like it feels like the number itself has meaning and importance, because the speed of light 300 million miles per second, the actual number of 300 million doesn't matter, because what matters is my definition of the meter.

And the second. If I change what a meter is, I get a different number. And so the number carries no importance. With a fine structure constant. The number seems to have importance because there are no units associated with it. Somehow, even though nobody asked the relationship between charge particles and electromagnetic radiation has this value that doesn't depend on anything else. And it doesn't depend on how you look at the world. Measure the world, standardize the world, doesn't depend on your unit system. It always just has this strength. And so, of course you're wondering. 1/137. Where's that come from? Sir Arthur ending the same guy who did that famous test of Einstein's relativity attempted this. He calculated the number of protons in the universe, and he estimated it to be, uh, 137 times two to the 256th power. So you can see he he arranged. He got a very large number and then rearranged it so that the 137 popped out. So he's like, There you go.

Fine structure. Constant is 1/137. Yeah, well, the number of protons in the UN is 137 times another large number. Uh, this was mocked at the time. There was another paper that came out. Uh, connecting the fine structure constant to the temperature of absolute zero is is meaningless. But But you can't blame someone like ending. Because when you see this number 1/137 1 that seems like really simple, really straightforward. There are no units. What is the meaning of this number? Why this number? The physicist Wolfgang Polly once collaborated with Psychoanalyst Carl Young to explore the significance of this number. I don't know if they got very far or not. These kinds of calculations continue to the present day Every once in a while, every year or so, there's some paper that claims to have a derivation of the fine structure. Constant. Ultimately, it come boils down to finding some random combination of numbers and and seemingly important things in the universe that that lead to 137. And you can do this too. If you want. You can, you know, Go ahead. Explain the importance of the number 137.

Why not 100 25? Why not do it? 476? Why not? Six pie? Why that number? Uh, but before you get too carried away there, my little Arthur Eddington's, um, it's it's fine structure. Constant is not exactly 1/137. Uh, the current measurement of the inverse of the fine structure constant is 137.035999206 plus or minus 11 in those last two digits. So you have a little bit tougher time. You can't just explain 137 you have to explain 137 and then a bunch of numbers following the decimal place. If you thought that was crazy, then I hope you're staying down for this. The fine structure constant isn't well, exactly constant. Yeah, you heard me, right? It's not even a constant. I mean, it stays the same through all time and space. As far as we can tell, we've We've measured this a lot at any time. There's an interaction between charge particles and electromagnetic radiation. The fine structure constant is involved.

It's the one governing how strong that relationship is. And so charge particles and electromagnetic ration they've been, uh, they've been interacting for quite a while now for 13.77 billion years and through the vast expanse of our cosmos. So any measurement we make of the deep universe is telling us about the fine structure Constant, Uh, like you can measure the polarization of of radio sources coming from different parts of the universe. You can look at the cosmic microwave background itself. You can do lab experiments to get more precision and a local measurement. As far as we can tell, tell the fine structure constant is the same through all of time and space, because you can plug it in and you say, OK, let's start varying alpha varying. The fine structure constant. You end up with different physics that violates observations. But this is a big but the fine structure. Constant changes with energy. One of the biggest realization with modern physics is that everything changes at higher energy levels.

The physics that we understand here in our everyday lives is not the same physics that happens at high energies. For example, the unification of the forces at low energies, everyday energies. We've got the electromagnetic force and the weak nuclear force. These are two totally separate forces. They don't even talk to each other anymore. They don't even acknowledge each other's existence as separate as separate. Could be. They look different. They act different. They smell different. But when you go up to higher energy scales, they merge together. There's not two forces of nature. There's a single force we call the electro weak force. That's a big change in physics, folks. That's a big change in physics, where even your fundamental forces are changing nature. It's not the same rules. And since the fine structure, constant is one of the rules of physics, you know, it tells you how strong charged particles interact with the electromagnetic field, the electromagnetic radiation. It isn't surprising that this number should change at higher energies. But to explain how we need, uh, we need to go to a party before I continue.

I want to let you know that this show is brought to you by the wonderful folks at better help. That's better. Help dot com I. I know a lot of you listen to this show as a form of therapy A as a way of, of escaping the world and and just going among the stars on this wonderful journey. Uh, I am a big advocate for therapy. I personally see a therapist, and you would be surprised if you don't currently see a therapist how much they can really help you Just navigate a difficult life just like you see a doctor to help you with physical conditions, you should see a therapist Better help dot com is a way to do that. That's convenient. It's affordable. Uh, these are professional counselors that you can connect to online a range of expertise worldwide. It really is an invaluable resource. Uh, as a listener, you can get 10% off your first month by visiting our sponsor at better help dot com slash spaceman. You can join 1 million people who have taken charge of their mental health again.

That's better help. HE LP dot com slash spaceman. See, we've been describing the fine structure constant as this constant that measures the strength of the relationship between charge particles and electromagnetic radiation. But that's all quantum mechanics. For a proper description, we need to upgrade our quantum mechanics to quantum field theory, Which is what happens when you marry quantum mechanics with special relativity. A very brief intro to quantum fields. I've done some episodes on this, Um uh, but basically every kind of particle, every electron, uh, top cork town neutrino there's a bunch of others is associated with a kind of field in the field completely soaks all of time and space throughout the universe. What we think of as particles are just little pieces of the field, little energetic vibrations of the field. Uh, it sounds super cool and out there, but it's backed up by observation and experiment. So quantum field theory it is.

And what we call physics is just the complicated interactions of all these fields happening all the time, and then what we see as electrons and atoms and chemistry and stellar furnaces and the cosmic microwave background and the emergence of life is all just a result of these complicated fields interacting in very complicated ways. The fine structure constant in this view of fields is the strength of the coupling between charged fields in the electromagnetic field. So same deal as before, I guess. But but the the math is way more complicated now. Trust me. In quantum field theory is, well, complicated because at low energies you can just focus on the one interaction you care about. Like like say, you got a very simple situation, an electron and a photon bouncing off of each other at low energies. You can just focus on what the electron field is doing and what the photon field is doing in that moment. But at high energies, the other fields of nature floating around also get to participate in the interaction because they have enough energy to do so.

So at high energies, it's not just a matter of an electron and a photo bouncing off of each other. Uh, the top quark field gets to play a role. The the town neutrino field gets to play a role uh, the W Boson field gets to play a role. They all they all start to talk to each other and they interfere. And they change the nature of that interaction because at high energies, they they have the energy to do it. And here's where the party comes in. Let's say you've got a really hot date. I'm talking dream material here, and you're trying to measure the, um, the chemistry between the two of you. How strong is your, um, coupling strength in this metaphor? You're an electron. Your hot data is a photon, and the chemistry between you is the vine structure, constant in a low energy setting like a quiet romantic dinner out. It's a dimly lit restaurant. There's candles, nice, flat wear. Everything's very romantic and nice.

You order a homage to get things going. You know, uh, you can measure your chemistry. There's the flirting, uh, the glances, uh, the the laughter, things that weren't really all that funny. Uh, the accidental touches of the hand. You can get a really, really good sense of the chemistry. Or or maybe it's bad chemistry. Maybe you Maybe your hot date is looking at the phone half the time. Maybe they're, you know, they're just happy with a salad. And then suddenly they have to go to the bathroom and then and And that was 10 minutes ago. Yeah, but But no matter what, in that quiet, intimate, low energy setting, you can measure your chemistry. But then, after the romantic candle at dinner, you head to a party, a very high energy setting, and you're still trying to measure that chemistry to see if the two of you are compatible. Uh, you know, see what you're coupling strength is, uh, but it's a lot harder. There's lots of people there that are talking to you, talking to your hot date, talking to both of you. At the same time. There's loud music, so it's hard to have a conversation.

Uh, maybe there's a little bit of libations involved, so you don't get a sense of what this person really is. Maybe your phone is blowing up with your DM and everything, and their hot day just got a phone call, and it's like it's a lot harder to measure that chemistry. There's so much going on in that high energy setting that your connection your coupling constant changes. Maybe it gets weaker because there's too much interference. And you know what? That hot date is more of a lukewarm date. Or maybe it gets stronger. Maybe the two of you really vibe with the energy in the room, and you and you just found a corner just dancing your heads off. And like like like the actual chemistry between you can change. This is what happens in high energy physics minus, uh, the dates and the romantic dinners and the the rocking parties. We say that the fine structure constant runs or changes its value at high energies because things like glue, watts and quarks start interfering with the interactions between the electron and the photon and changes how those interactions work.

In fact, we at in high energy settings we have measured the fine structure constant to not be 1/137 but 1/127 a completely different value. And we don't know where the fine structure constant is running to. We don't have an explanation for where the fine structure constant comes from. It doesn't emerge from a our theories. It appears in our theories, like Oh, OK, OK. There's a certain amount of chemistry between charge particles and the electromagnetic field. OK, but the only way to know that value is to measure it in an experiment that our actual theories don't produce that value ahead of time. They don't tell us what that coupling strength should be. It's like someone sets you up on a blind date and you're like, Well, are we compatible? And you're like, I don't know, go find out like that's That's the situation we're in And we don't have a high energy theory of unified physics. We can unify at certain energies, the electromagnetic in the weak nuclear force. We can measure what the fine structure constant looks like there.

But we have no sense or very little sense of what happens at even higher energies. And because the fine structure constant just plops itself into these equations and doesn't tell us ahead of time what its value should be. We we don't know what it what it should be. We don't know what it is at arbitrary energy levels. So not only do we lack an explanation of where the fine structure constant comes from, we don't even know it's correct value at all energy scales, which is why any attempt at deriving the fine structure constant with numerology is is probably bound to fail because that's not the only value it can have. It has different values and different energies. So what is it? What is the fine structure? Constant? Where does it come from? I mean, it's easy to put it into words. It's the strength of the connection between charged particles and electromagnetic radiation and quantum mechanics and quantum field theory or whatever. It doesn't matter. It's the strength of that connection. It's the chemistry between electrons and photons. It's just a number, a fundamental constant that we have to measure and stick into our mathematical models to get everything to come out right.

But why does it have that value and not a different value? We don't know if the fine structure content were different. Our universe would would radically change. Atoms would be a different size. Chemistry would be completely different. Stars would burn differently. Uh, life may not even be possible, and so this opens up questions about fine tuning. If the fine structure constant had a different value, we may not exist or any intelligent conscious observers may not exist in that kind of universe in order to measure it. So of course we see this one, because if it were different, we wouldn't be here and we couldn't measure it. That's called the anthropic principle, and it is not the best way to do science because there isn't a lot to falsify with that statement. Maybe there's something in a multiverse. If you have a whole bunch of different universes with all sorts of different physical constants, I need to do a whole episode on the origins of fundamental constants and what they mean. Go ahead. Someone asked me about fundamental constants.

Where do they come from? I would love to do an episode on that. We hope that a theory of everything a string theory or something else would be able to explain it, where we would just have to put in the number by hand where the theory itself will say yes, humans. The fine structure constant has this value, and it has this value for this fundamental reason, and it's all done. You don't need to measure it because I will tell you this. That's the voice of the theory of everything, by the way, in the amine structure. Constant just playing it drives us nuts. We can't explain it. We don't know why. It has the value that it does. The number itself seems important because there aren't any units associated with it. But we don't know why. It's that number and not a different number. I'll let Richard Feynman explain it better than me. Quote. There is the most profound and beautiful question associated with the observed coupling constant the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455.

My physicist friends won't recognize this number because they like to remember it as the inverse of it. Square. About 137.03597 with an uncertainty of about two in the last decimal place has been a mystery ever since it was discovered more than 50 years ago, and all good theoretical physicists put this number up on their wall and worry about it immediately. You would like to know where this number for a coupling comes from. Is it related to pi, or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics, a magic number that comes to us with no understanding by humans. You might say the hand of God wrote that number, and we don't know how he pushed his pencil. We know what kind of a dance to do to experimentally, to measure this number very accurately. But we don't know what kind of dance to do on the computer to make this number come out. That's where we are. End quote. By the way, Um, and that's where we are. No, he didn't say that. I said that. That's where we are. We don't know where the fine structure comes from.

It's an important number. If that number were different, a life, our entire universe, all of physics would be completely different. It seems to be important because it doesn't have any dimensions. So the number here is trying to tell us something, but we don't know what it's telling us. Thank you to Maria. A on email at Dan Van Tan on Twitter and at TW Dixon on Twitter for the questions that led to today's episode. Thank you to all my patreon contributors. I really do appreciate. I sincerely appreciate patreon dot com slash PM Sutter, especially my top contributors this month. Justin's G Chris Barbara K Duncan M Coy D, Justin ZNH in a Scott M, Rob H loyalty, Justin Lewis, M, Paul G, Don John W and Alexis is your contributions that keep this show going and I, I just can't thank you enough. I really do appreciate it. Hashtag ask the spaceman. Ask a spaceman at gmail dot com. Ask us spaceman dot com for the website. All the old episodes and you'll get a kick out of them. I hope.

Thank you for listening, and I will see you next time for more complete knowledge of time and space.

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