Daniel and Kelly’s Extraordinary Universe - What's the real speed limit of the Universe?

Episode Date: February 9, 2023

Daniel and Jorge talk about how close photons and protons can get to the speed of light, and what's stopping them!See omnystudio.com/listener for privacy information.

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Listen to the new season of Dacias Come Again on the IHeartRadio app, Apple Podcasts, or wherever you get your podcast. Hey, Jorge, do you find yourself speeding up or slowing down as we get older? Kind of both. Both. How's that possible? Well, I'm faster at falling asleep on the couch. That's true. I'm faster at finding a place to sit down as soon as I get somewhere. But I'm getting slower at the same time that time seems to go faster. Do you think there's like a maximum speed to that?

If we live to be like 900 years old like Yoda, would the years just pass by in a blink? Well, first of all, I definitely want to be Yoda. When I don't want to look like Yoda when I'm 900? Somebody needs to tell Yoda about sunscreen. Although my ears are getting bigger. But my lights hair skills are getting worse? As long as you can still do those flips. Well, you know what he said.

He said, do or do not, there is no try. Hi, I'm Jorge, I'm a cartoonist and the creator of PhD comics. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine. and I don't think I will ever do a backflip in my whole life. Oh, I feel bad for you. You've never done a backflip or a front flip. Except underwater.

I've done one underwater, but, you know, not like standing on the ground. And I feel like I've sort of passed the age where you could like learn to do that in the future. I still do backflips. You can do a standing backflip? Yeah. That's amazing. I think we have to see a video of that. Yeah.

Well, usually I do it at those trampoline places. Oh, okay. Yeah, I can do backflips. while skydiving. Yeah, have you skydive? I actually have jumped out of an airplane once. Did you do a backflip? We did all sorts of crazy maneuvers,

but I had somebody strapped to my back, so it was sort of like a double backflip. You had someone strapped to your back or somebody had you strapped to their front? It was basically like baby Bjorn skydiving. Welcome to our podcast, Daniel and Jorge, Explain the Universe, a production of iHeard Radio.

In which our goal is to make your brain do backflips, as you understand the incredible beauty and mystery of our universe. We seek to dive into all of the crazy mysteries about how things work, unravel the explanations that humanity has discovered for what's actually out there in the universe and what rules it is following. We talk about all of that on the podcast and make sure we can explain all of it to you. That's right. It is a vast universe moving slowly and fast at the same time. And we are here to help you do those mental gymnastics to put it all inside of your brain. We hope that you get that feeling of satisfaction when you land.

that triple backflip of understanding quantum mechanics and general relativity in squeezing all of that into your brain. Do you think we usually stick the landing on the podcast? I think we usually stick something somewhere. At the wall usually, yeah, we just throw bad puns at the wall and I hope something sticks. Thank God for good editors. But it is a wonderful and an interesting universe with all kinds of rules in it, it seems, that kind of govern how things can happen, what things can do, what particles and energy and forces

and waves can do out there that give us this interesting and very complex universe that we live in. And a very human thing to do when understanding the universe is to try to figure out what are the rules, what are the laws, what are the limits, what are the things that we are not allowed to do? It's like we're still children pushing up against the boundaries, trying to understand what's allowed and what's not. And now we're translating that to understanding what things in the universe can do. What is a particle allowed to do when it whizzes around a black hole? How fast can it go when it rides the shockwave from a supernova? Wait, are we trying to figure out the rules so we can break them or so we can avoid getting

into trouble? What does that mean to get into trouble? Is the universe going to punish us if we go faster than the speed of light? No dessert for a week? We might get a time out from the universe. Oh, wow. No screen time for a few millennia. Go orbit a black hole and have your time dilated.

No, I think we are trying to break the rules because that helps us understand what the rules are. I mean, if you think that there's a hard and fast rule in physics and then you break it, then you've discovered the universe is different from the way you thought it was. And that's exactly the process of science. That's what we are hoping to do, right? To pull back the veil of our ignorance and understand how the universe actually is. But wait, if you break a rule, then it wasn't really a rule, was it? No, it wasn't a rule. But then you try to figure out what the new rule is, what the real rule is. We hope we think that the universe does follow some set of rules and that we can approximate or learn those rules over time.

Well, the universe definitely rules, and there are lots of amazing things to consider and discover, including those rules themselves. It seems like the universe does kind of have limits about what you can and can't do in it. It certainly does. There are things that happen in the universe and things that just don't ever happen. And something we do a lot in science is take note of that and wonder like, hmm, why is it a muon doesn't ever decay directly to an electron? Why is it that the universe is made of these particles and never those kinds of.

of particles. And we think that all of these things are clues, that there are reasons for the universe to do one thing and never some other thing. And we're trying to uncover those rules and deduce from them what the underlying mechanics are of the workings of the universe. Daniel, wonder if that's a philosophically impossible task. I mean, isn't it impossible to prove a negative? Which means you can never prove that a rule can't be broken, which means you can't ever prove that something is a rule. That's certainly true. And a great example of that is a deep question about the nature of matter like is matter itself stable we are made of protons we think that protons might live forever but we don't know because we've never seen a proton fall apart like you put a proton

out into empty space we don't know how long they last we've watched a bunch of protons for a bunch of years and none of them fell apart that doesn't mean that eventually one day they might all fall apart we can't prove that they won't so we should just give up then you can never prove anything No, what we can do is make statistical limits. We can say we're very confident that the lifetime of a proton is longer than the current age of the universe. We don't know if it's infinity or if it's just very, very long, but that doesn't mean we don't know anything. We certainly know that the lifetime of a proton is not 10 minutes or one minute, right? Or we wouldn't even be here.

So we can certainly learn things about the universe, even if we can never know for sure what those rules are. I am 99% certain that is on Saturday. satisfactory answer. Welcome to philosophy. But the universe does seem to have sort of rules that things seem to fall on. One of them, maybe the biggest one that affects our everyday live is the speed of light. Does that limit you all the time? Like when you're going to the post office and stuff, you're like, oh, I wish I could drive there faster. But this dang speed of light. Yeah, I mean, it affects everything, right? It means there's a speed limit to how fast things can

happen because it doesn't just apply to light. It applies to everything in the universe, right? Yeah, that's true. It probably applies to the people listen to this podcast, because It limits how fast that download can happen. You write everything in the universe. All information and all matter is limited to the speed of light. That means if you want to download all of the Explain the Universe back catalog and it's 7.21 gigabytes or whatever, it's going to take a while because information takes time to transit.

I wonder how many people out there are cursing the speed of light because they can't hear our voices fast enough. One, maybe, or zero? I think that our voices arrive at just the right speed. We're like wizards in Lord of the Rings. We arrive precisely when we intended to arrive. Yeah, that's true. Although maybe people are out there listening to us at like 2x speed.

And so we already are breaking the rules. I wonder if anyone puts us at speed of light play. This podcast is finished as soon as you started it. Yeah, maybe before it started. Maybe people are out there listening to us at half speed because we're going too quickly. Or maybe somebody's playing us at negative speed, which would be. reveal some interesting and deep secrets about the universe. If you play the podcast backwards,

you actually hear the rules of the anti-matter universe. The anti-rules of the antimatter universe, which means what you should do, which maybe should be our new religion. I forgot what this podcast is supposed to be about. Now it's about anti-religion. I think we kind of went a little off-key there. It's about the speed of light and the speed of things in the universe

because it seems to be a very basic principle in the universe, right? The information, light, particles, they don't seem to be able to go faster than a very specific number out there in the universe. Yeah, this is a discovery made just about 120 years ago that the universe does seem to have a speed limit. No matter how fast you're going, you throw that baseball out of your spaceship, it will never go faster than a certain speed. No light, no photon, no particle, nothing in the universe,

no information even seems can transfer from one place in the universe to another faster than this stubborn speed limit. It's fascinating and it's forced us to rethink. think the nature of space and time and simultaneity and all sorts of crazy stuff. Or at least that's what it seems like. We haven't seen anything move faster than the speed of light. But you've got to wonder if maybe there are exceptions to that rule. It may there are special situations or circumstances in which that could happen.

And so today on the podcast, we'll be asking the question, What's the fastest that a charged particle can go? Now, charge is this like a particle that's had a lot of coffee? Or it's just pumped up with excitement? Or just the plain old electromagnetic charge. Yeah, I can't speak to the emotions of these particles. Or their caffeine intake. No, certainly not.

And I think, like, a molecule of caffeine is probably much, much bigger than an electron. So I don't even know how that would work. How do electrons sip coffee? There's a philosophy question for you without an answer. Maybe if the electron is part of the caffeine molecule, technically then it would be supercharged. Yeah, that's right. Are electrons that are part of caffeine, do they have a different experience than electrons that are part of something heavy and slow? Yeah, I guess it depends on whether they like coffee or not.

Are they part of a latte molecule or espresso molecule? I think they probably have a lot of fun. But back to the question at hand, it's interesting that there is an overall speed limit to the universe, something that nothing can ever exceed. But practically speaking, there are also other limits to how fast particles can go, especially if they have other attributes to them, mass or charge. And in this case, we're thinking about the old-fashioned electromagnetic charge. And so this is an interesting question.

And as usually, we're wondering how many people out there had thought about this, whether charged particles have a different speed limit than non-charge particles. So thank you very much to everybody out there who answers these questions on the podcast. It's a lot of fun for us to hear what you are thinking. And if you would like to share your thoughts on the podcast, please don't be shy. Write to us two questions at Danielanhorpe.com. Think about it for a second.

How fast do you think charge particles can go? Here's what people had to say. My quick answer, it will be like 99.99% of speed of light, but that's just a guess. Well, speed of light minus planks constant, multiply something that make units consistent. As far as I know, the maximum speed would be the speed of light, and it's only particles that have mass that cannot achieve speed of light,

so I think that would be the speed of light. I suppose my answer depends on whether or not charged particles have mass, and I'm honestly not sure if they do or not. If they are massless, I would guess that they travel at the speed of light, but if they do have mass and their mass is non-zero, I would say they travel at a significant fraction of the speed of light, maybe upwards of 99% the speed of light. The fastest charged particle could move in space,

I would think, would be the speed of light. If not, 0.99999.99% the speed of light. All right. Everyone seemed to have the speed of light as the limit, or at least 99.99. A lot of nines in these answers. I give it a 9 out of 10 for that vault attempt. Yeah, most people seem on board.

idea that the speed of light is the speed limit, but that massive particles can't reach the speed of light. So people definitely know there's a limit to things and that limit is less for things that have mass. And so the question is, does charge also give them a different speed limit? Well, let's dig into this topic. Generally speaking, Daniel, what is this speed limit that the universe seems to have? So special relativity, Einstein's description of space and time and motion and how all those things interact, tells us that the speed limit is the speed of light in a vacuum, which is about 300 million meters per second,

which is, first of all, a very, very fast number. It's huge, right? 300 million meters in a second is an extraordinary distance to traverse in just one second. And on the other hand, it's very, very slow because things in the universe are far apart. So even if you can fly 300 million meters in a second, it can still take you years to get to the next star,

thousands of years to get across the galaxy, and millions of years to get to other galaxies. Yeah, although assuming you don't want to go that far, it is pretty much instantaneous, right? If you're not the traveling type or want to go to another galaxy or planet, it's pretty much instantaneous, right? At least to our brains.

Yeah, it's pretty much instantaneous. You know, light takes about a nanosecond to go afoot. So if you're looking at something like your computer screen, that's about a foot away, you're seeing the computer screen as it looked a nanosecond ago. But, you know, the human eye also can't really distinguish things that happen faster than like 30 milliseconds. So for all extents and purposes, it's instantaneous on the sort of scale of things that we live in. Right, but I guess it is interesting this idea that there's nothing instantaneous kind of in the universe, right? That even light or pretty much anything, just information in general, things, events, the actual existence of things,

can't sort of move faster in this universe than the speed of light. Yeah, it makes our universe local. It means that you can only be influenced by things around you. And what we mean by around you depends on that speed of light. If the speed of light was much, much faster than things that could influence you, things that we would say are local, would be things that are also further away. If the speed of light was much, much slower, than the universe would be sort of more local. You could only be influenced by things that were closer to you.

We talked in the podcast several times about this concept. of a light cone, the sort of cone of things in your past that can influence you. Things that are nearby can influence you fairly recently. Things that are really, really far away can only influence you from the past. Things that happen in like Andromeda right now can't affect us. And that can be good news, right? If aliens are building a death ray and shooting at us, then it won't arrive here for quite a little while.

Yeah, I feel like it's a very philosophical question too and impact just on the very nature of existence. like a giant pink unicorn suddenly appeared on top of Jupiter. To us, that wouldn't really exist until several minutes later, right? Because that information would take some time to get to us. Yeah, I suppose it depends on what you mean by exists. We wouldn't know it existed. We couldn't prove that it existed.

So in that sense, it wouldn't be real in the way that it wouldn't appear in our experiments, right? But to somebody else on Jupiter, they would be able to see it, right? Yeah, that's what I mean. That for us, it wouldn't exist, right? Yeah. In the same way that if the sun disappeared, we wouldn't notice for eight minutes because it takes that long for light from the sun to reach here. So the universe as we see it is not the universe as it is right now. And more deeply, relativity says that there is no sort of universal definition of right now. That time in the universe depends on where you are and how fast you are going. This sort of requires us to give up this concept that there is a universe that's marching forward. in time uniformly, sort of an ancient Newtonian view. Right. And so it's called the speed of light, but it should actually be called the speed of anything

in the universe. We just call it the speed of light because basically light is the only thing we know that can go at that speed or the first thing we knew that could go at that speed. Yeah, it really should be called the speed of everything or maybe the speed of anything, but it's the sort of maximum speed limit of any kind of information. Any field, for example, in the universe when it wiggles, information can't move through that field faster than the speed of light. And so that limit applies to every field, including the electromagnetic field for which photons are a ripple in that field. And because they have no mass,

they can move at that maximum speed. It's true for any massless ripple in a field. So for example, we think that gravitational waves travel at the speed of light as well because those ripples in the gravitational field or equivalently ripples in the curvature of space. So we think those also move at the speed of light. And if there are other particles out there, we have in discovered that are massless, they would also move at the speed of light. Are there other particles we've discovered that are massless? Gluons, which are the particle that help transmit the strong force, they are also massless. So they move at the speed of light.

But gluons are weird because they interact very strongly with themselves. And so you never sort of see a gluon by itself. They can form weird states like glue balls. But those have energy inside of them. So they have mass. So glue balls don't move at the speed of light, even if individual gluons do. Hmm. Interesting. So photons are the only particles that we know of that can move at the speed of light. Well, I think gluons count as moving at the speed of light, even though they don't go very far.

Gravitational waves aren't a particle. If gravity is quantized and made of gravitons, then those are probably massless and would move at the speed of light. But we don't know if gravitons exist. Yeah, so technically photons are the only particle we know of. What do you have against gluons? Well, no, didn't you say a little while ago that they don't? Quite, you never see them. move at the speed of light? Yeah, you can't, like, shoot a gluon across the universe and have a travel like a photon. But, you know, a gluon, which is exchanged between two quarks, that does happen at the

speed of light. The speed of information of the strong force is the speed of light. All right. Well, photons and gluons, I guess they're stuck together in that category. But again, maybe give us an interest of sense, what does it mean to move at the speed of light? What is it like? It's a fun question.

What is it like to move at the speed of light? You would like to be able to put yourself in that frame and say, I'm moving along with a photon. What does the photon see? It's not something you can really do because photons don't have a frame. Like if a spaceship is flying by the Earth, you can put yourself in this frame

where the spaceship is at rest and say, okay, I'm moving with the spaceship. What do I see? I see the same thing as the spaceship. You can't do that with a photon because the photon is never at rest. There's no like frame you can put yourself in to say, I'm moving with the photon.

Photons always move at the speed of light relative to anybody. So no matter where you are in the universe how fast you're going, that photon is zipping away from you at the speed of light. And so you can't sort of like put yourself in the point of view of a photon. So there's sort of like pure motion, right? Because they don't have mass. So they don't have a substance to them. So all of their energy is in their speed.

Yeah. All of their energy is in their speed. Exactly. They are just motion. There is nothing to them. Like if you could catch up with a photon, it would sort of disappear in a puff of motionlessness. You know, they are. motion. But it's like a wiggle in the electrokinetic field, right? Yeah, it's the motion of

that field. But isn't it a wiggle, like a little perturbation? Yeah, pure kinetic energy, right? And people write in, they're confused about that because they say, well, it's energy and energy is MC squared, so doesn't that mean the photon has mass, right? And the wrinkle there is that E equals MC squared only applies to particles at rest because the M there applies to its rest mass. There's another term there, which we don't often talk about. The full equation is like e squared equals m squared c to the fourth plus p squared c squared. There's a term there for momentum. And so for a particle that has mass and momentum, there are two terms there.

There's the mass term and the momentum term. Photons don't have any mass. So they just have the momentum term. The equation for a photon is e equals p c, momentum times the speed of light. So photons are really weird because they don't have mass, but they do have. have momentum so they can like push things. Right. That's how solar sails work, right?

They catch sunlight and they transfer that momentum to motion. And that's how you can sail out of the solar system. So photons do have momentum and they go at the speed of light. But there are a couple of caveats to that. Maybe not just for photons, but for everything else. Let's dig into the ways that the rules don't apply. But first, let's take a quick break. Your entire identity has been fabricated.

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because I guess a charged particle is a little bit different. Yeah, particles that have charge also have mass. And the rules for massive particles and for charge particles are a little bit different than the rules for massless, chargeless photons. Yeah, we've been talking about how the speed limit applies to photons, which I guess it does, but it almost only applies to photons and I guess gluons, but it limits how fast photons can go.

But there are caveats to that rule, right? It's not necessarily the case that photons go at the speed of light. Yeah, there are caveats to that rule. When we say that photons always travel at the speed, of light. What we mean, but we don't often say is that that's true in your local inertial frame if space is not curved. Basically, the playground of special relativity. Operate in flat space and have things whizzing around near each other. That's what you're going to observe. But if space is curved or expanding or if things are really, really far away from you, then you can no longer

apply those rules and things start to get really weird. It seems like a very limiting caveat. I mean, local flat space, that's almost never true. I mean, if you're there, then you're bending space, which means it doesn't apply to you then. That's true, although you're not that massive, and so you don't really bend space. Oh, thanks. I've been working out. And no matter how curved the universe is,

you can always find a locally flat approximation to it. Space is always flat in a local approximation. You can always put a tangent on some surface and say, oh, in this vicinity, I can assume. I'm in flat space. And that's sort of the issue is that special relativity applies in our local vicinity where we can assume things are flat, but then over larger distances, we can't really make that assumption.

And that's why things break down. Well, I guess the question is, how do they break down? When space is not flat, when it's a little curved or a lot curve, does light go faster than the speed of light or slower than the speed of light? The space is curved between you and another galaxy. Then you have two different frames. You have your frame and you have the frame in that galaxy. And how you translate velocity from one frame to another is a little bit arbitrary.

You can do it in lots of different ways because space is curved between you. We talked about this once in the podcast. It has to do with like comparing whether two vectors are parallel and comparing their length. And if space is curved between two points, then how you like move that vector over that space depends on the path that you've taken. So it's sort of not well defined in the sense that there's like many ways that you could do it and get different answers. So you can't really compare velocities in two different frames if there's curvature or expansion between them. Yeah, it gets really tricky and complicated. And we spent a whole hour talking about this, I remember. But I guess what's the takeaway? There are many ways

to compute the velocity of a photon going from between here and another galaxy. But do some of these solutions tell you that this light is moving faster or slower than the speed of light? Or do they all tell you it's moving slower than the speed of light? Some of them tell you that those photons are moving faster than the speed of light. And some of them tell you that the photons are moving slower than the speed of light. So there's an infinite number of ways that you could do this compare velocities in one galaxy to another because there are different reference frames. There's also sort of a standard way that we do it, which is that we just try to like extrapolate our frame out to the end of the universe, even though we know that doesn't really work. And those galaxies are moving away from us faster than the speed of light. So things seem to be breaking that speed of light limit because you've done this thing of extending your inertial frame out to the end of the universe, which are not technically allowed to do. The other way you can look at it is to say they have their frame, we have our frame, and space is expanding between those frames. So nothing's breaking the speed of light limit. It's just that space itself is growing. And in its own frame, everything is moving less than the speed of light. That's what I mean when I say there's like different ways you could

assign that velocity. They're all sort of reasonable and give you different answers. So there are those important copyouts. But in your local inertial frame, like you're the laboratory, the measurements you're going to actually make, you're never going to observe anything going past it in the speed of light. I see. So even the local bending of space can only slow down the speed of light. Is that what you're saying? Like if I'm orbiting a black hole, for example, and space is really warped around me and I run

those experiments, what would I see? There I think you're breaking the assumption because we're talking about a local flat frame. And if you're near a black hole, then you're definitely not in a local flat frame. So I would say that if your space is pretty local and pretty flat, you're always going to see photons moving at the speed of light. though there's one caveat we haven't talked about yet, but if you are near a black hole or something else, then space is bendy and crazy and the velocities get insane. And you could see photons moving at zero velocity, for example, as a photon climbs out of the gravity well or tries to climb

out of the gravity well of a black hole, to you, it appears to go at zero velocity, right? Photons are contained within a black hole. How could they do that if they were moving at the speed of light? because the bendingness of space there makes all of these velocities a little wonky to calculate. But would you ever see it go faster? Probably not, right? That only happens when you have space expanding.

Yeah, I believe that's true. The bending of space can only effectively slow down the speed of light that you observe. In order for things to appear to go fast in the speed of light, you need space to expand rather than to curve. Well, there's another caveat to this also is that the space has to be empty.

Yes, that's right. The limit that we talk about is the speed of light in a very, vacuum, as if there's nothing out there in space for these photons to interact with. But we know that light slows down as it passes through materials. The index of refraction tells you the speed of light through that material. So light traveling through glass goes slower than light traveling through vacuum. Light traveling through air goes a little bit slower than light traveling through a vacuum. And that's not because somehow the air molecules or the glass molecules like affect the space

that the light travels in, it's because light keeps running into things, right? It's like trying to move through a crowded room. The photon keeps bumping into the air and glass molecules and then getting re-emitted on the other side, but it still has to sort of, something has to happen when they bump. The speed that we're talking about here

is basically the average speed from one side of the material to the other side of the material. You can think about it as a light sort of zigzagging between molecules or atoms that it's interacting with. Each of those zigs or each of those zags, it's still moving at the speed of light. a photon is always moving at the speed of light, but it sort of gets absorbed, it takes time to get re-emitted, and so that sort of slows it down. It's like if you send your teenager on an errand

to the store and they stop and chat at their friend's house every block, it's going to take them a lot longer to get there, even if they're driving at top speed between all of their friends' houses. That's an interesting neighborhood you live in where your teenage is driving and stopping to talk to their friends at the same time. Hopefully, they're being the speed limit there. Fortunately, I don't have teenagers who can drive yet. So maybe my analogies will improve when I have some data. So if space is empty and it's not bendy or distorted or expanding, then light goes at the speed of light. But now what about particles that are not light? Pretty much everything else besides gluons. What if a particle, for example, has mass? Yeah, so photons can go at the speed

of light if they're in a vacuum and not near a black hole, for example. But electrons, particles with mass, they can never actually reach the speed of light. Oh, yeah? Is there a particular reason for that? It's sort of interesting and philosophical. It's not like there's a lower speed limit for electrons. It's not like electrons can only go 99% of the speed of light, and they're always pegged there. It's just that they asymptotically can approach the speed of light. So there's no actual limit there. They just get closer and closer and closer to the speed of light as you add more energy, but they never actually get to the speed of light.

Yeah, that's weird. So you're saying that it's a speed limit, not because if I just create an electron or a proton or a core going at the speed of light, maybe that can happen. It's just that for any electron or particle with mass that starts at rest, I can never get it to the speed of light. A particle with mass moving at the speed of light would have infinite kinetic energy. So if you could create a particle with infinite kinetic energy, then yes, it would be moving at the speed of light. Otherwise, taking a particle and getting it to the speed of light would require giving it infinite kinetic energy. And the key concept, of course, is that these particles have mass. So why is it that having mass means that you require infinite energy to get to the speed of light, whereas a photon with a non-infident energy can move at the speed of light, right? And the key concept there, of course, is the mass of the particle. Mass is this property of particles to like resist changes to their motion.

So you have an electron. It's going to stay at rest unless you give it a push and it's going to stay at a certain velocity unless you give it a push. And mass is that ability to resist changes in motion. So it takes energy to speed it up. So you give the electron a push, it speeds up. As it gets faster and faster, though, it takes bigger pushes, more energy to take it up the next level in speed.

It's not a linear relationship. Right. And that's just kind of how the universe is, right? Like, that's just what mass is. It's not like they have mass and therefore they're hard to push the more you go. It's like the definition of mass is the fact that some particles gets harder and harder to push. Yeah, I think it's important to understand what things we understand and what things we just like observe and define. Right.

We have observed that things that have internal energy in them have this property of inertia. And electron has some internal energy to it. protons have some internal energy to it, the mass of the corks and then also the mass of the binding energy between the corks. Anything with internal energy seems to have this property of inertia, of resisting changes to its motion. So yeah, sort of a deep philosophical mystery of why that is, why do we live in the universe that way and not some other way, but it's something that we've observed in the universe and try to describe in our theories and those theories are very effective when we test them out in nature. So that's why we believe they are true, even if we don't know

why the universe is this way and not some other way. Yeah, it's a massive issue. And how is this related to the Higgs boson and the Higgs field? Because I know everyone talks about how the Higgs field is what gives particles mass. Is this inertial mass that's related to the speed of light related to the Higgs field and Higgs boson? So most generally, mass is just internal stored energy of some kind. And most of the mass in your body doesn't come from the mass of the particles of your body. So, for example, you're mostly protons and neutrons.

And those protons have masses from their quarks, but they also have mass from how those corks are bound together. So the internal stored energy, the proton is mostly the energy of those particles bound together. A little bit of the mass of the proton does come from the mass of those particles, like the corks that are inside the proton. And those quarks, they get their inertial mass from the Higgs boson. But again, it's internal stored energy. The quarks themselves, like the true theoretical object is massless. But as the cork moves through the universe, it interacts with this Higgs field and it creates this like effective quark, this object which is moving differently because of its interactions with the Higgs field in such a way that it moves as if it had mass. So it is inertial mass that we're talking about.

And some of the inertial mass in the universe comes from the Higgs boson, but not all of it. Right. In fact, most of it doesn't come from the Higgs field and Higgs boson. Most of it just comes from this fact of the universe that things with energy are hard to move in the universe. and impossible to get moving at the speed of light. Yeah, exactly. You often hear the refrain that as things approach the speed of light, they get more massive, as if like an electron is getting as heavy as a car,

for example, if it goes near the speed of light. And it's an old-fashioned idea that's trying to convey to you this concept that as something approaches a speed of light, it takes more energy to move it up in velocity than it did when it was moving slower. We don't really think about things literally gaining mass. It's just that it takes a bigger push to notch them up to the next level of velocity. Right. Although it's kind of true, right?

I mean, the idea is that mass is the resistance to movement or to increasing your movement, then yeah, as it gets harder because the universe says it gets harder, technically it is sort of gaining that mass, right? It doesn't really hang together, though. Like if you want to use that mass in F equals MA, it doesn't really work because then that mass is like weirdly directionally dependent. Because if you're moving along the X axis, for example, now you have like a lot of mass along the x-axis, but you don't have that mass along

the y-axis, right? Like, somebody can give you a push along the y-axis with a certain force and you get one acceleration, but if they give you a push along the x-axis with that same force, they get a different acceleration. The more general way to think about it is just in terms of momentum. This is equation for relativistic momentum, which includes this factor. So we just leave mass as the rest mass of an object, like how massive would it be if it was at rest? And this extra resistance to accelerating at high speeds, we fold that into the definition of momentum, which then helps fix up F equals M.A., which in the end is just F equals the derivative of momentum with respect to time. So this is this whole topic of relativistic kinematics, which I think we dug

into in another episode. Yeah. I think what you're trying to say is that an electron looks less massive depending on which angle you're looking at it. Like the electron has a good angle and a bad angle. I think the concept of relativistic mass, things actually getting heavier as you get to higher mass doesn't really hang it together if you try to propagate it through all the equations. But it's sort of an old-fashioned way of thinking about things. All right. That's how mass affects how fast you can go in the universe. Now let's talk about how other things might affect how fast you can move through the universe, including whether space is empty or not. So let's get into that. But first, let's take another quick break.

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All right, we're asking the question, what is the fastest that a charged particle or pretty much any particle can go, right? Because there are a lot of caveats to this idea that nothing can move faster than the speed of light. One of those caveats was that space had to be empty. But what happens if space is not empty?

Yeah, we talked about photons moving through glass and photons moving through water. But you might imagine, well, what about space between here and Andromeda, for example? That's mostly empty, right? Or what about the space outside of Earth in our solar system? That's mostly empty, right? Photons surely spend most of their time whizzing around basically at the speed of light. Well, it turns out, space is almost never empty.

The space in our solar system is filled with particles from the sun. The sun pumps out a solar wind of protons and electrons and other stuff that's always blowing through the solar system. So photons traveling through our solar system are constantly running into these protons and these electrons and interacting with them. Really interesting. So you're saying like the space between us and the sun is not perfectly clear. There's all kinds of stuff in it, which means that the speed of light in our solar system is slower than the speed of light. A tiny, tiny, tiny little bit slower. This is very dilute.

There's like not very many protons per cubic meter, you know, between us and Jupiter, for example. But there are some. And so if you're talking technically like our photons that bounce on. have Jupiter then come back to Earth. Are those moving at the speed of light? Technically, they're moving at a little bit less than the speed of light. And that's also true for photons from Andromeda, for example, because the space between us and other galaxies is also not empty. Right. Yeah, because there's a lot of stuff in between us and Andromeda, even though it's hard to see with the naked eye. You probably imagine the universe is these clusters of stars

grouped into galaxies. And that's basically where everything is. But don't forget that the universe is mostly gas, right? Stars are a tiny fraction in the universe. So really you should be thinking about the gas in those galaxies. And there's also gas between the galaxies. Think of the universe not as a bunch of dots of stars clustered into galaxies, but like a cosmic web of gas filaments. And where those filaments overlap and intersect, then you have these deep pools that form stars and visible light and all that cool stuff. But between the galaxies, there are these very long tendrils of gas between us and Andromeda, for example. huge amount of gas. They estimate like a significant fraction of all the matter in the universe,

our kind of matter, is actually between galaxies, not in galaxies. Yeah, like 50% of the matter in the universe is basically smog, right? Yeah, they call this the warm, hot, intergalactic medium. I'm not even going to talk about why they call it warm hot. But the acronym for it is W-H-I-M, which, you know, they didn't choose on a whim. But they did, because it spells out whim. It's just a whimsical name, you know, for something that's warm hot. Now, why do they call it warm hot? Because it's not a cool warm.

They call it warm, hot because it's sort of between warm and hot. And remember, if you were out there in space, you would freeze your tushy off. But these particles are fairly high speed. And so we say that they have a fairly high temperature. This intergalactic plasma can actually be fairly hot on a temperature scale, even though it's very, very dilute. So it doesn't contain a lot of heat. heat, but because of the speed of the particles, they say it's fairly hot, not fast enough

to call it actually hot, not slow enough to call it just warm. So it's sort of like warm too hot. So they call it warm hot. It's not a whim or a hem. It's a whim. It should be W-T-H-I-M, but then it would be like within. I guess the lukewarm intergalactic medium wouldn't really fly there. No, I suppose not. And so that slows down photons that are moving through the universe, you know, between galaxies. So when you're looking up at the night sky, know that all the photons that are traveling towards you are traveling a little bit less than the speed of light,

even the ones coming from other galaxies. But wait, wait, wait, isn't the space between our galaxies also expanding? So space everywhere is expanding, right? The expansion happens simultaneously at every point in space at the same rate. For things that are near each other, however, that's a pretty small effect. And also things that are near each other have gravity. So the gravity of the dachometer is actually pulling it towards us faster than space is expanding between us.

So you can basically ignore the expansion of space when you're thinking about photons from Andromeda because they're like in our little local gravitational bubble. Right, but it's still expanding, which is speeding up to speed of light a little bit. But you're saying that the effect of the whimsical gas in between is slowing it down more than the expansion is speeding it up. Yes, so the expansion would be moving Indromeda away from us,

but gravity's holding Andromeda in place, sort of the same way that gravity holds the Earth around the sun. You're right, though, the photons from Andromeda are moving through expanding space because they're moving towards us, that would actually be slowing down their effective speed. Okay, now let's talk about charged particles. We know that particles with mass have extra limitation with respect to the speed of light, and we know that space is not empty.

Does having a charge affect you more than having mass? Like, does it somehow give you a boost through this plasma or does it slow you down more? Well, interestingly, there are no particles that have charge and don't have mass. So the photon has no charge and no mass. But if you're a charged particle, number one, that means that you have mass, like the electron and the quarks, all the particles that have charge also have mass. So that right away means if you have charge, you can't go at the speed of light. Really?

Wouldn't that mean you think they're somehow related? Yeah, it's a really fascinating clue and one that we just don't understand at all. It's possible that one day in the future, we will discover a massless charged particle, but none exist currently in our universe that we know about. Well, gluons have charge. They just don't have electromagnetic charge, right? That's right. They have color charge, charged for the strong force.

Yeah, that's a really good point. And we do sometimes discover new categories of particles, like the Higgs boson, was a particle like no particle we had seen before. It's the first scalar particle that we've ever found before, a particle without any spin. And so it's possible to discover new categories of particles that we haven't seen before in the universe, or we might discover that that's impossible for some reason we haven't learned yet. The Higgs boson has mass to it, right?

It interacts with itself, but does the Higgs boson have charge? The Higgs boson doesn't have electric charge, no. But it was interesting because it also doesn't have quantum spin like all the other particles do. So the Higgs boson does have mass, but no charge. The Higgs boson has mass but no charge, but we don't have any particles that have charge but no mass. Oh, I see. So if you have charge, then you usually have mass. That's the pattern so far.

We don't know if that's a hard and fast rule or just sort of like a coincidence. Or electromagnetic charge, I should say, right? Yes, exactly, electromagnetic charge. So now if you're a proton flying through space, an electron flying through space, you obviously can't move at the speed of light just because you have mass. So if you're a charged particle, that also means you have mass, which means you can't travel at the speed of light. How does the charge affect your motion?

Does it make you go faster or slower through this plasma in the universe? Well, both. First of all, it allows you to go really fast because having a charge means that you can get accelerated by cosmic electric field. or magnetic fields. For example, you can be near a black hole or a pulsar, which have very, very strong magnetic fields, and you can gain huge acceleration.

And so it allows you to sort of like tap into cosmic accelerators to get to really, really high energies. But then on the flip side, it also slows you down because particles that have charge interact with photons. And the universe is filled with photons. We have photons left over from the Big Bang, from the cosmic microwave background radiation that's everywhere in the universe.

And so charged particles flying through the universe interact with those photons which constantly sap their energy. I think you're saying that if you have charge, that means that you can be pulled by something that has the opposite charge ahead of you, right? But it could also maybe slow you down if the thing is behind you.

Absolutely could. Yeah, magnetic fields and electric fields from cosmic objects can accelerate or decelerate these particles. But also just the whole universe is filled with a fog. If you're an electron, you're flying through the, universe, there really is no empty space. You see photons everywhere and they're all interacting with you. And there's this effect that if a particle is moving really, really, really, really fast, then it tends to interact with this cosmic microwave background photons in a way that saps its

energy and turns it into other particles. And so there's basically like an effective limit to how fast a charged particle can move through the universe because of its interaction with the cosmic microwave background radiation. Meaning like if I'm a proton flying, through space and I hit a photon head on, it's going to slow me down, right? Because the photon has momentum, right? You're going to interact with that photon and some of your energy is going to get used up to create a new particle, like a delta particle or some other low mass particle. And then you can go fly off in another direction, but you've lost some of that energy. What if the photon hits you from behind? Wouldn't it push you? Yeah, that's possible. And photons move faster than protons. So they can

catch up to a proton and give it a little push. But the overall effect from a proton like flying through this fog of photons is that it gets slowed down. It's like compressing the space in front of it. You mean like there's an average speed of all the photons in the universe and if you're going faster than that average speed, then you'll hit the photons kind of like bugs in your windshield. I'm not sure how to calculate the average speed of a photon, but think about like the number of directions that a photon could hit you. In most of those ways, it would slow you down and only a few ways it would speed you up. Because you're moving in a certain direction relative to the, maybe the average direction of all the photons.

Yeah, that's right. And also as you move really fast through space, you tend to contract the space in front of you, which increases the density of the photons in front of you that you're hitting. So there's a special relativistic effect there also. And what this means is that really, really high energy particles get slowed down. So we have cosmic accelerators out there, the centers of galaxies and pulsars, whatever,

spewing out super high energy charged particles, but then they basically screech to a halt. It's really, really hard to have charged particles, a crazy high energy in the universe because the universe is kind of like sticky for those charged particles. And that means something really cool. It means that if you see one of these particles,

it can't have come from very far away because very, very high energy particles can't go very far in our universe. They're sort of local. Or they started off with a super duper, duper, crazy amount of energy to start with. Yeah, exactly. They would have to have double bonkers energy

if they come from really far away. So you're saying that the whole universe is filled with a little bit of light pollution. which kind of slows everything down, makes it even harder to go at the speed of light. And as time goes on, that light pollution, the cosmic microwave background radiation, is cooling. And so this effect is fading because the universe is expanding,

that light is cooling, it's getting more and more dilute. So as time goes on, the universe gets like less sticky for charge particles, which means that these charged particles, these protons, coming out of cosmic accelerators, can go faster and faster as time goes on, or further and further at their top speed. You mean like this light pollution of the universe is kind of dissipating in a way? Yeah, precisely.

The fog is clearing very, very slowly. Isn't the universe also filled with like quantum vacuum energy, like particles popping in and out? Yeah, all space has quantum fields in it and those quantum fields can never relax down to zero. So there's always some energy in space. We think that's very, very small. We also think that might be what's causing the expansion of the universe. it's not something that we understand very well. So then if something is flying through space,

does it interact with those, that vacuum quantum field particles popping up? It doesn't necessarily slow it down. It just gives it inertia. So interacting with the Higgs field is how the particle gets mass and doesn't have to slow it down. So it's possible to interact with these quantum fields

without slowing down. All right. Well, then now to wrap it up and to answer the question we set out to answer at the beginning, Daniel, what's the fastest that a charged particle can go? Super duper, dober, dober, duper, fast, but not actually the speed of light and not for very far in the universe. You mean 0.99999.9.9.9%. Yeah, there's no actual limit, right? These particles can keep approaching the speed of light but never

actually get there. And for charge particles, they just can't do it for very far. So even if I did a perfect backflip at the Olympics, you would only give me a 9.999.9.9. I would give you a warm hot score, yes. All right. Well, another reminder that the universe has these strange rules, if you think about them, they're kind of strange. But that's kind of the job that we as humans have is to figure out what are the rules and when can you break them. And that's the job of us experimentalists to go out there and actually try to break the rules of the universe. All right. Well, we hope you enjoyed that. Thanks for joining us. See you next time.

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