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Good job. Thanks, Hey Daniel, Has particle physics done anything useful lately?

Good job. Thanks, Hey Daniel, Has particle physics done anything useful lately?

You mean, other than revealing the fundamental nature of reality?

You mean, other than revealing the fundamental nature of reality?

Have you done that?

Have you done that?

I mean it's a project.

I mean it's a project.

I mean that's all nice and cool, but it doesn't really help me, you know, with the dishes or you know, with my diet.

I mean that's all nice and cool, but it doesn't really help me, you know, with the dishes or you know, with my diet.

I guess we did also invent the World Wide Web.

I guess we did also invent the World Wide Web.

That's pretty helpful, you mean web surfing. I's say, that's not the most helpful thing in my life, but that was a long time ago. Anyways, what have you done for us recently?

That's pretty helpful, you mean web surfing. I's say, that's not the most helpful thing in my life, but that was a long time ago. Anyways, what have you done for us recently?

Yeah?

Yeah?

Maybe we should be coming up with like a fundamental physics diet plan.

Maybe we should be coming up with like a fundamental physics diet plan.

It's just coffee and doughnuts all the.

It's just coffee and doughnuts all the.

Time, existential angst about the nature of the universe.

Time, existential angst about the nature of the universe.

I guess the problem with physics is that it says that the faster you go, the more massive you get. Right, that's kind of an anti diet.

I guess the problem with physics is that it says that the faster you go, the more massive you get. Right, that's kind of an anti diet.

I guess I was thinking, you know, black holes something something something liposuction, black holes. I don't know. I didn't really have it worked out.

I guess I was thinking, you know, black holes something something something liposuction, black holes. I don't know. I didn't really have it worked out.

Quantum cosmetic surgery, whoa.

Quantum cosmetic surgery, whoa.

Orange County is definitely the place for that.

Orange County is definitely the place for that.

And you can get a ten to the color baite h Ii am orhammy cartoonist and the creator of PhD comics.

And you can get a ten to the color baite h Ii am orhammy cartoonist and the creator of PhD comics.

Hi.

Hi.

I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I was shocked when a pediatrician offered my one year old plastic surgery.

I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I was shocked when a pediatrician offered my one year old plastic surgery.

Wait what they do that on one year old?

Wait what they do that on one year old?

In Orange County? You're never too young for plastic surgery.

In Orange County? You're never too young for plastic surgery.

Oh boy. I get to the offer like a subscription service, like a membership or something.

Oh boy. I get to the offer like a subscription service, like a membership or something.

It's a long term relationship. No, our son had like a vein on his eyelid, and the doctor was like do you want me to remove that? And we were like, no, please.

It's a long term relationship. No, our son had like a vein on his eyelid, and the doctor was like do you want me to remove that? And we were like, no, please.

Do not.

Do not.

Wait the eyelid or the vein. You're like, I think my son needs it's his Eyelidly.

Wait the eyelid or the vein. You're like, I think my son needs it's his Eyelidly.

We were like, I'm pretty sure that's going to be fine, And newsflash, he's fine.

We were like, I'm pretty sure that's going to be fine, And newsflash, he's fine.

Were you like, I'm a real doctor, I don't think he needs any surgery.

Were you like, I'm a real doctor, I don't think he needs any surgery.

I'm not a real doctor, but I'm pretty sure he didn't need any surgery.

I'm not a real doctor, but I'm pretty sure he didn't need any surgery.

Like, I'm not a real doctor, I just play one in the lab. But anyways, Welcome to our podcast, Daniel and Jorge Explain the Universe, a production of iHeartRadio.

Like, I'm not a real doctor, I just play one in the lab. But anyways, Welcome to our podcast, Daniel and Jorge Explain the Universe, a production of iHeartRadio.

In which we try to show you the nature of the universe in all of its unvarnished glory. We don't want to edit out the ugly bits and smooth over the bumps and wrinkles. We want to show you the universe the way it actually is, even when it conflicts with our intuition and runs aground for our preconceived ideas for how things move and flow and dance in the universe.

In which we try to show you the nature of the universe in all of its unvarnished glory. We don't want to edit out the ugly bits and smooth over the bumps and wrinkles. We want to show you the universe the way it actually is, even when it conflicts with our intuition and runs aground for our preconceived ideas for how things move and flow and dance in the universe.

That's right, that's because we love the universe just the way it is. We love the og universe, the original organic version of the universe. Untreated, unvarnished, and pretty mysterious.

That's right, that's because we love the universe just the way it is. We love the og universe, the original organic version of the universe. Untreated, unvarnished, and pretty mysterious.

That's right. We prefer the granola crunchy Berkeley version, with all of its hair and all the original places, even on all of its black holes.

That's right. We prefer the granola crunchy Berkeley version, with all of its hair and all the original places, even on all of its black holes.

Well, let's not go too far there. I mean, I'm a big fan of socks and sandals, but you know, there's a time in a place.

Well, let's not go too far there. I mean, I'm a big fan of socks and sandals, but you know, there's a time in a place.

I'm all for accepting people and universes just the way they are.

I'm all for accepting people and universes just the way they are.

But it is a wonderful and beautiful universe. It doesn't need any cosmic surgery because when we look at it, we're just stricken with awe an amazement at how wonderfully complex and intriguing it all is.

But it is a wonderful and beautiful universe. It doesn't need any cosmic surgery because when we look at it, we're just stricken with awe an amazement at how wonderfully complex and intriguing it all is.

And one of my favorite things about the universe is that it's surprising. It's not like we look out into the universe and we're like, oh, yeah, that's pretty much how I expected, or oh yeah, there's nothing new out there to discover. Every time we dig deep into something, every time we scratch under the surface, we find out, Wow, the universe is quite different from the way that we imagined it, which is wonderful because it's an opportunity to learn to discover the truth instead of just coasting on our intuition.

And one of my favorite things about the universe is that it's surprising. It's not like we look out into the universe and we're like, oh, yeah, that's pretty much how I expected, or oh yeah, there's nothing new out there to discover. Every time we dig deep into something, every time we scratch under the surface, we find out, Wow, the universe is quite different from the way that we imagined it, which is wonderful because it's an opportunity to learn to discover the truth instead of just coasting on our intuition.

Yeah, the universe is very different out there in space, beyond our galaxy, beyond our cluster of galaxies, and it's also very different at the molecular and atomic and particle scales. Things are actually very different than our everyday experience.

Yeah, the universe is very different out there in space, beyond our galaxy, beyond our cluster of galaxies, and it's also very different at the molecular and atomic and particle scales. Things are actually very different than our everyday experience.

And we're tempted when we discover these new weird wrinkles in the universe too explain them in terms of things that we know, things we understand. It's a very natural a way to try to understand the universe, to describe it in terms of the language that you already have. Sometimes, though, that gets awkward. It's hard to understand how quantum particles dance around if you're thinking about them as little dots of stuff, and that's because they're not really little dots of stuff. And it's hard to think about velocity and energy and mass as things approach the speed of life because the definitions of those things have to change, and the way things move and bounce against each other and transfer energy and momentum is really very different at high speeds than it is down here in the slow motion life on Earth.

And we're tempted when we discover these new weird wrinkles in the universe too explain them in terms of things that we know, things we understand. It's a very natural a way to try to understand the universe, to describe it in terms of the language that you already have. Sometimes, though, that gets awkward. It's hard to understand how quantum particles dance around if you're thinking about them as little dots of stuff, and that's because they're not really little dots of stuff. And it's hard to think about velocity and energy and mass as things approach the speed of life because the definitions of those things have to change, and the way things move and bounce against each other and transfer energy and momentum is really very different at high speeds than it is down here in the slow motion life on Earth.

Yeah, thinks are very weird and awkward in general. When you talk to physicists I feel not just when you learn learn what they have to say.

Yeah, thinks are very weird and awkward in general. When you talk to physicists I feel not just when you learn learn what they have to say.

All right, this is not a therapy podcast. We're talking about the nature of the universe here.

All right, this is not a therapy podcast. We're talking about the nature of the universe here.

That's right, that's right in the universe is not awkward or weird. It's just the way it is. And I guess it's us that are weird and awkward, right, because we have this picture of how the world works, but that may not be how the universe actually works.

That's right, that's right in the universe is not awkward or weird. It's just the way it is. And I guess it's us that are weird and awkward, right, because we have this picture of how the world works, but that may not be how the universe actually works.

Yeah, And in physics, our project is to build a mathematical discription of how things work in the universe, something that lets us make predictions and gives us a peek at the machinery behind the curtains that deciding, like what happens when two balls bounce against each other. But that doesn't always translate in an easy or simple way to English, the language that most humans speak. So when physicists are trying to explain how things work when the universe gets weird, they use the terms that we're familiar with, mass and energy, momentum, et cetera, and try to translate the weirdness in those terms. And so you hear a lot of explanations for what happens when things get fast. Some of those explanations are bang on, and some of them are a little bit misleading.

Yeah, And in physics, our project is to build a mathematical discription of how things work in the universe, something that lets us make predictions and gives us a peek at the machinery behind the curtains that deciding, like what happens when two balls bounce against each other. But that doesn't always translate in an easy or simple way to English, the language that most humans speak. So when physicists are trying to explain how things work when the universe gets weird, they use the terms that we're familiar with, mass and energy, momentum, et cetera, and try to translate the weirdness in those terms. And so you hear a lot of explanations for what happens when things get fast. Some of those explanations are bang on, and some of them are a little bit misleading.

Yeah, because I guess one of the biggest mind bending moments and autism and strangest moments in the history of science was when we found out that the universe is kind of difference once you start moving really fast exactly.

Yeah, because I guess one of the biggest mind bending moments and autism and strangest moments in the history of science was when we found out that the universe is kind of difference once you start moving really fast exactly.

We've had Newtonian and Gallean mechanics for centuries, things that did a very good job of explaining what happens when two balls bounce against each other, and how momentum is transferred, and how things look when you're going fast. If you're driving in a car thirty miles an hour and you for a ball at thirty miles an hour, then you know that ball should be moving at sixty miles an hour relative to the ground. All that stuff made sense for a long time until we started looking at things that were moving really, really fast. We discovered there's a speed limit to the universe, and that really changed everything we thought about the nature of space and time and velocity and gives rise to all sorts of weird stuff that's very tricky to unpack.

We've had Newtonian and Gallean mechanics for centuries, things that did a very good job of explaining what happens when two balls bounce against each other, and how momentum is transferred, and how things look when you're going fast. If you're driving in a car thirty miles an hour and you for a ball at thirty miles an hour, then you know that ball should be moving at sixty miles an hour relative to the ground. All that stuff made sense for a long time until we started looking at things that were moving really, really fast. We discovered there's a speed limit to the universe, and that really changed everything we thought about the nature of space and time and velocity and gives rise to all sorts of weird stuff that's very tricky to unpack.

Yeah, it gets super tricky. Well, first of all, the idea that we have a speed limit in the universe is kind of wild. Like, you know, you sort of grew up thinking that disguise the limit. The more that you push something, the faster you go. But at some point the universe says, I think that's fast enough. It doesn't let you go faster than a certain speed.

Yeah, it gets super tricky. Well, first of all, the idea that we have a speed limit in the universe is kind of wild. Like, you know, you sort of grew up thinking that disguise the limit. The more that you push something, the faster you go. But at some point the universe says, I think that's fast enough. It doesn't let you go faster than a certain speed.

Yeah, it's a really bizarre feature of our universe, one that we've discovered experimentally. Right. The Michaelson Morley experiments proved that light travels the same speed in every direction and effectively demonstrating that there is no absolute reference, framing that there is a maximum speed of information and transmission in the universe, which leads to all sorts of weird consequences. Changes what we think about time and the nature of simultaneity. Things that happen at the same time for one person might happen in a different order for somebody else. The whole nature of reality becomes different when there is a maximum speed limit to the universe.

Yeah, it's a really bizarre feature of our universe, one that we've discovered experimentally. Right. The Michaelson Morley experiments proved that light travels the same speed in every direction and effectively demonstrating that there is no absolute reference, framing that there is a maximum speed of information and transmission in the universe, which leads to all sorts of weird consequences. Changes what we think about time and the nature of simultaneity. Things that happen at the same time for one person might happen in a different order for somebody else. The whole nature of reality becomes different when there is a maximum speed limit to the universe.

Yeah, and I think it kind of makes people wonder what would happen if you try to go faster than the speed of light? Does a universe police come and flag you down and stop you, or you hit a wall?

Yeah, and I think it kind of makes people wonder what would happen if you try to go faster than the speed of light? Does a universe police come and flag you down and stop you, or you hit a wall?

Or what are you considering trying to break some laws of the universe be asking for physics legal advice.

Or what are you considering trying to break some laws of the universe be asking for physics legal advice.

Well, I'm trying to toe the line, you know. I'm kind of max out of my life here. I need to know how far I can go.

Well, I'm trying to toe the line, you know. I'm kind of max out of my life here. I need to know how far I can go.

I just don't want to be held responsible if you get thrown in physics.

I just don't want to be held responsible if you get thrown in physics.

Jail when I need a physics lawyer.

Jail when I need a physics lawyer.

I wonder if people who are lawyers are always going to look at for like, is this person asking me legal advice? I'm not going to get them in trouble if I say the wrong thing. I don't usually have to worry about that because most people aren't capable of trying to break the laws of the universe.

I wonder if people who are lawyers are always going to look at for like, is this person asking me legal advice? I'm not going to get them in trouble if I say the wrong thing. I don't usually have to worry about that because most people aren't capable of trying to break the laws of the universe.

I think most lawyers don't really care that much.

I think most lawyers don't really care that much.

But no, there is no physics police that are just going to pull you over. It's just that acceleration and momentums start working differently at high speeds, so you discover that you can pour energy into a particle, it just doesn't go much faster. So you can discover that as things approach the speed of light, you can keep pouring energy into something a rock, a particle of spaceship, whatever, It just doesn't go much faster. The same amount of energy doesn't get you increases in velocity the same rate. It's no longer linear, it becomes asymptotic.

But no, there is no physics police that are just going to pull you over. It's just that acceleration and momentums start working differently at high speeds, so you discover that you can pour energy into a particle, it just doesn't go much faster. So you can discover that as things approach the speed of light, you can keep pouring energy into something a rock, a particle of spaceship, whatever, It just doesn't go much faster. The same amount of energy doesn't get you increases in velocity the same rate. It's no longer linear, it becomes asymptotic.

So today podcast we'll be tackling the question do things get more massive the faster they move? This is kind of like the anti diet, or at least I feel like it justifies maybe sitting down on your couch all the time, because if I get up up for my couch and I move, then I'm just going to gain more mass. Right, technically, that's true.

So today podcast we'll be tackling the question do things get more massive the faster they move? This is kind of like the anti diet, or at least I feel like it justifies maybe sitting down on your couch all the time, because if I get up up for my couch and I move, then I'm just going to gain more mass. Right, technically, that's true.

Well, what we're going to learn on the podcast today is that it's a little bit more complicated than that. This is the kind of popular science thing you hear all the time and people write in and ask me about, and I think it was wide they taught in textbooks until about thirty forty years ago, the feeling that everything gets weird as you approach the speed of light, and then even your mass might change. Things might get like infinitely heavy as you approach the speed of light. It's an attractive concept for people, I think, because it gives you a sense of the strange. But as we'll talk about today on the podcast, it's a little bit more complicated than that, and it's actually something of an outdated notion.

Well, what we're going to learn on the podcast today is that it's a little bit more complicated than that. This is the kind of popular science thing you hear all the time and people write in and ask me about, and I think it was wide they taught in textbooks until about thirty forty years ago, the feeling that everything gets weird as you approach the speed of light, and then even your mass might change. Things might get like infinitely heavy as you approach the speed of light. It's an attractive concept for people, I think, because it gives you a sense of the strange. But as we'll talk about today on the podcast, it's a little bit more complicated than that, and it's actually something of an outdated notion.

Wait, wait, are you saying it's a massive lie?

Wait, wait, are you saying it's a massive lie?

You know, there's a lot of different ways you can try to translate the crisp mathematics of relativity into English and into popular culture. This was one attempt early on that I don't think really works very well.

You know, there's a lot of different ways you can try to translate the crisp mathematics of relativity into English and into popular culture. This was one attempt early on that I don't think really works very well.

I see, it was just heavily exaggerated. Well as usual, we were wondering how many people had wondered about this question at ask this about themselves, about the universe, about what happens when you try to go faster and faster, And so Daniel went out there into the internet to ask people do you think things get more massive as you approach the speed of light?

I see, it was just heavily exaggerated. Well as usual, we were wondering how many people had wondered about this question at ask this about themselves, about the universe, about what happens when you try to go faster and faster, And so Daniel went out there into the internet to ask people do you think things get more massive as you approach the speed of light?

I am so grateful to everybody who answers these questions. They gave me a sense for what people already know, and they give listeners a sense for what everybody else is they If you would like to participate, please don't be shy. You're really very welcome to join the club. To just write to me two questions at Danielandjorge dot com.

I am so grateful to everybody who answers these questions. They gave me a sense for what people already know, and they give listeners a sense for what everybody else is they If you would like to participate, please don't be shy. You're really very welcome to join the club. To just write to me two questions at Danielandjorge dot com.

So think about it for a second. Do you think you should stay in your couch if you don't want to gain any mess. Here's what people had to say.

So think about it for a second. Do you think you should stay in your couch if you don't want to gain any mess. Here's what people had to say.

This question just blows my mind. I'm just stumped. Do they get more massive? I guess maybe. I don't know how, but maybe something related to quantum mechanics.

This question just blows my mind. I'm just stumped. Do they get more massive? I guess maybe. I don't know how, but maybe something related to quantum mechanics.

I don't know.

I don't know.

As you approached the speed of light, I thought Einstein's equations told us that you would gain mess, But to an outside observer, I don't think you would actually look bigger.

As you approached the speed of light, I thought Einstein's equations told us that you would gain mess, But to an outside observer, I don't think you would actually look bigger.

I mean, at the speed of lifetime was slower. Maybe space gets contracted, So I'm kind of reinstorming here. Maybe if that is true, then you will have a higher density and in that sense, will be more massive.

I mean, at the speed of lifetime was slower. Maybe space gets contracted, So I'm kind of reinstorming here. Maybe if that is true, then you will have a higher density and in that sense, will be more massive.

Not sure.

Not sure.

I think they do get more massive, but because it's it gets harder to move things at that speed, and not because they get more the feet.

I think they do get more massive, but because it's it gets harder to move things at that speed, and not because they get more the feet.

My understanding is mass and energy are interchangeable, so the more energy you have to pump into something to accelerate it closer and closer to the speed of light is really no different than making it more massive to begin with. So I think, yes, it gets more massive as you approach the speed of light, just because mass and energy are essentially the same thing.

My understanding is mass and energy are interchangeable, so the more energy you have to pump into something to accelerate it closer and closer to the speed of light is really no different than making it more massive to begin with. So I think, yes, it gets more massive as you approach the speed of light, just because mass and energy are essentially the same thing.

I think I remember hearing that they do get more massive as they approach the speed of light, I think it takes more energy to increase the speed and like, yeah, they just can't really get to the speed of light unless it's like, you know, massless.

I think I remember hearing that they do get more massive as they approach the speed of light, I think it takes more energy to increase the speed and like, yeah, they just can't really get to the speed of light unless it's like, you know, massless.

I guess so based on the question. I'm not sure exactly why, but if it has something to do with like the kinetic energy of something affecting its mass, then I would guess so.

I guess so based on the question. I'm not sure exactly why, but if it has something to do with like the kinetic energy of something affecting its mass, then I would guess so.

I think the answer is yes. First, I was taught it that way. I've since heard that's an old school way of thinking about it. But definitely if we consider energy as being mass, you know the way it works relativistically, you can concentrate energy as well as matter, and that is all mass energy. Then as you add velocity, you're adding energy and you become more massive.

I think the answer is yes. First, I was taught it that way. I've since heard that's an old school way of thinking about it. But definitely if we consider energy as being mass, you know the way it works relativistically, you can concentrate energy as well as matter, and that is all mass energy. Then as you add velocity, you're adding energy and you become more massive.

All Right, a lot of great answers here. I feel like some people were blown away and some people were like, oh, I've heard of this. The answer is yes or no.

All Right, a lot of great answers here. I feel like some people were blown away and some people were like, oh, I've heard of this. The answer is yes or no.

Yeah, I thought this was really interesting. There's a lot of different ideas here about what energy is and what mass is. Very few people mentioned momentum even, but there's definitely this understanding that things change as you approach the speed of light, and that it's harder to go faster.

Yeah, I thought this was really interesting. There's a lot of different ideas here about what energy is and what mass is. Very few people mentioned momentum even, but there's definitely this understanding that things change as you approach the speed of light, and that it's harder to go faster.

Yeah, somebody, one of the listeners said that it's kind of strange that your mass would change, right.

Yeah, somebody, one of the listeners said that it's kind of strange that your mass would change, right.

And that goes to the heart of what we mean by mass. I think a lot of people think of mass as like the amount of stuff they have, and so it's really weird for them to imagine them getting like more stuff as they approach to the speed of light. And that's one reason why I really don't like this concept of relativistic mass. It gives people the impression that something physical is happening, which isn't interesting.

And that goes to the heart of what we mean by mass. I think a lot of people think of mass as like the amount of stuff they have, and so it's really weird for them to imagine them getting like more stuff as they approach to the speed of light. And that's one reason why I really don't like this concept of relativistic mass. It gives people the impression that something physical is happening, which isn't interesting.

All right, well, let's dig into it, and I guess let's start with the basics. As you said, let's start with the concept of mass. Now. I know mass is kind of a big mystery. We talked about it in our book, like what is mass? Anyways? We have a whole chapter about how we don't kind of know what mass is. But Daniel maybe step us through it. What do we know about what mass is?

All right, well, let's dig into it, and I guess let's start with the basics. As you said, let's start with the concept of mass. Now. I know mass is kind of a big mystery. We talked about it in our book, like what is mass? Anyways? We have a whole chapter about how we don't kind of know what mass is. But Daniel maybe step us through it. What do we know about what mass is?

I think in the context of relativity and motion, the most important thing to think about is inertia, like the fact that it's not easy to change your velocity you're flying through the universe at some speed in order to change that speed, you need a push, right. That's really what F equals ma is trying to say that to accelerate, you need to have a force applied to you, and that M in that equation in F equals ma is the mass. It relates how much acceleration you get for how much force. We've all heard, for example, that the Earth's gravity on you is the same as you gravity on the Earth, right, But we feel a much stronger force than the Earth does because the Earth has a huge mass. So we feel a much stronger acceleration than the Earth does because the Earth has a huge mass, and so its acceleration is tiny, even though the force is the same. So a really important concept in mass is inertia. That's really what mass is about when we're talking about motion, and that's connected to this idea of momentum. Right. Another way to think about F equals ma is that f is actually a change in momentum. When you're flying through the universe at a certain velocity, you have a certain momentum. In order to change your momentum, you need to have a force applied. So mass is this concept that tells us basically how hard it is to change your momentum.

I think in the context of relativity and motion, the most important thing to think about is inertia, like the fact that it's not easy to change your velocity you're flying through the universe at some speed in order to change that speed, you need a push, right. That's really what F equals ma is trying to say that to accelerate, you need to have a force applied to you, and that M in that equation in F equals ma is the mass. It relates how much acceleration you get for how much force. We've all heard, for example, that the Earth's gravity on you is the same as you gravity on the Earth, right, But we feel a much stronger force than the Earth does because the Earth has a huge mass. So we feel a much stronger acceleration than the Earth does because the Earth has a huge mass, and so its acceleration is tiny, even though the force is the same. So a really important concept in mass is inertia. That's really what mass is about when we're talking about motion, and that's connected to this idea of momentum. Right. Another way to think about F equals ma is that f is actually a change in momentum. When you're flying through the universe at a certain velocity, you have a certain momentum. In order to change your momentum, you need to have a force applied. So mass is this concept that tells us basically how hard it is to change your momentum.

I feel like you're making us go down a rabbit hole a little bit, because then it makes me wonder, like, what is momentum anyways?

I feel like you're making us go down a rabbit hole a little bit, because then it makes me wonder, like, what is momentum anyways?

Yeah, a momentum is something we know is important in the universe. It's a quantity that's conserved. Like we look at in the universe, we watch stuff, we see things happen, and we look for patterns, and a very important pattern are concertation loss things that don't change. So two balls bounce against each other, for example, you calculate all the momentum beforehand and all the momentum afterwards, and you notice it's the same. It is conserved. We actually know that there's a deep reason for why momentum is conserved. It's because space is the same everywhere. We did a whole fun podcast on Nother's theorem, which tells you that because space is the same everywhere, momentum has to be conserved. This is deep link there. So momentum is an important physical quantity in the universe. It's something that's really powerful and it really gives us insight into what's happened. And momentum is flowing through a system, right, but it's conserved in the universe. The universe at least thinks momentum is important, so maybe we should.

Yeah, a momentum is something we know is important in the universe. It's a quantity that's conserved. Like we look at in the universe, we watch stuff, we see things happen, and we look for patterns, and a very important pattern are concertation loss things that don't change. So two balls bounce against each other, for example, you calculate all the momentum beforehand and all the momentum afterwards, and you notice it's the same. It is conserved. We actually know that there's a deep reason for why momentum is conserved. It's because space is the same everywhere. We did a whole fun podcast on Nother's theorem, which tells you that because space is the same everywhere, momentum has to be conserved. This is deep link there. So momentum is an important physical quantity in the universe. It's something that's really powerful and it really gives us insight into what's happened. And momentum is flowing through a system, right, but it's conserved in the universe. The universe at least thinks momentum is important, so maybe we should.

Also well, how is it different from like energy? And is momentum the same as energy. Is the momentum of a particle or a baseball the same as its kinetic energy? How do the two connect?

Also well, how is it different from like energy? And is momentum the same as energy. Is the momentum of a particle or a baseball the same as its kinetic energy? How do the two connect?

Yeah? Great question. First of all, momentum has directionality. You can have momentum in one direction or momentum in another direction. It's a vector it points in. For example, the Earth has a constant magnitude momentum, but the direction of its momentum is changing as it goes around the Sun. It's like an arrow that tells you which way the Earth is headed, and that's constantly changing. So the length of that vector isn't changing, but the direction of it is. And that's why it takes acceleration to move around the Sun, because you're changing the direction of that momentum vector. So momentum is a direction, right. Energy doesn't have a direction, it's just a number.

Yeah? Great question. First of all, momentum has directionality. You can have momentum in one direction or momentum in another direction. It's a vector it points in. For example, the Earth has a constant magnitude momentum, but the direction of its momentum is changing as it goes around the Sun. It's like an arrow that tells you which way the Earth is headed, and that's constantly changing. So the length of that vector isn't changing, but the direction of it is. And that's why it takes acceleration to move around the Sun, because you're changing the direction of that momentum vector. So momentum is a direction, right. Energy doesn't have a direction, it's just a number.

Right.

Right.

And also, and energy includes something else. The energy of an object has two components. There's the internal energy what we call it's inertial mass, and the energy of its motion, it's kinetic energy. So there's two separate components there. So things can have energy when they're not moving, like an electron just sitting there has some mass, then that corresponds to some energy, and there's also energy of motion. Things can have only energy of motion, like a photon is just motion energy has no mass, or they can have both, like an electron flying through the universe has mass and that's energy and also has kinetic energy. So energy has two components. There's the mass and there's a contribution from the momentum, which we also call kinetic energy.

And also, and energy includes something else. The energy of an object has two components. There's the internal energy what we call it's inertial mass, and the energy of its motion, it's kinetic energy. So there's two separate components there. So things can have energy when they're not moving, like an electron just sitting there has some mass, then that corresponds to some energy, and there's also energy of motion. Things can have only energy of motion, like a photon is just motion energy has no mass, or they can have both, like an electron flying through the universe has mass and that's energy and also has kinetic energy. So energy has two components. There's the mass and there's a contribution from the momentum, which we also call kinetic energy.

And so the universe conserves both things, right, Like it somehow conserves momentum and it also conserves energy, but not necessarily the same way I think.

And so the universe conserves both things, right, Like it somehow conserves momentum and it also conserves energy, but not necessarily the same way I think.

Right, So there's a little asterisk there in flat space. Yes, energy is conserved in the global universe. As space expands, actually energy increases, so energy is not strictly conserved in the universe. There's a whole podcast episode we did about that if you want to dig into it. But let's just assume we're like living in flat space and we're bouncing balls and particles off each other. We wouldn't notice the expansion of the universe. So let's just say for the sake of this discussion that yes, energy is conserved, and so you're right, momentum is conserved and energy is conserved, and those are actually related. Those are four separate conservation laws because energy is one number and momentum is three numbers. Because we have three dimensions of space, and momentum is conserved separately in each of those dimensions. So we have four conservation laws, three from momentum and one from energy. And in particle physics at least we group energy and momentum together into something we call four momentum, like the four dimensions of space time, and we say there's conservation of for momentum, which combines momentum and energy into one conservation law.

Right, So there's a little asterisk there in flat space. Yes, energy is conserved in the global universe. As space expands, actually energy increases, so energy is not strictly conserved in the universe. There's a whole podcast episode we did about that if you want to dig into it. But let's just assume we're like living in flat space and we're bouncing balls and particles off each other. We wouldn't notice the expansion of the universe. So let's just say for the sake of this discussion that yes, energy is conserved, and so you're right, momentum is conserved and energy is conserved, and those are actually related. Those are four separate conservation laws because energy is one number and momentum is three numbers. Because we have three dimensions of space, and momentum is conserved separately in each of those dimensions. So we have four conservation laws, three from momentum and one from energy. And in particle physics at least we group energy and momentum together into something we call four momentum, like the four dimensions of space time, and we say there's conservation of for momentum, which combines momentum and energy into one conservation law.

So then mass is related to both things like mass makes your momentum go higher and it makes your energy go higher.

So then mass is related to both things like mass makes your momentum go higher and it makes your energy go higher.

Yeah, that's right. So mass is like your internal stored energy. Take a proton, for example, it has a bunch of mass. Where does that mass come from. It comes from the internal energy of the proton. Like there's the mass of the quarks. They get their mass from the Higgs boson. Then there's the mass of the binding of those quarks together. And that's where most of the mass of the proton comes from. So that proton has mass, and you're right, that's part of its energy, and the proton could also have momentum that's another part of its energy. So we think of the mass as the thing that makes it hard to push on something or easier to push on something, but it has low mass, and then there's also energy stored in its motion.

Yeah, that's right. So mass is like your internal stored energy. Take a proton, for example, it has a bunch of mass. Where does that mass come from. It comes from the internal energy of the proton. Like there's the mass of the quarks. They get their mass from the Higgs boson. Then there's the mass of the binding of those quarks together. And that's where most of the mass of the proton comes from. So that proton has mass, and you're right, that's part of its energy, and the proton could also have momentum that's another part of its energy. So we think of the mass as the thing that makes it hard to push on something or easier to push on something, but it has low mass, and then there's also energy stored in its motion.

Okay, So then generally speaking, mass is just what makes things harder to move, right.

Okay, So then generally speaking, mass is just what makes things harder to move, right.

Basically, that's exactly right. That's the concept of inertial mass basically relate to the object's inertia, which tells you how how hard is it to change its momentum?

Basically, that's exactly right. That's the concept of inertial mass basically relate to the object's inertia, which tells you how how hard is it to change its momentum?

Right, And then there's a concept of gravitational mass, which is a different concept, but it's the same number.

Right, And then there's a concept of gravitational mass, which is a different concept, but it's the same number.

Yeah, And there's a bunch of really fascinating wrinkles here. Like in Newton's world, he had f equals maa, which tells you about how hard it is to push something. And he also had this number m in his gravitational law gmm over r square, which tells you the force between two objects. And in Newtonian physics these two things are different numbers. They're written in the same way. The same letter M in f equals ma and m in gmm over r squared, But in principle they could have been totally different.

Yeah, And there's a bunch of really fascinating wrinkles here. Like in Newton's world, he had f equals maa, which tells you about how hard it is to push something. And he also had this number m in his gravitational law gmm over r square, which tells you the force between two objects. And in Newtonian physics these two things are different numbers. They're written in the same way. The same letter M in f equals ma and m in gmm over r squared, But in principle they could have been totally different.

Right.

Right.

It was a bit of a mystery in Newtonian physics why these two numbers always seem to have the same value. Einstein unified these things in general relativity and told us that actually inertial gravitational masses have to be the same because, according to Einstein, there is no acceleration due to gravity. There is no force due to gravity. It's just inertial motion through curved space time. That when you are having inertial motion, there's no forces on you through space time. That's what gravity looks like. So motion due to gravity is actually just inertial motion and you're just really in free fall.

It was a bit of a mystery in Newtonian physics why these two numbers always seem to have the same value. Einstein unified these things in general relativity and told us that actually inertial gravitational masses have to be the same because, according to Einstein, there is no acceleration due to gravity. There is no force due to gravity. It's just inertial motion through curved space time. That when you are having inertial motion, there's no forces on you through space time. That's what gravity looks like. So motion due to gravity is actually just inertial motion and you're just really in free fall.

Right.

Right.

So like, for example, the Earth orbiting around the Sun, it's not like there's a force pulling the Earth towards the Sun, or there's no centripetal force. There is just that the space around the Sun for the Earth is sort of curved and it's shaped like a circle basically.

So like, for example, the Earth orbiting around the Sun, it's not like there's a force pulling the Earth towards the Sun, or there's no centripetal force. There is just that the space around the Sun for the Earth is sort of curved and it's shaped like a circle basically.

Right, Yeah, that's right. If space were flat, everything we just move in what looks to us like straight lines. But when space is curved, things move differently and it looks like there's a force there bending their paths, but really it's just motion through curved space because we can't see that curvature. You can like look through space and see the curvature of space the way you can see the curvature of a road. It seems like a bit of a mystery why things are moving in curves, and of course is that space is curved, so there's an apparent force there.

Right, Yeah, that's right. If space were flat, everything we just move in what looks to us like straight lines. But when space is curved, things move differently and it looks like there's a force there bending their paths, but really it's just motion through curved space because we can't see that curvature. You can like look through space and see the curvature of space the way you can see the curvature of a road. It seems like a bit of a mystery why things are moving in curves, and of course is that space is curved, so there's an apparent force there.

Or more accurately, you mean like space time, right, Like maybe space is not curve, but space time is.

Or more accurately, you mean like space time, right, Like maybe space is not curve, but space time is.

It's definitely more coherent to think about relativity in terms of space because the way like energy and momentum are linked, space and time are definitely linked. You can't talk about the curvature of space as well and the curvature of time separately. They make more sense when you think about them together. But yes, space itself can also be curved, but space time as well.

It's definitely more coherent to think about relativity in terms of space because the way like energy and momentum are linked, space and time are definitely linked. You can't talk about the curvature of space as well and the curvature of time separately. They make more sense when you think about them together. But yes, space itself can also be curved, but space time as well.

All right, So then that's mess. It's how hard it is to push on something, and it's also sort of like the effect something has on space time around it.

All right, So then that's mess. It's how hard it is to push on something, and it's also sort of like the effect something has on space time around it.

Yeah, and this is very intuitive. If you're like playing billiards or you're shooting a basketball or you're rolling rocks down hills, and it aligns with our sense that like things that have more stuff to them are harder to push, and that all makes sense at low speeds. Things change a little bit as you get very high velocity, and then you have a question for like, what do you change? You change momentum, do you change mass, do you change energy? What's the most sensible way to think about these things?

Yeah, and this is very intuitive. If you're like playing billiards or you're shooting a basketball or you're rolling rocks down hills, and it aligns with our sense that like things that have more stuff to them are harder to push, and that all makes sense at low speeds. Things change a little bit as you get very high velocity, and then you have a question for like, what do you change? You change momentum, do you change mass, do you change energy? What's the most sensible way to think about these things?

Yeah, because as we mentioned, there's the idea out there that the faster you go, and as your approach the speed of light, your mass starts to get bigger and bigger, which is a problem for us who are trying to stay slim. And so let's dig into that scenario and the problems with that scenario and what it all means about the loss of the universe. But first, let's take a quick break.

Yeah, because as we mentioned, there's the idea out there that the faster you go, and as your approach the speed of light, your mass starts to get bigger and bigger, which is a problem for us who are trying to stay slim. And so let's dig into that scenario and the problems with that scenario and what it all means about the loss of the universe. But first, let's take a quick break.

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All right, we are talking about a massive topic here, and it's going by really fast, and it's about how really massive things go really fast get massive as they go really fast.

All right, we are talking about a massive topic here, and it's going by really fast, and it's about how really massive things go really fast get massive as they go really fast.

Yeah, things definitely do change as you approach the speed of light, and a lot of your intuition goes out the window. You can just lean into the mathematics and say, well, there are new formulas and I can just use them and calculate stuff. But we also want to have like an understanding of how the universe works. We want to develop a new intuition. So it's important that we make sense of what the words mean as things change.

Yeah, things definitely do change as you approach the speed of light, and a lot of your intuition goes out the window. You can just lean into the mathematics and say, well, there are new formulas and I can just use them and calculate stuff. But we also want to have like an understanding of how the universe works. We want to develop a new intuition. So it's important that we make sense of what the words mean as things change.

Okay, so let's talk about change. I guess now, before when we just had Newtonian physics, things were kind of simple, like if you wanted to change the velocity of something, you had to apply a certain force, and a certain force would always give you the same amount of velocity change, kind like no matter if you're standing still or if you're going fast. If you applied and have you always got that change in velocity acceleration.

Okay, so let's talk about change. I guess now, before when we just had Newtonian physics, things were kind of simple, like if you wanted to change the velocity of something, you had to apply a certain force, and a certain force would always give you the same amount of velocity change, kind like no matter if you're standing still or if you're going fast. If you applied and have you always got that change in velocity acceleration.

Yeah, that's right, F used to equal M in a very simple and straightforward way. Or equivalently, we could say F is the change in momentum.

Yeah, that's right, F used to equal M in a very simple and straightforward way. Or equivalently, we could say F is the change in momentum.

Right, So that's Newtonian physics. But then we sort of learned a little bit more about relativity, which says that that's not quite true.

Right, So that's Newtonian physics. But then we sort of learned a little bit more about relativity, which says that that's not quite true.

Yeah, because there is a maximum speed to the universe. If you pour energy into something to try to get it going faster, you don't always get the same amount of speed up, which means like it's harder to add velocity in the direction something is moving. You have rocket ship and it's already going at ninety percent of the speed of light, and you fire the engines the same amount you did earlier, you're not going to get the same amount of speed up even if you're applying the same.

Yeah, because there is a maximum speed to the universe. If you pour energy into something to try to get it going faster, you don't always get the same amount of speed up, which means like it's harder to add velocity in the direction something is moving. You have rocket ship and it's already going at ninety percent of the speed of light, and you fire the engines the same amount you did earlier, you're not going to get the same amount of speed up even if you're applying the same.

Force, right, Because I guess under Newtonian physics, you could technically go infinitely fast, right, Like if you just kept pushing on an object over a long long period of time, we just keep going faster and faster and faster because F equals m A. And so if I apply a constant force to something. The velocity is just going to keep increasing, increasing and increasing, and eventually it would go faster than the speed of light in a Newtonian universe.

Force, right, Because I guess under Newtonian physics, you could technically go infinitely fast, right, Like if you just kept pushing on an object over a long long period of time, we just keep going faster and faster and faster because F equals m A. And so if I apply a constant force to something. The velocity is just going to keep increasing, increasing and increasing, and eventually it would go faster than the speed of light in a Newtonian universe.

Yeah, that's exactly right.

Yeah, that's exactly right.

But we seem to have this speed limit that says you can go faster and faster, and so I guess my question is what happened then? Did we have to adjust our math or does the math tell you why you can't go faster than the speed of light.

But we seem to have this speed limit that says you can go faster and faster, and so I guess my question is what happened then? Did we have to adjust our math or does the math tell you why you can't go faster than the speed of light.

We definitely had to adjust our math, right, because those formulas are wrong. As you say, they predict you could go infinitely fast. So what was wrong about those formulas? Well, it turns out our formula form momentum was wrong. We thought momentum was just like mass times velocity, and then we thought that quantity was conserved in the universe. Turns out we were missing a term. There's another term in that equation, this thing we call the boost factor. We write it as gamma in relativity. It's just a number, but if you're going at slow speeds, that number is basically one, so it doesn't change your equation. But as you approach to speed of light, that number grows to infinity. So what it means is momentum is different from what we thought it was. We talked about how momentum is this important quantity in the universe that's conserved. That's true, but it's not M times V. There's a different expression for momentum, and that's the thing that's actually conserved in the universe. It turns out M times V times this gamma factor. So momentum changes as you approach the speed of light, and that's why it's hard to increase your velocity as you approach the speed of light because your momentum is changing. It requires a larger force to change your momentum.

We definitely had to adjust our math, right, because those formulas are wrong. As you say, they predict you could go infinitely fast. So what was wrong about those formulas? Well, it turns out our formula form momentum was wrong. We thought momentum was just like mass times velocity, and then we thought that quantity was conserved in the universe. Turns out we were missing a term. There's another term in that equation, this thing we call the boost factor. We write it as gamma in relativity. It's just a number, but if you're going at slow speeds, that number is basically one, so it doesn't change your equation. But as you approach to speed of light, that number grows to infinity. So what it means is momentum is different from what we thought it was. We talked about how momentum is this important quantity in the universe that's conserved. That's true, but it's not M times V. There's a different expression for momentum, and that's the thing that's actually conserved in the universe. It turns out M times V times this gamma factor. So momentum changes as you approach the speed of light, and that's why it's hard to increase your velocity as you approach the speed of light because your momentum is changing. It requires a larger force to change your momentum.

I guess this is where it gets kind of confusing, because, first of all, like you're saying that as I go faster, my momentum decreases, But doesn't that depend on how fast I'm going relative to who or what like? To me, I'm not going fast at all if I'm going really fast. To me, it just looks like the universe is moving around me.

I guess this is where it gets kind of confusing, because, first of all, like you're saying that as I go faster, my momentum decreases, But doesn't that depend on how fast I'm going relative to who or what like? To me, I'm not going fast at all if I'm going really fast. To me, it just looks like the universe is moving around me.

So, first of all, as you go faster, your momentum still increases. That's always true, it's just not a linear increase. And you're absolutely right that all of these things depend on your frame, right, depends on who's watching. Somebody who's in a spaceship with you is going to see you at zero velocity, and somebody who's on Earth as you zip by, it's going to see you moving at very high speed. So you're absolutely right. There's no sense of talking about like, what is my velocity in an absolute way. It's always measured relative to some observer. So there's an important difference between things that are invariant, where everybody agrees on them no matter their velocity, and things that are conserved, things that don't change any frame of reference. So momentum, for example, is conserved for some observer. You always see momentum conserved before collision. After collision is the same momentum, but momentum is not invariant. Another observer moving at a different speed will see a different set of momenta, but they will also see momentum conserved. So momentum is conserved, meaning for a given observer it doesn't ever disappear or appear, but it's not invariant, meaning different people will measure different amounts at different velocities.

So, first of all, as you go faster, your momentum still increases. That's always true, it's just not a linear increase. And you're absolutely right that all of these things depend on your frame, right, depends on who's watching. Somebody who's in a spaceship with you is going to see you at zero velocity, and somebody who's on Earth as you zip by, it's going to see you moving at very high speed. So you're absolutely right. There's no sense of talking about like, what is my velocity in an absolute way. It's always measured relative to some observer. So there's an important difference between things that are invariant, where everybody agrees on them no matter their velocity, and things that are conserved, things that don't change any frame of reference. So momentum, for example, is conserved for some observer. You always see momentum conserved before collision. After collision is the same momentum, but momentum is not invariant. Another observer moving at a different speed will see a different set of momenta, but they will also see momentum conserved. So momentum is conserved, meaning for a given observer it doesn't ever disappear or appear, but it's not invariant, meaning different people will measure different amounts at different velocities.

Okay, so then I think what you're saying is that momentum is not linear, it gets kind of wonky the faster you go. And the way it gets wonky is that it gets kind of ridiculously big as you get closer to the speed of light. Right, you said, momentum equals mass time velocity times gamma, and gamma is basically one when we're standing still, but it gets to infinity as we get closer to the speed of light.

Okay, so then I think what you're saying is that momentum is not linear, it gets kind of wonky the faster you go. And the way it gets wonky is that it gets kind of ridiculously big as you get closer to the speed of light. Right, you said, momentum equals mass time velocity times gamma, and gamma is basically one when we're standing still, but it gets to infinity as we get closer to the speed of light.

Exactly. And if you think about force not just as mass times acceleration, but as the change in momentum, than if your momentum is really really big, then it becomes hard to change your momentum. You need to apply a really really big force to change your momentum. And your momentum grows very very quickly near the speed of light. As you say, it approaches infinity as velocity approaches the speed of light.

Exactly. And if you think about force not just as mass times acceleration, but as the change in momentum, than if your momentum is really really big, then it becomes hard to change your momentum. You need to apply a really really big force to change your momentum. And your momentum grows very very quickly near the speed of light. As you say, it approaches infinity as velocity approaches the speed of light.

So I guess, but I get more concretely, it would mean like my couch, me sitting in my couch, my momentum would be my mass times my velocity, which in this case I guess it's zero, but it would just in my mass timeline my velocity. But if I was moving at two hundred thousand kilometers per second, then my momentum would be not just my mass times my velocity, but it'd be my mass time my velocity times a really big number, which is this adjustment factor that gets bigger the closer you move to the speed of light.

So I guess, but I get more concretely, it would mean like my couch, me sitting in my couch, my momentum would be my mass times my velocity, which in this case I guess it's zero, but it would just in my mass timeline my velocity. But if I was moving at two hundred thousand kilometers per second, then my momentum would be not just my mass times my velocity, but it'd be my mass time my velocity times a really big number, which is this adjustment factor that gets bigger the closer you move to the speed of light.

Exactly. This gamma factor is the thing that Newton missed in momentum basically, and he missed it because for everything he measured and he saw, it was just one, so it didn't change any of his calculations. Any number multiplied by one is just itself. So you have like a hidden factor in your equation that's always one. You can't discover it. You can only discover it when it changes from one, and that only changes from one as you approach the speed of light.

Exactly. This gamma factor is the thing that Newton missed in momentum basically, and he missed it because for everything he measured and he saw, it was just one, so it didn't change any of his calculations. Any number multiplied by one is just itself. So you have like a hidden factor in your equation that's always one. You can't discover it. You can only discover it when it changes from one, and that only changes from one as you approach the speed of light.

So I think kind of the message is that the universe is kind of like, Okay, if you want to move something from your couch through your kitchen, that's fine, you can do that. It's going to cost you this much. But if you want to move it from you know, your couch to almost to the speed of light or super duper fast, it's going to cost you that plus an extra like universe tax or something exactly that says that, oh, that's going to cost you a lot a lot, and somehow the idea is that it that kind of lets the universe prevent you from going faster than the speed of light.

So I think kind of the message is that the universe is kind of like, Okay, if you want to move something from your couch through your kitchen, that's fine, you can do that. It's going to cost you this much. But if you want to move it from you know, your couch to almost to the speed of light or super duper fast, it's going to cost you that plus an extra like universe tax or something exactly that says that, oh, that's going to cost you a lot a lot, and somehow the idea is that it that kind of lets the universe prevent you from going faster than the speed of light.

Yeah, and the universe tax it's basically zero if you're not moving very fast. Even if you're moving at like half the speed of light, this gamma factor, this boost, this universe tax is like fifteen percent. So even at half the speed of light, it's barely noticeable. As you get to like ninety percent of the speed of light, it's like two point three. And if you get to like ninety nine percent of the speed of light, it's like seven ninety nine point nine percent of the speed of light. It's like twenty two. Increases very very quickly as things get fast.

Yeah, and the universe tax it's basically zero if you're not moving very fast. Even if you're moving at like half the speed of light, this gamma factor, this boost, this universe tax is like fifteen percent. So even at half the speed of light, it's barely noticeable. As you get to like ninety percent of the speed of light, it's like two point three. And if you get to like ninety nine percent of the speed of light, it's like seven ninety nine point nine percent of the speed of light. It's like twenty two. Increases very very quickly as things get fast.

Well, I didn't know the universe was so progressive.

Well, I didn't know the universe was so progressive.

Exactly. Momentum, billionaires, the universe is coming for you. Yeah, And so really that's fundamentally what's happening. We like to think about momentum because that's something the universe conserves. That's something that's important to the universe, energy and momentum, and that's really what's driving this experience that it's harder to accelerate as you get towards the speed of light. And remember that momentum is directional, right, and so adding velocity in the direction you're already going takes actually different amounts of momentum than adding velocity like perpendicular to your motion. It gets very complicated.

Exactly. Momentum, billionaires, the universe is coming for you. Yeah, And so really that's fundamentally what's happening. We like to think about momentum because that's something the universe conserves. That's something that's important to the universe, energy and momentum, and that's really what's driving this experience that it's harder to accelerate as you get towards the speed of light. And remember that momentum is directional, right, and so adding velocity in the direction you're already going takes actually different amounts of momentum than adding velocity like perpendicular to your motion. It gets very complicated.