The world out there is a wonderful, intriguing puzzle. Sometimes it feels like it makes little sense, constantly refusing to obey our intuition or behave the way that we expect it to. Quantum mechanics tells us electrons don't follow smooth paths, relativity tells us time doesn't flow the same way for everyone, And yet we can make some sense of it. We have math that describes it and predicts it. It's incredible
that the universe is so finely balanced. It's complicated enough that it's taking us thousands of years to unravel its truths, but it's simple enough that our tiny brains can make progress year after year. So let's keep hoping that truant continues. But even when we have wrangled a bit of math that seems to work, it doesn't mean our intuition goes along for the ride. Sometimes when we translate the math into popular science intuition and dramatic clickbait, the reality is lost.
You've heard that a potato approaching the speed of light can turn into a black hole, or that photons don't experience time. Unfortunately, neither of those things are accurate. Today, we're going to try to untangle some of these widespread misconceptions about special relativity and show you that the truth of the universe is plenty weird and wonderful without clickbait. Do Photon's experience time. Does a potato become a black
hole if it goes fast enough? Welcome to Daniel and Kelly's extraordinary but amazingly comprehensible universe.
Hello, I'm Kelly Widerspin. I'm a biologist, and I am super excited to let Daniel be the wet blanket today.
Hi, I'm Daniel. I'm a particle physicist, and I'm not going to throw a wet blanket on the universe. I'm going to show you how it's even weirder than what you've been told.
Yeah, that's what I do all the time. Also, Daniel, it's all about packaging the idea.
That's right, exactly, make it sound positive, that's right.
So my question for you today is when you were a kid and you watched like physics y kinds of movies, were you concerned with whether or not they were accurate or did kid Daniel just enjoy whatever he was watching.
Hey, there's an implication there that adult Daniel can't enjoy movies. I don't appreciate that. That's not true.
Go ahead and tell us about the trajectory of your life and how it has evolved with movie watching.
You know, when I watched movies like that as a kid, I was just amazed and odd. I thought it was fantastic to think about these things and to push against the edge of our knowledge. Could we live in four dimensional space? Could aliens be six dimensional beings? Is it possible to travel through time? I thought those movies were wonderful because they pushed us past the edge of our current knowledge and imagined how the universe could be different.
And now, of course, as a grown up scientist, I know something about what we do and don't know, and which of those ideas are possible and which of those ideas are not really possible. But I appreciate the creativity in that. I think it's important that we push past that and then we try to break outside of the box of our current ideas.
So you could watch a movie that clearly had an incorrect physics concept and straight up enjoy it. Is that right?
You know, if they're going to embrace life in a different universe with different laws, that's fine. Go for it. But if they're going to pretend to be in this universe and then they drop a bunch of like pop sign nonsense to make it sound like they talk to a physicist when they didn't, and they're all higgs bos on this and quantum fluctuation that, then yeah, that's annoying because like, hey, reach out to a scientist. It's not
so hard to get like actual realistic scientific babble. Instead appear nonsense from your chat GPT, like come on email me, I'll answer. I'll help you get actual science into your movie.
I think the one time where I was like, maybe I'm going to ask for my money back? What was? The movie was with John Cusack and I loved John Cusack, but it was like the new Trinos have mutated and everything. I was like, oh, can I get past this? I don't think I can. It was one of those like Ends of the World disaster movies.
The new Trenos are going to kill us, all that's right.
I was like, they're neutral, guys, It's all right anyway.
Yeah. I mean, if people want to embrace something awesome and new, that's fantastic. And I think that being created that way is cool but if you want to use real physics, like reach out to a real scientist. There's so many folks who would happily help you make the science in your show real. And you know, then it's even better because the people who are listening and know something are then like not jerked out of their experience by the bizarre nonsense you just injected into their brains.
We would all love to be involved in TV shows and movies that makes us like the cool kid in the room, So like, give us the chance to be the cool kid man.
Yeah, Christopher Nolan write to me, come.
On, that's right, that's right, And there's got to be a bunch of parasite movies that people could be, you know, talking to me about. But all right, well, today we're focusing on two very specific ideas that are often wrong in popsid.
Yeah, that's right, because there's a lot of popular science descriptions of special relativity what happens as you approach the speed of light and what's it like to be a photon and all this kind of stuff, and some of it sounds really cool and it's really fun to read about, but it's actually kind of nonsense, and the worst part is that it's obscuring the reality, the awesomeness of our universe, and the truth is always so much weirder than the nonsense,
which I love. And so because people write in quite often asking these kinds of questions, I thought it'd be fun to try to disentangle some of the common misconceptions about special relativity. But before we dig into those particular topics, I was curious what people thought were the most popular misconceptions about special relativity, the things that people didn't understand
about it. So I went out and asked our listeners if you would like to join our group of volunteers, please don't be shy or right to us two questions at Danielankelly dot org.
We were going through and Daniel and I really to survey, which you can get on our website Daniel and Kelly dot com. And I was going through some of the answers.
Daniel and Kelly dot org unless you're a guest at Daniel and Kelly's wedding, in which case go to Daniel Kelly dot com. Congratulations you too, love he thank you for the correction.
Yeah, I was looking through the answers and somebody wrote to say that they would like to hear a lot more female voices for this question and answer session, and so if you are a woman who is on that list, we would really love to hear from you. Or if you're a woman who would like to answer these questions, we would really love to hear from you. I had a journalist reach out to me the other day and I told them, oh, sorry, I'm not an expert in that area, so I'm gonna pass. And they wrote back
and they said, men never pass. Women are the ones who are like, oh, I'm not quite sure I'm an expert in this. And so what I'm saying is, ladies, let's go all in on the confidence and just answer it. And if the answer is I don't know, that's fine too. Let's get your voice out there.
Absolutely, ladies, please chime in. All right, without further ado, here's what our listeners had to say.
Whether I'm thinking of special general relativity a time dilation.
If you put a gun to my head, I couldn't tell you.
The difference between special and general relativity time dilation.
That if you somehow get into a ship and approach the speed of light or close to the speed of light, that your clock or un slower.
The speed of light is constant for all observers, regardless of their motion or location or whatever. Why does the speed of light always appear to be at the speed of light regardless of my speed? Well, I'm ashamed to say I can't remember the difference between special and general relativity. How to become special enough to be recognized by the Special relativity crew. The visualizations of invisible fabrics, as well as two dimensional sheets used to explain four dimensional curvature,
makes wascetime more confusing. Why is it special?
There's more photons than anything else, so when that kind to be a general thing?
How observers can see events in different orders.
That if you exceed light speed the time will run backwards.
I've never understood why we say the universe is about fourteen billion years old, but a photon traveling at the speed of light since the Big Bang has experienced no change in.
Time god fact of the speed of light. Why is the speed of light three times twenty eighth meters per second and not some other number.
I don't understand how, despite the variables, light can never exceed three hundred thousand kilometers per second, that.
The speed of light is constant, no matter where you're observing it from or how fast you're going.
It's the fact that the speed of light is a constant. Misunderstood is E equals mc squared because most people think it's got something to do with relativity.
That there is no god beside the universe with an absolute clock who judges who was right.
Fixed speed in a vacuum, no matter what your speed is, All.
Right, some great answers. And I got to say, every time we have a conversation, I get closer to understanding relativity, but not all of it sticks. And so I'm looking forward to being reminded of the difference between special and general relativity today.
Right, So today we're only digging into special relativity. General relativity is a whole other hairy beast we're not even going to try to tackle today because special relativity, even though it's simpler than general relativity, is plenty confusing. You know, it already requires you to distort how your brain works and accept the time flows differently for people in different
parts of the universe. Briefly, special relativity is physics in flat space, where there's no curvature, there's no mass, there's no gravity, it's just like beams of light and clocks and things moving fast, and it tells us how time flows and how things are relative, even outside of like black holes and all that weirdness.
So this is not dealing with any bending of space or time.
That's right, Yeah, exactly. Imagine space is purely flat and we got a bunch of physics nerds doing experiments with lasers and clocks and cats and all sorts of stuff. But we've got no black holes, no gravity, nothing like that.
All right, great, I think I can wrap my head around that. Where do we start.
Then, Well, my favorite thing about special relativity is that it lets you dig deep into your understanding of like the very fabric of reality. And I know that sounds like pomps and grandiose, but it's true because that's what it's dealing with. It's describing space and time and helping us grapple with like what that really means. And you know, philosophically, it's awesome that you can say, hey, here's a mathematical model that describes what's happening out there in the universe.
And if it works, if it describes the universe faithfully, then I can look at that model and say, hmm, maybe I can learn something about the universe by studying this model. If I have a mathematical description of the universe, does that description reveal something about reality to me? That's the juice in all of this physics. And you know, one of the most important things to understand and in special relativity are very basic things like location, like velocity,
like acceleration. Like what do these things mean in special relativity? And how are they different from how Newton or Archimedes or Aristotle thought about these very basic concepts.
A while back, we had two topics that I think would be helpful intros to this, if anybody wants to go back and get some more background. We had an episode on what is time and what is space? And as I was looking at your outline, I thought, oh, that's helpful background information for this discussion.
Yeah, And so the headlines for special relativity are that location and velocity are purely relative. There's no absolute measure of location velocity, but acceleration is not. Acceleration is an absolute quantity. So let's start with location. What do we mean when we say location is relative? It just means that your location can only be described relative to other stuff. There's no like set of markers in the universe, no like axis glowing in space where you can say my
location is in this quadrant. It's always like I am five kilometers from that, or I am two meters from this. That's the only way to define your location in space. There's no reference points. Another way to think about this is that location is a property of a pair of points, not a single object. Like a single object doesn't have a location. Two objects have a distance between them, But there's no meaning to say my coffee is at this location.
You can say my coffee is a meter from the ground, or my coffee is six thousand kilometers from the center of the Earth. But my coffee has no location on its own, and.
There's no greater question than where is my coffee? So thank you physicists.
Exactly. I mean, I'm trying to be practical here. You know, it's not all space ships and cats flying through space. And this is sort of hard for a lot of people to wrap their minds around because they think of locations as absolute the way Newton did. Right. Newton thought of space as absolutely thought. Even if there's nothing in
the universe, there is still space. But you know, we think of space as just the distance between things, and that's really important framework for understanding general relativity if you get there, because the bending of space can be understood not as like the curature of space relative to some other external metric. There is no other external metric, but just the changing distances between things, because that's all we have.
So it's important to remember that distances are just relative. Right, your location is just relative, And that's also true about velocity. Velocity also purely a relative quantity. This one, I think is even harder for people to grapple with.
So you said, there's no like grid, and this is a stupid question, but like, would our understanding of location change if we had infinite money and we put a grid in space and like you know, every one light year we put like a blinking buoy like in the ocean. How would we still be in the same position even if we had that grid.
Yeah, if we had infinite money, wouldn't coommend spending it on that grid because it wouldn't change our relationship with space, Like you could still define your location relative to a point on that grid. That's fine, But now you've created an object. You've put it there, and you said I'm going to create axis at this location, and therefore I can define my distance from this buoy or from that booey or from the other thing. That's no different from saying here I am relative to my coffee or a
relative to the center of the earth. But you haven't anchored those booies to like space itself. Right. You could shift all of space over and nothing would change in your measurements because space itself doesn't have a location. There's no frame to space itself. Right. You can't say my booys are here relative to space. That means nothing, right, space has no frame.
You just saved us all a lot of money.
I'd like to take five percent of that infinite dollars divert it to my own research.
You might need it, all right, So let's move on to velocity and acceleration. And I'm going to be honest, I often forget the definition of velocity and the definition of acceleration. So let's just start there.
Okay, cool, Well, velocity and principle is very simple. It's how is your location changing? Okap. Location is in units of like distance, meters, kilometers, whatever. Velocity is distance per time, right, So meters per second? How is your location changing? So if you're in a car on the ground, your location is where are you relative to your house, for example,
and your velocity is how quickly is that location changing? Right, So that's why you measure it in like meters per second or kilometers per hour something.
Okay, So the way you just said it, it's also relative to something.
You don't have an absolute velocity exactly. You always measure relative to something because there are no absolute references, right, How could you measure it in an absolute sense? If space itself is not absolute, if there's nothing to grab
onto on space, nothing everybody can agree on. So you and I can measure the speed of a passing baseball and we can disagree because maybe you're in a car and I'm on the ground, and so you measure the baseball traveling at one speed and I'm measured traveling at another speed. The baseball has no speed inherently. It has a speed relative to you and a speed relative to me. I think that makes sense to people, but it tells us that speeding in is not a property of the object.
It's a property of a pair of objects. And I think most people are totally cool with that, and I see you nodding. But then you get a lot of people talking about what happens when you're moving near the speed of light. My question is always near the speed of light relative to what There is no I'm moving near the speed of light or I'm not moving near the speed of light. You're already moving near the speed of light relative to particles that are shooting at the Earth.
If those particles are moving towards the Earth at near the speed of light, the Earth is moving towards them at near the speed of light. So you're already moving near the speed of light. You're also moving at zero velocity relative to your shoes right, which are probably I hope attached to you, or to your head, let's say your head, for example. So you have multiple speeds. You
have speed relative to any potential observer. So it makes no sense to say I'm moving near the speed of light or I'm not moving near the speed of light. You're moving at any speed relative to any observer that could be observing you.
I didn't realize I could claim that I was going so fast. I'm gonna go ahead and across the exercise box off of my new year's resolution list. I am speeding around this universe.
I always tell people you're very quick.
Yes, you're very quick too, We're all very quick. It depends on what you're comparing to.
Yeah, exactly. And this is an amazing and confusing thing about special relativity because time depends on this speed. Right. What we say in special relativity is that moving clocks run slow. So if there's a spaceship zooming past the Earth and it has high speed relative to the Earth, right, people writing with relativity questions and they say a spaceship is moving near the speed of light, and I say near the speed of light relative to who? Right, relative
to what? In this case, the spaceship is moving near the speed of light relative to the Earth. The Earth sees a space ship's clocks as running slowly. That might make sense. People are cool with that. But then because it's symmetric, because the spaceship also sees the Earth as moving near the speed of light. Because hey, we just told you velocity is relative, right, That means that the spaceship sees the Earth's clocks as running slow. And that's
the amazing thing about special relativity. If you really grasp the relativity of velocity. It means that you can't have the same clock everywhere, that everybody doesn't have to agree about how time flows. I'm right that the spaceship's clocks are running slow. The spaceship is right that my clocks are running slow. That's both true because we don't have to have the same story about what's happening in the universe.
Special relativity tells us there's no absolute space, there's no absolute time, there is no absolute history of the universe. Boom boom.
Now that does seem like a good place to start a movie or a sci fi novel. So I can see why this comes up so often.
Right, So keep that in mind when we're later talking about whether potatoes can into black holes or what it's like to be a photon. But there is one thing in the universe which really amazingly, fascinatingly is absolute about the universe, and that's acceleration. So we started with location. That's just like, where are you relative to some arbitrary grid where you anchorated some object. You know, distance from my coffee cup, or distance from my toes, or distance
from the center of the sun. That's location. Velocity is how is your location changing acceleration is how is your velocity changing. So for the math nerds out there, we're now two derivatives. In right, velocity is the slope or derivative of your location. If you're plotting where is your location versus time, then velocity is the slope of that plot. If you then plot your velocity, acceleration is the slope of the velocity plot. So it's just like, how much
is velocity changing? Velocity is how much is location changing?
Got it? I kind of liked calculus.
I love the connection between calculus and physics, right, Like knowing this makes physics so simple and straightforward. You're like, oh, acceleration is just the derivative of velocity, which is just the derivative of location. So I can just like derive my equations of emotions from one fact like a constant acceleration. Boom, I know the accelerations emotion, Just integrate twice to get the position. Boom, You're done.
Elementary maybe not quite that easy.
But I had this great moment because my son is taking physics right now, and he's also taking calculus, and so he knows these tools and he was learning about equations of motion and I was like dude, you can just integrate this twice and get that answer. And he was like, oh, and that's why it's one half at squared. I get it. Cool. And he had this like moment, We're all clicked in his mind, and I was like, dude, math and physics dancing together to explain the universe.
Aw. That must have been a proud moment as a father to be able to observe that.
It was twenty years in the making, but it was cool.
Sometimes you got to wait a long time for the payoffs, but you got there.
But the amazing thing about acceleration is that it is absolute. It's the one thing which does belong to you. Right. Your location is relative, it's a property of a pair of objects. Your velocity is relative. It only has meaning in relation to something else you're measuring with respect to acceleration is something you own. Your acceleration is just your own. You don't need to measure it relative to anything else.
And this is Einstein's famous thought experiment. Right in a box, you can't tell where you are or how fast you're going because those things only have meaning relative to stuff outside the box. But inside the box, you can measure your acceleration.
My first question is, so is it because the reference point is now what you were doing like a second ago, and because that's like an internal comparison, that's why it's not relative silences. I always think, was this a great question or a really dumb question? Dane was trying to figure out, how do I not insult Kelly's intelligence?
No, not at all. The fun moments for me and teaching are hearing somebody's question and then trying to work backwards to what is going on in your mind that made you ask that question, so that my an or is the most helpful, and for me, like that's the fun part about teaching. That's always the puzzle.
I enjoy giving you lots of those opportunities.
Daniel, You know, it's a really amazing property of the universe, and it's not something I think we understand philosophically. It's just something we observe, like this is our description of the universe as we experience it. We know that you cannot measure your velocity or your location, but you can measure your acceleration, So fundamentally, this is a description of something we see in the universe, and this is one of those moments when you can say, Okay, this is
the description of the universe. What does it mean about the universe that velocity is relative and acceleration is not. And it's actually one of the connections to general relativity because acceleration can be seen as equivalent to curvature. Acceleration has all the same effects on the motion of an object as curvature. In fact, we describe curvature sometimes as a pseudo force, right, that's what gravity is. Curvature is gravity,
and gravity is a pseudoforce that generates apparent acceleration. So that's actually a much more complex topic and connect special in general relativity. So I think for the purposes of today's conversation, let's just say this is something we observe in the universe, and we do our best to describe it. And I think the best way to get your handle on the intuition for acceleration is to imagine, like, well,
how would you measure it? I told you you can't measure your velocity accept relative to other stuff, And you can imagine, like being in a box flying through space where you don't have access to anything outside, how would you measure your velocity? There's no experiment you can come up with that can measure your velocity because you need access to stuff outside because that's the only way to define your velocity. But you can measure your acceleration inside that box.
And how would I do that? Like say I was standing in there with the ball, would that help me?
Yes? Absolutely? Just drop the ball. See what happens right now. If you're not accelerating, the ball will just hang there with you. If you are accelerating, then the ball will move because there'll be a pseudo force generated by your acceleration. And we do this all the time. You feel this every time you drive somewhere. Right, If you're driving the car and somebody hits the accelerator right, then what happens. You feel pressed back into your seat. If you dropped
a ball right, then the ball would fly backwards. If somebody hits the brakes, which is also an acceleration, then you feel pushed forwards.
Right.
There's a phudo force there as you're pushed forward. If you dropped the ball, it would fly forwards. Right. The reason you have a seat belt is because of this effect. So it's very easy to tell whether you're accelerating. Just bring a ball or bring a scale. Right, a scale,
it literally is measuring acceleration. That's why, for example, when you stand on a scale in space, you measure nothing because you're in free fall, there is no acceleration, whereas if you stand on the surface of the Earth, you do measure acceleration. You're measuring the Earth accelerating up and out to keep you from falling towards the center of the Earth.
We are recording this pretty close to the end of the holiday, so I'm going to stick with the ball instead of the scale. Let's take a break, and when we get back from the break, going to talk about whether or not potatoes turn into black holes if they're going fast enough. Okay, Daniel, So here's my question for you. Do things change their mass as you approach the speed of lie?
Yeah? Right? And this question was inspired by a listener who wrote in and heard on another podcast that potatoes, if they approach the speed of light, were turned into
black holes. And like, I won't comment on whether you might turn into a black hole if you eat too many potatoes after the holidays, but I do want to dig into this question of what happens to a potato immediately your eyebras scrunch up when you hear this question, because even the question like what happens to a potato when approaches the speed of light, you might think like, well, the speed of light relative to what? Right? Because velocity
is not the property of a potato. So it doesn't make sense to even talk about a potato having a speed. Is it moving at that speed relative to the Earth, relative to a spaceship, relative to some particle? The question itself already doesn't make sense, and that tells you that the answer can't.
Be yes and we're done.
I mean, for example, like take a potato. Maybe have a potato in your kitchen. What is the velocity of that potato? Well, it's moving at zero relative to your kitchen. Probably it's already moving near the speed of light relative to anything that's moving towards the Earth at near the speed of light. And there's lots of stuff moving towards the Earth at near the speed of light. There's particles shooting from space at super high energy. Is at ninety
nine point nine percent of the speed of light. Your potato is moving near the speed of light relative to that particle. Is your potato a black hole?
No?
So the answer. Everybody who has a potato is doing this experiment right now, so we know your potato is not turning into a black hole. And the amazing thing about black holes is that they are observer independent. Some of the things we talked about earlier are observer dependent, like I see your clock as slowing down if I see you moving quickly, and that's observer dependent because it depends on my velocity relative to you. But black holes
are not observer dependent. They exist in every frame, if they exist at all. So it's not like I can see the potato as a black hole because it's moving fast relative to me, but you don't see the potato as a black hole because it's sitting next to you. Everybody has to agree whether it's a black hole or not.
So if we assumed that when they were talking about the speed of the potato it was relative to Earth, does that solve because we all have the same frame of reference.
No, because you can always possibly some observer are moving with the potato somewhere else. Yeah, exactly, and there's always some particle there to do that observing. And the root of this comes from a historically sort of fascinating idea about mass. You often hear that mass increases as your approach to the speed of light. And again, I hope your ears to turn up at that and go like, hmm,
who's measuring the speed in that case? And though this is often quoted, it makes little sense, right, because it doesn't make sense for mass to be observer dependent. If you're moving past me near the speed of light, does it make sense for me to measure mass as larger than somebody else to measure your mass? Right? Mass can't be observed dependent if it has consequences like if you have enough of it you turn into a black hole, right,
And we know that's not observer dependent. So what's going on here is an old concept in relativity which are sort of picked up on and propagated and been repeated over and over and over again, even though it doesn't really make much sense.
What is the old idea that's being repeated.
So this is basically all Einstein's fault, because when Einstein was developing relativity, he had to think about how some of these basic concepts change in this new notion, in this new perspective of the universe, right, And so he was thinking about speed and momentum and energy and mass, And you know, some of these things are the same for Newton, and some of these things are different. Right, velocity is similar, but it has a maximum value now,
and so that changes. And what does that mean about changing energy and changing momentum, Because like energy doesn't have a maximum value. You can have an infinite amount of energy even if your speed only approaches a certain value. So like the relationship between these quantities have to change.
And so Einstein had to reimagine what these quantities were, and for a moment, he came up with this idea of relativistic mass, saying like, well, let's treat an object as if it had more mass if its velocity is greater. And so in his early writing he came up with this concept, and he wrote the equations for mass increasing with velocity.
So anyone who was confused a moment ago about whether or not mass changes with velocity can feel good knowing that Einstein was making the same mistake.
Yes, exactly, And you know it's fair like you're exploring these new concepts, you're wondering, like, how do we generalize We went from one idea to another. What gets change, what doesn't get change? What's the most sensible way for things to change, and it's fine for your first idea to not be the best idea. The problem with relativistic mass is that it doesn't really make sense and it's not really necessary. Doesn't really make sense because it means
that your mass now depends on your velocity. So like that potato would have more mass or less mass based on who's measuring it, and also it would have different masses in different directions, right, Like, what does happen to the potato as we see it approach to the speed of light relative to us is that it gets harder
to accelerate in one direction and not in others. Like, if the potato is already going at ninety nine percent of the speed of light as it whizzes by us, then it's harder for us to increase its velocity in the direction it's already moving, right, because it's already going near the speed of light in that direction. It's easier for me to push it perpendicular to its motion because it's not already moving at a very high velocity.
It's easier for you to push it perpendicular because it's not already moving at a high velocity.
Yeah, relativity velocity has this weird maximum. Right, nothing can go faster than the speed of light relative to anything else. And as you approach the speed of light relative to something, you can pour additional energy into that object. You can give it a push without increasing its velocity as much. Like if I apply the same force to a potato that said zero meters per second relative to me, it's
going to speed up. And if I apply that same force to a potato that's already ninety nine point nine to nine percent of the speed of light relative to me, it's not going to speed up as much. It's just like not room for it to speed up as much. So I can pour energy into it without getting the same velocity return.
Sure, but what was the perpendicular part?
So if you try to think of that as, oh, the potato has additional mass, it's harder to accelerate because it's more massive, then you might think initially, okay, that makes sense. I can describe this as additional mass. It's harder to accelerate the potato if it's always already going really fast, so the same force doesn't give the same increase in velocity. That kind of makes sense, right, except that only makes sense in the direction the potato is going,
because the potato can have no velocity in other directions. Right, so I'm free to apply a force to the potato in another direction and I get the same boost as I always did. And so now the potato has to have like a mass in this direction because it's hard to speed it up in that direction, and a mass in other directions where it's easier to speed it up. And so now mass has to have like directionality to it, right, instead of just being like a property of the object.
I feel like I just felt the pieces click like in my hand. There. Okay, let's keep going.
And so there is a way that could make sense if you're willing to have mass be this weird directional thing. But Einstein was like, Okay, actually, this doesn't make any sense, and you don't need it because you already have a concept of energy, the total energy. The object already captures this behavior, So you don't need this new weird directional relativistic mass. It doesn't give you anything, it doesn't help
you at all. Let that be part of energy. And then Einstein and others decided, well, let's just keep mass to be a number and it'll be the amount of energy something has when it's at rest. So it's like the rest energy of the object, and that makes it invariant because you defined it to be the amount at rest. And so this is what we call invariant mass, and it means that energy is now nicely broken in two parts. The energy you have a rest which you call the
invariant mass. So take for example, an electron. It has a mass even if you're holding it in your hand, right, that's what we call the invariant mass. That's the rest mass of the object. And you can also have energy if it's in motion, so that's its momentum. So energy now has two components, the rest mass, the invariant mass, and the motion part right, the energy of its motion.
So those are two separate things. And the invariant mass by definition, doesn't grow with velocity because you measure it when it's at rest. So you might think that's just defining stuff, you're just defining it to be invariant trick. Yeah, yes, that's true. We're defining it to be at rest. That's really what mass is. And we're free to invent these quantities to be useful and to make sense to us, because hey, we're the audience of.
It, right, right, we're creating tools that help us with stuff, so why not?
Yeah, And if you're following along, remember our original question is does a potato turn into a black hole near the speed of light? And our answer so far is, let's be careful when we talk about energy of mass and energy of momentum. Energy momentum is relative, energy of mass is not. So listeners following along might be like, Okay, Daniels told us about the definition of energy and how it might be mass and how it might be menum.
But in general relativity, we know that curvature space depends just on energy, right, It doesn't depend only on mass. It depends on more complex notions of energy. Because like photons can help bend space and they have no mass. So why don't potatoes create enough curvature if they have enough velocity, they have enough momentum, why can't that energy density then create black holes? And I have two answers
to that. One is this is a really really complicated calculation to do because in general relativity, it's not just like a number. It's not like Newton's gravity where you have mass and more mass means more gravity. Einstein's equations are tensor equations, which means they're matrices. Is all sorts of complicated stuff, and different kinds of energy enter in different ways, So energy of mass enters differently from energy
of velocity, and so it's a really complicated calculation. And we know that the answer has to be the same for a potato at rest and a potato in motion because black holes are not observer dependent. That's just like a bedrock fact in general relativity. So instead of doing a really complicated calculation where the potato is in motion, we know we'll get the same answer when the potato
is at rest. And if the potato at rest doesn't give you a black hole, then the potato at motion can't give you a black hole, and it can't go through all the complicated math here on the podcast. But that's the sort of the end run around having to do all that math. We know a potato turning into a black hole if it's not already a black hole in.
Your kitchen, So I don't have to live in fear of my potatoes. That is a relief.
Well, potatoes going to hurt you in lots of ways, but they're not going to turn into black.
Holes, that's right, all right. So we have struck down one misconception about potatoes and black holes, which I'm sure everybody woke up this morning thinking that they'd hear about potatoes and black holes. And when we get back, we're going to ask do photons experience time? All right? Daniel? You know I've often heard it said that light doesn't experience time? Is that right?
Have you heard it said that photons experience our podcast and enjoy it? Are they faithful listeners?
I mean, Daniel, how could they not everything from super organisms down to the smallest particles enjoy dk EU. How could they not?
Exactly? And we're so good looking, right, and what do photons do if not appreciate our looks?
Right?
Yeah?
Sure, I think we're getting on something ic here. But let's move forward, all.
Right before we undermine our credibility too far. Yes, this is something you see in popular science all the time. Photons fly through the universe not experiencing time. So let's try and understand where this comes from, and then let's talk about what we actually know about it.
All right?
Where does this come from?
So it's a not unreasonable extrapolation of what we know about special relativity, we say that moving clocks run slow. So I put Kelly and her potato on a spaceship with a clock, and I tell them to accelerate. They're going now near the speed of light relative to me. I look at their clock through a telescope. I see that it ticks more slowly than a clock sitting next
to me. So two clocks, one that has no volo city relative to me, taking one second per second, and Kelly's clock near the speed of light relative to me, ticking at one second per year or something. And that's cool, that's fascinating, that's amazing, right, whoop.
So I'll note if you have Kelly and a potato pretty soon, and you're only going to have Kelly, but are fascinating and amazing.
Yeah, And special relativity tells me how to calculate that. It says, okay, Kelly's moving fast. I can calculate how quickly her clock is ticking. And I can also go to Kelly's reference frame. Because Kelly has a reference frame, she has a potatoes, she's a clock. She is sitting in her spaceship sipping her coffee. I can go from her reference frame to my reference frame. And that's really the core of special relativities. It tells you how to
translate from one reference frame to another. Right, I create mine. We said there is no absolute space. But I can create a reference frame and say, here's my origin. Here's location equals zero, here's location equals one. I can measure location and velocity relative to my reference frame. Like if we spent a zillion dollars building your grid, that would be Kelly's reference frame. Wouldn't be special or absolute in anyway,
but it'd be yours, and it'd be wonderful. I'm sure it'd be special to me and special to you, but not special to the universe, all right. They wouldn't change the laws of physics in any way. And so I have a reference frame, You have a reference frame, and special relativity tells us how to transform between these different reference frames. And special relativity tells us that as the velocity of two reference frames grows to near the speed of light, which is the maximum, the time that they
see each other's clocks ticking goes to zero. If you're at ninety nine percent of the speed of light, I see your clock ticking like one second per day. If you go to ninety nine point ninety nine percent of it, I see your clock ticking. It's one second per year. If you go at ninety nine point nine and whatever percent of the speed of light, maybe I see your clock ticking one second every thousand years. So it's tempting to extrapolate this and say, well, what happens if you
go at the speed of light? Do I see your time as stopping. That's where this comes from because photons we move at the speed of light, and so people imagine, oh, okay, put a photon in a spaceship, take that spaceship to the speed of light. If the photon has a little clock next to it, what does that clock read? Well, it's very tempting to say, at the speed of light, time stops.
All right, so is this going to be a speed of light relative to something? I'm not going to try to jump the gun? What do we talk about next, Daniel.
So it's very fun to say that time stops with that photon, but it's not really true because that photon doesn't have a reference frame.
Well, that's what I was trying to get at. Y I'm brilliant, all right, Sorry, go ahead, PhD In physics.
Yeah, because photons don't have a reference frame. Photons move at the speed of light relative to every observer. So I see the move at the speed of light. You see the move at the speed of light. You have this confusing scenario where you're in your spaceship moving really fast, you turn on a flashlight. You see the photons moving relative to you at the speed of light. I see the photons moving relative to you at the speed of light, even though I also see you moving at nine of
the speed of light. It's very confused. But the thing about photons, the reason they move at the speed of light relative to everybody, is that you can never catch them. You can't like zoom up next to a photon and say like, hey, look there's a photon the way you can relative to a potato, for example, or relative to Kelly's ship. This weird fact that two observers always see light moving at the speed of light, even if they have a high velocity relative to each other. This is
not like a little detail. It's the whole foundation of special relativity. From this one fact and the assumption that the laws of physics are the same everywhere, you can derive all of special relativity, time dilation, length contraction, Lorentz transformations all over. That depends on this Why is that
the case? Why is there a universe this way? Well, we aren't actually sure, but it is an observed fact we have verified with experiments, and everything flows from it, and it has all of these weird consequences, including that you can't catch up to a photon. You can't ever join a photon in its reference frame and say, hey, what's it like to be a photon? And that's kind of the short answer is that photons have no reference frame, and so it makes no sense to say, what does
a photon experience? Does a photon experience time? Photons don't experience anything the way like lumps of coal don't have political views. Right, It's sort of like a category error to even ask the question.
Unfortunately, Okay, I'm taking a second to wrap my head around the fact that photons have no reference frame because essentially, for any reference frame you pick, they're always moving at the speed a light.
Yes, exactly, And special relativity, this calculation on which this whole idea is based, can only translate between reference frames. It says, my potatoes reference frame, Kelly's reference frame, my coffee is reference rame, my cats reference frame. I can tell you how clocks in any of those reference frame appear in my reference frame, or I can tell you how my clocks appear in those reference frames. But photons don't have a reference frame. There is no axis moving
with the photon where the photon is at rest. There's no special set of buize for that photon that move along with it where it has no velocity. Right, no matter what set of booies you build, photons will always be moving at the speed of light relative to those booies. So there is no reference frame, so you can't use special relativity to calculate what's it like to be a photon.
I think my brain feels like physics should be intuitive because I exist in this universe and feel like I understand it. But the more I talk to you, the more I feel like it's not necessarily intuitive, which makes it all the more amazing that we have figured it out. And so I totally get why people jumped to photons don't experience time, because intuitively, that does feel right to me. I'll be sleeping tonight thinking about photons not having a
reference frame. Yeah, is this intuitive to you? Or is this it makes sense now because you've been thinking about it for so long.
It makes sense mathematically. Intuitively, it's always a struggle it makes sense of the universe. The way I think about it is that there's a very tempting intuitive path which is wrong, which is to think about photons as the extrapolation of what happens when you go really really fast, because they're moving at the speed of light, and we can go almost to the speed of light, and so it seems like they're right there, like at the end of that curve, right, But they're not. They're really in
a different category. So even though you might want to organize them like at the end of that curve they're similar to a spaceship moving really really fast, they're not. They're really in a completely different regime because they have no mass. Right, So you can't like build a clock in this photons reference frame. You can't build a clock out of pure photons. There's nothing it's like to be a photon. It's really a completely different kind of object
than anything that does have mass. So think about two different categories. Has mass, doesn't have mass. Special relativity can tell you about the experience and how time clicks for anything that has mass, anything that doesn't have mass. There's no reference frame there. So special relativity has no handle on it. It can't tell you at all what it's like to be a photon. Does that mean photons don't
have an experience? You know, maybe alien philosophers when they come and it tell us about how the universe works, will have some way thinking about what it's like to be a photon, you know, the way Thomas Nagel struggled with what it's like to be a bat. So I don't want to totally rule it out. And you know, maybe there are crazy aliens out there whose minds are just made out of photons somehow, or ripples and electromagnetism, and so I don't want to piss them off either.
You're really hedging your bets here, Dan.
Hey.
You know, like at the beginning of the podcast, we've got to be open minded, and we don't want to be full of hubris and declare that we know everything about the universe. So I think the crispest thing we can say is that special relativity can't say anything about what it's like to be a photon. It certainly doesn't tell us that photons experience zero time. And you know that already, because if you take that idea to its
logical conclusion, then there's all sorts of confusing contradictions. Like a photon that's omitted instantly is across the universe, right like, it doesn't that feel like it violates all sorts of principles and transformation of information, and you get quickly into paradoxes and confusions about causality. It really doesn't make sense at all. And for those of you who are students of special relativity, photons do take time to fly through
the universe. They have this thing called a space time interval which is zero, which just means that they follow the shortest path through space time, but they still take time to move through space. And so, you know, special relativity is our best description of how space works, and it tells us a lot about the nature of space and the nature of velocity and the nature of acceleration even but it doesn't tell us what it's like to be a photon.
Got it all right? Just like we'll never know what the bees see with the colors that they can see and we stand, we'll never know what it's like to be a photon. I gotta be honest, I'm a little sad that I'll never know what it's like to be a bee, but I can live without knowing what it's like to be a photon. But maybe this is a fundamental difference between biologists and physicists.
But hey, if you're a photon and you've been listening to this podcast and we offended you right in, tell us what is it like to be a photon and be pissed off at the podcast? I want to know. Also, if you're a bee right in, because Kelly wants to hear.
From you, that's right, it will have you on the show.
And if you're not a photon and you're not a bee, and you're somehow a human listening to this podcast, we still want to hear from you. Did this make sense to you? Did this help you understand why potatoes are not black holes? And what it's like to be a photon? Did we just confuse you? Send us some feedback, Send us some love, send us some grumpy emails. Whatever. We love to hear from you. Write to us to Danielankelly dot org. Don't send hard physics questions to Daniel and
Kelly dot com. I don't think they know the answers.
They might just might not appreciate it. You know, a lot of work was at the planning a wedding. They're very busy people.
That's right, Yeah, exactly. They got a full spreadsheet. They don't need your question on top of the to do list.
Good luck, Daniel and Kelly.
Congratulations.
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