What is a space-time interval?

Daniel and Kelly break space, twist time, and then put it back together to explain the most important concept in relativity you've never heard of. See omnystudio.com/listener https://omnystudio.com/listener for privacy information.

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Daniel Whiteson?

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• 3:17Daniel Whiteson?

  Special Relativity brings space and time together, and in the darkness, binds them into spacetime. That sounds pretty awesome, and it was fun to say, like, something that could only happen in Mordor or during the Big Bang. But what does it actually mean? What is spacetime? How do you measure distances in four-dimensional spacetime? And why would you? Physicists are always saying that space and time are like two sides of the same coin, making more sense together. What are they talking about?

• 4:01Daniel Whiteson?

  In what way do they make more sense together? Today, we're going to blow up all of those analogies and give you a real conceptual understanding of how relativity breaks space and twists time, but then clicks them back together into a harmonious whole. We'll talk about what that really means and the crucial, but rarely explained, concept at the heart of it all, the spacetime interval. Welcome to Daniel and Kelly's Spacey, Timey Universe.

• 4:31Kelly Weinersmith?

  Hello, I'm Kelly Weiner-Smith. I study parasites and space, and I have fun in all spaces and at all times.

• 4:50Daniel Whiteson?

  Hi, I'm Daniel. I'm a particle physicist who likes to think about aliens, and I was having fun this morning until Kelly showed me the Crusher.

• 5:04Kelly Weinersmith?

  Oh, I wasn't sure you were going to mention the Crusher on the show.

• 5:09Daniel Whiteson?

  It's the only thing I can think about now. Thank you very much. Kelly, tell everybody, what does the Crusher crush?

• 5:15Kelly Weinersmith?

  The tube that goes to the testicle and connects it to the rest of the body. I am looking into methods for what we'll say, weathering our male goats. And I'm trying to figure out what method I would feel comfortable doing, or if I need to call the vets. And wow, the Crusher is a big piece of equipment that, once I have it in my hands, I am not sure that I am up for actually using.

• 5:41Daniel Whiteson?

  But you were up for brandishing it on our video call this morning with Glee.

• 5:46Kelly Weinersmith?

  This thing is huge. Everybody needs to see it.

• 5:48Daniel Whiteson?

  Oh, stop it. Put it away.

• 5:50Kelly Weinersmith?

  The Crusher. All right.

• 5:52Daniel Whiteson?

  But today, we are not crushing goats or any of their bits. We are crushing your confusion. We are explaining the way the universe works.

• 5:59Kelly Weinersmith?

  You always pull us back somehow. Okay. So today, we're talking about spacetime.

• 6:07Daniel Whiteson?

  Yes.

• 6:08Kelly Weinersmith?

  Which got me thinking about all of space and all of time. And so, Daniel, if you could snap your fingers, and for five minutes, you would be in a protective bubble, and you could go anywhere in space, but you couldn't change the time, like, you had to just pop up right there now, what would you want to see?

• 6:25Daniel Whiteson?

  Kelly, you need this episode, because if you had heard this episode already, you would know that that question is incoherent, because there is no universal now.

• 6:34Kelly Weinersmith?

  That's right.

• 6:35Daniel Whiteson?

  Right? There's no sense of time across the whole universe where you can say, this now is the same as that now. It's observer-dependent, as we're going to talk about.

• 6:43Kelly Weinersmith?

  And you know what? I should have known that from our What is Time? and What is Space? episode series. But, okay, so is there some way to constrain it so I can say, like, you can't go back to the beginning of the universe? I was trying to, like...

• 6:55Daniel Whiteson?

  Why do you want to stop me from going back to the beginning of the universe?

• 6:58Kelly Weinersmith?

  Well, because that's what I thought you'd say.

• 6:59Daniel Whiteson?

  You were totally right. That is what I was going to say.

• 7:02Kelly Weinersmith?

  But you've said that on the show before. So I'm trying to figure out what you think is the most interesting thing happening now. And my guess is that you were going to say black holes.

• 7:10Daniel Whiteson?

  I'm going to go to the factory that makes the Crusher, and I'm going to burn it down.

• 7:14Kelly Weinersmith?

  Okay.

• 7:15Daniel Whiteson?

  No, but if I could go somewhere in the modern universe, then for sure, I would like to see not only what's inside a black hole, but the immediate vicinity of a black hole would be super fascinating, to see frame dragging, and to see all that time dilation, and all the extreme events around a black hole. I think my second choice would be the heart of a neutron star, because when every other defense against gravity has already collapsed, and matter becomes insanely dense, so that protons and electrons eat each other and become neutrons, then you have this fascinating environment where quantum mechanics and gravity are at about the same strength, and we don't

• 7:59Daniel Whiteson?

  know what's going on at the heart of neutron stars, because we can't calculate that stuff, because we don't have a theory of quantum gravity. We'll never go inside a black hole, so that's sort of just like, fun to say but hopeless. But the inside of a neutron star is out there and real, and on the outside of event horizon. So in principle, we could one day see it, and that could be the key to unlocking quantum gravity.

• 8:21Kelly Weinersmith?

  Whoa. Okay, so how could I have worded the question to constrain your ability to see the Big Bang? What would have been the right way to word that?

• 8:29Daniel Whiteson?

  Daniel, what would you like to see in the universe except for the Big Bang?

• 8:34Kelly Weinersmith?

  Wouldn't you have to go backwards in time to see the Big Bang?

• 8:40Daniel Whiteson?

  It depends a little bit what you mean by "see." I mean, the information from the Big Bang is out there. In some respects, people often say seeing, the CMB is like seeing the Big Bang, though it actually comes from 380,000 years later. There is information from the Big Bang out there, and gravitational waves. And so, like, seeing it means detecting those and reconstructing what happened. We can do that today without, like, being there during the Big Bang. In that sense, everything you see happened in the past already, so...

• 9:10Kelly Weinersmith?

  But I feel like you understand that that's not what I mean. Like, yes, you can see evidence from it.

• 9:18Daniel Whiteson?

  Yes.

• 9:19Kelly Weinersmith?

  But like, I don't, you know, so if I go to a Civil War site and I find a, like, bullet case, that's like evidence that it happened.

• 9:26Daniel Whiteson?

  Yeah.

• 9:27Kelly Weinersmith?

  But it's not the same as being there and watching both sides run across a field and start fighting each other, right?

• 9:34Daniel Whiteson?

  No, but it's sort of like going really, really far away instantaneously and capturing the light that left that Civil War battlefield contemporaneously, and using it to watch in real time the battle, which is something you could literally do, right?

• 9:48Kelly Weinersmith?

  All right, all right, all right. Well, I'm going to have to be more careful next time I ask you a question. But we've all learned something from Kelly's bad question, which is why Kelly's here. So...

• 9:59Daniel Whiteson?

  And these are really fun topics to think about, because our intuition is broken about how all of this stuff works. We tend to think that time flows the same way for everyone. We tend to think that distances are real, and they're universal. When it turns out the universe operates in a way that's fundamentally in conflict with our intuition, but amazingly, does make sense. So we have this task ahead of us to, like, incorporate this new intuition about the universe into our minds. But often, this means just, like, read a bunch of equations and use them to predict what happens. But I think it's possible to develop a new kind of intuition, a conceptual understanding for how the universe really does work. And that's what we're going to try to do today by introducing you to one of the most

• 10:42Daniel Whiteson?

  important concepts in special relativity that almost nobody talks about, and that we've never covered on this show.

• 10:48Kelly Weinersmith?

  What? What?

• 10:50Daniel Whiteson?

  Yes.

• 10:51Kelly Weinersmith?

  Well, this is a very exciting day here at DKEU. And let's see if our audience heard about this thing that pretty much no one talks about. And so, we asked our audience, what is a spacetime interval?

• 11:04Speaker 06

  Well, I would expect that that would be the reduction of Einstein's spacetime into a quantum-type interval, but I'm really not too sure.

• 11:17Daniel Whiteson?

  It's the time between two objects in space, maybe? I don't know. Could a spacetime interval be the point where... One max plank length ends and one begins? I'm not sure.

• 11:32Speaker 07

  A spacetime interval is the required timeframe between semi convincing, scientific mumbo jumbo that you hear on sci fi shows and movies. But seriously, maybe it's some form of the smallest unit of spacetime, uh, length and distance, kind of almost a singularity, but not quite.

• 11:53Daniel Whiteson?

  I've never actually heard the term spacetime interval before, but guessing from context, I would imagine a spacetime interval is one like frame of the universe. So, you know, you move forward one unit of time and look at the way everything else changed. That's one interval of spacetime.

• 12:15Kelly Weinersmith?

  All right, Daniel, I asked a question that belied my ignorance. And so I'm not going to even attempt to, to say if I think the audience was correct or not, uh, with this question, how, how close were they?

• 12:28Daniel Whiteson?

  Pretty much zero points all around. A few points for people thinking this is a kind of distance because that's the closest. It has nothing to do with the plank length or frames of the universe or minimum distances or anything like that. It's really an analog to what we think of as distance, but now in four dimensional spacetime with an uncomfortable twist in it that we're going to get to.

• 12:53Kelly Weinersmith?

  Good news, everybody. We all need this episode. So here we go. And we are going to start from the beginning because clearly Kelly needs to go back to first principles. So what I want you to explain to me, Daniel, so space time sounds like space and time and distance. And there's like, so what is distance? Let's start there.

• 13:14Daniel Whiteson?

  Yeah, let's build our intuition with stuff that makes sense to us. And let's start easy. Let's start in one dimension, right? So imagine, for example, you have a pencil and you have a ruler and you want to know how long is my pencil? What do you do? Well, you put it along the ruler, you're operating in one dimension, right? So the pencil and the ruler are lined up. And you say, well, the back of the pencil, you know, is at two centimeters on the ruler and the front of the pencil is at eight centimeters on the ruler. And then you subtract, it's like eight minus two, six centimeters long.

• 13:46Kelly Weinersmith?

  I don't know why you wouldn't just put it at the beginning of the ruler and then you don't have to do any subtraction.

• 13:50Daniel Whiteson?

  Exactly. You could put it at the beginning of the ruler so that you get zero and six, but what happens? You get the same answer, right? If you put the pencil at the beginning or if you slide it along, it doesn't matter. The answer you get does not depend on where on the ruler your pencil is, right? It's invariant.

• 14:06Kelly Weinersmith?

  Okay.

• 14:07Daniel Whiteson?

  That's cool. That all makes sense. It's makes so much sense. It's kind of blindingly obvious, which is where we want to begin, right? With like firmly grounded in our intuition.

• 14:15Kelly Weinersmith?

  This is very comforting, unlike the crusher.

• 14:20Daniel Whiteson?

  Okay. So why do you keep bringing that up, Kelly? You just like really want to throw me off.

• 14:25Kelly Weinersmith?

  I wasn't going to mention it on this episode, but you brought it up.

• 14:29Daniel Whiteson?

  Because you did the whole crushing thing on the video before the episode. And now there's nothing else in my mind. I'm trying to get spacetime in my brain, but that's all I can see.

• 14:38Kelly Weinersmith?

  I'm so sorry. I'm sorry.

• 14:40Daniel Whiteson?

  It's fine. All right. So now let's go to two dimensions. How do things change? Well, imagine you have like a piece of graph paper. And the little squares on the graph paper are one centimeter by one centimeter. And you drop your pencil onto the graph paper and I ask you, how long is your pencil? So how do you figure out how far it is from one side of the pencil to the other?

• 15:01Kelly Weinersmith?

  Pythagorean theorem.

• 15:03Daniel Whiteson?

  Yes, exactly. So you say, well, how many squares does a cross in one direction and how many squares in the other direction? And now you have a right triangle where the pencil is the hypotenuse, right? It's the long part of the right triangle. And we can calculate one side because it's just counting squares. We can calculate the length of the other side, just counting squares. And then the diagonal, which is the length of the pencil, that's the Pythagorean theorem, right? So a squared plus b squared equals c squared. Boom. We have an answer. And just like in the one dimensional case, it doesn't matter where the pencil was on the graph paper. If you dropped it in a different direction, you might've gotten more squares on one side and fewer on the other, but the answer wouldn't change.

• 15:46Daniel Whiteson?

  Or even if by chance you happen to drop the pencil so it lined up perfectly in one direction, right? Like along the X axis conceptually, right? Then it's basically back to the one dimensional problem or the other axis. The point is, in this picture, distance is real. It's invariant. It does not depend on where you dropped the pencil or like the size of these squares. If you made them two centimeters or five centimeters or like a furlong or whatever, all those are just arbitrary choices humans have imposed. The pencil distance is the real thing, right?

• 16:20Kelly Weinersmith?

  Yes, this is very comforting. Can we stay here for the rest of the episode? No, let's push our boundaries. Let's keep going.

• 16:28Daniel Whiteson?

  All right. And so now it's easy to imagine how we might extend this to three dimensions or really any number of dimensions. Like if you have your pencil and it's not on the paper, but it's like floating in space, we're on the space station now, right? And the pencil is floating in space. And you imagine like not graph paper, but like laser lines through space. And you want to measure how long is it from one edge of my pencil to the other? Well, you play the same game, but now you have three directions of counting squares. And you can still do Pythagorean theorem. It's just a squared plus b squared plus c squared equals d squared, right? It's the same game fundamentally. The geometry has not changed because the nature of these dimensions are all the same. And so we can just keep doing this. And if you wanted to work in 11 dimensional space

• 17:12Daniel Whiteson?

  or 26 dimensional space, the concept of distance wouldn't change mathematically or intuitively, because the distance is the real thing, right? Everything else is just bookkeeping.

• 17:24Kelly Weinersmith?

  Okay. So I'm trying to imagine a pencil floating in space. And now a squared plus b squared plus c squared equals the length of the pencil squared.

• 17:34Daniel Whiteson?

  Yeah.

• 17:34Kelly Weinersmith?

  My gut feels like the more dimensions you add, the bigger the pencil is going to get. Cause you've got all these extra squared terms that are going to keep getting added. But that's not true because why?

• 17:46Daniel Whiteson?

  Yeah, that's not true because the pencil is a certain length. And if you add squares in one of the dimensions, the other ones will shrink.

• 17:54Kelly Weinersmith?

  Okay.

• 17:55Daniel Whiteson?

  Just like if the pencil falls to the floor and it's now on a two dimensional surface, you only have two contributions or the third one is just zero, right? And those are longer than if it's floating up above the graph and it gets a third dimension, the first two dimensions are going to shrink a little bit. So they all act in harmony to make sure the distance never changes. You like flip a pencil from one astronaut to another. So it's like rotating through space. You know, your intuition tells you the length of the pencil is not changing. The difference between its front and its back along some axis might change, right? It might go up and down and be negative or whatever. But the length of the pencil doesn't change because all three dimensions are working in harmony to contribute various pieces to the length.

• 18:40Daniel Whiteson?

  And it always adds up to the same number because that's the physical thing. Everything else is just bookkeeping. It wouldn't make sense if the length of the pencil depended on like where the graph paper was, right? Or which ruler you used. It's a real thing in the universe.

• 18:55Kelly Weinersmith?

  All right. But I bet that if I were to say, Daniel, you can travel a billion, a trillion, a quadrillion miles away in any direction in space. What is it that you want to see within that area? I was gonna say, everybody should know what I'm talking about. Are you going to tell me that, uh, that something about that doesn't work like the pencil?

• 19:15Daniel Whiteson?

  I see. You're asking me to be the physics wet blanket here?

• 19:19Kelly Weinersmith?

  I mean, we have to take turns there, right?

• 19:23Daniel Whiteson?

  Well, if you said I could go a quadrillion miles with respect to Earth, then you've given me a frame of reference in which that is well defined.

• 19:31Kelly Weinersmith?

  Okay.

• 19:32Daniel Whiteson?

  So yeah, I could totally do that.

• 19:34Kelly Weinersmith?

  All right. That's what I should have asked. Anyway, all right, moving on.

• 19:37Daniel Whiteson?

  And so we have three dimensions of space. We're comfortable with the idea of distance in space. Cool. Let's put that aside for now and think about time. Time is one dimensional, right? We don't have like two clocks going on. We don't think so. It's actually a super fun theory we can explore. And we did an episode a couple of years ago about two dimensions of time. But for now, let's just think about one dimension of time, right? And so for example, you can click your stopwatch when this episode starts and when the episode ends, and you can ask, how long is this episode of the pod? And you can look at the difference and that's the length, right? Totally obvious, basic subtraction.

• 20:15Kelly Weinersmith?

  Perfect. Yes. For our poor audio guy, it probably feels like an hour is infinite, but it is still just an hour.

• 20:21Daniel Whiteson?

  Exactly. And in the same way, it doesn't actually matter when you hit the stopwatch to start, as long as you noted when the episode started. If you accidentally hit your stopwatch like an hour before, as long as you wrote down, oh, the episode started at one hour in, you could still measure the length of the episode by looking at the difference, right? Because when you started it is arbitrary. What you're interested in is the physical thing, which is the difference between the start and the end of the episode. So intervals in time are also physical in that sense, right? They're real. It's not just bookkeeping.

• 20:54Kelly Weinersmith?

  What does physical mean in this case? Like physical, I think of as something I can touch.

• 20:58Daniel Whiteson?

  Oh, I see.

• 20:59Kelly Weinersmith?

  You mean physics all?

• 21:03Daniel Whiteson?

  I mean, it's a part of the universe.

• 21:04Kelly Weinersmith?

  Okay.

• 21:04Daniel Whiteson?

  It's not part of our measurement system.

• 21:06Kelly Weinersmith?

  Okay.

• 21:06Daniel Whiteson?

  Right? And it's invariant in that way. And here so far, all these definitions are in a classical world, right? Before relativity, this is Newton's idea about how time and distance worked, right? That anybody could measure the difference between two things that happened in the universe and the time difference or the space difference, and they would always get the same answer. That's the way Newton thought the universe worked and that's the way I operate and you operate. And this whole segment of the pod has been like, let's confirm our intuition about how distances work. And it's all very comforting until we learn that it's all wrong.

• 21:42Kelly Weinersmith?

  Oh no, you pulled the soft blanket of Newtonian physics off.

• 21:48Daniel Whiteson?

  Yeah.

• 21:48Kelly Weinersmith?

  And now it's cold and unwelcoming. Let's take a break before we have to sit with our discomfort for too long. And when we get back, we'll hear what Einstein had to add.

• 22:09Speaker 03

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• 22:29Kelly Weinersmith?

  To this day, Ordinary would not have done anything, and I would have not been able to put it out if Book Talk didn't back it up, and if my wife and her friend didn't back it up. So, pretty crazy how like, just one thing.

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  I mean, you, I bet you, we could point to nine different things in our careers, where it's just one thing, all of a sudden, if that one thing didn't happen, then I wouldn't be here.

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• 23:05Kelly Weinersmith?

  It's just insane.

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• 25:05Kelly Weinersmith?

  And we're back. We had a very comforting discussion about distance and time, where everything felt like it made sense. And now we are at the point of the episode where we are going to expand our brains and learn something new. So, all right, Daniel, make us uncomfortable.

• 25:18Daniel Whiteson?

  All right, so.

• 25:20Kelly Weinersmith?

  Not crusher-level uncomfortable.

• 25:21Daniel Whiteson?

  Well, in 1905, Einstein pulled out the metaphorical crusher. And he said to Newton, he said, you know, put your theories in this, buddy, because here I come.

• 25:31Kelly Weinersmith?

  It took me a second. Sorry for the delay. I was drinking water. It almost totally destroyed my computer. All right, go on.

• 25:40Daniel Whiteson?

  And, you know, these intuitive notions of how the universe works, they do work for us at our basic level. But Einstein discovered that when speeds get high, relative speeds get high, then they don't work. The universe is broken. It actually works in a fundamentally different way. And it's important to understand where this comes from. It all comes from the same source, which is the fact that the speed of light is constant for all observers. That is at the heart of everything. If you accept that the speed of light is the same number, no matter who measures it, no matter how fast they are moving with respect to, like, the flashlight that gave off that beam, then you'll see that everything breaks. And we're going to walk you through that, and how it crushes your intuition.

• 26:23Kelly Weinersmith?

  All right, crush away.

• 26:27Daniel Whiteson?

  So imagine, here's the setup. Kelly gives two flashlights to her goats, and puts those goats in a crate, and puts that crate on a self-driving tractor to the vet, to, you know, have their problems taken care of with great anesthetic, of course, and very humanely.

• 26:43Kelly Weinersmith?

  Good, good.

• 26:43Daniel Whiteson?

  All right. And so, they have two flashlights, and one is pointed towards the front of the crate, and one is pointed towards the back of the crate. Okay? And they turn the flashlights on at the same moment. So they click both buttons. And then, we're interested in, like, well, how long does it take for that beam of light to hit the front of the crate versus the back of the crate? So what would you say, Kelly? Goats are in the center of the crate. They turn on both flashlights at the same time. Do those beams reach the front and the back of the crate at the same time? Yes or no?

• 27:12Kelly Weinersmith?

  I feel like they should, but it's moving forward, right? And so, does that mess up the answer?

• 27:20Daniel Whiteson?

  That's very good intuition, but we're asking right now from the goat's point of view, right? So yes, the goat is in the crate, and it's on the back of the self-driving tractor, and it's driving itself towards the vet. But the goat doesn't know how fast the tractor is moving relative to you. You're outside the tractor. It's inside the crate, and the crate is not moving with respect to the goat.

• 27:40Kelly Weinersmith?

  Okay, so it reaches the front and the back at the same time?

• 27:43Daniel Whiteson?

  Yes, you're exactly right. The goat says that the light reaches the front and the back at the same time. And that makes perfect sense, because it's going at light speed forward and light speed backwards. And it hits the front and the back, which are the same distance away, in the same time. Distance is rate times time. Very simple, right? Nothing complicated.

• 28:00Kelly Weinersmith?

  That's right.

• 28:00Daniel Whiteson?

  All right. But Kelly is also watching. She sent the goats on this self-driving tractor, and she doesn't want them to get hurt, except maybe get crushed when they get there. But she's paying attention to what happened. And for her, unlike the goats who see the walls of the crate at rest, for Kelly, the crate is moving forward. And she says, hold on a second. I also see light traveling at the speed of light forwards, and at the speed of light backwards. But I see the front of the crate is moving forward from the point where the light was emanated. So it's moving away from the source at the same time as the light is chasing it, so it takes longer. And the back of the crate, you see moving towards where the light was emitted. So that distance is effectively shorter. And so you

• 28:45Daniel Whiteson?

  say, no, no, no, the light hits the back of the crate first, and the front of the crate second.

• 28:51Kelly Weinersmith?

  And then I look at the goats, and I say, you guys are bad at this.

• 28:55Daniel Whiteson?

  And meanwhile, Zach, who's in his Ferrari, is zipping by at 100 miles an hour to do who knows what. And he says, I see the opposite, right? Because from his point of view, the crate is going backwards. And so he says, no, no, the back of the crate is running away from the light, and the front of the crate is moving towards the light. So Zach sees the front of the crate get hit before the back of the crate.

• 29:18Kelly Weinersmith?

  Ever since that lucrative Doritos sponsorship, he's been able to afford fast cars.

• 29:25Daniel Whiteson?

  Exactly. And so, even though he's got one hand in the Doritos bag, and one hand on the wheel, he's able to make these measurements. And so, what's going on here? The issue comes down to the fact that everybody, the goat, Zach, and Kelly, all see light moving at the same speed, no matter what. If you replicated this experiment with sound instead of with light, then everybody would agree on what happened. Why is that? Because the speed of sound is not the same for all observers. Like, if the goats are bleeding, if they're going bah inside the crate, then they're going to see their sound hit the front and the back at the same time. Kelly, who sees the crate moving, is going to see the sound going forward

• 30:07Daniel Whiteson?

  faster than it's going backwards, because the sound is moving with the same speed with respect to the air in the crate. And so, like, if Zach has a speed relative to that air, or Kelly has a speed relative to that air, then they see the sound moving at different speeds, right? So the front and the back move at different speeds, which accounts for everything, and closes the loop. So because light moves at the same speed with respect to all observers, everybody sees light moving forwards or backwards at the same speed, even if they have velocity relative to the goats, then that's why people see things happen in different orders, right? That's why they can't agree on whether the light hits the front or the back of the crate at the same time. So the takeaway here is the

• 30:48Daniel Whiteson?

  fact that the speed of light is constant for everybody breaks this notion of simultaneity, that if two things happen at the same time for Kelly, they also happen at the same time for the goats, and they happen at the same time for Zach, or for anybody else paying attention. That's no longer true because of this one crucial fact, that the speed of light is the same for all observers.

• 31:10Kelly Weinersmith?

  I don't like it, but I accept it. It's confusing. It's not confusing. You explained it clearly. It remains sort of counterintuitive.

• 31:18Daniel Whiteson?

  It is.

• 31:19Kelly Weinersmith?

  But I followed that explanation. I'm with you.

• 31:21Daniel Whiteson?

  It is. And it's somehow reassuring if you know where it comes from. Like, it comes from this speed of light fact. It's not just some, like, arbitrary thing about the universe. In fact, in order for the universe to make sense, to accommodate this speed of light being universal, time has to not be universal for everybody. It doesn't make sense for time to be universal. And this is why we have things like time dilation, right? When we say, moving clocks run slow, it's really another statement of the same thing. If I see somebody in a spaceship, and they have a clock, and they're moving at half the speed of light relative to me, I will see their clock ticking slowly, and they will see my clock ticking slowly.

• 32:02Daniel Whiteson?

  And all of the surprising counterintuitive facts about relativity come from this one fact, that the speed of light is constant for all observers, which means simultaneity is not universal, which means clocks run slow or fast depending on your speed relative to them. And so what that means is what we said earlier about how everybody will agree about how long the podcast is, that is not true.

• 32:25Kelly Weinersmith?

  What?

• 32:25Daniel Whiteson?

  The distance in time between two events is not universal. And it's not just because somebody's listening to the pod at 1.5x or whatever, or at half x because we talk too fast or whatever. It's because for them clocks run faster or slower depending on their velocity relative to them.

• 32:42Kelly Weinersmith?

  Okay, so it can be nearly infinite for Matt when he's editing our episodes.

• 32:48Daniel Whiteson?

  Depending on his velocity with respect to the equipment. Yeah, exactly.

• 32:52Kelly Weinersmith?

  So we've gone over all of this in the past, which I'm, and I, it is always useful to go over this again, especially when your co-host is as smart as a rock. But when do we get to how this is different?

• 33:05Daniel Whiteson?

  So remember at the end of last segment, we were saying, distance and time in classical physics are physical. And we're like, what does physical mean? And I was saying, it's, it's a part of the universe. It doesn't depend on where your graph paper is or who's doing the measurement. It's a real thing everybody should agree on. Now we're saying that's not true, right? Time is not universal. It's not physical. It's observer dependent. It does depend on where you put the graph paper. It does depend on how fast the graph paper is going. So now we're sort of unmoored. We're like, oh no, what's real out there in the universe?

• 33:35Kelly Weinersmith?

  Daniel was gaslighting me.

• 33:37Daniel Whiteson?

  So where we're going to get to is that time is broken and space is broken, but we can put them back together.

• 33:43Kelly Weinersmith?

  Oh, good.

• 33:44Daniel Whiteson?

  And there is a concept of distance in spacetime, which is called the spacetime interval, which is physical, which is real, which everybody can agree about. So don't worry, we're going to get there.

• 33:55Kelly Weinersmith?

  Yes.

• 33:56Daniel Whiteson?

  We've just broken time and we're going to use that to break space. And then we're going to put them back together with super glue.

• 34:02Kelly Weinersmith?

  Awesome. All right, now let's talk about space then.

• 34:05Daniel Whiteson?

  Yeah. So remember we were saying earlier, like the length of the pencil, that's physical. It doesn't matter if it's rotating. It doesn't matter if your graph is moving. It doesn't matter what ruler you use. It is a number and everybody should agree on it, right? Well, it turns out that's not true. And it's for the same fundamental reason that the speed of light is universal, which breaks time, which is then going to break distance. Because think about how we measure distance. How do we measure distance is you measure where the back end of the pencil is and you measure where the front end of the pencil is, and then you subtract. Very basic, right? How could that go wrong? How could that depend on clocks in any way? Well, implicit in that definition is I'm measuring the back and the front end of the pencil at the same time.

• 34:48Daniel Whiteson?

  Because if the pencil is moving and I measure the back end of the pencil now and the front end of the pencil later, then I'm going to get two numbers that are much further apart and the pencil is going to look too long. Right? And so I have to measure the front and the back at the same time.

• 35:02Kelly Weinersmith?

  And you can't cheat by saying, I'm in the tractor, the tractor's moving forward, but I'm going to take a picture of the pencil so that I can measure from the front and the back at the same time. Now you've got a different frame of reference because it's a picture and that's cheating. Is that right?

• 35:15Daniel Whiteson?

  Okay, yeah, great question. And I love the idea of using a camera. The camera actually makes this more complicated instead of simpler because now you have the additional issue of how long did it take the information to arrive from the back or the front of the pencil to the camera? And if your cam is not like centered along the pencil, then you're going to get like out of date information in one direction. And usually when we talk about special relativity, we try to remove all of those effects, the effect of like light traveling from the event to the observer, because that's a completely separate, different kind of effect. And so all the things we're talking about today assume that basically you have an infinite number of observers at every location who could always measure things locally. So there's no time delay due to the speed of light.

• 36:00Daniel Whiteson?

  So the camera is really tempting, but it actually adds a bunch of confusion. And we can dig into special relativity, including those time delays, but it's sort of like a different rabbit hole.

• 36:09Kelly Weinersmith?

  All right, different episode.

• 36:10Daniel Whiteson?

  So let's instead say Kelly has two goats and she can measure the front and back of the pencil with her two goat assistants. And they record, you know, where on the ruler it was, and then she subtracts it and she gets a number, right?

• 36:23Kelly Weinersmith?

  Thanks, shortbread and numino.

• 36:25Daniel Whiteson?

  That's right. But Zach is watching from his Ferrari and he says, look, one goat was off. Your goats didn't measure the front and the back at the same time. Because remember Zach doesn't think two things happening at the same time for Kelly are happening at the same time for him.

• 36:39Kelly Weinersmith?

  Typical.

• 36:42Daniel Whiteson?

  So see how the speed of light being constant breaks the universality of simultaneity, which breaks the universality of distance, right? People disagree about when you measure the front and when you measure the back. And that changes your measured distance of these things. To give just one more simple example, go back to the pencil. If you measured the back of the pencil to be at two centimeters and the front to be at eight centimeters, so you said it was six centimeters long, eight minus two. But what if the pencil was moving and you had measured the front before you measured the back, not at the same time? Then the reason the pencil is at eight centimeters when you measured it is because it moved.

• 37:22Daniel Whiteson?

  So because different people disagree about what at the same time means, because speed breaks simultaneity, then people disagree about when to measure the front and the back. And so they disagree about length because length depends on simultaneity. That's why breaking time also breaks distance.

• 37:44Kelly Weinersmith?

  All right, so we can't depend on time. We can't depend on distance.

• 37:48Daniel Whiteson?

  Yeah.

• 37:48Kelly Weinersmith?

  I'm with you.

• 37:49Daniel Whiteson?

  So all of these things are now broken, right? Einstein revealed that time is not universal, space is not universal. So the comfortable footing we were on a few minutes ago seems to have evaporated behind us, right? And so who comes to the rescue but math profs?

• 38:05Kelly Weinersmith?

  Oh.

• 38:09Kelly Weinersmith?

  Math profs. All right, none of us come to D K E U to be comfortable. We come here to be challenged. So tell me what the math prof had to say.

• 38:17Daniel Whiteson?

  So this is after Einstein had introduced special relativity, which showed us that distance is not universal, that time is not universal, right? And so then Herman Minkowski, who's famous for introducing this concept of Minkowski space, and he was a math professor, he actually taught Einstein. And Einstein famously skipped some of his lectures and Minkowski thought Einstein was a quote lazy dog.

• 38:44Daniel Whiteson?

  So Minkowski gives this talk a few years later, and he starts off with this famous line saying, quote, henceforth, space by itself and time by itself are doomed to fade away into mere shadows. And only a kind of union of the two will preserve an independent reality. So it's a famous line because what he's saying is space is not real, time is not real by themselves. But you know what we can do is we can link them together and build something new, which is physical, which is real, which we can count on.

• 39:19Kelly Weinersmith?

  I think 99% of us can work without spacetime, but I'm glad the physicists have spacetime.

• 39:27Daniel Whiteson?

  It's sort of like if you're studying elephants, you know, and elephants are lined up so you can either see the head or the tail, right? And you like measure the number of heads and you measure the number of elephants' tails and you have no idea that heads and tails are connected. And you're just like noting, okay, today I see 90 heads and 10 tails. You come back tomorrow and you see 60 tails and 40 heads. And you're like, what is going on? The number of elephant heads is changing. The number of elephant tails is changing. What is going on with these elephant heads and tails? And then somebody comes along and tells you, heads and tails, neither of these are fundamental. They're both parts of the same thing. And what's really constant here is the number of elephants, the sum of the heads and the tails of the elephants. They just turn around and so you can measure different numbers of heads or tails that

• 40:09Daniel Whiteson?

  you can see, but that doesn't change the number of elephants. That's what's physical, what's real. And that's what Minkowski did. He said, let me bring space and time together. The reason space looks broken and the reason time looks broken is that you're just looking at one part of a larger object that's rotating. So as you see space changing, time is changing in a way that's compensating for space changing. You're just not paying attention to it. It's sort of like your question earlier about the pencil in three dimensional space, right? You're like, if the pencil floats up from the graph paper and now it has three dimensions instead of two, how do I know that those two dimensions are compensating correctly to make sure the distance is the same?

• 40:51Daniel Whiteson?

  A two dimensional physicist who only could see like two of those dimensions as the pencil floats up, he would say, no, the pencil is getting shorter. You'd be like, that's just because you forgot to account for the third dimension, right? The pencil is the same length. That's what's happening here. Space may be getting weird and short, but time is out there compensating for it. So if we put space and time together in some way, then we can build a new sense of distance, which really is universal, which really is invariant, which really is physical.

• 41:20Kelly Weinersmith?

  Well, one, I love when you recontextualize my dumb questions to make them seem insightful. Much appreciated. And two, let's take some time to think about space and we're going to take a break. And when we get back, Daniel is going to really dig in to what a spacetime interval is.

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• 44:35Kelly Weinersmith?

  All right, we are having fun at this space in this time, and Daniel is going to help us understand the complicated concept that is spacetime interval. So space and time make sense for all of us again.

• 44:46Daniel Whiteson?

  Mm-hmm. All right, so we are building spacetime. We have three dimensions. We want to add time to it. Earlier, I said, it's no big deal to add more dimensions. You can just add them to our Pythagorean theorem, right? You have x squared plus y squared. No problem, we can add z squared. It's all cozy, it's all happy, it's easy. So probably you're thinking, great, now we just have to add time. We have x squared plus y squared plus z squared plus t squared, right?

• 45:13Kelly Weinersmith?

  Yes.

• 45:14Daniel Whiteson?

  Minkowski says, no, that's wrong. We do have to account for time, but time enters with a negative.

• 45:22Kelly Weinersmith?

  What?

• 45:22Daniel Whiteson?

  So the concept of a spacetime interval is distance in space minus the distance in time. It's x squared plus y squared plus z squared minus t squared.

• 45:33Kelly Weinersmith?

  What?

• 45:34Daniel Whiteson?

  This weird negative sign. Yes, exactly.

• 45:37Kelly Weinersmith?

  All right, so I'm thinking about the lights in the box. I'm thinking about my goats in the box. Does subtracting time depend on like what distance you're moving in? Because like I'm imagining, you know, when we measured the pencil and the distance was shorter because you had been moving in a certain direction. Does that have anything to do with why time is negative? Or is my intuition, yet again, totally off here?

• 46:00Daniel Whiteson?

  No, your intuition is right on. It all comes from the same origin of how space and time connect to each other, which is fundamentally because of how the speed of light is invariant for all observers. But there's a little bit of a twist here. What we're building, this spacetime interval, is not exactly like a four-dimensional analog of distance, right? It's not like how far apart these two points are. So let's make that explicit. Let's say, what are we talking about here? What is a spacetime interval? Imagine you have some event. So a goat is born. That happens at a location and a time.

• 46:35Kelly Weinersmith?

  Yay, we all celebrate.

• 46:36Daniel Whiteson?

  Then you have another event. A goat is crushed, right?

• 46:40Kelly Weinersmith?

  Oh.

• 46:40Daniel Whiteson?

  That happens at some location and at some time, right? And we can talk about the distance between those two events, right? Maybe the goat was born on Kelly's farm, and the goat was crushed at the vet. There's a certain distance there. And we can talk about the time interval between those two, right? The goat was born, and three weeks later, it was crushed, or whatever. Now, we can also talk about the spacetime interval between those two events, those spacetime events. And now, four-dimensional coordinates in spacetime, we can talk about the spacetime interval. And that has the distance component and the time component, but in a negative, right? So the time adds in a negative. It's not just like a straight-up distance. And you might think, well, why would you do that? Why would you add the negative?

• 47:24Daniel Whiteson?

  That doesn't give me some concept of distance. Now, it's like space and time playing off each other, right? Well, the reason is that that's the physical thing. That's what the universe wants. That's the thing that's invariant. If I calculate the distance in space and I calculate the distance in time from my point of view, I'm going to get a number for the interval. If Kelly does it, she's going to get the same number. If Zach in his Ferrari does it, he's going to get the same number. We're all going to disagree on distances. We're all going to disagree on times. But when we put them together into spacetime interval, we're all going to get the same number. The same way that like the pencil has a length in space. It doesn't matter, right? Who's measuring it, or how it's rotating, or whatever. The spacetime interval is the physical thing in spacetime.

• 48:09Daniel Whiteson?

  It's what the universe respects. So us little humans, we want senses of distance. We'd love to add time to space with a positive number. So we have like a four-dimensional Pythagorean theorem. But no, the universe says, this is the thing that's important.

• 48:24Kelly Weinersmith?

  Is it reasonable to think about it as like distance standardized by time, or not quite? I feel like the answer is not quite.

• 48:31Daniel Whiteson?

  Right, so we've answered one question, which is like, what is the spacetime interval? It's this weird mathematical construction where you have space and time playing against each other. And we've said it's important because the universe respects it. Now, the question is like, well, what is this thing, right? Like, what do I do with this thing? How do I think about it? So it's not a distance, again, because time is playing in the interval. The way to think about it is causal separation, all right? Because there are three different kinds of spacetime intervals. You can have a spacetime interval that's zero, which is what we call light-like, and that's when the space and the time balance each other. So like the distance minus the time, because you know, you have a positive and negative, they can be zero.

• 49:15Daniel Whiteson?

  Two events have a spacetime interval of zero if light can leave one and arrive at the other. So for example, Kelly turns on a flashlight, and then the flashlight arrives at the end of a barn. Those two events have a zero spacetime interval because they're exactly causally connected, right? The interval between them is exactly how long it would take light to go from one to the other. So events have zero spacetime intervals if they are perfectly causally linked, just enough time and not too much. A message departing and arriving are two spacetime events with zero spacetime interval. They have a distance in space and a distance in time,

• 49:58Daniel Whiteson?

  but those balance to give no interval. Events that have a zero spacetime interval from you are events that you can exactly reach with your beam of light. Close-by things in the near future have a zero spacetime interval. Far-away things in the far future. It's basically your forward light cone.

• 50:17Kelly Weinersmith?

  Okay.

• 50:18Daniel Whiteson?

  You can also have positive spacetime intervals, right? So for example, Andromeda, right now, is too far away for us to affect it causally. Kelly turns on her death ray from her farm. She cannot zap in the aliens in Andromeda right now because the death ray is still traveling there. So the distance between Kelly's farm and Andromeda has a positive spacetime interval. It's outside the realm of anything she can influence because her death ray, which moves at the speed of light, can't reach it until the future. Even moving at the speed of light is not fast enough. It's just too far away.

• 50:55Kelly Weinersmith?

  But so when I'm standing in a barn, and I turn on my flashlight, and the light hits the opposite wall, that happens in the future too, but it's just a shorter future.

• 51:04Daniel Whiteson?

  It happens in the future, but you're right, it's a shorter future. And so you can imagine, we talk sometimes about a light cone, right? Think about the future that you can influence, okay? You can influence exactly where you are right now, or you can influence things that are one light second away in one light second, or things that are one light year away in a year, right? That's your future light cone. That light cone has spacetime interval of zero.

• 51:30Kelly Weinersmith?

  Okay.

• 51:30Daniel Whiteson?

  Because the speed of light is the same for all observers. Everybody agrees on what Kelly's light cone is. You turn on the flashlight, and it does hit the side of the barn. And that event where the light reaches the other side of the barn is on your future light cone. It's in your causal reach. It has zero spacetime interval.

• 51:50Daniel Whiteson?

  And an event much further away at that same moment is outside your light cone. You can't affect it. Light doesn't have time to reach it. It has a positive spacetime interval and everyone agrees on that. Unlike distance and time, the spacetime interval is the invariant thing. Can Kelly zap this alien? And when is a number everybody agrees on, no matter where they are in the universe or how fast they're going. Everything outside that cone, Kelly cannot zap. It's beyond her causal reach. Everything within that cone has a negative spacetime interval. So that's what the spacetime interval is about. It's about what can you influence? Where is your causal reach?

• 52:34Daniel Whiteson?

  Spacetime intervals that are negative are time like things you can reach. Spacetime intervals that are zero are where light will reach. And spacetime intervals that are positive are outside of your reach. You cannot influence them because light cannot get from you to them in time. So it's sort of like a sense of distance, but it's more like a sense of causal distance. It's like, is this something I can influence in the future?

• 53:00Kelly Weinersmith?

  I think I'm still a little caught up on like, so if I turn on a laser, it's going to get to Andromeda eventually.

• 53:06Daniel Whiteson?

  Yes.

• 53:07Kelly Weinersmith?

  And so why can't we just wait more time?

• 53:10Daniel Whiteson?

  You can wait more time, absolutely. But you have to wait more time to get further. And so you can't zap Andromeda now. You have to zap it in the future, just like you can't zap the other side of your barn. Now you have to wait for light to get there. So there's no limit on how far you can zap, but there is a limit on how far you can zap in a given time, in a second or in 10 seconds or whatever. If the universe wasn't expanding, then the whole universe is eventually in your light cone, your future light cone, right? You could zap anybody. It just takes time for those death rays to get there. But everywhere along the bleeding edge of your death rays has the same spacetime interval.

• 53:54Daniel Whiteson?

  That's zero, because this distance and the time portions balance perfectly. Because we're adding up distance and we're subtracting time. And the spacetime conversion we use to subtract time is the speed of light that enters into that equation. And so the spacetime interval between two events basically tells you, could light have gotten here between these two events or not? If it's zero, then light has just enough time to get there. If it's positive, then it's too far for light to get to. You can't influence it. If it's negative, then light can definitely influence it.

• 54:24Kelly Weinersmith?

  So is Andromeda moving away from me faster than my laser is going?

• 54:29Daniel Whiteson?

  Andromeda is actually moving towards us, right? Because of gravity. So it's going to collide with us in a few years. But that's sort of adding a few billion years. I say few years, a few billion years. We got time. Don't worry about it. And please don't build a laser and point it at the aliens. We hope the aliens are friendly. I'm just using that as an example.

• 54:47Kelly Weinersmith?

  Yeah, yeah.

• 54:48Daniel Whiteson?

  And this isn't about Andromeda moving. It's not that it's escaping your laser. It's just that it's too far away for you to hit it now or in a year. Your laser won't get there for millions of years. And so the events your laser can visit are only in the future. Those are the ones with spacetime interval zero.

• 55:08Kelly Weinersmith?

  Okay, so I get one spacetime value for shining a laser at my barn and a different spacetime interval value by shining a laser at Andromeda. And I'm still not understanding why they have different signs. I can't remember if one was zero, one was positive. I've lost track, but like, why are those different?

• 55:28Daniel Whiteson?

  Okay, well, let's stick with your barn for now and then we'll get to Andromeda.

• 55:31Kelly Weinersmith?

  Okay.

• 55:32Daniel Whiteson?

  So if you turn your flashlight on now and you shine it at the other wall, right? Then you can ask, what is the spacetime interval between me turning on my light and the other side of my barn right now, before the light has a chance to get there? And that has a positive spacetime interval because the light has not had a chance to get to the other side of the barn.

• 55:54Kelly Weinersmith?

  Okay.

• 55:54Daniel Whiteson?

  Right? But if you ask, what is the spacetime interval between me turning on my flashlight and the other side of my barn in one millisecond, right? Or however long it takes light to get there, that has a zero spacetime interval. So there's two different spacetime intervals there. There's the one between your flashlight now and the other side of the barn now, or between your flashlight now and the other side of your barn when the light gets there in the future.

• 56:20Kelly Weinersmith?

  Okay.

• 56:21Daniel Whiteson?

  So one is zero because light has had a chance to get there. But if you ask, what is the spacetime interval between my flashlight and the other side of the barn now, before light has had a chance to get there? That's a positive spacetime interval. That's outside of your light cone. So the same location can be inside or on or outside the light cone, depending on the time. Because the light cone expands with time. Same is true for Andromeda, right? If you fire your death ray right now and ask, is Andromeda within my light cone? Well, it isn't right now, but in five million years or whatever it will be. So that has a spacetime interval that's zero. But firing your death ray right now and Andromeda right now, that has a positive spacetime interval.

• 57:03Daniel Whiteson?

  So basically just tells you which parts of the universe can you zap? Which parts are accessible to you because of this limited speed of light?

• 57:11Kelly Weinersmith?

  Got it.

• 57:12Daniel Whiteson?

  So that's something interesting about the universe, right? Like, we should listen when the universe tells us, hey, this is the physical thing. This is what's invariant. This is what's important. Like when we notice that momentum is conserved, we say, okay, that means something useful about the universe. And it does. It tells us something fascinating about space. Check out our episode about Noether's theorem to understand the connections between symmetries and conservation laws. But this is a really good way to get deep insights about the nature of the universe is to say, what does the universe respect? What does it conserve? What does it keep constant? In this case, we're not talking about conservation. We're talking about invariance. What does the universe say everybody has to agree on, right? No matter how fast your Ferrari or your spaceship is, everybody's going to agree

• 57:57Daniel Whiteson?

  on Kelly's light cone. Can she reach Andromeda with her death ray? Not now, but yes, in the future. That's something everybody agrees on, no matter how fast they're going. And so that's interesting. That's fascinating. And it's connected to the idea of distance, right? But it's clear that like spatial distance itself is not something the universe insists everybody agree on. It's all twisted and broken by high speeds and relativity. So this is something the universe respects, and that means that it's closer to the truth. It's like at the heart of the universe. Fundamentally, it tells us something about the geometry of the universe. Remember when we were adding up the pieces of the Pythagorean theorem for space?

• 58:40Daniel Whiteson?

  And as we add more dimensions, we just add them the same way, because all the dimensions are the same, X and Y and Z, they don't matter. Well, time is a dimension and it's a part of spacetime, which is four dimensional, but it's different. The geometry of time and space are different with respect to each other. That's what the universe is saying here.

• 59:00Kelly Weinersmith?

  Okay. So as you said, this is like fundamental and important. But when we get the explanation about how distance is invariant and time is invariant, it's not usually followed by this explanation for, well, how do you make it all variant? Or whatever.

• 59:15Daniel Whiteson?

  Yeah.

• 59:16Kelly Weinersmith?

  Why, why don't we usually get that other step? Is it just because it's hard to explain? Or what do you think?

• 59:21Daniel Whiteson?

  Yeah, I think this concept of a spacetime interval is a little bit abstract because there's no real intuitive analog for it. Like, what is this thing we're talking about? Like, yes, the universe respects it, but it's not something that lines up with our notions very nicely. And so I think that's why it's not typically like introduced in pop sci. Whereas, you know, like the universe respects energy or doesn't respect energy or momentum. These are things we can get a handle on, so it's easier to talk about. But the spacetime interval really is foundational to the whole concept of the geometry of the universe, which is what relativity is all about. That's really what Minkowski was saying to Einstein. Yeah, you broke space and you broke time, but really you showed us that these are two sides of a more complicated object.

• 1:00:06Daniel Whiteson?

  You don't stick them together trivially. You stick them together backwards. And the universe has this weird geometry. And that's how it organizes itself. That's the internal mechanism of the mathematics of the universe. And this turned out to be really crucial for Einstein's next step in general relativity. Because in special relativity, these interval formulas are pretty simple. You just take the differences in each spatial dimension. You take the difference in the time dimension. You add them up with a negative and you do the Pythagorean theorem. You're good. In general relativity, the locations don't add up all the same way. Some locations add up more and some locations add up less. That's what we mean by the metric we talk about sometimes in general relativity. How is space curved in this location?

• 1:00:48Daniel Whiteson?

  How much spacetime interval do you accrue by passing through this space versus passing through that space? And so this concept of having a geometry to the universe and then having that geometry be non-trivial, that's how you go from special relativity to general relativity. But you've got to get your brain to like the geometry of the universe first before you can even get to general relativity.

• 1:01:10Kelly Weinersmith?

  Well, this conversation didn't crush my spirits. It lifted them up. And now I have, I guess you can't really make a positive spacetime, because then that would be too far to travel. And so I'm still going to be thinking about this tonight, but I totally followed the explanation. And that's awesome. I learned something new today.

• 1:01:28Daniel Whiteson?

  And one more speed bump to avoid is you often hear people saying that photons do not experience time. And here, what we're saying is light can go from A to B with no spacetime interval, right? It's light like, it's a zero spacetime interval along the light cone. That's not the same as saying photons do not experience time, right? Saying photons have a zero spacetime interval is very different from saying photons do not experience time. There's a whole separate pop sci rabbit hole, but photons do take time to move across the universe. They just don't take spacetime.

• 1:02:03Kelly Weinersmith?

  I'm realizing I want to ask if spacetime intervals have units? Does it make sense to think of it as a measurement with a unit?

• 1:02:13Daniel Whiteson?

  Yes, it does. And the units we use are distance, right? Like length, like meters, for example. And time enters with a conversion factor, which is the speed of light. So it's not really time. It's the speed of light times time, CT, which is why photons have a spacetime interval of zero, because they move at the speed of light. So that conversion factor ensures that the space and the time parts balance perfectly.

• 1:02:37Kelly Weinersmith?

  Way to go math.

• 1:02:38Daniel Whiteson?

  Harmonious mathematics.

• 1:02:41Kelly Weinersmith?

  Love it.

• 1:02:42Daniel Whiteson?

  All right. Well, thank you, everybody, for going on this journey through space and time and through spacetime. Thank you, Kelly, for all the great questions and for not using the crusher on today's episode.

• 1:02:52Kelly Weinersmith?

  Thank you, Daniel, for the great explanation. I will keep the crusher at home with me.

• 1:02:57Daniel Whiteson?

  You guys hear the sound of that thing? Oh, my gosh. Oh, gosh. All right. And that's me signing off with a shiver.

• 1:03:06Kelly Weinersmith?

  Yep, that's me signing off as well. I don't think I'm going to be able to use this thing on anything actually living without. Yeah, I'm not doing it. All right, everybody. Until next time. Have a good space and have a good time.

• 1:03:25Daniel Whiteson?

  Thanks, everybody for listening. Please go and do us a favor and rate the show on whatever podcast app you're using. It really helps people find us.

• 1:03:32Kelly Weinersmith?

  Daniel and Kelly's Extraordinary Universe is edited by the amazing Matt Kesselman.

• 1:03:37Daniel Whiteson?

  He really is a wizard. You can also find us online on Blue Sky, Instagram, and X, D and K Universe. Come engage with us.

• 1:03:47Kelly Weinersmith?

  You can email us at questions at danielandkelly.org. We really do want to hear from you.

• 1:03:53Daniel Whiteson?

  And you can find our website, www.danielandkelly.org, where you'll also find an invitation to join our Discord, where everybody comes and talks about the amazing universe.

• 1:04:04Kelly Weinersmith?

  And we also have the most amazing moderators. This is an iHeart Podcast. Thanks for joining us.

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