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Speaker 1: Special relativity brings space and time together and in the

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Speaker 1: darkness binds them into space time. That sounds pretty awesome,

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Speaker 1: and it was fun to say, like something that could

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Speaker 1: only happen in Mordoor or during the Big Bang. But

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Speaker 1: what does it actually mean? What is space time? How

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Speaker 1: do you measure distances in four dimensional space time? And

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Speaker 1: why would you? Physicists are always saying that space and

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Speaker 1: time are like two sides of the same coin making

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Speaker 1: more sense together. What are they talking about? In what

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Speaker 1: way do they make more sense together? Today We're gonna

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Speaker 1: blow up all of those analogies and give you a

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Speaker 1: real conceptual understanding of how relativity breaks space and twists time,

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Speaker 1: but then clicks them back together into a harmonious hole.

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Speaker 1: We'll talk about what that really means and the crucial

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Speaker 1: but rarely explain concept at the heart of it all

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Speaker 1: the space time interval. Welcome to Daniel and Kelly's spacey

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Speaker 1: timey Universe.

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Speaker 2: Hello.

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Speaker 3: I'm Kelly Wiener Smith. I study parasites and space, and

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Speaker 3: I have fun in all spaces and at all times. Hi.

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Speaker 1: I'm Daniel. I'm a particle physicist who likes to think

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Speaker 1: about aliens, and I was having fun this morning until

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Speaker 1: Kelly showed me the crusher.

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Speaker 3: Oh was it sure you were going to mention the

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Speaker 3: crusher on the show.

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Speaker 1: It's the only thing I can think about now, Thank

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Speaker 1: you very much. Kelly. Tell everybody what does the crusher crush.

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Speaker 3: The tube that goes to the testicle and connects it

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Speaker 3: to the rest of the body. I am looking into

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Speaker 3: methods for what we'll say, weathering are male goats, and

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Speaker 3: I'm trying to figure out what method I would feel

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Speaker 3: comfortable doing, or if I need to call the vets

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Speaker 3: and Wow, the crusher is a big piece of equipment

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Speaker 3: that once I have it in my hands, I am

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Speaker 3: not sure that I am up for actually using.

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Speaker 1: But you were up for brandishing it on our video

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Speaker 1: call this morning.

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Speaker 3: Everybody needs to stop it.

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Speaker 1: Away the crusher, all right, But today we are not

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Speaker 1: crushing goats or any of their bits. We are crushing

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Speaker 1: your confusion. We are explaining the way the universe works.

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Speaker 3: You always pull us back somehow, Okay, So today we're

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Speaker 3: talking about space time, yes, which got me thinking about

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Speaker 3: all of space and all of time. And so, Daniel,

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Speaker 3: if you could snap your fingers and for five minutes,

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Speaker 3: you would be in a protective bubble, and you could

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Speaker 3: go anywhere in space, but you couldn't change the time,

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Speaker 3: like you had to just pop up right there. Now,

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Speaker 3: what would you want to see?

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Speaker 1: Kelly? You need this episode because if you had heard

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Speaker 1: this episode already, you would know that that question is

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Speaker 1: incoherent because there is no universal now. That's right, right,

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Speaker 1: there's no sense of time across the whole universe where

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Speaker 1: you can say this now is the same as that now.

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Speaker 1: It's observer dependent. We're gonna talk about and.

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Speaker 3: You know what, I should have known that from our

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Speaker 3: What Is Time and What Is Space? Episode series? But okay,

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Speaker 3: so is there some way to constrain it so I

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Speaker 3: can say, like, you can't go back to the beginning

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Speaker 3: of the universe. I was trying to, like, why do.

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Speaker 1: You want to stop me from going back to the

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Speaker 1: beginning of the.

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Speaker 3: Universe, because that's what I thought you'd say.

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Speaker 1: You were totally right, that is what I was gonna.

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Speaker 3: Say, But you said that on the show before. So

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Speaker 3: trying to figure out what you think is the most

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Speaker 3: interesting thing happening now. And my guess is that you

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Speaker 3: were gonna say black holes.

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Speaker 1: I'm gonna go to the factory that makes the crusher

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Speaker 1: and I'm gonna burn it down. Okay, No, but if

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Speaker 1: I could go somewhere in the modern universe, then for

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Speaker 1: sure I would like to see not only what's inside

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Speaker 1: a black hole, but the immediate vicinity of a black

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Speaker 1: hole would be super fascinating to see frame dragging and

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Speaker 1: to see all that time dilation and all the extreme

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Speaker 1: events around a black hole. I think my second choice

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Speaker 1: would be the heart of a neutron star, because when

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Speaker 1: every other defense against gravity has already collapsed and matter

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Speaker 1: becomes insanely dense so the protons and electrons eat each

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Speaker 1: other and become neutrons, then you have this fascinating environment

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Speaker 1: where quantum mechanics and gravity are at about the same strength.

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Speaker 1: And we don't know what's going on at the heart

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Speaker 1: of neutron stars because we can't calculate that stuff because

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Speaker 1: we don't have a theory of quantum gravity. We'll never

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Speaker 1: go inside a black hole, so that's sort of just

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Speaker 1: like fun to say, but hopeless. But the inside of

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Speaker 1: a neutron star is out there and real and on

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Speaker 1: the outside of event horizon, so in principle we could

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Speaker 1: one day see it, and that be the key to

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Speaker 1: unlocking quantum gravity.

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Speaker 3: WHOA Okay, So, how could I have worded the question

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Speaker 3: to constrain your ability to see the Big Bang? What

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Speaker 3: would have been the right way to word that?

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Speaker 1: Of Daniel? What would you like to see in the

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Speaker 1: universe except for the Big Bang?

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Speaker 3: Well, wouldn't you have to go backwards in time to

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Speaker 3: see the Big Bang?

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Speaker 1: It depends a little bit of what you mean by sea.

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Speaker 1: I mean the information from the Big Bang is out

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Speaker 1: there in some respects. People often say seeing the CMB

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Speaker 1: is like seeing the Big Bang, though it actually comes

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Speaker 1: from three hundred and eighty thousand years later. There is

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Speaker 1: information from the Big Bang out there and gravitational waves,

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Speaker 1: and so like seeing it means detecting those and reconstructing

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Speaker 1: what happened. We can do that today without like being

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Speaker 1: there during the Big Bang. In that sense, everything you

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Speaker 1: see happened in the past already.

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Speaker 3: So but I feel like you understand that that's not

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Speaker 3: what I mean like that, like, like, yes, you can

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Speaker 3: see evidence from it, yes, but like I don't you know,

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Speaker 3: So if I go to a civil war site and

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Speaker 3: I find a like bullet case, that's like evidence that

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Speaker 3: it happened. Yeah, but it's not the same as being

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Speaker 3: there and watching both sides run across a field and

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Speaker 3: start fighting each other.

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Speaker 1: Right, No, but it's sort of like going really really

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Speaker 1: far away instantaneously and capturing the light that left that

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Speaker 1: Civil War battlefield contemporaneously and using it to watch in

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Speaker 1: real time the battle, which is something you could literally.

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Speaker 3: Do, right, All right, all right, all right, Well I'm

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Speaker 3: gonna have you be more careful next time I ask you

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Speaker 3: a question. But we've all learned something from Kelly's bad question,

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Speaker 3: which is why Kelly's here.

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Speaker 1: So, and these are really fun topics to think about

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Speaker 1: because our intuition is broken about how all of this

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Speaker 1: stuff works. We tend to think that time flows the

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Speaker 1: same way for everyone. We tend to think that distances

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Speaker 1: are real and they're universal. When it turns out the

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Speaker 1: universe operates in a way that's fundamentally in conflict with

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Speaker 1: our intuition but amazingly does make sense. So we have

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Speaker 1: this task ahead of us to incorporate this new intuition

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Speaker 1: about the universe into our minds. But often this means

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Speaker 1: just like, read a bunch of equations and use them

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Speaker 1: to predict what happens. But I think it's possible to

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Speaker 1: develop a new kind of intuition, a conceptual understanding for

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Speaker 1: how the universe really does work. And that's what we're

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Speaker 1: going to try to do today by introducing you to

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Speaker 1: one of the most important concepts in special relativity that

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Speaker 1: almost nobody talks about and that we've never covered on

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Speaker 1: this show.

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Speaker 3: What. Yes, Well, this is a very exciting day here

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Speaker 3: at dk EU, and let's see if our audience heard

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Speaker 3: about this thing that pretty much no one talks about.

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Speaker 3: And so we asked our audience, what is a space

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Speaker 3: time interval?

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Speaker 2: Well, I would expect that that would be the reduction

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Speaker 2: of Einstein's space time into a quantum type interval, but

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Speaker 2: I'm really not too sure. It's the between two objects

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Speaker 2: and space.

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Speaker 4: Maybe I don't know.

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Speaker 1: Could a space time interval be the point where one

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Speaker 1: max plank length ends and one begins.

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Speaker 5: I'm not sure a space time interval is the required

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Speaker 5: time frame between semi convincing scientific mumbo jumbo that you

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Speaker 5: hear on sci fi shows and movies. But seriously, maybe

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Speaker 5: it's some form of the smallest unit of space time

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Speaker 5: length and distance, kind of almost a singularity, but not quite.

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Speaker 4: I've never actually heard the term space time interval before,

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Speaker 4: but guessing from context, I would imagine a space time

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Speaker 4: interval is one like frame of the universe. So you know,

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Speaker 4: you move forward one unit of time and look at

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Speaker 4: the way everything else changed. That's one interval of space type.

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Speaker 3: All right, Daniel, I asked a question that belied my ignorance,

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Speaker 3: and so I'm not going to even attempt to say

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Speaker 3: if I think the audience was correct or not with

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Speaker 3: this question. How close were they?

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Speaker 1: Pretty much? Zero points all around? A few points for

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Speaker 1: people thinking this is a kind of distance, because that's

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Speaker 1: the closest. It has nothing to do with the plank

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Speaker 1: length or frames of the universe or minimum distances or

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Speaker 1: anything like that. It's really an analog to what we

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Speaker 1: think of as distance, but now in four dimensional space

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Speaker 1: time with an uncomfortable twist in it. That we're going

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Speaker 1: to get.

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Speaker 3: To good news everybody. We all need this episode. So

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Speaker 3: here we go, and we are going to start from

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Speaker 3: the beginning, because clearly Kelly needs to go back to

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Speaker 3: first principles. So what I want you to explain to me, Daniel?

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Speaker 3: So space time sounds like space and time and distance,

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Speaker 3: and there's like, so what is distance? Let's start there.

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Speaker 1: Yeah, let's build our intuition with stuff that makes sense

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Speaker 1: to us. And let's start easy. Let's start in one dimension, right.

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Speaker 1: So imagine, for example, you have a pencil and you

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Speaker 1: have a ruler, and you want to know how long

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Speaker 1: is my pencil? What do you do? Well, you put

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Speaker 1: it along the ruler. You're operating in one dimension, right,

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Speaker 1: So the pencil and the ruler are lined up, and

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Speaker 1: you say, well, the back of the pencil, you know,

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Speaker 1: is that two centimeters on the ruler, and the front

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Speaker 1: of the pencil is that eight centimeters on the ruler.

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Speaker 1: And then you subtract it's like eight minus two six

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Speaker 1: centimeters long.

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Speaker 3: I don't know why you wouldn't just put it at

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Speaker 3: the beginning of the ruler and then you don't have

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Speaker 3: to do any subtraction.

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Speaker 1: Exactly. You could put it at the beginning of the

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Speaker 1: ruler so that you get zero and six. But what

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Speaker 1: happens You get the same answer, right, if you put

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Speaker 1: the pencil at the beginning or if you slide it along,

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Speaker 1: It doesn't matter. The answer you get does not depend

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Speaker 1: on where on the ruler of your pencil is. Right,

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Speaker 1: It's invariant. Okay, that's cool. That all makes sense. It's

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Speaker 1: makes so much sense. It's kind of blindingly obvious, which

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Speaker 1: is where we want to begin, right with, like firmly

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Speaker 1: grounded in our intuition.

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Speaker 3: This is very comforting, unlike the crusher.

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Speaker 1: Okay, so why do you keep bringing that up? Kelly?

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Speaker 1: You just like I don't want to throw me off.

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Speaker 3: I wasn't going to mention it on this episode, but

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Speaker 3: you brought it up because you did the whole crushing

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Speaker 3: thing on the video before the episode, And now there's

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Speaker 3: nothing else in my mind.

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Speaker 1: I'm trying to get space time in my brain, but

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Speaker 1: that's all I can see you.

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Speaker 3: I'm so sorry. I'm sorry.

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Speaker 1: It's fine, all right. So now let's go to two dimensions.

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Speaker 1: How do things change? Well, imagine you have like a

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Speaker 1: piece of graph paper and the little squares on the

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Speaker 1: graph paper are one centimeter by one centimeter, and you

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Speaker 1: drop your pencil onto the graph paper and ask you

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Speaker 1: how long is your pencil? So how do you figure

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Speaker 1: out how far it is from one side of the

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Speaker 1: pencil to the other.

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Speaker 3: But the Agrean theorem.

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Speaker 1: Yes exactly, So you say, well, how many squares does

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Speaker 1: it cross in one direction and how many squares in

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Speaker 1: the other? Direction, and now you have a right triangle

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Speaker 1: where the pencil is the hyphpot news right, it's the

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Speaker 1: long part of the right triangle, and we can calculate

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Speaker 1: one side because it's just counting squares. We can calculate

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Speaker 1: the length may the other side just counting squares, and

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Speaker 1: then the diagonal, which is the length of the pencil.

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Speaker 1: That's the Pythagorean theorem. Right, So a squared plus b

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Speaker 1: squared equal c square. Boom, we have an answer. And

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Speaker 1: just like in the one dimensional case, it doesn't matter

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Speaker 1: where the pencil was on the graph paper. If you

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Speaker 1: dropped it in a different direction, you might have gotten

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Speaker 1: more squares on one side and few or on the other,

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Speaker 1: but the answer wouldn't change. Or even if by chance

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Speaker 1: you happen to drop the pencil so it liigned up

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Speaker 1: perfectly in one direction right like along the X axis

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Speaker 1: conceptually right, then it's basically back to the one dimensional

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Speaker 1: problem or the other axis. The point is in this picture,

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Speaker 1: distance is real. It's invariant. It does not depend on

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Speaker 1: where you drop the pencil, or like the size of

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Speaker 1: these squares, if you made them two centimeters or five centimeters,

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Speaker 1: or like a furlong or whatever. All those are just

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Speaker 1: arbitrary choices humans have imposed. The pencil distance is the real.

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Speaker 3: Thing, right, Yes, this is very comforting. Can we stay

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Speaker 3: here for the rest of the episode. No, let's push

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Speaker 3: our boundaries.

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Speaker 1: Let's keep going, all right, And so now it's easy

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Speaker 1: to imagine how we might extend this to three dimensions,

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Speaker 1: or really any number of dimensions. Like if you have

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Speaker 1: your pencil and it's not on the paper, but it's

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Speaker 1: like floating in space. We're on the space station now, right,

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Speaker 1: and the pencils floating in space, and you imagine like

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Speaker 1: not graph paper, but like laser lines through space, and

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Speaker 1: you want to measure how long is it from one

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Speaker 1: edge of my pencil to the other. Well, you play

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Speaker 1: the same game, but now you have three directions of

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Speaker 1: counting squares and you can still do the pythagoranth theorem.

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Speaker 1: It's just A squared plus B squared plus C squared

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Speaker 1: equals D squared. Right, it's the same game fundamentally that

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Speaker 1: the geometry has not changed because the nature of these

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Speaker 1: dimensions are all the same, And so we can just

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Speaker 1: keep doing this. And if you wanted to work in

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Speaker 1: eleven dimensional space or twenty six dimensional space, the concept

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Speaker 1: of distance wouldn't change mathematically or in intuitively, because the

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Speaker 1: distance is the real thing, right, Everything else is just bookkeeping.

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Speaker 3: Okay, So I'm trying to imagine a pencil floating in space,

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Speaker 3: and now a squared plus B squared plus b squared

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Speaker 3: equals the length of the pencil squared. Yeah, my gut

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Speaker 3: feels like the more dimensions you add, the bigger the

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Speaker 3: pencil's going to get because you've got all these extra

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Speaker 3: squared terms that are gonna keep getting added. But that's

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Speaker 3: not true because why.

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Speaker 1: Yeah, that's not true because the pencil is a certain length,

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Speaker 1: and if you add squares in one of the dimensions,

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Speaker 1: the other ones will shrink. Okay, Just like if the

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Speaker 1: pencil falls to the floor and it's now on a

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Speaker 1: two dimensional surface, you only have two contributions, or the

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Speaker 1: third one is just zero, right, and those are longer

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Speaker 1: than if it's floating up above the graph and it

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Speaker 1: gets a third dimension, the first two dimensions are going

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Speaker 1: to shrink a little bit. So they all act in

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Speaker 1: harmony to make sure the distance never changes. You like

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Speaker 1: flip a pencil from one astronaut to another se so

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Speaker 1: it's like rotating through space. You know, your intuition tells

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Speaker 1: you the length of the pencil is not changing. The

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Speaker 1: difference between its front and its back along some axis

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Speaker 1: might change, right, it might go up and down and

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Speaker 1: be negative or whatever, But the length of the pencil

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Speaker 1: doesn't change because all three dimensions are working in harmony

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Speaker 1: to contribute various pieces to the length, and it always

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Speaker 1: adds up to the same number. Because that's the physical thing.

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Speaker 1: Everything else is just bookkeeping. It wouldn't make sense if

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Speaker 1: the length of the pencil depended on like where the

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Speaker 1: graph paper was right, or which ruler you used. It's

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Speaker 1: a real thing in the universe.

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Speaker 3: All right. But I bet that if I were to say, Daniel,

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Speaker 3: you can travel a billion, a trillion, a quadrillion miles

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Speaker 3: away in any direction in space. What is it that

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Speaker 3: you want to see within that area? Everybody should know

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Speaker 3: what I'm talking about. Are you going to tell me

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Speaker 3: that something about that doesn't work? Like the pencil?

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Speaker 1: I see, you're asking me to be the physics sweat

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Speaker 1: blanket here.

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Speaker 3: I mean we have to take turns there, right.

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Speaker 1: Well, if you said I could go at quadrillion miles

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Speaker 1: with respect to Earth, then you've given me a frame

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Speaker 1: of reference. In which that is well defined. Okay, so yeah,

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Speaker 1: I could totally do that, all.

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Speaker 3: Right, that's what I should have asked anyway.

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Speaker 1: All right, moving on, and so we have three dimensions

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Speaker 1: of space. We're comfortable with the idea of distance in space. Cool,

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Speaker 1: let's put that aside for now and think about time.

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Speaker 1: Time is one dimensional, right, We don't have like two

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Speaker 1: clocks going on, we don't think, so it's actually a

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Speaker 1: super fun theory we can explore. And we did an

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Speaker 1: episode a couple of years ago about two dimensions of time.

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Speaker 1: But for now, let's just think about one dimension of time, right,

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Speaker 1: And so, for example, you can click your stop watch

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Speaker 1: when this episode starts and when the episode ends, and

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Speaker 1: you can ask how long is this episode of the

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Speaker 1: pod and you can look at the difference, and that's

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Speaker 1: the length, right, totally obvious, basic subtraction.

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Speaker 3: Perfect. Yes, for our poor audio guy, it probably feels

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Speaker 3: like an hour is infinite, but it is still just

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Speaker 3: an hour exactly.

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Speaker 1: And in the same way, it doesn't actually matter when

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Speaker 1: you hit the stopwatch to start, as long as you

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Speaker 1: noted when the episode started. If you'd accidentally hit your

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Speaker 1: stopwatch like an hour before, as long as you wrote down. Oh,

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Speaker 1: the episode started at one hour in you could still

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Speaker 1: measure the length of the episode by looking at the difference, right,

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Speaker 1: because when you started it is arbitrary. What you're interested

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Speaker 1: in is the physical thing, which is the difference between

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Speaker 1: the start and the end of the episode. So intervals

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Speaker 1: and time are also physical in that sense, right, They're real,

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Speaker 1: It's not just bookkeeping.

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Speaker 3: What does physical mean in this case? Like physical I

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Speaker 3: think of as something I can touch. Oh, I see,

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Speaker 3: you mean physics all.

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Speaker 1: I mean it's a part of the universe. It's not

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Speaker 1: part of our measurement system, and it's invariant in that way.

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Speaker 1: And here so far, all these definitions are in a

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Speaker 1: classical world, right before relativity. This is Newton's idea about

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Speaker 1: how time and distance were worked, Right, that anybody could

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Speaker 1: measure the difference between two things that happened in the

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Speaker 1: universe and the time difference or the space difference, and

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Speaker 1: they would always get the same answer. That's the way

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Speaker 1: Newton thoughts the universe worked, and that's the way I

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Speaker 1: operate and you operate. And this whole segment of the

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Speaker 1: pod has been like, let's confirm our intuition about how

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Speaker 1: distances work and that's all very comforting until we learn

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Speaker 1: that it's all wrong.

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Speaker 3: Oh no, you pulled the soft blanket of Newtonian physics off. Yeah,

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Speaker 3: and now it's cold and unwelcoming. Let's take a break

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Speaker 3: before we have to sit with our discomfort for too long.

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Speaker 3: And when we get back, we'll hear what Einstein had

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Speaker 3: to add. And we're back. We had a very comforting

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Speaker 3: discussion about distance and time where everything felt like it

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Speaker 3: made sense. And now we're at the point of the

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Speaker 3: episode where we are going to expand our brains and

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Speaker 3: learn something new. So all right, Daniel, make us uncomfortable,

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Speaker 3: all right, So not crusher level uncomfortable.

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Speaker 1: Well, in nineteen oh five, Einstein pulled out the metaphorical

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Speaker 1: crusher and he said to Newton, he said, you know,

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Speaker 1: put your theories in this, buddy, because here I come.

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Speaker 3: It took me a second. Sorry for the delay. I

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Speaker 3: was drinking water. It almost totally destroyed my computer.

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Speaker 1: All right, go on, and you know these intuitive notions

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Speaker 1: of how the universe works, they do work for us

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Speaker 1: at our basic level. But Einstein discovered that when speeds

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Speaker 1: get high relative speeds get high, then they don't work.

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Speaker 1: The universe is broken. It actually works in a fundamentally

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Speaker 1: different way. And it's important to understand where this comes from.

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Speaker 1: It all comes from the same source, which is the

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Speaker 1: fact that the speed of light is constant for all observed.

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Speaker 1: That is at the heart of everything. If you accept

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Speaker 1: that the speed of light is the same number no

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Speaker 1: matter who measures it, no matter how fast they are

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Speaker 1: moving with respect to like the flashlight that gave off

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Speaker 1: that beam, then you'll see that everything breaks. And we're

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Speaker 1: going to walk you through that and how it crushes

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Speaker 1: your intuition, all.

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Speaker 3: Right, crush away.

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Speaker 1: So imagine here's the setup. Kelly gives two flashlights to

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Speaker 1: her goats and puts those goats in a crate and

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Speaker 1: puts that crate on a self driving tractor to the

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Speaker 1: vet to you know, have their problems taken care of

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Speaker 1: with great anesthetic, of course, and very humanely good, all right.

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Speaker 1: And so they have two flashlights and one is pointed

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Speaker 1: towards the front of the crate and one is pointed

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Speaker 1: towards the back of the crate. Okay, and they turn

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Speaker 1: the flashlights on at the same moment, so they click

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Speaker 1: both buttons. And then we're interested in, like, well, how

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Speaker 1: long does it take for that beam of light to

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Speaker 1: hit the front of the crate versus the back of

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Speaker 1: the crate. So what would you say, Kelly ghost during

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Speaker 1: the center of the crate, they turn on both flashlights

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Speaker 1: at the same time. Do those beams reach the front

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Speaker 1: and the back of the crate at the same time? Yes?

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Speaker 1: Or no?

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Speaker 3: I feel like they should. But it's moving forward, right,

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Speaker 3: and so does that mess up the answer?

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Speaker 1: That's very good intuition. But we're asking right now from

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Speaker 1: the goat's point of view, right, So, yes, the goat

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Speaker 1: is in the crate, and it's on the back of

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Speaker 1: the self driving tractor and it's driving itself towards the vet.

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Speaker 1: But the goat doesn't know how fast the tractor is

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Speaker 1: moving relative to you. You're outside the tractor. It's inside

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Speaker 1: the crate, and the crate is not moving with respect

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Speaker 1: to the goat.

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Speaker 3: Okay, so it reaches the front and the back at

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Speaker 3: the same time.

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Speaker 1: Yes, you're exactly right. The goat says that the light

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Speaker 1: reaches the front and the back at the same time,

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Speaker 1: and that makes perfect sense because it's going at light

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Speaker 1: speed forward and light speed backwards, and it hits the

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Speaker 1: front and the back, which are the same distance. Away

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Speaker 1: in the same time. Distance is great, time's time, very simple, right,

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Speaker 1: nothing complicated, that's right, all right. But Kelly is also watching.

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Speaker 1: She sent the goats this self driving tractor, and she

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Speaker 1: doesn't want them to get hurt, except maybe get crushed

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Speaker 1: when they get there. But she's paying attention to what happened.

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Speaker 1: And for her, unlike the goats who see the walls

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Speaker 1: of the crate at rest, for Kelly, the crate is

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Speaker 1: moving forward, and she says, hold on a second. I

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Speaker 1: also see light traveling at the speed of light forwards

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Speaker 1: and at the speed of light backwards. But I see

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Speaker 1: the front of the crate is moving forward from the

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Speaker 1: point where the light was emanated, so it's moving away

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Speaker 1: from the source at the same time as the light

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Speaker 1: is chasing it, so it takes longer. And the back

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Speaker 1: of the crate you see, moving towards where the light

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00:22:37,200 --> 00:22:40,159
Speaker 1: was emitted, so that distance is effectively shorter. And so

439
00:22:40,280 --> 00:22:43,200
Speaker 1: you say, no, no, no. The light hits the back

440
00:22:43,200 --> 00:22:45,840
Speaker 1: of the crate first and the front of the crate second.

441
00:22:46,240 --> 00:22:47,560
Speaker 3: And then I look at the goats and I say,

442
00:22:47,560 --> 00:22:49,000
Speaker 3: you guys are bad at this.

443
00:22:50,640 --> 00:22:53,520
Speaker 1: And meanwhile, Zach, who's in his ferrari is zipping by

444
00:22:53,520 --> 00:22:55,320
Speaker 1: it one hundred miles an hour to do who knows what.

445
00:22:55,880 --> 00:22:59,000
Speaker 1: And he says, I see the opposite right, because from

446
00:22:59,040 --> 00:23:02,479
Speaker 1: his point of view, the crate is going backwards, and

447
00:23:02,520 --> 00:23:04,680
Speaker 1: so he says, no, no, the back of the crate

448
00:23:04,720 --> 00:23:06,720
Speaker 1: is running away from the light and the front of

449
00:23:06,760 --> 00:23:10,080
Speaker 1: the crate is moving towards the light. So Zach sees

450
00:23:10,200 --> 00:23:12,600
Speaker 1: the front of the crate get hit before the back

451
00:23:12,640 --> 00:23:13,119
Speaker 1: of the crate.

452
00:23:13,480 --> 00:23:16,520
Speaker 3: Ever since that lucrative Dorito sponsorship, he's been able to

453
00:23:16,600 --> 00:23:18,200
Speaker 3: afford fast cars.

454
00:23:20,240 --> 00:23:23,240
Speaker 1: Exactly, And so even though he's got one hand in

455
00:23:23,280 --> 00:23:25,800
Speaker 1: the Dorito's bag and one hand on the wheel, he's

456
00:23:25,880 --> 00:23:28,760
Speaker 1: able to make these measurements. And so what's going on here?

457
00:23:29,240 --> 00:23:32,320
Speaker 1: The issue comes down to the fact that everybody, the goat, Zach,

458
00:23:32,400 --> 00:23:35,040
Speaker 1: and Kelly all see light moving at the same speed,

459
00:23:35,119 --> 00:23:38,560
Speaker 1: no matter what. If you replicated this experiment with sound

460
00:23:38,880 --> 00:23:43,240
Speaker 1: instead of with light, then everybody would agree on what happened.

461
00:23:43,720 --> 00:23:45,840
Speaker 1: Why is that because the speed of sound is not

462
00:23:45,960 --> 00:23:49,680
Speaker 1: the same for all observers, Like if the goats are bleeding,

463
00:23:49,720 --> 00:23:53,040
Speaker 1: if they're going back inside the crate, then they're going

464
00:23:53,119 --> 00:23:55,280
Speaker 1: to see their sound hit the front in the back

465
00:23:55,320 --> 00:23:59,000
Speaker 1: of the same time, Kelly, who sees the crate moving,

466
00:23:59,520 --> 00:24:02,760
Speaker 1: is going to see the sound going forward faster than

467
00:24:02,800 --> 00:24:05,240
Speaker 1: it's going backwards, because the sound is moving with the

468
00:24:05,240 --> 00:24:07,760
Speaker 1: same speed with respect to the air in the crate,

469
00:24:08,080 --> 00:24:10,359
Speaker 1: and so like, if Zack has a speed relative to

470
00:24:10,400 --> 00:24:12,760
Speaker 1: that air or Kelly has a speed relative to that air,

471
00:24:13,119 --> 00:24:16,640
Speaker 1: then they see the sound moving at different speeds. Right,

472
00:24:16,680 --> 00:24:18,560
Speaker 1: So the front and the back move at different speeds,

473
00:24:18,560 --> 00:24:21,919
Speaker 1: which accounts for everything and closes the loop. So, because

474
00:24:22,040 --> 00:24:25,520
Speaker 1: light moves at the same speed with respect to all observers,

475
00:24:25,520 --> 00:24:28,520
Speaker 1: everybody sees light moving forwards or backwards at the same speed,

476
00:24:29,000 --> 00:24:32,840
Speaker 1: even if they have velocity relative to the goats. Then

477
00:24:33,040 --> 00:24:36,400
Speaker 1: that's why people see things happen in different orders, right,

478
00:24:36,400 --> 00:24:38,920
Speaker 1: That's why they can't agree on whether the light hits

479
00:24:38,920 --> 00:24:40,600
Speaker 1: the front or the back of the crate at the

480
00:24:40,640 --> 00:24:44,119
Speaker 1: same time. So the takeaway here is the fact that

481
00:24:44,160 --> 00:24:47,119
Speaker 1: the speed of light is constant for everybody. Breaks this

482
00:24:47,280 --> 00:24:50,440
Speaker 1: notion of simultaneity that if two things happen at the

483
00:24:50,480 --> 00:24:52,720
Speaker 1: same time for Kelly, they also happen at the same

484
00:24:52,720 --> 00:24:54,680
Speaker 1: time for the goats, and they happen at the same

485
00:24:54,680 --> 00:24:57,879
Speaker 1: time for Zack or for anybody else. Paying attention. That's

486
00:24:57,960 --> 00:25:02,320
Speaker 1: no longer true because of this one crucial fact that

487
00:25:02,400 --> 00:25:04,680
Speaker 1: the speed of light is the same for all observers.

488
00:25:05,359 --> 00:25:08,840
Speaker 3: I don't like it, but I accept it. It's confusing,

489
00:25:09,160 --> 00:25:12,360
Speaker 3: it's not confusing. You explained it clearly. It remains sort

490
00:25:12,400 --> 00:25:16,320
Speaker 3: of counterintuitive. It is, but I followed that explanation. I'm

491
00:25:16,320 --> 00:25:16,560
Speaker 3: with you.

492
00:25:17,080 --> 00:25:19,600
Speaker 1: It is, and it's somehow reassuring if you know where

493
00:25:19,640 --> 00:25:22,320
Speaker 1: it comes from, like it comes from this speed of

494
00:25:22,400 --> 00:25:25,920
Speaker 1: light fact. It's not just some like arbitrary thing about

495
00:25:25,960 --> 00:25:29,199
Speaker 1: the universe. In fact, in order for the universe to

496
00:25:29,280 --> 00:25:32,960
Speaker 1: make sense, to accommodate this speed of light being universal,

497
00:25:33,240 --> 00:25:35,840
Speaker 1: time has to not be universal for everybody. It doesn't

498
00:25:35,880 --> 00:25:39,119
Speaker 1: make sense for time to be universal. And this is

499
00:25:39,160 --> 00:25:42,159
Speaker 1: why we have things like time dilation. Right when we

500
00:25:42,200 --> 00:25:46,359
Speaker 1: say moving clocks run slow, it's really another statement of

501
00:25:46,400 --> 00:25:48,960
Speaker 1: the same thing. If I see somebody in a spaceship

502
00:25:49,000 --> 00:25:51,080
Speaker 1: and they have a clock and they're moving at half

503
00:25:51,119 --> 00:25:53,000
Speaker 1: the speed of light relative to me, I will see

504
00:25:53,000 --> 00:25:55,320
Speaker 1: their clock ticking slowly, and they will see my clock

505
00:25:55,359 --> 00:25:59,680
Speaker 1: ticking slowly. And all of the surprising counterintuitive facts about

506
00:25:59,680 --> 00:26:03,040
Speaker 1: relativetivity come from this one fact that the speed of

507
00:26:03,119 --> 00:26:06,840
Speaker 1: light is constant for all observers, which means simultaneidi is

508
00:26:06,880 --> 00:26:10,920
Speaker 1: not universal, which means clocks run slow or fast depending

509
00:26:11,000 --> 00:26:13,720
Speaker 1: on your speed relative to them. And so what that

510
00:26:13,880 --> 00:26:16,880
Speaker 1: means is what we said earlier about how everybody will

511
00:26:16,920 --> 00:26:19,879
Speaker 1: agree about how long the podcast is. That is not true.

512
00:26:19,960 --> 00:26:23,920
Speaker 1: What the distance in time between two events is not universal.

513
00:26:24,240 --> 00:26:25,960
Speaker 1: And it's not just because somebody is listening to the

514
00:26:26,000 --> 00:26:29,040
Speaker 1: pod at one point five X or whatever, or at

515
00:26:29,040 --> 00:26:31,920
Speaker 1: half X because we talked too fast or whatever. It's

516
00:26:31,960 --> 00:26:35,159
Speaker 1: because for them, clocks run faster or slower depending on

517
00:26:35,240 --> 00:26:37,200
Speaker 1: their velocity relative to them.

518
00:26:37,680 --> 00:26:40,520
Speaker 3: Okay, so it can be nearly infinite for Matt when

519
00:26:40,560 --> 00:26:41,639
Speaker 3: he's editing our.

520
00:26:41,560 --> 00:26:46,640
Speaker 1: Episodes, depending on his velocity with respective of the equipment.

521
00:26:46,720 --> 00:26:47,400
Speaker 2: Yeah, exactly.

522
00:26:47,800 --> 00:26:50,760
Speaker 3: So we've gone over all of this in the past,

523
00:26:50,880 --> 00:26:53,159
Speaker 3: which i'm and i'm it is always useful to go

524
00:26:53,200 --> 00:26:56,399
Speaker 3: over this again, especially when your co host is as

525
00:26:56,440 --> 00:26:59,040
Speaker 3: smart as a rock. But when do we get to

526
00:26:59,160 --> 00:27:00,600
Speaker 3: how this right is different?

527
00:27:00,680 --> 00:27:02,280
Speaker 1: So remember at the end of last segment we were

528
00:27:02,280 --> 00:27:05,600
Speaker 1: saying distance in time and classical physics are physical, and

529
00:27:05,640 --> 00:27:07,679
Speaker 1: we're like, what does physical mean? And I'm saying it's

530
00:27:07,920 --> 00:27:10,040
Speaker 1: it's a part of the universe. It doesn't depend on

531
00:27:10,400 --> 00:27:13,000
Speaker 1: where your graph paper is or who's doing the measurement.

532
00:27:13,040 --> 00:27:16,040
Speaker 1: It's a real thing everybody should agree on. Now we're

533
00:27:16,080 --> 00:27:19,360
Speaker 1: saying that's not true. Right. Time is not universal, it's

534
00:27:19,400 --> 00:27:22,280
Speaker 1: not physical, it's observer dependent. It does depend on where

535
00:27:22,320 --> 00:27:24,280
Speaker 1: you put the graph paper. It does depend on how

536
00:27:24,280 --> 00:27:26,800
Speaker 1: fast the graph paper is going. So now we're sort

537
00:27:26,800 --> 00:27:29,320
Speaker 1: of unmoored. We're like, oh no, what's real out there

538
00:27:29,359 --> 00:27:30,080
Speaker 1: in the universe.

539
00:27:30,200 --> 00:27:31,359
Speaker 3: Daniel was gaslating this.

540
00:27:32,640 --> 00:27:35,040
Speaker 1: So what we're going to get to is that time

541
00:27:35,119 --> 00:27:37,520
Speaker 1: is broken and space is broken, but we can put

542
00:27:37,520 --> 00:27:41,600
Speaker 1: them back together. And there is a concept of distance

543
00:27:41,800 --> 00:27:44,120
Speaker 1: in space time which is called the space time interval,

544
00:27:44,440 --> 00:27:47,800
Speaker 1: which is physical, which is real, which everybody can agree about.

545
00:27:48,240 --> 00:27:51,160
Speaker 1: So don't worry. We're going to get there. Yes, we've

546
00:27:51,240 --> 00:27:53,320
Speaker 1: just broken time and we're going to use that to

547
00:27:53,320 --> 00:27:55,120
Speaker 1: break space and then we're going to put them back

548
00:27:55,160 --> 00:27:56,920
Speaker 1: together with super glue.

549
00:27:57,160 --> 00:27:59,720
Speaker 3: Awesome, All right, now let's talk about space then.

550
00:28:00,160 --> 00:28:03,120
Speaker 1: Yeah. So remember we were saying earlier, like the length

551
00:28:03,119 --> 00:28:05,880
Speaker 1: of the pencil, that's physical. It doesn't matter if it's rotating,

552
00:28:05,920 --> 00:28:07,920
Speaker 1: it doesn't matter if your graph is moving, it doesn't

553
00:28:07,920 --> 00:28:10,199
Speaker 1: matter what rule you use. It is a number and

554
00:28:10,200 --> 00:28:11,359
Speaker 1: everybody should agree on it.

555
00:28:11,480 --> 00:28:11,720
Speaker 2: Right.

556
00:28:12,359 --> 00:28:14,959
Speaker 1: Well, it turns out that's not true, and it's for

557
00:28:15,000 --> 00:28:18,440
Speaker 1: the same fundamental reason that the speed of light is universal,

558
00:28:18,520 --> 00:28:21,520
Speaker 1: which breaks time, which is then going to break distance.

559
00:28:21,960 --> 00:28:25,000
Speaker 1: Because think about how we measure distance. How do we

560
00:28:25,040 --> 00:28:27,920
Speaker 1: measure distance? Is you measure where the back end of

561
00:28:27,960 --> 00:28:29,719
Speaker 1: the pencil is, and you measure where the front end

562
00:28:29,720 --> 00:28:32,360
Speaker 1: of the pencil is, and then you subtract. Very basic, right,

563
00:28:32,400 --> 00:28:34,879
Speaker 1: How could that go wrong? How could that depend on

564
00:28:35,119 --> 00:28:39,560
Speaker 1: clocks in any way? Well, implicit in that definition is

565
00:28:39,800 --> 00:28:41,480
Speaker 1: I'm measuring the back and the front end of the

566
00:28:41,480 --> 00:28:44,640
Speaker 1: pencil at the same time. Because if the pencil is

567
00:28:44,720 --> 00:28:46,760
Speaker 1: moving and I measure the back end of the pencil

568
00:28:46,800 --> 00:28:49,160
Speaker 1: now in the front end of the pencil later, then

569
00:28:49,200 --> 00:28:51,520
Speaker 1: I'm going to get two numbers that are much further apart,

570
00:28:51,520 --> 00:28:53,800
Speaker 1: and the pencil is going to look too long, right,

571
00:28:53,880 --> 00:28:55,360
Speaker 1: And so I have to measure the front in the

572
00:28:55,400 --> 00:28:56,720
Speaker 1: back at the same time.

573
00:28:57,000 --> 00:29:00,000
Speaker 3: And you can't cheap by saying I'm in the track

574
00:29:00,240 --> 00:29:02,000
Speaker 3: the tractors moving forward. But I'm going to take a

575
00:29:02,040 --> 00:29:04,280
Speaker 3: picture of the pencil so that i can measure from

576
00:29:04,320 --> 00:29:06,320
Speaker 3: the front in the back at the same time. Now

577
00:29:06,360 --> 00:29:08,600
Speaker 3: you've got a different frame of reference because it's a picture,

578
00:29:09,080 --> 00:29:10,600
Speaker 3: and that's cheating, is that right?

579
00:29:10,680 --> 00:29:12,920
Speaker 1: Okay, yeah, great question. And I love the idea of

580
00:29:12,960 --> 00:29:15,800
Speaker 1: using a camera. The camera actually makes this more complicated

581
00:29:15,840 --> 00:29:19,000
Speaker 1: instead of simpler, because now you have the additional issue

582
00:29:19,120 --> 00:29:22,480
Speaker 1: of how long did it take the information to arrive

583
00:29:23,240 --> 00:29:25,880
Speaker 1: from the back or the front of the pencil to

584
00:29:26,000 --> 00:29:28,560
Speaker 1: the camera, And if your camera is not like centered

585
00:29:28,600 --> 00:29:30,800
Speaker 1: along the pencil, then you're going to get like out

586
00:29:30,840 --> 00:29:33,480
Speaker 1: of date information in one direction. And usually when we

587
00:29:33,480 --> 00:29:35,800
Speaker 1: talk about special relativity, we try to remove all of

588
00:29:35,800 --> 00:29:39,080
Speaker 1: those effects, the effect of light traveling from the event

589
00:29:39,440 --> 00:29:43,160
Speaker 1: to the observer, because that's a completely separate, different kind

590
00:29:43,160 --> 00:29:45,600
Speaker 1: of effect, and so all the things we're talking about

591
00:29:45,640 --> 00:29:48,960
Speaker 1: today assume that basically you have an infinite number of

592
00:29:49,040 --> 00:29:52,160
Speaker 1: observers at every location who can always measure things locally,

593
00:29:52,240 --> 00:29:55,240
Speaker 1: so there's no time delay due to the speed of light.

594
00:29:55,560 --> 00:29:58,160
Speaker 1: So the camera is really tempting, but it actually adds

595
00:29:58,200 --> 00:30:00,920
Speaker 1: a bunch of confusion, and we can dig into special relativity,

596
00:30:00,960 --> 00:30:03,000
Speaker 1: including those time delays, but it's sort of like a.

597
00:30:02,920 --> 00:30:04,880
Speaker 3: Different rabbit hole, all right, different episode.

598
00:30:04,960 --> 00:30:08,320
Speaker 1: So let's instead say Kelly has two goats, and she

599
00:30:08,320 --> 00:30:10,320
Speaker 1: can measure the front and back of the pencil with

600
00:30:10,360 --> 00:30:13,960
Speaker 1: her two goat assistants, and they record, you know where

601
00:30:14,120 --> 00:30:16,400
Speaker 1: on the ruler it was, and then she subtracts it

602
00:30:16,400 --> 00:30:17,360
Speaker 1: and she gets a number.

603
00:30:17,760 --> 00:30:19,160
Speaker 3: Right, thanks short Bread and Newman.

604
00:30:19,240 --> 00:30:22,560
Speaker 1: No, that's right. But Zack is watching from his ferrari

605
00:30:22,920 --> 00:30:25,920
Speaker 1: and he says, look, one goat was off. Your goats

606
00:30:25,920 --> 00:30:28,040
Speaker 1: didn't measure the front in the back of the same time.

607
00:30:28,240 --> 00:30:31,240
Speaker 1: Because remember Zach doesn't think two things happening at the

608
00:30:31,280 --> 00:30:33,400
Speaker 1: same time for Kelly are happening at the same time

609
00:30:33,520 --> 00:30:33,920
Speaker 1: for him.

610
00:30:34,160 --> 00:30:34,640
Speaker 3: Typical.

611
00:30:37,080 --> 00:30:40,360
Speaker 1: So see how the speed of light being constant breaks

612
00:30:40,360 --> 00:30:45,440
Speaker 1: the universality of simultaneti, which breaks the universality of distance. Right,

613
00:30:45,880 --> 00:30:48,800
Speaker 1: people disagree about when you measure the front and when

614
00:30:48,840 --> 00:30:52,240
Speaker 1: you measure the back, and that changes you measured distance

615
00:30:52,320 --> 00:30:55,280
Speaker 1: of these things. So you give just one more simple example.

616
00:30:55,520 --> 00:30:58,240
Speaker 1: Go back to the pencil. If you measured the back

617
00:30:58,280 --> 00:31:00,480
Speaker 1: of the pencil to be a two centimeter and the

618
00:31:00,520 --> 00:31:02,760
Speaker 1: front to be eight centimeters, so you said it was

619
00:31:02,800 --> 00:31:05,760
Speaker 1: six centimeters long eight minus two. But what if the

620
00:31:05,800 --> 00:31:09,160
Speaker 1: pencil was moving and you had measured the front before

621
00:31:09,320 --> 00:31:12,560
Speaker 1: you measured the back, not at the same time. Then

622
00:31:12,600 --> 00:31:14,680
Speaker 1: the reason the pencil is that eight centimeters when you

623
00:31:14,720 --> 00:31:19,000
Speaker 1: measured it is because it moved. So because different people

624
00:31:19,040 --> 00:31:23,520
Speaker 1: disagree about what at the same time means. Because speed

625
00:31:23,640 --> 00:31:28,280
Speaker 1: breaks simultaneity, then people disagree about when to measure the

626
00:31:28,320 --> 00:31:31,479
Speaker 1: front and the back, and so they disagree about length

627
00:31:31,920 --> 00:31:37,200
Speaker 1: because length depends on simultaneity. That's why breaking time also

628
00:31:37,480 --> 00:31:38,520
Speaker 1: breaks distance.

629
00:31:39,000 --> 00:31:41,440
Speaker 3: All right, So we can't depend on time, we can't

630
00:31:41,480 --> 00:31:42,560
Speaker 3: depend on distance.

631
00:31:43,280 --> 00:31:45,960
Speaker 1: Yeah, so all of these things are now broken. Right.

632
00:31:46,000 --> 00:31:50,560
Speaker 1: Einstein revealed that time is not universal, space is not universal.

633
00:31:50,880 --> 00:31:52,920
Speaker 1: So the comfortable footing we were on a few minutes

634
00:31:52,920 --> 00:31:56,320
Speaker 1: ago seems to have evaporated behind us, right, and so

635
00:31:56,880 --> 00:31:59,280
Speaker 1: who comes to the rescue but mass.

636
00:31:59,000 --> 00:32:06,520
Speaker 3: Price math proffs, all right, none of us come to

637
00:32:06,600 --> 00:32:09,400
Speaker 3: DKAU to be comfortable. We come here to be challenged.

638
00:32:09,680 --> 00:32:12,360
Speaker 3: So tell me what the math proff had to say.

639
00:32:12,680 --> 00:32:15,840
Speaker 1: So this is after Einstein had introduced special relativity, which

640
00:32:15,840 --> 00:32:18,520
Speaker 1: showed us that distance is not universal, that time is

641
00:32:18,560 --> 00:32:22,959
Speaker 1: not universal. Right, and so then Hermann Minkowski, who's famous

642
00:32:23,000 --> 00:32:26,480
Speaker 1: for introducing this concept of Minkowski space, and he was

643
00:32:26,520 --> 00:32:30,480
Speaker 1: a math professor. He actually taught Einstein and Einstein famously

644
00:32:30,520 --> 00:32:33,240
Speaker 1: skipped some of his lectures, and Minkowski thought Einstein was

645
00:32:33,280 --> 00:32:40,400
Speaker 1: a quote lazy dog. Anyway, So Minkowski gives this talk

646
00:32:40,760 --> 00:32:42,959
Speaker 1: a few years later, and he starts off with his

647
00:32:43,000 --> 00:32:47,920
Speaker 1: famous line saying, quote, henceforth, space by itself and time

648
00:32:48,000 --> 00:32:51,920
Speaker 1: by itself are doomed to fade away into mere shadows,

649
00:32:52,440 --> 00:32:55,680
Speaker 1: and only a kind of union of the two will

650
00:32:55,720 --> 00:32:59,760
Speaker 1: preserve an independent reality. So it's a famous line because

651
00:32:59,760 --> 00:33:02,800
Speaker 1: what he I'm saying is space is not real. Time

652
00:33:02,880 --> 00:33:05,520
Speaker 1: is not real by themselves. But you know what we

653
00:33:05,560 --> 00:33:08,840
Speaker 1: can do is we can link them together and build

654
00:33:08,960 --> 00:33:12,600
Speaker 1: something new which is physical, which is real, which we

655
00:33:12,680 --> 00:33:13,600
Speaker 1: can count on.

656
00:33:14,120 --> 00:33:17,120
Speaker 3: I think ninety nine percent of us can work without

657
00:33:17,160 --> 00:33:21,120
Speaker 3: space time. But I'm glad the physicists have space suns.

658
00:33:21,920 --> 00:33:24,080
Speaker 1: It's sort of like if you're studying elephants, you know,

659
00:33:24,080 --> 00:33:25,840
Speaker 1: and elephants are lined up, so you can either see

660
00:33:25,880 --> 00:33:28,320
Speaker 1: the head or the tail right, and you like measure

661
00:33:28,320 --> 00:33:30,160
Speaker 1: the number of heads, and you measure the number of

662
00:33:30,160 --> 00:33:32,240
Speaker 1: elephants tails, and you have no idea that heads and

663
00:33:32,240 --> 00:33:35,120
Speaker 1: tails are connected, and you're just like noting, Okay, today,

664
00:33:35,120 --> 00:33:37,040
Speaker 1: I see ninety heads and ten tails. You come back

665
00:33:37,080 --> 00:33:40,240
Speaker 1: tomorrow and you see sixty tails and forty heads, and

666
00:33:40,240 --> 00:33:42,480
Speaker 1: you're like, what is going on the number of elephant

667
00:33:42,480 --> 00:33:45,240
Speaker 1: heads is changing, the number of elephant tails is changing.

668
00:33:45,560 --> 00:33:47,680
Speaker 1: What is going on with these elephant heads and tails?

669
00:33:47,720 --> 00:33:51,000
Speaker 1: And then somebody comes along and tells you heads and tails,

670
00:33:51,120 --> 00:33:53,640
Speaker 1: neither of these are fundamental. They're at both parts of

671
00:33:53,720 --> 00:33:56,600
Speaker 1: the same thing. And what's really constant here is the

672
00:33:56,720 --> 00:33:59,440
Speaker 1: number of elephants, the sum of the heads and the tails.

673
00:33:59,440 --> 00:34:01,960
Speaker 1: At the elephant. They just turn around, and so you

674
00:34:01,960 --> 00:34:04,880
Speaker 1: can measure different numbers of heads or tails that you

675
00:34:04,880 --> 00:34:07,880
Speaker 1: can see, but that doesn't change the number of elephants.

676
00:34:08,239 --> 00:34:11,879
Speaker 1: That's what's physical, what's real, And that's what Minkowski did.

677
00:34:11,920 --> 00:34:15,040
Speaker 1: He said, let me bring space and time together. The

678
00:34:15,120 --> 00:34:17,920
Speaker 1: reason space looks broken and the reason time looks broken

679
00:34:18,400 --> 00:34:20,239
Speaker 1: is that you're just looking at one part of a

680
00:34:20,320 --> 00:34:23,960
Speaker 1: larger object that's rotating. So as you see space changing,

681
00:34:24,200 --> 00:34:28,160
Speaker 1: time is changing in a way that's compensating for space changing.

682
00:34:28,200 --> 00:34:30,600
Speaker 1: You're just not paying attention to it. It's sort of

683
00:34:30,680 --> 00:34:33,719
Speaker 1: like your question earlier about the pencil in three dimensional space, right,

684
00:34:34,120 --> 00:34:36,560
Speaker 1: You're like, if the pencil floats up from the graph

685
00:34:36,600 --> 00:34:39,840
Speaker 1: paper and now it has three dimensions instead of two.

686
00:34:39,920 --> 00:34:42,799
Speaker 1: How do I know that those two dimensions are compensating

687
00:34:42,840 --> 00:34:46,120
Speaker 1: correctly to make sure the distance is the same. A

688
00:34:46,160 --> 00:34:49,400
Speaker 1: two dimensional physicist who only could see like two of

689
00:34:49,440 --> 00:34:51,880
Speaker 1: those dimensions. As the pencil floats up, he would say, no,

690
00:34:51,880 --> 00:34:54,120
Speaker 1: the pencil is getting shorter. You'd be like, that's just

691
00:34:54,120 --> 00:34:56,680
Speaker 1: because you forgot to account for the third dimension. Right,

692
00:34:56,840 --> 00:34:59,439
Speaker 1: the pencil is the same length. That's what's happening here.

693
00:35:00,000 --> 00:35:02,640
Speaker 1: Spa may be getting weird and short, but time is

694
00:35:02,680 --> 00:35:04,720
Speaker 1: out there compensating for it. So if we put space

695
00:35:04,760 --> 00:35:08,600
Speaker 1: and time together in some way, then we can build

696
00:35:08,640 --> 00:35:12,120
Speaker 1: a new sense of distance, which really is universal, which

697
00:35:12,160 --> 00:35:14,719
Speaker 1: really is invariant, which really is physical.

698
00:35:15,200 --> 00:35:19,080
Speaker 3: Well, One, I love when you recontextualize my dumb questions

699
00:35:19,080 --> 00:35:23,279
Speaker 3: to make them seem insightful, much appreciated. And two, let's

700
00:35:23,320 --> 00:35:25,480
Speaker 3: take some time to think about space. And we're going

701
00:35:25,560 --> 00:35:27,880
Speaker 3: to take a break, and when we get back, Daniel

702
00:35:27,920 --> 00:35:30,800
Speaker 3: is going to really dig in to what a space

703
00:35:30,880 --> 00:35:53,440
Speaker 3: time interval is. All Right, we are having fun at

704
00:35:53,440 --> 00:35:56,239
Speaker 3: this space in this time, and Daniel is going to

705
00:35:56,280 --> 00:36:00,680
Speaker 3: help us understand the complicated concept that is space time interval.

706
00:36:00,760 --> 00:36:02,719
Speaker 3: So space and time makes sense for all of us again.

707
00:36:03,760 --> 00:36:06,239
Speaker 1: All right, so we are building space time. We have

708
00:36:06,320 --> 00:36:09,240
Speaker 1: three dimensions. We want to add time to it. Earlier

709
00:36:09,280 --> 00:36:12,040
Speaker 1: I said, it's no big deal to add more dimensions.

710
00:36:12,239 --> 00:36:14,960
Speaker 1: You can just add them to our Pythagorea and theorem. Right,

711
00:36:15,480 --> 00:36:17,759
Speaker 1: you have X squarre plus y squared. No problem, we

712
00:36:17,760 --> 00:36:20,080
Speaker 1: can add z squared. It's all cozy, it's all happy,

713
00:36:20,400 --> 00:36:23,759
Speaker 1: it's easy. So probably you're thinking, great, now we just

714
00:36:23,800 --> 00:36:26,360
Speaker 1: have to add time. We have X squared plus y

715
00:36:26,360 --> 00:36:31,800
Speaker 1: squared plus D squared plus t squared. Right, Yes, Minkowski says, no,

716
00:36:32,040 --> 00:36:35,799
Speaker 1: that's wrong. We do have to account for time, but

717
00:36:35,920 --> 00:36:39,279
Speaker 1: time enters with a negative. So the concept of a

718
00:36:39,320 --> 00:36:44,080
Speaker 1: space time interval is distance in space minus the distance

719
00:36:44,200 --> 00:36:47,080
Speaker 1: in time. It's x squared plus y squared plus z

720
00:36:47,160 --> 00:36:53,080
Speaker 1: squared minus t squared. What this weird negative sign? Yes, exactly,

721
00:36:53,360 --> 00:36:53,759
Speaker 1: all right, So.

722
00:36:53,760 --> 00:36:56,560
Speaker 3: I'm thinking about the lights in the box. I'm thinking

723
00:36:56,560 --> 00:36:59,600
Speaker 3: about my goats in the box. Do subtracting time depend

724
00:36:59,680 --> 00:37:03,440
Speaker 3: on like what distance you're moving in because, like I'm imagining,

725
00:37:04,160 --> 00:37:06,680
Speaker 3: you know, when we measured the pencil and the distance

726
00:37:06,840 --> 00:37:09,480
Speaker 3: was shorter because you had been moving in a certain direction.

727
00:37:09,560 --> 00:37:11,120
Speaker 3: Does that have anything to do with why time is

728
00:37:11,160 --> 00:37:14,719
Speaker 3: negative or is my intuition yet again totally off here.

729
00:37:16,640 --> 00:37:19,319
Speaker 1: Now your intuition is right on. It all comes from

730
00:37:19,360 --> 00:37:22,360
Speaker 1: the same origin of how space and time connect to

731
00:37:22,400 --> 00:37:26,480
Speaker 1: each other, which is fundamentally because of how the speed

732
00:37:26,480 --> 00:37:30,080
Speaker 1: of light is invariant for all observers. But there's a

733
00:37:30,080 --> 00:37:32,560
Speaker 1: little bit of a twist here. What we're building, this

734
00:37:32,640 --> 00:37:36,320
Speaker 1: space time interval is not exactly like a four dimensional

735
00:37:36,400 --> 00:37:40,000
Speaker 1: analog of distance, right, It's not like how far apart

736
00:37:40,440 --> 00:37:43,680
Speaker 1: these two points are. So let's make that explicitly. Say

737
00:37:43,680 --> 00:37:45,439
Speaker 1: what are we talking about here? What is it space

738
00:37:45,480 --> 00:37:48,560
Speaker 1: time interval? Imagine you have some event, So a goat

739
00:37:48,600 --> 00:37:51,440
Speaker 1: is born, that happens at a location and a time.

740
00:37:51,640 --> 00:37:52,760
Speaker 3: Yay, we all celebrate.

741
00:37:52,800 --> 00:37:55,919
Speaker 1: And you have another event, a goat is crushed. Right,

742
00:37:56,440 --> 00:37:59,719
Speaker 1: That happens at some location and at some time. Right,

743
00:38:00,239 --> 00:38:03,239
Speaker 1: And we can talk about the distance between those two events. Right,

744
00:38:03,320 --> 00:38:05,520
Speaker 1: Maybe the goat was born in Kelly's farm and the

745
00:38:05,560 --> 00:38:08,640
Speaker 1: goat was crushed at the vet. There's a certain distance there,

746
00:38:08,800 --> 00:38:12,080
Speaker 1: and we can talk about the time interval between those two. Right,

747
00:38:12,160 --> 00:38:14,239
Speaker 1: the goat was born and three weeks later it was

748
00:38:14,320 --> 00:38:17,319
Speaker 1: crushed or whatever. Now we can also talk about the

749
00:38:17,360 --> 00:38:21,640
Speaker 1: space time interval between those two events, those space time events,

750
00:38:21,680 --> 00:38:24,920
Speaker 1: and now four dimensional coordinates in space time, we can

751
00:38:24,960 --> 00:38:28,040
Speaker 1: talk about the space time interval, and that has the

752
00:38:28,120 --> 00:38:32,279
Speaker 1: distance component and the time component, but in a negative, right,

753
00:38:32,320 --> 00:38:34,319
Speaker 1: So the time adds in a negative. It's not just

754
00:38:34,400 --> 00:38:37,600
Speaker 1: like a straight up distance. And you might think, well,

755
00:38:37,680 --> 00:38:40,120
Speaker 1: why would you do that? Why would you add the negative?

756
00:38:40,239 --> 00:38:43,279
Speaker 1: That doesn't give me some concept of distance? Now, it's

757
00:38:43,280 --> 00:38:45,960
Speaker 1: like space and time playing off each other, right, Well,

758
00:38:46,000 --> 00:38:48,640
Speaker 1: the reason is that that's the physical thing. That's what

759
00:38:48,680 --> 00:38:52,200
Speaker 1: the universe wants. That's the thing that's invariant. If I

760
00:38:52,400 --> 00:38:55,920
Speaker 1: calculate the distance in space and I calculate the distance

761
00:38:55,960 --> 00:38:57,719
Speaker 1: in time, from my point of view, I'm going to

762
00:38:57,800 --> 00:39:00,879
Speaker 1: get a number for the interval. Does it, She's going

763
00:39:00,920 --> 00:39:03,360
Speaker 1: to get the same number. If Zach and his Ferrari

764
00:39:03,440 --> 00:39:05,839
Speaker 1: does it, he's going to get the same number. We're

765
00:39:05,840 --> 00:39:08,279
Speaker 1: all going to disagree on distances, we're all going to

766
00:39:08,320 --> 00:39:10,920
Speaker 1: disagree on times, but when we put them together into

767
00:39:10,920 --> 00:39:12,840
Speaker 1: the space time interval, we're all going to get the

768
00:39:12,880 --> 00:39:15,919
Speaker 1: same number. The same way that, like the pencil has

769
00:39:15,920 --> 00:39:19,360
Speaker 1: a length in space, it doesn't matter right who's measuring

770
00:39:19,400 --> 00:39:21,960
Speaker 1: it or how it's rotating or whatever. The space time

771
00:39:22,080 --> 00:39:25,799
Speaker 1: interval is the physical thing in space time. It's what

772
00:39:25,840 --> 00:39:29,800
Speaker 1: the universe respects. So us little humans we want senses

773
00:39:29,800 --> 00:39:32,160
Speaker 1: of distance, and we'd love to add time to space

774
00:39:32,400 --> 00:39:34,319
Speaker 1: with a positive number, so we have like a four

775
00:39:34,320 --> 00:39:38,279
Speaker 1: dimensional pythagorea in theorem. But no, the universe says this

776
00:39:38,480 --> 00:39:39,800
Speaker 1: is the thing that's important.

777
00:39:40,280 --> 00:39:43,000
Speaker 3: Is it reasonable to think about it as like distance

778
00:39:43,040 --> 00:39:46,480
Speaker 3: standardized by time or not quite? I feel like the

779
00:39:46,520 --> 00:39:48,080
Speaker 3: answer is not quite right.

780
00:39:48,200 --> 00:39:50,640
Speaker 1: So we've answered one question, which is like what is

781
00:39:50,680 --> 00:39:53,960
Speaker 1: the space time interval. It's this weird mathematical construction where

782
00:39:54,000 --> 00:39:56,600
Speaker 1: you have space and time playing against each other. And

783
00:39:56,640 --> 00:40:00,439
Speaker 1: we've said it's important because the universe respects it. Now

784
00:40:00,440 --> 00:40:03,200
Speaker 1: the question is like, well what is this thing? Right?

785
00:40:03,280 --> 00:40:05,000
Speaker 1: Like what do I do with this thing? How do

786
00:40:05,080 --> 00:40:08,640
Speaker 1: I think about it? So it's not a distance again

787
00:40:08,680 --> 00:40:11,120
Speaker 1: because time is playing in the interval. The way to

788
00:40:11,160 --> 00:40:15,399
Speaker 1: think about it is causal separation, right, because there are

789
00:40:15,440 --> 00:40:19,239
Speaker 1: three different kinds of space time intervals. You can have

790
00:40:19,239 --> 00:40:22,719
Speaker 1: a space time interval that's zero, which is what we

791
00:40:22,800 --> 00:40:24,440
Speaker 1: call light light, and that's when the space and the

792
00:40:24,520 --> 00:40:27,960
Speaker 1: time balance each other. So like the distance minus the

793
00:40:28,040 --> 00:40:30,680
Speaker 1: time because you have a positive and negative they can

794
00:40:30,719 --> 00:40:34,279
Speaker 1: be zero. Two events have a space time interval of

795
00:40:34,360 --> 00:40:37,279
Speaker 1: zero if light can leave one and arrive at the other.

796
00:40:37,840 --> 00:40:41,359
Speaker 1: So for example, Kelly turns on a flashlight and then

797
00:40:41,400 --> 00:40:44,520
Speaker 1: the flashlight arrives at the end of a barn. Those

798
00:40:44,560 --> 00:40:49,560
Speaker 1: two events have a zero spacetime interval because they're exactly

799
00:40:49,680 --> 00:40:53,480
Speaker 1: causally connected. Right the interval between them is exactly how

800
00:40:53,520 --> 00:40:55,080
Speaker 1: long it would take light to go from one to

801
00:40:55,120 --> 00:40:58,880
Speaker 1: the other. So events have zero space time intervals if

802
00:40:58,880 --> 00:41:02,560
Speaker 1: they are perfectly causally linked, just enough time and not

803
00:41:02,680 --> 00:41:07,120
Speaker 1: too much a message. Departing and arriving are two space

804
00:41:07,200 --> 00:41:11,440
Speaker 1: time events with zero space time interval. They have a

805
00:41:11,520 --> 00:41:14,919
Speaker 1: distance in space and a distance in time, but those

806
00:41:15,000 --> 00:41:18,560
Speaker 1: balance to give no interval. Events that have a zero

807
00:41:18,680 --> 00:41:22,640
Speaker 1: space time interval from you are events that you can

808
00:41:22,719 --> 00:41:26,000
Speaker 1: exactly reach with your beam of light. Close by things

809
00:41:26,040 --> 00:41:28,560
Speaker 1: in the near future have a zero space time interval.

810
00:41:28,840 --> 00:41:32,120
Speaker 1: Far away things in the far future. It's basically your

811
00:41:32,160 --> 00:41:36,120
Speaker 1: forward light cone. Okay, you can also have positive space

812
00:41:36,200 --> 00:41:41,200
Speaker 1: time intervals right So, for example, Andromeda right now is

813
00:41:41,280 --> 00:41:44,440
Speaker 1: too far away for us to affect it causally, Kelly

814
00:41:44,480 --> 00:41:47,560
Speaker 1: turns on her death ray from her farm. She cannot

815
00:41:47,640 --> 00:41:50,239
Speaker 1: zap in the aliens in Andromeda right now because the

816
00:41:50,280 --> 00:41:53,640
Speaker 1: death ray is still traveling there. So the distance between

817
00:41:53,920 --> 00:41:58,520
Speaker 1: Kelly's farm and Andromeda has a positive space time interval.

818
00:41:58,800 --> 00:42:02,680
Speaker 1: It's outside the realm of anything she can influence because

819
00:42:03,120 --> 00:42:05,479
Speaker 1: her death ray, which with the speed of light, can't

820
00:42:05,520 --> 00:42:08,520
Speaker 1: reach it until the future. Even moving at the speed

821
00:42:08,560 --> 00:42:11,480
Speaker 1: of light is not fast enough. It's just too far away.

822
00:42:11,760 --> 00:42:13,879
Speaker 3: But so when I'm standing in a barn, I turn

823
00:42:13,920 --> 00:42:16,120
Speaker 3: on my flashlight and the light hits the opposite wall.

824
00:42:17,000 --> 00:42:18,960
Speaker 3: That happens in the future too, but it's just a

825
00:42:19,000 --> 00:42:19,800
Speaker 3: shorter future.

826
00:42:20,080 --> 00:42:21,640
Speaker 1: It happens in the future. But you're right, it's a

827
00:42:21,680 --> 00:42:24,520
Speaker 1: shorter future. And so you can imagine. We talk sometimes

828
00:42:24,560 --> 00:42:26,920
Speaker 1: about a light cone. Right, think about the future that

829
00:42:26,960 --> 00:42:30,719
Speaker 1: you can influence. Okay, you can influence exactly where you

830
00:42:30,760 --> 00:42:33,759
Speaker 1: are right now, or you can influence things that are

831
00:42:34,080 --> 00:42:37,720
Speaker 1: one light second away in one light second, or things

832
00:42:37,760 --> 00:42:41,320
Speaker 1: that are one light year away in a year. Right,

833
00:42:41,680 --> 00:42:44,920
Speaker 1: that's your future light cone. That light cone has space

834
00:42:45,000 --> 00:42:47,800
Speaker 1: time interval of zero because the speed of light is

835
00:42:47,840 --> 00:42:50,840
Speaker 1: the same for all observers. Everybody agrees on what Kelly's

836
00:42:50,880 --> 00:42:53,640
Speaker 1: light cone is you turn on the flashlight and it

837
00:42:53,680 --> 00:42:56,400
Speaker 1: does hit the side of the barn, and that event

838
00:42:56,719 --> 00:42:59,560
Speaker 1: where the light reaches the other side of the barn

839
00:42:59,840 --> 00:43:02,279
Speaker 1: is on your future l like cone. It's in your

840
00:43:02,440 --> 00:43:07,200
Speaker 1: causal reach. It has zero space time interval, and an

841
00:43:07,239 --> 00:43:11,359
Speaker 1: event much further away at that same moment is outside

842
00:43:11,400 --> 00:43:14,279
Speaker 1: your light cone. You can't affect it. Light doesn't have

843
00:43:14,400 --> 00:43:17,800
Speaker 1: time to reach it. It has a positive space time interval,

844
00:43:18,120 --> 00:43:22,840
Speaker 1: and everyone agrees on that. Unlike distance and time, the

845
00:43:22,960 --> 00:43:27,360
Speaker 1: space time interval is the invariant thing. Can Kelly zapp

846
00:43:27,400 --> 00:43:30,400
Speaker 1: this alien and when is a number everybody agrees on,

847
00:43:30,480 --> 00:43:32,680
Speaker 1: no matter where they are in the universe or how

848
00:43:32,719 --> 00:43:36,960
Speaker 1: fast they're going. Everything outside that cone, Kelly cannot zap.

849
00:43:37,160 --> 00:43:41,919
Speaker 1: It's beyond her causal reach. Everything within that cone has

850
00:43:41,960 --> 00:43:45,200
Speaker 1: a negative space time interval. So that's what the space

851
00:43:45,239 --> 00:43:48,280
Speaker 1: time interval is about. It's about what can you influence

852
00:43:48,520 --> 00:43:51,600
Speaker 1: where is your causal reach. Space time intervals that are

853
00:43:51,640 --> 00:43:54,960
Speaker 1: negative are time like things you can reach. Space time

854
00:43:55,000 --> 00:43:57,840
Speaker 1: intervals that are zero are where light will reach, and

855
00:43:57,880 --> 00:44:01,719
Speaker 1: space time intervals that are positive are outside of your reak.

856
00:44:01,840 --> 00:44:04,520
Speaker 1: You cannot influence them because life cannot get from you

857
00:44:04,640 --> 00:44:08,360
Speaker 1: to them in time. So it's sort of like a

858
00:44:08,400 --> 00:44:10,480
Speaker 1: sense of distance, but it's more like a sense of

859
00:44:10,960 --> 00:44:14,759
Speaker 1: causal distance. It's like, is this something I can influence

860
00:44:14,840 --> 00:44:15,719
Speaker 1: in the future.

861
00:44:16,239 --> 00:44:18,400
Speaker 3: I think I'm still a little caught up on Like,

862
00:44:18,440 --> 00:44:21,040
Speaker 3: so if I turn on a laser, it's gonna get

863
00:44:21,040 --> 00:44:25,440
Speaker 3: to Andrameda eventually, Yes, And so why can't we just

864
00:44:25,480 --> 00:44:26,320
Speaker 3: wait more time?

865
00:44:26,680 --> 00:44:29,080
Speaker 1: You can wait more time, absolutely, but you have to

866
00:44:29,120 --> 00:44:33,040
Speaker 1: wait more time to get further. And so you can't

867
00:44:33,160 --> 00:44:37,240
Speaker 1: zap Andrameda now. You have to zap it in the future,

868
00:44:37,280 --> 00:44:39,160
Speaker 1: just like you can't zap the other side of your

869
00:44:39,200 --> 00:44:42,560
Speaker 1: barn now. You have to wait for life to get there.

870
00:44:42,960 --> 00:44:45,480
Speaker 1: So there's no limit on how far you can zap,

871
00:44:45,719 --> 00:44:48,200
Speaker 1: but there is a limit on how far you can

872
00:44:48,280 --> 00:44:50,880
Speaker 1: zap in a given time, in a second or in

873
00:44:50,960 --> 00:44:54,680
Speaker 1: ten seconds or whatever. If the universe wasn't expanding, then

874
00:44:54,680 --> 00:44:58,120
Speaker 1: the whole universe is eventually in your light cone, your

875
00:44:58,120 --> 00:45:01,720
Speaker 1: future light cone, right, is that anybody? It just takes

876
00:45:01,880 --> 00:45:05,480
Speaker 1: time for those death rays to get there. But everywhere

877
00:45:05,480 --> 00:45:08,840
Speaker 1: along the bleeding edge of your death rays has the

878
00:45:08,880 --> 00:45:12,640
Speaker 1: same space time interval. That's zero because the distance and

879
00:45:12,680 --> 00:45:16,080
Speaker 1: the time portions balance perfectly. Because we're outing up distance

880
00:45:16,120 --> 00:45:18,960
Speaker 1: and we're subtracting time, and the space time conversion we

881
00:45:19,080 --> 00:45:21,759
Speaker 1: used to subtract time is the speed of light that

882
00:45:21,920 --> 00:45:25,160
Speaker 1: enters into that equation. And so the space time interval

883
00:45:25,239 --> 00:45:28,200
Speaker 1: between two events basically tells you, kid, light have gotten

884
00:45:28,239 --> 00:45:31,319
Speaker 1: here between these two events or not. If it's zero,

885
00:45:31,480 --> 00:45:33,879
Speaker 1: then light has just enough time to get there. If

886
00:45:33,880 --> 00:45:36,560
Speaker 1: it's positive, then it's too far for light to get to.

887
00:45:36,680 --> 00:45:39,359
Speaker 1: You can't influence it. If it's negative, then light can

888
00:45:39,400 --> 00:45:40,440
Speaker 1: definitely influence it.

889
00:45:40,680 --> 00:45:44,040
Speaker 3: So is Andromeda moving away from me faster than my

890
00:45:44,160 --> 00:45:45,360
Speaker 3: laser is going.

891
00:45:45,600 --> 00:45:49,080
Speaker 1: And Drama is actually moving towards us right because of gravity,

892
00:45:49,200 --> 00:45:51,120
Speaker 1: So it's going to collide with us in a few years.

893
00:45:51,480 --> 00:45:54,360
Speaker 1: But that's sort of adding a few billion years. I

894
00:45:54,400 --> 00:45:58,160
Speaker 1: say a few years. We got time, don't worry about it.

895
00:45:58,200 --> 00:46:00,800
Speaker 1: And please don't build a laser in points at the aliens.

896
00:46:00,880 --> 00:46:02,799
Speaker 1: We hope the aliens are friendly. I'm just using that

897
00:46:02,840 --> 00:46:06,560
Speaker 1: as an example. Yeah, yeah, And this isn't about Andromeda moving.

898
00:46:06,680 --> 00:46:09,719
Speaker 1: It's not that it's escaping your laser. It's just that

899
00:46:09,760 --> 00:46:12,200
Speaker 1: it's too far away for you to hit it now

900
00:46:12,400 --> 00:46:15,239
Speaker 1: or in a year, your laser won't get there. For

901
00:46:15,400 --> 00:46:18,839
Speaker 1: millions of years, and so the events your laser can

902
00:46:19,040 --> 00:46:22,640
Speaker 1: visit are only in the future. Those are the ones

903
00:46:22,680 --> 00:46:24,360
Speaker 1: with space time interval zero.

904
00:46:24,680 --> 00:46:28,120
Speaker 3: Okay, So I get one space time value for shining

905
00:46:28,120 --> 00:46:32,439
Speaker 3: a laser at my barn and a different space time

906
00:46:32,480 --> 00:46:36,319
Speaker 3: interval value by shining a laser at Andromeda. And I'm

907
00:46:36,360 --> 00:46:39,799
Speaker 3: still not understanding why they have different signs. I can't

908
00:46:39,840 --> 00:46:42,600
Speaker 3: remember if one was zero one was probably I've lost track,

909
00:46:42,680 --> 00:46:44,160
Speaker 3: but like, why are those different?

910
00:46:44,640 --> 00:46:46,560
Speaker 1: Okay, Well, let's stick with your barn for now, and

911
00:46:46,600 --> 00:46:47,719
Speaker 1: then we'll get to Andromeda.

912
00:46:47,800 --> 00:46:48,040
Speaker 2: Okay.

913
00:46:48,320 --> 00:46:52,319
Speaker 1: So if you turn your flashlight on now and you

914
00:46:52,360 --> 00:46:55,560
Speaker 1: shine it at the other wall right, then you can

915
00:46:55,640 --> 00:46:59,320
Speaker 1: ask what is the space time interval between me turning

916
00:46:59,360 --> 00:47:02,760
Speaker 1: on my life and the other side of my barn

917
00:47:02,960 --> 00:47:05,520
Speaker 1: right now before the light has a chance to get there?

918
00:47:05,760 --> 00:47:07,960
Speaker 1: And that is a positive space time interval because the

919
00:47:08,000 --> 00:47:09,480
Speaker 1: light has not had a chance to get to the

920
00:47:09,480 --> 00:47:12,279
Speaker 1: other side of the barn. Right. But if you ask,

921
00:47:12,360 --> 00:47:14,640
Speaker 1: what is this space time interval between me turning on

922
00:47:14,719 --> 00:47:17,600
Speaker 1: my flashlight and the other side of my barn in

923
00:47:18,080 --> 00:47:21,799
Speaker 1: one millisecond right or wherever long it takes light to

924
00:47:21,840 --> 00:47:24,920
Speaker 1: get there, that has a zero space time interval. So

925
00:47:24,960 --> 00:47:27,719
Speaker 1: there's two different space time intervals there. There's the one

926
00:47:27,760 --> 00:47:30,560
Speaker 1: between your flashlight now and the other side of the

927
00:47:30,560 --> 00:47:33,040
Speaker 1: barn now, or between your flashlight now and the other

928
00:47:33,080 --> 00:47:35,480
Speaker 1: side of your barn when the light gets there in

929
00:47:35,520 --> 00:47:39,719
Speaker 1: the future. Okay, so one is zero because light has

930
00:47:39,719 --> 00:47:41,520
Speaker 1: had a chance to get there. But if you ask,

931
00:47:42,120 --> 00:47:45,480
Speaker 1: what is the space time interval between my flashlight and

932
00:47:45,520 --> 00:47:47,799
Speaker 1: the other side of the barn now before light has

933
00:47:47,840 --> 00:47:49,799
Speaker 1: had a chance to get there, that's a positive space

934
00:47:49,840 --> 00:47:52,239
Speaker 1: time interval. That's outside of your light cone. So the

935
00:47:52,239 --> 00:47:55,400
Speaker 1: same location can be inside or on or outside the

936
00:47:55,440 --> 00:47:58,239
Speaker 1: light cone, depending on the time, because the light cone

937
00:47:58,280 --> 00:48:02,600
Speaker 1: expands with Time's true for Andromeda, right if you fire

938
00:48:02,640 --> 00:48:05,360
Speaker 1: your deathray right now and ask is Andromeda within my

939
00:48:05,440 --> 00:48:08,640
Speaker 1: light cone, well it isn't right now, but in five

940
00:48:08,680 --> 00:48:11,839
Speaker 1: million years or whatever, it will be, So that has

941
00:48:11,840 --> 00:48:15,440
Speaker 1: a space time interval that's zero. But firing your deathray

942
00:48:15,520 --> 00:48:18,240
Speaker 1: right now and Andromeda right now, that has a positive

943
00:48:18,280 --> 00:48:21,960
Speaker 1: space time interval. So basically just tells you which parts

944
00:48:21,960 --> 00:48:24,920
Speaker 1: of the universe can use ZAM, which parts are accessible

945
00:48:24,960 --> 00:48:27,359
Speaker 1: to you because of this limited speed of light.

946
00:48:27,719 --> 00:48:28,080
Speaker 3: Got it.

947
00:48:28,200 --> 00:48:31,960
Speaker 1: So that's something interesting about the universe, right, Like we

948
00:48:32,080 --> 00:48:34,960
Speaker 1: should listen when the universe tells us, hey, this is

949
00:48:35,000 --> 00:48:38,440
Speaker 1: the physical thing, this is what's invariant, this is what's important.

950
00:48:38,960 --> 00:48:41,399
Speaker 1: Like when we notice that momentum is conserved, we say, okay,

951
00:48:41,440 --> 00:48:44,600
Speaker 1: that means something useful about the universe, and it does.

952
00:48:44,640 --> 00:48:47,840
Speaker 1: It tells us something fascinating about space. Check out our

953
00:48:47,880 --> 00:48:51,200
Speaker 1: episode about Noether's theorem to understand the connections between symmetries

954
00:48:51,200 --> 00:48:53,640
Speaker 1: and conservation laws. But this is a really good way

955
00:48:53,640 --> 00:48:56,200
Speaker 1: to get deep insights about the nature of the universe

956
00:48:56,320 --> 00:48:58,960
Speaker 1: is to say, what does the universe respect, what does

957
00:48:59,000 --> 00:49:02,160
Speaker 1: it conserve, what does it keep constant? In this case,

958
00:49:02,200 --> 00:49:05,160
Speaker 1: we're not talking about conservation, we're talking about invariance. What

959
00:49:05,239 --> 00:49:08,799
Speaker 1: does the universe say everybody has to agree on no

960
00:49:08,840 --> 00:49:12,319
Speaker 1: matter how fast your ferrari or your spaceship is, everybody's

961
00:49:12,360 --> 00:49:15,879
Speaker 1: going to agree on Kelly's light cone, can she reach

962
00:49:15,920 --> 00:49:18,960
Speaker 1: Andromeda worth her death ray? Not now, but yes, in

963
00:49:19,000 --> 00:49:22,080
Speaker 1: the future. That's something everybody agrees on, no matter how

964
00:49:22,120 --> 00:49:26,200
Speaker 1: fast they're going. And so that's interesting, that's fascinating, and

965
00:49:26,239 --> 00:49:29,719
Speaker 1: it's connected to the idea of distance, right. But it's

966
00:49:29,719 --> 00:49:33,640
Speaker 1: clear that like spatial distance itself is not something the

967
00:49:33,760 --> 00:49:37,760
Speaker 1: universe insists everybody agree on. It's all twisted and broken

968
00:49:38,000 --> 00:49:41,880
Speaker 1: by high speeds and relativity. So this is something the

969
00:49:42,000 --> 00:49:45,920
Speaker 1: universe respects, and that means that it's closer to the truth.

970
00:49:46,000 --> 00:49:49,080
Speaker 1: It's like at the heart of the universe. Fundamentally, it

971
00:49:49,120 --> 00:49:53,160
Speaker 1: tells us something about the geometry of the universe. Remember

972
00:49:53,160 --> 00:49:55,080
Speaker 1: when we were adding up the pieces of the Pythagorean

973
00:49:55,160 --> 00:49:57,880
Speaker 1: theorem for space, and as we add more dimensions, we

974
00:49:57,960 --> 00:50:00,760
Speaker 1: just add them the same way. Because all the dimensions

975
00:50:00,760 --> 00:50:03,560
Speaker 1: are the same x and y and z, it don't matter. Well,

976
00:50:03,840 --> 00:50:07,200
Speaker 1: time is a dimension and it's a part of space time,

977
00:50:07,239 --> 00:50:10,560
Speaker 1: which is four dimensional, but it's different. The geometry of

978
00:50:10,600 --> 00:50:13,719
Speaker 1: time and space are different with respect to each other.

979
00:50:14,080 --> 00:50:15,840
Speaker 1: That's what the universe is saying here.

980
00:50:16,200 --> 00:50:19,480
Speaker 3: Okay, so, as you said, this is like fundamental and important.

981
00:50:20,400 --> 00:50:23,880
Speaker 3: But when we get the explanation about how distance is

982
00:50:23,920 --> 00:50:27,680
Speaker 3: invariant and time is invariant, it's not usually followed by

983
00:50:27,680 --> 00:50:29,919
Speaker 3: this explanation for well, how do you make it all

984
00:50:30,520 --> 00:50:34,400
Speaker 3: variant or whatever? Why don't we usually get that other step?

985
00:50:34,440 --> 00:50:36,680
Speaker 3: Is it just because it's hard to explain or what

986
00:50:36,719 --> 00:50:37,200
Speaker 3: do you think?

987
00:50:37,600 --> 00:50:39,640
Speaker 1: Yeah, I think this concept of a space time interval

988
00:50:39,680 --> 00:50:42,600
Speaker 1: is a little bit abstract because there's no real intuitive

989
00:50:42,640 --> 00:50:44,920
Speaker 1: and analog for it, Like, what is this thing we're

990
00:50:44,960 --> 00:50:48,359
Speaker 1: talking about, Like, yes, the universe respects it, but it's

991
00:50:48,400 --> 00:50:51,320
Speaker 1: not something that lines up with our notions very nicely.

992
00:50:51,920 --> 00:50:54,040
Speaker 1: And so I think that's why it's not typically like

993
00:50:54,120 --> 00:50:58,240
Speaker 1: introduced in POPSI, whereas you know, like the universe respects

994
00:50:58,360 --> 00:51:00,839
Speaker 1: energy or doesn't respect energy or momentum. These are things

995
00:51:00,920 --> 00:51:03,719
Speaker 1: we can get a handle on, so it's easier to

996
00:51:03,760 --> 00:51:07,080
Speaker 1: talk about. But the space time interval really is foundational

997
00:51:07,120 --> 00:51:09,880
Speaker 1: to the whole concept of the geometry of the universe,

998
00:51:09,880 --> 00:51:12,839
Speaker 1: which is what relativity is all about. That's really what

999
00:51:12,960 --> 00:51:16,600
Speaker 1: Menkowski was saying to Einstein. Yeah, you broke space and

1000
00:51:16,640 --> 00:51:19,480
Speaker 1: you broke time, but really you showed us that these

1001
00:51:19,520 --> 00:51:22,279
Speaker 1: are two sides of a more complicated object. You don't

1002
00:51:22,280 --> 00:51:26,000
Speaker 1: stick them together trivially. You stick them together backwards, and

1003
00:51:26,360 --> 00:51:29,440
Speaker 1: the universe has this weird geometry and that's how it

1004
00:51:29,560 --> 00:51:33,400
Speaker 1: organizes itself. That's the internal mechanism of the mathematics of

1005
00:51:33,480 --> 00:51:36,600
Speaker 1: the universe. And this turned out to be really crucial

1006
00:51:36,640 --> 00:51:41,400
Speaker 1: for Einstein's next step in general relativity, because in special relativity,

1007
00:51:41,400 --> 00:51:44,040
Speaker 1: these interval formulas are pretty simple. You just take the

1008
00:51:44,080 --> 00:51:46,560
Speaker 1: differences in each spatial dimension, you take the difference in

1009
00:51:46,600 --> 00:51:49,160
Speaker 1: the time dimension, you add them up with a negative,

1010
00:51:49,280 --> 00:51:52,239
Speaker 1: and you do the pythegonorary and theorem. You're good. In

1011
00:51:52,280 --> 00:51:55,279
Speaker 1: general relativity, the locations don't add up all the same way.

1012
00:51:55,360 --> 00:51:58,120
Speaker 1: Some locations add up more and some locations add up less.

1013
00:51:58,360 --> 00:52:00,760
Speaker 1: That's what we mean by the metrical talk about sometimes

1014
00:52:00,760 --> 00:52:03,880
Speaker 1: in general relativity, how is space curved in this location?

1015
00:52:04,160 --> 00:52:07,000
Speaker 1: How much space time interval do you crew by passing

1016
00:52:07,000 --> 00:52:10,400
Speaker 1: through this space versus passing through that space? And so

1017
00:52:11,120 --> 00:52:13,920
Speaker 1: this concept of having a geometry to the universe and

1018
00:52:13,920 --> 00:52:17,279
Speaker 1: then having that geometry be non trivial, that's how you

1019
00:52:17,320 --> 00:52:20,560
Speaker 1: go from special relativity to general relativity. But you got

1020
00:52:20,560 --> 00:52:23,480
Speaker 1: to get your brain like the geometry of the universe

1021
00:52:23,560 --> 00:52:26,239
Speaker 1: first before you can even get to general relativity.

1022
00:52:26,600 --> 00:52:30,680
Speaker 3: Well, this conversation didn't crush my spirits. It lifted them up.

1023
00:52:30,760 --> 00:52:32,920
Speaker 3: And now I have I guess you can't really make

1024
00:52:32,960 --> 00:52:35,120
Speaker 3: a positive space time because then that would be too

1025
00:52:35,200 --> 00:52:38,000
Speaker 3: far to travel. And so I'm still going to be

1026
00:52:38,080 --> 00:52:40,920
Speaker 3: thinking about this tonight. But I totally followed the explanation,

1027
00:52:41,719 --> 00:52:43,600
Speaker 3: and that's awesome. I learned something new today.

1028
00:52:44,040 --> 00:52:46,439
Speaker 1: And one more speed bump to avoid is you often

1029
00:52:46,480 --> 00:52:49,360
Speaker 1: hear people saying that photons do not experience time. And

1030
00:52:49,880 --> 00:52:52,719
Speaker 1: here what we're saying is light can go from A

1031
00:52:52,880 --> 00:52:57,120
Speaker 1: to B with no space time interval. Right, it's lightlight,

1032
00:52:57,360 --> 00:53:01,040
Speaker 1: it's a zero space time interval along the light. That's

1033
00:53:01,120 --> 00:53:04,120
Speaker 1: not the same as saying photons do not experience time.

1034
00:53:04,760 --> 00:53:04,880
Speaker 2: Right.

1035
00:53:05,280 --> 00:53:08,560
Speaker 1: Saying photons have a zero space time interval is very

1036
00:53:08,560 --> 00:53:11,920
Speaker 1: different from saying photons do not experience time. There's a

1037
00:53:11,920 --> 00:53:15,880
Speaker 1: whole separate POPSI rabbit hole. But photons do take time

1038
00:53:15,960 --> 00:53:19,400
Speaker 1: to move across the universe. They just don't take space time.

1039
00:53:19,920 --> 00:53:24,239
Speaker 3: I'm realizing. I want to ask, if space time intervals

1040
00:53:24,280 --> 00:53:26,520
Speaker 3: have units, does it make sense to think of it

1041
00:53:26,560 --> 00:53:28,840
Speaker 3: as a measurement with a unit.

1042
00:53:29,440 --> 00:53:32,240
Speaker 1: Yes, it does. In the units we use are distance

1043
00:53:32,719 --> 00:53:36,560
Speaker 1: right like length like meters for example, and time enters

1044
00:53:36,880 --> 00:53:39,120
Speaker 1: with a conversion factor, which is the speed of light.

1045
00:53:39,400 --> 00:53:41,520
Speaker 1: So it's not really time, it's the speed of light.

1046
00:53:41,600 --> 00:53:45,320
Speaker 1: Time's time ct which is why photons have a space

1047
00:53:45,360 --> 00:53:48,239
Speaker 1: time interval of zero, because they move at the speed

1048
00:53:48,239 --> 00:53:51,080
Speaker 1: of light, so that conversion factor ensures that the space

1049
00:53:51,160 --> 00:53:54,799
Speaker 1: and the time parts balance perfectly. Way to go, mass

1050
00:53:54,840 --> 00:53:59,520
Speaker 1: harmonious mathematics. Love it all right? Well, thank you everybody

1051
00:53:59,560 --> 00:54:02,239
Speaker 1: for going on this journey through space and time and

1052
00:54:02,360 --> 00:54:04,680
Speaker 1: through space time. Thank you Kelly for all the great

1053
00:54:04,760 --> 00:54:07,960
Speaker 1: questions and for not using the crusher on today's episode.

1054
00:54:08,000 --> 00:54:10,879
Speaker 3: Thank you Daniel for the great explanation. I will keep

1055
00:54:10,920 --> 00:54:12,560
Speaker 3: the crusher at home with me.

1056
00:54:13,719 --> 00:54:15,279
Speaker 1: You guys, hear the sound of that thing.

1057
00:54:15,480 --> 00:54:18,840
Speaker 2: Oh my gosh, oh gosh.

1058
00:54:18,920 --> 00:54:21,200
Speaker 1: All right, and that's me signing off with a shiver.

1059
00:54:22,960 --> 00:54:24,640
Speaker 3: Yep, that's me signing off as well. I don't think

1060
00:54:24,640 --> 00:54:26,440
Speaker 3: I'm gonna be able to use this thing on anything

1061
00:54:26,760 --> 00:54:30,600
Speaker 3: actually living without Yeah, I'm not doing it. All right, everybody,

1062
00:54:30,640 --> 00:54:33,719
Speaker 3: Until next time, have a good space and have a

1063
00:54:33,719 --> 00:54:34,200
Speaker 3: good time.

1064
00:54:41,000 --> 00:54:43,440
Speaker 1: Thanks everybody for listening. Please go and do us a

1065
00:54:43,440 --> 00:54:46,680
Speaker 1: favor and rate the show on whatever podcast app you're using.

1066
00:54:46,800 --> 00:54:48,359
Speaker 1: It really helps people find us.

1067
00:54:48,920 --> 00:54:52,840
Speaker 3: Daniel and Kelly's Extraordinary Universe is edited by the amazing

1068
00:54:52,880 --> 00:54:53,600
Speaker 3: Matt Kesselman.

1069
00:54:53,800 --> 00:54:57,080
Speaker 1: He really is a wizard. You can also find us

1070
00:54:57,160 --> 00:55:02,240
Speaker 1: online on Blue Sky, Instagram, and d and K Universe.

1071
00:55:02,320 --> 00:55:03,560
Speaker 1: Come engage with us.

1072
00:55:03,800 --> 00:55:07,120
Speaker 3: You can email us at questions at Danielankelly dot org.

1073
00:55:07,239 --> 00:55:09,400
Speaker 3: We really do want to hear from you, and you.

1074
00:55:09,400 --> 00:55:13,399
Speaker 1: Can find our website www dot danieland Kelly dot org,

1075
00:55:13,680 --> 00:55:16,799
Speaker 1: where you'll also find an invitation to join our discord

1076
00:55:16,880 --> 00:55:20,560
Speaker 1: where everybody comes and talks about the amazing universe.

1077
00:55:20,360 --> 00:55:24,320
Speaker 3: And we also have the most amazing moderators. This is

1078
00:55:24,360 --> 00:55:26,920
Speaker 3: an iHeart podcast. Thanks for joining us.