Physicist Explains Dimensions in 5 Levels of Difficulty | WIRED

hi I'm Sean Carroll I'm a theoretical physicist here at the California Institute of Technology I've been challenged to explain dimensions to five different levels the idea of a dimension sometimes in pop culture is misunderstood like there's an extra place you can go a mystical dimension or something like that to a physicist or a mathematician a dimension is just a direction you can go in up down left right forward backward do you and me we think there's three dimensions around us but then physicists start talking about extra dimensions how can you hide them you know where might they be I'm hopeful that we'll learn something at each level we're gonna talk about some science do you like science yes a lot oh very good you come to the right place so we're gonna think about physics have you heard the word physics before do you know what that is what's your idea what physics is I'm not so sure okay I just think of physics as you know the study of everything what stuff is what stuff does so today we're going to talk about space and in particular the idea of dimensions have have you heard about dimensions I think I mean I ain't enough 3d printing 3d printing good no I own keys the size all I have to do with the shape but you know what 3d means it's free dimensional three dimensional as opposed to what is ordinary printing so ordinary printing would be 2 d what do you say when something is one-dimensional what's an example of something it's one-dimensional a line is the perfect example because it's one thing that's straight right so here's some toys we're gonna build some dimensions right so what would you say about this that's 1 exactly it's not really one dimensional everything has to be one or two dimensional before it's free dimensional and how would you find yourself like if someone said where are you like could you use some words or ideas to say where you are on that line I think I would be a maybe there since I'm facing it but here's what I wanted to think about if I say I'm at this point on the line I could translate that into saying I'm at the three-centimeter point if I were here I via the four-centimeter point the five-centimeter point right so every point every location on our little line has its own unit as its own unit has one number we need one number to tell you where we are that's one dimension that's what it means to be one dimensional I only need to tell you one number to figure out where we are because if it's like a sphere you kind of have to start using points there you go exactly we're gonna build a little two dimensional space you wanna do it you wanna do the honors here why don't you put those two lines together if you make it mental is this a corner exactly another way is if you are two spacing between is an angle I think you should be in this chair and he should be explaining this to me you're much better than this than I am yeah so those are the dimensions that's how we think about dimensions remember we just needed one number to find ourselves on the line we need two numbers to find ourselves on the plane I think that would be an X or Y axis there you go so do you think we could have more than three dimensions 3d is the maximum of dimensions for shapes well as far as we know this is why physicists think about things we don't know about we're wondering whether it could be extra dimensions you've never seen that are tinier than atoms so okay so what have you learned what do you know about dimensions now how do you think about dimensions in a slightly different way than you did before so at least everything has a certain dimension yeah do you think he'd be excited a physicist said that they found extra dimensions of space that would be the news would be spreaded around the world rocket I think so I think you're right all right Hank we want you to you know keep up studying learn a lot of math and physics and help us discover new dimensions someday does that sound like a fun idea yeah do you like science doesn't think about what kind of science I like biology and computer science all right you're in the wrong place we're not gonna be talking about biology computer science so we want to talk about the idea of dimensions the other dimension is how you define dimensions I guess I don't know how to exactly define it but I know like the first floor right you know the difference between like one dimension dimensions three dimensions etc so let's do a little experiment here so there's one dimension I'll give that to you now here's here's your task I'm gonna give you another dimension and I'm gonna ask hold those two things at right angles to each other it's easy to do so there's no trace here I'm not trying to pull you here okay now this will be slightly trickier I'm going to give you this I want you to hold all three of them at right angles to all the others at the same time there you go so what that's doing is when you had just two that was describing a two-dimensional plane right like the two things pick out a plane the three things pick out all three dimensional space now we'll give you one more I'm gonna ask you to hold that fourth one so that it's at a right angle to all the other three at the same time all right now I am can't be done you can't do it so we just experimentally proved that space is three-dimensional that's sort of what it means to be three-dimensional that there are three different directions you can move in and there's not four or five or six directions you can move in okay there you go three dimensional space right mm-hmm so have you thought about using coordinates in three dimensions yeah I was actually doing SAT prep there you go it showed like the x y&z axis as well that's right so that's exactly what these would be have you heard that there are other coordinate systems other than XYZ no but we could also say how far we are away from the center just the distance and then the angle that our little line makes with that's a B X ax yeah so that's a different way of giving you two numbers and locating yourself and we called polar coordinates is a different coordinate system well we want to do as physicist is look for extra dimensions can you imagine can you think of any way that there could be extra dimensions time time yes Einstein that said that we can think of time as a fourth dimension and that's a very fascinating thing that we could talk about all by itself but what about space what about the solar system like if you wanted to tell me where a certain star was in the sky do you know what how we do that I have no idea it's it's exactly the same thing as latitude and longitude but we put coordinates on the sky so astronomers call them right Ascension and declination which are two terrible words but basically you've seen you know on the globe where you draw latitude and longitude what it looks like yeah there are the peals of an orange kind of thing right yeah so you can define something as well you know how high above a certain location on earth it is but the earth is rotating and revolving around the Sun so we have to define separate celestial coordinates so there's like mold how many dimensions would there be we don't know you know the optimistic view is that there are six but the thing is some of them might be really really really really really small like way too small for us to ever see yeah and some of them might be medium sized that hopefully we can see okay so since it's all theoretical like this could not be three dimension and this is sort of the state of uncertainty that physicists are stuck living out you know honestly out there if you go out onto campus and talk to the physicists half of them will say probably extra dimensions exist and have them say no that's just nonsense okay after all this yeah someone comes up to you on the street and says what's a dimension oh man I mean I guess what I've learned today is just that there are not just three dimensions or at least we think I mean everything's theoretical it's all just really kind of confusing that's right and you know if they're still bugging you you can just like give them some sticks and act as we're together and that would shut them up yeah where do you go to school and what do you study I'm gonna be a sophomore from ona college and I study math and physics Oh math and physics okay what kind of physicists do you want to be you know I really don't know I like theory and experimental so it's kind of tough for me to say usually if it's math and physics you end up as a theoretical physicist right yeah experimental one so our theme here today is dimensions and so this is great that you have some math background some mathematicians think about dimensions in a different way yeah so how would you explain to you know your friends who are not math and physics majors like what is it dimension yourself my first intuitive thought is water like the coordinates you know so if we were looking at things we're looking like a dot that's like one or a line rather that's one dimensional because we can only measure it one way but now if we look at like a square then we're increasing like that so it's like all basically the what coordinates we can use to measure something that's exactly right and so you've heard of space time yeah being four-dimensional right now in some sense that's kind of trivial to you and me because of course you have space which is three-dimensional you have time which is one dimensional so space-time is four-dimensional but it didn't turn out it didn't occur to anyone that that was a sensible way to talk until really relativity this is the crucial thing right is that what Einstein realized is that sure there's both time and space but how we divide space time into time and space can be different for different people and really there's a real sense in which four-dimensional space-time is kind of a generalization of three-dimensional space and I think to really explain this we're gonna need a blackboard okay let's bring what it all right think about relativity is that they really want you to think of space-time as one four-dimensional thing right it's kind of like space it's not just three dimensions of space in one dimension of time why though why this is a very good question so let's just start with space right you know a little bit about space so here's my simple-minded way of drawing space two dimensions because that's how many I can draw on the blackboard let's say x and y and what is special about space there's many things but one is that if I have you know a curve or a path between two points there's a distance that you can calculate right and the distance between those two points doesn't depend on your coordinates it doesn't depend on whether you're in radial coordinates or Cartesian coordinates or whatever I'm allowed to imagine a curve that does something like this between those two points and if I were a person walking on that curve I would have an a domitor with me maybe and I would know you you would know even without having done that this path has always going to be longer than that there's a formula I thank you mrs. theorem it tells you what the shortest distance path is that's the point the physicalness of what is real is the distance along a certain curve so space-time is like that that's why it is useful to think about space okay so let me draw space-time is how we usually draw it I'll just say X but all of space is condensed this one direction and this is time okay so if you're a little person you start at some event so you start you're located somewhere in space somewhere the three coordinates of space and whether you like it or not you're moving through space-time just by getting older yeah when people ask me can you travel through time I say yes yesterday I traveled 24 hours into the future and Here I am you know the day later so that's just this okay you're moving through time like that so what Einstein says is look I can travel through space-time in different ways like I could hop in a rocket ship and fly out and then fly back and then I can meet you there so this is a different trajectory through space-time right yeah and it's almost exactly like the space story the space story says there's a distance distance is different along different Irv's Einstein says there's something that measures the length of these curves and we call it the proper time it is literally the time that you would read on your wristwatch so it's kind of like our like fundamental time I got face time well kind of what Einstein wants to get across this there's no such thing as fundamental like there's the universe is time this big letter T that might you know tell you how old the universe is but then every individual has a clock with them and they measure their own time depending on how they're moving through the universes and the crucial difference is the time is not the same for this person who stayed behind and sat in their chair and this person who zoomed out there why is that this one is shorter than there is what we call a metric on space time and when we talk about Euclidean space versus a curved space versus a sphere or something that's a different metric and space-time has its own metric which says the following thing that the path between two events in space-time that is a straight line will always be the longest time I see okay that's the difference all right so what when I had this idea Oh gravity could be related to the curvature of space-time he did some equations okay so he got it that's a long story will satisfy what he figured out was that rather than gravity living on top of space-time it's a manifestation of the curvature of space-time so when you have like the earth the Sun the moon they cause a gravitational field they're actually warping the space-time around them they're giving it a different geometry would it be if I had like a spring off or not a spring like a like a sheet and I dropped like a book in the sheet curves down yeah exactly if you if you had a sheet that was originally flat and you know you sent a marble on it would go in a straight line then if you put something on it so it warps it that marble is now gonna be deflected I see Einstein says the gravity is just like that I see but there are no straight lines because space-time itself is curved so do you think if you had to explain relativity what would you say I think I'd go with like the kind of like the Train paradox let's say I'm stationary and someone's moving past me on the train they think they're stationary on the train like they think that they're not accelerating but if they start walking through the train cars then they are accelerating in their frame but then from my outside frame where I'm completely removed I see they're accelerating so I guess that relativity is all about perspective I guess in a way yeah that's right and it goes exactly back to what we drew on the board and we're how those two people in the Train and on the ground would divide space-time up differently you have to space in time that's pretty good yeah it's a lot of fun stuff to talk about so observational cosmology so like what would he look at so I work on two ground-based surveys and the optical and we're basically trying to make huge maps of the universe so that we can study dark energy I'm sure you've heard about extra dimensions a little bit I've heard it yeah I'm thinking about the idea that there might be more than three dimensions of space what is your impression of theoretical physicists who think about things like extra dimensions of space that they haven't ever seen I get a little scared cuz I think oh how can you prove these theories right one theory I've heard of I don't know if this fits in with that is bubble universes it's not an extra dimension does that fit into that or is that something it does in fact one way that different universes might sort of be created and be different from each other is that different universes could have effectively different numbers of dimensions like we have three dimensions around us but there's people out there aliens who could live in five dimensional universes and are each of those dimensions do are they governed by the same laws of physics or is there like a separate lagrangian for each universe yeah how does that work we think that it would be you know all this is incredibly speculative and we don't know for sure but the idea is that there is some deep down underlying laws that are universal and the same but they show up differently so they appear different so the specific particles and forces and masses would be completely different in different parts of the multiverse okay why in the world would you think that there are extra dimensions right so you've heard of string theory I have so the string theory is basically a theory of quantum gravity mm-hmm so we have quantum mechanics right the theory of you know atoms and so forth and how those work and then we have gravity and gravity doesn't seem to fit in it's the one force of nature that we can't really easily fit into this quantum mechanical so string theory is one of the best right ideas that's the good news the bad news is that it only seems to work if space-time is ten dimensional so you would say well then it's wrong it can't be right space-time is not 10 dimensional space-time is four dimensional you've observed that but instead we say if space-time looks four dimensional to us but string theory which might be the best theory we have of quantum gravity says it must be 10 dimensional maybe we could hide those extra six dimensions somehow so here's how we could get lucky we could imagine that there are extra dimensions of space that are curled up somehow that are so small that we can't see them this is actually an old idea it goes back to Colusa and klein right after general relativity was invented in 1915 but there's a more recent idea that says there could actually be relatively large extra dimensions there could be extra dimensions that are actually that big like a millimeter across that you would not have noticed but here's the new exciting idea so let's imagine okay there's a piece of paper but let's imagine this is our entire world so in other words our real world is three dimensional but let's imagine that we're just idealizing it down to two dimensions so we all live here you and I live here but let's imagine that we're embedded in this bigger space so there are extra dimensions that are actually big ok let's imagine that when I say we live on this three dimensional world what I mean is imagine that the particles that you and I are made of right the quarks the leptons the electrons and everything all the forces we know about electromagnetism the weak nuclear force the strong nuclear force imagine that they can't leave this surface this is what will we call a brain BR ane have you heard this word before right yes do you know where it comes from no from membranes you know we have lines one dimension we have two-dimensional surfaces so if you have a line that is a vibrating physical thing you call it a string right right if you have a two-dimensional surface that vibrates and is a physical thing we call that a membrane membrane theory goes back it never was as popular as string theory but it's been around for a while but if you have extra dimensions of space then you can have three-dimensional vibrating things and four-dimensional vibrating things so how do these strings give rise to things like mass in charge and basically give us the properties of the particles we see well basically the strings are the particles that we see it's exactly the same thing as we said you know for the straw if you look at it far away it looks one-dimensional a little loop of string so a little one-dimensional circle that is vibrating if you look at it from very very far away it just looks like a particle so in string theory an electron is a little string a photon is a little string so is string theory part of what they call the grand unified theory is it's supposed to be the the last thing that sort of unifies all the forces together yeah string theory is even better so the phrase grand unified theory was coined in the 1970s for theories that joined electricity and magnetism so a good string theory is gravity plus a grand unified theory that's even better is the theory of everything what would you tell a friend of yours if they asked you what dimensions are what extra dimensions are what a brain is so we have three spatial dimensions a brain is sort of the next level so a brain is a higher dimensional object that vibrates through space that's right and we could live there the world we see around us the three dimensions of space around us could reflect the fact that we are somehow stuck on a three dimensional brain trying to escape it was really cool to learn about strings and brains and how looking at gravity on small scales is actually connected to what I do and looking at gravity on these cosmological scales and it's definitely something I'm going to think about in my research you're a string theorist so tell us like what kind of string theory you do what it means to be you string theorists one of the things that's key in the whole story of string theory is the piece of it that talks about quantum theories of gravity so I'm very excited about what happens to space-time what does even mean at the quantum level cool so do you think a lot about extra dimensions in your everyday life yes I do and so when you think about extra dimensions you put them together with brains and different fields wrapping around the extra dimensions and so forth right yes you know a lot of people a lot of string theorists they care a lot about all the different ways in which we could hide the extra dimensions as someone who cares about cosmology I want to start asking why are the extra dimensions small at all how did happen is this something you think about yourself yes well ultimately we'd like to understand the observable universe if string theory turns out to be the thing that the universe cares about we'd like to know with all of these possibilities of the in string theory how do we get the one that looks like the world we live in the thing I want to talk about is this paper I wrote with Matt Johnson and Lisa Randall where we realized there's another way to compactify extra dimensions spontaneously dynamically if you imagine starting with this big piece of paper you couldn't wrap up everything but within some region of space you could make a tube okay right and down there in the tube it looks like you're a long thing that is compactified in one direction and infinitely extend in the other direction so there's one less macroscopic dimension of space okay I think that sounds plausible to you it sounds like fun what I would immediately ask is whether the large dimensions come from in the first place is that something you address or you just assume that large debate all the dimensions are large as a starting point yeah so we certainly assume that they're all large as a starting point and it's worse than that so in our paper we imagine you start in de sitter space you start in a universe with no matter no anything like that just empty space but with an energy that is positive and all the dimensions are large but where do they come from it was always there why why not okay this is replacing one prejudice for the different prejudice I would say that we shouldn't be prejudiced one way or the other just a large you know 10 or 11 dimensions with the cosmological constant doesn't seem like a fundamental starting point it's it sounds like there needs to be something to underlie that but it's a fun scenario yeah so let me tell you a little bit more about the scenario so you know there are black holes good right I've heard of them there are black brains as well why don't you explain to us what a black brain is well in some ways it's very much like a black hole and that you have far away from it you have these large just you know flat dimensions as you move in there's there's something in the it has itself higher dimensions and so because physicists love to joke they thought well it's like a membrane but it can have many different dimensions let's use P to stand in for those number of dimensions and so they call them P brain yeah I've been trying to explain them to lower levels and they always look at me like I like your a little bit or is this the real thing that they use yes it is the real thing they use we study these brains in de sitter space and so we what we found is that there are black brain solutions which instead of having a singularity inside our non singular and stable and compactified is this a familiar thing I know things like this have been discussed yeah yeah so a lot of the brains that are relevant for studying things to do with anti-de sitter spacetime x' in various dimensions actually start out as these non singular type brains and then you find in the core there's actually an entity sitter spacetime right imagine that rather than going down to a point it just ask some totes to some fixed radius and continues infinitely far down but then you can ask okay what about the rest of the university have like some sphere some two dimensions compactified and the balance between the cosmological constant and the electromagnetic field keeps it at a distance but then the other dimensions the transverse dimensions don't need to be anti-de sitter they can have either positive 0 or negative cosmological constant so you can basically get any sort of cosmological solution times a compactified sphere is it that these have the lowest action of all the things that could possibly all the possible solutions I guess I mean maybe maybe you think otherwise again or maybe we could change my mind I think that as long as it can happen it will happen some of the time right you mean the one of the things that could happen so I mean obviously you know we know one of them baby I stole that from Kenna Reeves I'm afraid someone probably wrote it for you so it's possible that if you do have this starting point of an empty de sitter space with positive cosmos constant some field flying around you inevitably get a multiverse it just happened you know it's just part of quantum nucleation two different things and then maybe you need to explain why we live in this universe rather than some other one via the anthropic principle or something like that so how does how does our kind of you know Tech old-fashioned way of making new universes intersect with the kinds of things you'd think about well it's interesting because there's a lot of activity going on inspired by things we learned from working in anti-de sitter space where the cosmological constant has you know right wrong sign so you will find that there are a number of papers as many of which you've probably read probably you've read more of them that I have which try then to take different kinds of brains these extended solutions or and there many different kinds doing different things we understand them well enough now that we can put them together in various ways they intersect they dissolve inside each other they and you do them all in all sorts of different ways and shows that you can construct four-dimensional universes with a cosmological constant of your desire depending upon how you did the construction not everyone buys that there's a big discussion in the literature right now and if we put aside for the second the concerns of our colleagues in other parts of physics and it's just amongst us chickens what do you think about the future of cosmology and string theory and the dynamics of these extra dimensions I think it's gonna get way more interesting than then we're currently able to grapple with right now and I think there are hints of it there could be a description of the physics that might be our early universe that is like that molecular description and then from that emerges flat space times maybe for maybe some mechanism tells you it's for not something else I think that's where we're going if the viewers want to know more about how space-time can emerge from quantum mechanics they could read the graphic novel you just wrote right yes I wrote in drew a graphic novel called the dialogues conversations about the nature of the universe and I just wrote a book called something deeply hidden about many worlds quantum mechanics and how space-time can emerge from it plenty reading material for the audience out there excellent so that was fun I hope that everyone did learn something I know that I did it was very nice to see how the idea of dimensions and space resonates in different ways with different people all the way up to talking to Clifford about the forefront of modern research I really do think that we're not done understanding how dimensions work there are three dimensions of space why that why not - why not 27 I think that we really don't yet have the data or ideas to think about this but we're creeping up on it I'm optimistic about progress in the near future I'm a professor at the University of Waterloo and I'm a sleep scientist at UCSF today I've been challenged to explain lasers to explain the topic of sleep at five different levels [Music]

Channel: WIRED

Views: 5,545,129

Rating: 4.941503 out of 5

Keywords: dimensions, dimension, theoretical physicist, sean carroll dimensions, sean carroll, dimensions explained, dimensions explanation, explanation on dimensions, dimension explanation, explanation on dimension, dimension explained, explained dimensions, wired dimension, wired explanation dimensions, 3d explained, 2d explained, physicist explains dimensions, physicist explains, physics, physics explanation, physicist, physicist sean dimension, wired

Id: 3KC32Vymo0Q

Length: 28min 24sec (1704 seconds)

Published: Wed Oct 16 2019

Reddit Comments

[u/derioderio]

Fun video. Also the last conversation shows how high-level theoretical physics can blend into philosophy:

Why can you do that?

Why not?

[u/uncasripley]

The Expert made me laugh. Great video.

If you like Sean Caroll, he has a podcast called Mindscape.

[u/zebroar123]

Physics is fucking nuts

[u/tomishiy0]

The sarcasm with which the string theorist replied that he heard about black holes almost generated a gravitational colapse.

[u/spauldeagle]

Aw that kid is awesome. Cool to see someone so young go along with something abstract.

[u/chibicody]

I'm a bit angry at whoever did the editing for making Sean tell us that a GUT is the unification of electricity, magnetism and nothing else because we don't have time for all those forces!

[u/mdivan]

Kid is fucking genius :D

[u/Fizzkicks]

Oh hey I know that grad student! I officially know someone famous.

[u/jwkennington]

+1 for Sean Carroll