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Sal Khan 创建




right now the prevailing theory of how the universe came about is commonly called the Big Bang Theory Big Bang Theory and really is just this idea that the universe started is kind of this infinitely small point this infinitely small singularity and then it just had a Big Bang or just expanded from that state to the universe that we know right now and and when I first imagined this and I think it's it's also a byproduct of how it's named a Big Bang you kind of imagine this this type of explosion you kind of imagined this type of explosion that everything was infinitely packed in together and then it exploded and then it exploded outward and then as all of the matter explore exploded outward it started to condense and then you have these little galaxies and superclusters of galaxies and they started to condense and then within them a planets condensed and stars condensed and that we have the type of universe that we have right now but this model for visualizing the Big Bang has a couple of problems one is when we talk about the Big Bang we're not talking about the matter just the the mass or just the matter in the universe being in one point we're talking about actual space expanding so we're not just talking about something inside of space like the physical mass the physical matter expanding we're talking bout space itself and so when you have this type of model you have all of this stuff expanding but you're like well look isn't it expanding into something else isn't you know maybe if if the the furthest out parts of this matter is right over here is right over here what's this stuff over here and until you say well you know wouldn't that be space so how can you say space itself is expanding and another idea that a Big Bang also implies is if this is the furthest stuff out there would this be would this be the edge of the universe does the universe have an edge and the answer to either those questions is that's right what we're going to try to tackle on this is that one the universe does not have an edge and two there is no outside space we are not expanding into another space and I'm gonna explain that hopefully we'll see why that is the case right now so the best way to view it and we're gonna view it by analogy we're gonna Butte by a knowledge if I were to tell you that I have a a two dimensional a two dimensional space a two dimensional space two dimensional space that has a finite area so it has a finite area finite area so it's not infinite and it also has no edge it also has no edge this once again at first when you first look at it seems difficult how do i construct something that has a finite area but still has no edge every time I try to draw an area it looks like I have to have some edges and then you might remember what if that two-dimensional space is curved what happens and I think the easiest example of that is the surface of a sphere the surface of a sphere let me draw a sphere over here so this right here is a sphere let me draw some some equal longitude and latitude and the lines on this sphere on this sphere all of a sudden and I'll shade it in a little bit make it look nice this type of a sphere you have a finite a finite area you could imagine the surface of a balloon or the surface of a bubble or the surface of the earth you have a finite area but you have no edge if you keep going forever in one direction if you keep going forever in one direction you're just gonna keep me and go all the way around and come back and come back to the other side now to imagine a three-dimensional space that has these same properties a finite area and and I want I don't want to say find out area anymore because we're not talking about a three-dimensional space let me draw it over here so let's think about a three dimensional space so three three-dimensional three-dimensional space instead of area since we're in three three dimensions now I want to talk about a finite volume finite finite volume and no edge how do I do that and when you think about it superficially well look if I have a finite volume it's gonna be in you know maybe it'll be can contain some type of a cube and then and we clearly have edges in those situations or you could even think about a finite volume as being the inside of a sphere and that clearly has an edge this entire surface over there so how do you construct a three-dimensional space that has finite volume and no edge and that I'm gonna tell you right now it's very hard for us to visualize it but in order to visualize it I'm gonna draw the same thing as I drew right here what we would you're what you have to imagine and you almost have to imagine it by analogy unless you have some type of a profound brain wired for more than three - more than three spatial dimensions is a sphere but so let me make it clear this is a this is a two-dimensional surface two-dimensional surface right on the surface of the sphere you can only move in two directions - two perpendicular directions you can move like that or you can move like that you can move left and right or you can move up and down so it's a two-dimensional surface of a three-dimensional a three-dimensional sphere so if we take it by analogy let's imagine and it's hard to imagine a three-dimensional surface a three-dimensional surface and you can do it mathematically the math here is actually not that difficult it's a three-dimensional surface of a four dimensional sphere of a four-dimensional four dimensional sphere and I'm gonna draw it the same way so if we kind of view those three dimensions or just these two dimensions of the surface the same thing it's the same thing and if you imagine that I'm not saying that this is actually the shape of the universe we don't know the actual shape but we do know that it does have a slight curvature but we don't know the actual shape but a sphere is the simplest there's other ones we could do a toroid would also fit the bill of having a finite volume with no edge and another thing I want to make it clear we actually don't even know whether it has just a finite volume that's still an open question but what I want to do is show you that it can have a finite volume and also have no edge and most that most people believe and I want to say believe here because you know we can just go based on evidence and all of that that we are talking about something with a finite volume especially when you talk about the Big Bang Theory that kind of on some on some dimension implies a finite volume although it could be a super large unfathomably large volume it is finite now if if you have this let's imagine this sphere let's imagine this sphere once again if you're on this surface of this four dimensional sphere I obviously can't not I cannot draw four dimensional sphere but if you're on the surface of this four-dimensional sphere if you go in any direction you will come back out and come back to where you started if you go that way you'll come back around here now the universe is super huge so even light maybe light itself would take an unbelievable amount of time to traverse it and if this sphere if the sphere itself is expanding it might be expanding so fast that light might not ever be able to come back around it but in theory if something were fast enough if something were to keep going around it could eventually go back to this point now when we talk about a three dimensional surface it's a three dimensional surface of a four dimensional sphere that means that any of the three dimensions over here on the surface I can only draw two but that means if this is true if we if the universe is a three-dimensional surface of a four dimensional sphere that means that if you go if you go up and you just keep going up you'll eventually come back from the bottom so if you keep going if you keep going all the way up you'll eventually come back to the point that you were it might be an unbelievably large distance but you'll eventually get back where you were if you go to the right you'll eventually come back all the way around to the point where you were and if you were to go into the page so if you were to go into the page let me draw it that way if you were to go into the page you would eventually come back from above the page and come back to the point that you are so that's what this implication would be that you would eventually get back to where you are so let's go back to the question of an expanding universe a you know expanding universe that's not expanding into any other space that is all of the space but it's still expanding well this is the model so you could imagine shortly after the Big Bang our four dimensional sphere look like this maybe it was a little small four dimensional sphere at some you know maybe it you know right at the Big Bang it was like this little unbelievably small sphere then a little bit later it's this larger sphere let me just shade it in to show you that it has three that it has that it's kind of popping out of the page and it's a sphere and then at a later time the sphere might look like this the sphere might look like this now your your temptation might be to say what we'd sell isn't this stuff outside of the sphere isn't that some type of a space that's expanding into isn't that somehow part of the universe and I would say if you're if you're talking in three dimensions no it's not the entire universe is this surface it is this surface of this four dimensional sphere if you start talking about more dimensions then yes you could talk about maybe things outside of our three-dimensional universe so as this expands in space-time so you cannot you know one way to view the fourth dimension is it is time itself things are just getting further and further apart and I'll talk about more evidence in future videos for why we why the Big Bang is the best theory we have out there right now but as you can imagine if - if we have two points on this fear that are that far apart as this sphere expands this four-dimensional sphere as this bubble blows up where this balloon blows up those two points are just let me draw three points let's say those are three points those three points are just gonna get further and further apart and that's actually one of the main points that that or one of the one of the first reasons why it made sense to leave in the Big Bang is that everything is expanding not from some central point but everything is expanding from everything that if you put any direction from any point in the universe everything else is expanding away and the further away you go it looks like the far the faster its expanding away from you so I'll leave you there something for you to kind of think about a little bit and then and then we'll build on some of this to think about what it means to kind of observe the observable universe