A universe smaller than the observable

Every video until now, we've been working from the assumption that the observable universe is smaller than the entire universe. And if you go by the cosmic inflation theory-- and it was founded by Alan Guth. And I have almost personal connection to Alan Guth. When I was at MIT, I always used to go to this Chinese food truck. And I always used to show up at the food truck like two seconds before Alan Guth. Like he was always one or two people behind me in line. But anyway, he was the founder of the cosmic inflation theory, which is basically this idea that in the very early moments or the very early period after the Big Bang, we went through this major inflation in the expansion of space. But anyway, based on the theory of cosmic inflation, then the observable universe is on the order of-- or maybe another way to say it, the entire universe is on the order of-- 10 to the 23 times the size of the observable universe. So that would mean that this is just a tiny, tiny fraction. I mean, this is an unimaginable large number. In fact, it is unimaginable. So already everything we've talked about, this itself is a huge-- this is an incomprehensible amount of space. But this is an incomprehensible multiple of this incomprehensible amount of space. And that's just based on that theory. But it is possible-- we cannot rule out even the idea-- that the actual universe is smaller than the observable universe. And that one is in some ways even more mind blowing than the idea that the universe is this big, the fact that what we're observing is actually larger than the actual universe. And so you might say, well, Sal, that's impossible. But just think about it a little bit. This is the observable universe. And the way we've depicted it, it's based on how long the light has taken to reach us. We've already covered before that this point in space is now 46 billion light years away, not 13.7, the way it looks right over here. It just took 13.7 billion years to reach us. If there's any photon that would take longer than 13.7 billion years to reach us, it hasn't reached just yet. Because it could have only started 13.7 billion years ago. So they're on their way. And they started at some point outside of our observable universe. So our observable universe will grow over time. But with that said, let's imagine that the actual universe is a subset of this observable universe. Let's say it's roughly half the diameter. So let's say it looks like this. Maybe I'll make it a little bit of an oval. Maybe the actual universe-- and this is just to be a little bit provocative. And it's not impossible. Let's say that this is the actual universe. And the way I drew it, it makes it look like Earth is the center. That we're the center of it. But remember, this is very likely to be the surface-- or it is curved. It has a slight curvature. But it could very well be the surface of a four-dimensional object. And maybe the simplest one to visualize is four-dimensional sphere. So if you really wanted to visualize this right, this whole volume-- and remember this whole picture, it keeps looking two-dimensional. But it has depth. It is a volume of space, an incredibly vast volume of space. And so what I've done here is this is an ellipsoid right here. It's elliptical volume of space that I've bubbled out right over here. But if this was really the entire universe, and if the entire universe really were the surface of a four-dimensional sphere, then the reality is that this entire space could be represented like this. It could be represented as the surface. If this was a four-dimensional sphere-- obviously, I can only draw three-dimensional spheres. But let me show you that it's not just a circle, that it actually has some depth to it. And I can even shade it right over here. And so you can imagine that this point over here is actually the same thing as that point over there. That they have wrapped around and that they're connected right at the back over here-- let me go behind-- that they're connected right over there. And that this point and this point are actually the same point, that they've wrapped around. Maybe they've wrapped around. Actually, the way I've drawn it right here, they would actually all wrap around right back there at that point, if I'm visualizing properly. But if you go in any one direction, you would come back on the other side of the surface. Let's say that Earth is right here. The way we depicted it, Earth is the center. But we see that when you look I like this, there is no center to the surface of a sphere, even a four-dimensional sphere. So in this sense, if you go in any one direction, you'll come back out the other side. So if you start from Earth and you go in that direction, once you get there, you're really here again. And then you would come back to Earth. And so if this were the case, if the actual volume of the true universe was smaller than what it looks like, the observable universe, then what's all this stuff on the outside? And to think about it, think about what would happen if 13.7 billion years ago, when we were in that primitive state, where that background radiation, those photons are being-- those electromagnetic waves are being released, let's say they get released. And those photons on their first pass-- and I think you know where this is going-- on their first pass, they would get to us in about-- this looks like a distance of about, I don't know, this looks like about 6 billion years. Then they would pass us up. And then they would get back to this point again in another 6 billion years. And then they would come back here. And so that very first past photon are going to be right over here. And from our point of view, we're not going to see them for a couple of billion years. And so when we do see them, we're going to perceive them-- we're going to say, wow, it took 15, 16 billion years for that photon to get to me. That must be from something out here. But the reality is it's a photon from something within a smaller physical universe, within a smaller actual universe, that's just taken several passes by us. And we're just seeing a pass after 14 billion years. We just think it's from something further out. Now the other thing is you say, well, if this was the case, if we could just go in one direction of the universe and then come out of the other side, and if all of that was within the observable universe, wouldn't we be able to tell? Wouldn't we be able to look in two directions and see the same thing from a different perspective? And the answer there is to think about what happens-- or actually, wouldn't we even be able to see ourselves? Because we emit some light, and it would take maybe-- I don't know how far that is. Let's say that's 6 or 7 billion light years to get right over here, which would be right over there. And then it would take another 6 or 7 billion light years to get over there. So maybe that background radiation we're seeing is actually background radiation emitted from that exact point in space that we are right now, or from a very similar point in space, to where we are right now. Or part of the background radiation is from a similar point in space that we are right now. So how come we can't just see ourselves? Well, I kind of just answered the question. That second pass, if you're observing the same point in space, if you're observing light from the same point in space on a previous pass, that light was emitted a long, long, long time ago, maybe 13 billion years ago. And so it would be unrecognizable. This region of space, the region of space that we are in right now, if we saw the same region of space 13 billion years ago, we just wouldn't recognize it. Now, there are some people attempting to see if there are some patterns, see if you can model how the universe would change and if you see patterns. And maybe the actual universe is a subset of the observable. We just haven't seen it yet. But it's completely a possibility. Hopefully, I didn't confuse you. I actually find this kind of an interesting idea. That this light that has taken 13-- let's say the light that's taken us 8 billion years to reach us. We think it's from something, based on this scale, 8 billion light years out. It's actually further because the universe is expanding. So it would have actually traversed more space than that. But we think it's from something like that. But it could've been something further in, if the actual universe is smaller. And it's just on its second pass. It's actually coming back again. And that's why it took 8 billion years to reach us. And we don't even recognize it because it looks very different than that region of space right now. Or that region of space after 4 billion years looks completely different than it did when it first released. Anyway, hopefully I didn't confuse you too much. But I think this is a fascinating, fascinating topic.