Radius of observable universe

Right now, the best estimate of when the Big Bang occurred-- and once again, I don't like the term that much because it kind of implies some type of explosion. But what it really is is kind of an expansion of space, when space started to really start to expand from a singularity. But our best estimate of when this occurred is 13.7 billion years ago. And even though we're used to dealing with numbers in the billions, especially when we talk about large amounts of money and what not, this is an unbelievable amount of time. It seems like something that is tractable, but it really isn't. And in future videos, I'm actually going to talk about the time scale. So we can really appreciate how long, or even start to appreciate, or appreciate that we can't appreciate how long 13.7 billion years is. And I also want to emphasize that this is the current best estimate. Even in my lifetime, even in my lifetime that I actually knew about the Big Bang and that I would pay attention to what the best estimate was, this number's been moving around. So I suspect that in the future, this number might become more accurate or might move around some. But this is our best guess. Now with that said, I want to think about what this tells us about the size of the observable universe. So if all of the expansion started 13.7 billion years ago, that 13.7 billion years ago, everything we know in our three-dimensional universe was in a single point, the longest that any photon of light could be traveling that's reaching us right now-- so let's say that that is my eye right over here. That's my eyelashes, just like that-- so some photon of light is just to getting to my eye or maybe it's just getting to the lens of a telescope. The longest that that could have been traveling is 13.7 billion years. So it could be traveling 13.7 billion years. So when we looked at that depiction-- this I think was two or three videos ago, of the observable universe-- I drew, it was this circle. And when we see light coming from these remote objects-- that light is getting to us right here. This is where we are. This is where I guess in the depiction the remote object was. But the light from that remote object is just now getting to us. And that light took 13.7 billion years to get to us. Now, what I'm going to hesitate to do, because we're talking over such large distances and we're talking on such large time scales and time scales over which space itself is expanding-- we're going to see in this video that you cannot say that this object over here, this is not necessarily, this is NOT, I'll put it in caps, this is NOT 13.7 billion light years away. If we were talking about smaller time scales or I guess smaller distances, you could say approximately that. The expansion of the universe itself would not make as much of a difference. And let me make it even more clear. I'm talking about an object over there. But we could even talk about that coordinate in space. And actually, I should say that coordinate in space-time, because we're viewing it at a certain instant as well. But that coordinate is not 13.7 billion light years away from our current coordinate. And there's a couple of reasons to think about it. First of all, think about it, that light was emitted 13.7 billion years ago. When that light was emitted, we were much closer to that coordinate. This coordinate was much closer to that. Where we are in the universe right now was much closer to that point in the universe. The other thing to think about is as this-- let me actually draw it. So let's go 300,000 years after that initial expansion of that singularity. So we're just 300,000 years into the universe's history right now. So this is roughly 300,000 years into the universe's life. I guess we could view it that way. And first of all, at that point things haven't differentiated in a meaningful way yet right now. And we'll talk more about this when we talk about the cosmic microwave background radiation. But at this point in the universe, it was kind of this almost uniform white-hot plasma of hydrogen. And then we're going to talk about it. It was emitting microwave radiation. And we'll talk more about that in a future video. But let's just think about two points in this early universe. So in this early universe, let's say you have that point. And let's say you have the coordinate where we are right now. You have the coordinate where we are right now. And in fact, I'll just make that roughly-- I won't make it the center just because I think it makes it easier to visualize if it's not the center. And let's say at that very early stage in the universe, if you were able to just take some rulers instantaneously and measure that, you would measure this distance to be 30 million light years. And let's just say right at that point, this object over here-- I'll do it in magenta-- this object over here emits a photon, maybe in the microwave frequency range. And we'll see that that was the range that it was emitting in. But it emits a photon. And that photon is traveling at the speed of light. It is light. And so that photon, says, you know what, I only got 30 million light years to travel. That's not too bad. I'm going to get there in 30 million years. And I'm going to do it discrete. The math is more complicated than what I'm doing here. But I really just want to give you the idea of what's going on here. So let's just say, well, that photon says in about 10 million years, in roughly 10 million years, I should be right about at that coordinate. I should be about one third of the distance. But what happens over the course of those 10 million years? Well, over the course of those 10 million years, the universe has expanded some. The universe has expanded maybe a good deal. So let me draw the expanded universe. So after 10 million years, the universe might look like this. Actually it might even be bigger than that. Let me draw it like this. After 10 million years, the universe might have expanded a good bit. So this is 10 million years into the future. Still on a cosmological time scale, still almost at kind of the infancy of the universe because we're talking about 13.7 billion years. So let's say 10 million years. 10 million years go by. The universe has expanded. This coordinate, where we're sitting today at the present time, is now all the way over here. That coordinate where the photon was originally emitted is now going to be sitting right over here. And that photon, it said, OK, after 10 million light years, I'm going to get over there. And I'm approximating. I'm doing it in a very discrete way. But I really just want to give you the idea. So that coordinate, where the photon roughly gets in 10 million light years, is about right over here. The whole universe has expanded. All the coordinates have gotten further away from each other. Now, what just happened here? The universe has expanded. This distance that was 30 million light years now-- and I'm just making rough numbers here. I don't know the actual numbers here. Now, it is actually-- this is really just for the sake of giving you the idea of why-- well, giving you the intuition of what's going on. This distance now is no longer 30 million light years. Maybe it's 100 million. So this is now 100 million light years away from each other. The universe is expanding. These coordinates, the space is actually spreading out. You could imagine it's kind of a trampoline or the surface of a balloon. It's getting stretched thin. And so this coordinate where the light happens to be after 10 million years, it has been traveling for 10 million years, but it's gone a much larger distance. That distance now might be on the order of-- maybe it's on the order of 30 million light years. And the math isn't exact here. I haven't done the math to figure it out. So it's done 30 million light years. And actually I shouldn't even make it the same proportion. Because the distance it's gone and the distance it has to go, because of the stretching, it's not going to be completely linear. At least when I'm thinking about it in my head, it shouldn't be, I think. But I'm going to make a hard statement about that. But the distance that it reversed, maybe this distance right here is now 20 million light years because it got there. Every time it moved some distance, the space that it had traversed is now stretched. So even though its traveled for 10 million years, the space that it traversed is no longer just 10 million light years. It's now stretched to 20 million light years. And the space that it has left to traverse is no longer only 20 million light years. It might now be 80 million light years. It is now 80 million light years. And so this photon might be getting frustrated. There's an optimistic way of viewing it. It is like, wow, I was able to cover 20 million light years in only 10 million years. It looks like I'm moving faster than the speed of light. The reality is it's not because the space coordinates themselves are spreading out. Those are getting thin. So the photon is just moving at the speed of light. But the distance that it actually traversed in 10 million years is more than 10 million light years. It's 20 million light years. So you can't just multiply a rate times time on these cosmological scales, especially when the coordinates themselves, the distance coordinates are actually moving away from each other. But I think you see, or maybe you might see, where this is going. OK, this photon says, oh, in another-- let me write this. This is 80 million light years-- in another 40 million light years, maybe I'm going to get over here. But the reality is over that next 40 million light years-- sorry, in 40 million years, I might get right over here, because this is 80 million light years. But the reality is after 40 million years-- so another 40 million years go by-- now, all of a sudden, the universe has expanded even more. I won't even draw the whole bubble. But the place where the photon was emitted from might be over here. And now our current position is over here. Where the light got after 10 million years is now over here. And now, where the light is after 40 million years, maybe it's over here. So now this distance, the distance between these two points, when we started, it was 10 million light years. Then it became 20 million light years. Maybe now, it's on the order of-- I don't know-- maybe it's a billion light years. Maybe now it's a billion light years. And maybe this distance over here-- and I'm just making up these numbers. In fact, that's probably be too big for that point-- maybe this is now 100 million light years. This is now 100 million light years. And now, maybe this distance right here is-- I don't know-- 500 million light years. And maybe now the total distance between the two points is a billion light years. So as you can see, the photon might getting frustrated. As it covers more and more distance, it looks back and says, wow, in only 50 million years, I've been able to cover 600 million light years. That's pretty good. But it's frustrated because what it thought was it only had to cover 30 million light years in distance. That keeps stretching out because space itself is stretching. So the reality, just going to the original idea, this photon that is just reaching us, that's been traveling for-- let's say it's been traveling for 13.4 billion years. So it's reaching us is just now. So let me just fast forward 13.4 billion years from this point now to get to the present day. So if I draw the whole visible universe right over here, this point right over here is going to be-- where it was emitted from is right over there. We are sitting right over there. And actually, let me make something clear. If I'm drawing the whole observable universe, the center actually should be where we are. Because we can observe an equal distance. If things aren't really strange, we can observe an equal distance in any direction. So actually maybe we should put us at the center. So if this was the entire observable universe, and the photon was emitted from here 13.4 billion years ago-- so 300,000 years after that initial Big Bang, and it's just getting to us, it is true that the photon has been traveling for 13.7 billion years. But what's kind of nutty about it is this object, since we've been expanding away from each other, this object is now, in our best estimates, this object is going to be about 46 billion light years away from us. And I want to make it very clear. This object is now 46 billion light years away from us. When we just use light to observe it, it looks like, just based on light years, hey, this light has been traveling 13.7 billion years to reach us. That's our only way of kind with light to kind of think about the distance. So maybe it's 13.4 or whatever-- I keep changing the decimal-- but 13.4 billion light years away. But the reality is if you had a ruler today, light year rulers, this space here has stretched so much that this is now 46 billion light years. And just to give you a hint of when we talk about the cosmic microwave background radiation, what will this point in space look like, this thing that's actually 46 billion light years away, but the photon only took 13.7 billion years to reach us? What will this look like? Well, when we say look like, it's based on the photons that are reaching us right now. Those photons left 13.4 billion years ago. So those photons are the photons being emitted from this primitive structure, from this white-hot haze of hydrogen plasma. So what we're going to see is this white-hot haze. So we're going to see this kind of white-hot plasma, white hot, undifferentiated not differentiated into proper stable atoms, much less stars and galaxies, but white hot. We're going to see this white-hot plasma. The reality today is that point in space that's 46 billion years from now, it's probably differentiated into stable atoms, and stars, and planets, and galaxies. And frankly, if that person, that person, if there is a civilization there right now and if they're sitting right there, and they're observing photons being emitted from our coordinate, from our point in space right now, they're not going to see us. They're going to see us 13.4 billion years ago. They're going to see the super primitive state of our region of space when it really was just a white-hot plasma. And we're going to talk more about this in the next video. But think about it. Any photon that's coming from that period in time, so from any direction, that's been traveling for 13.4 billion years from any direction, it's going to come from that primitive state or it would have been emitted when the universe was in that primitive state, when it was just that white-hot plasma, this undifferentiated mass. And hopefully, that will give you a sense of where the cosmic microwave background radiation comes from.