Saturday, September 25, 2021

Where did the Big Bang happen?

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

The universe started with a Big Bang and it’s expanded ever since. You probably know this. You probably also know that the universe doesn’t have a center. But where did the big bang happen, if not in the center of the universe? And if the universe expands, doesn’t that mean that matter on the average doesn’t move, contrary to what Einstein said, that absolute rest doesn’t exist? I get these questions a lot. And at the end of this video, you’ll know the answers.

First of all, what’s the Big Bang? The Big Bang, The Big Bang is what you get if you take Einstein’s equations and extrapolate the present state of the universe back in time. The universe presently expands, so if you go back in time it contracts, and the matter in it becomes more and more compressed. The equations say that when you’ve gone back about thirteen point seven billion years you run into a singularity at which the density of matter must have been infinitely large. This moment is what we call the “Big Bang”.

There are two warnings I have to add when it comes to the “Big Bang”. First, I don’t know anybody who actually believes that this singularity is physically real. It probably just means that Einstein’s equations break down and must be replaced by something else. For this reason, physicists use the term “Big Bang” to refer to whatever it is that replaces the singularity to within a Planck time or so. A Planck time is about ten to the minus forty-four seconds.

Second, we don’t actually know that this extrapolation all the way back to the Big Bang is correct because we have no observations dating back to before roughly the creation of atomic nuclei. It could be that Einstein’s equations actually aren’t the right ones for the very early universe. So instead of a Big Bang it could also be that an earlier universe collapsed and then expanded again which is called a Big Bounce. Or there could have been an infinitely long time in which not much happened after which expansion suddenly began. That would also look much like a big bang. We just don’t know which one’s right. The “Big Bang” is just the simplest scenario you get when you naively extrapolate the equations back in time.

But if the Big Bang did happen, where did it happen? It seems that if the universe expands, it must have come out of some place, right? Well, no. Like so many popular science confusions, this one is created by the attempt to visualize what can’t be visualized.

To begin with, as I explained in an earlier video, the universe doesn’t expand into anything. So the image of an inflating balloon is very misleading. When we say that the universe expands, we’re talking about what happens inside the universe.

Therefore, that the universe expands is not a statement about the size of the universe as a whole. That wouldn’t make sense because in Einstein’s theory, the universe is infinitely large. It is infinitely large now and has always been infinitely large. That the universe expands means that the distances between locations in the universe increase. And that can happen even though the size is infinite.

Suppose you have an elastic strap with buttons on it, and imagine the strap is space and the buttons are galaxy clusters. If you stretch the strap, the distances between the buttons increase. That’s what it means for the universe to expand. It’s the intergalactic space that expands. Now just imagine the strap is 3-dimensional and infinitely large.

Okay, easier said than done, I know, but this is how the mathematics works. If you go back in time to the Big Bang, all distances, areas, and volumes go to zero. But this happens at every point in space. And the size of the universe is still infinite. How can the size of the universe possibly be infinite if all distances go to zero? Well, have a look at this line. That’s a stretch of the real numbers from zero to 1. That’s a set of infinitely many points, each of which has size zero. And yet the line doesn’t have length zero. Infinity is weird. If you add up infinitely many zeros you can get anything, including infinity. I talked more about infinity in an earlier video.

But in all honesty, I also find it somewhat hard to interpret the Big Bang in terms of distances. That’s why I prefer to think of it as the moment when the density of matter in the universe goes to infinity – everywhere.

But wait, didn’t you hear someone say that the universe was the size of a grapefruit at the Big Bang? They were referring only to the part of the universe that we can see today. The part that we can see has a finite size because light had only those 13.7 billion years to travel, so anything farther away from us than that, we can’t see it. We are in the middle of the part we can see just because light travels the same in all directions. The mass in the visible part of the universe is finite. And, yes, if there really was a Big Bang then all that mass was once compressed into a volume similar to that of a grapefruit or really whatever fruit you want. But the Big Bang still happened everywhere in that grapefruit.

Okay, but that brings up another problem. If the universe expands the same everywhere, then doesn’t this define a frame of absolute rest. Think back of that elastic band again. If you sit on one of the buttons, then you move “with the expansion of the universe” in some sense. It seems fair to say that this would correspond to zero velocity. But didn’t Einstein say that velocities are relative, and that you’re not supposed to talk about absolute velocities. I mean, that’s why it’s called “relativity” right? Well, yes and no.

If you remember, Einstein really had two theories, first special relativity and then general relativity. Special relativity is the theory in which there is no such thing as absolute rest and you can only talk about relative velocities. But this theory does not contain gravity, which Einstein described as the curvature of space and time. If you want to describe gravity and the expansion of the universe, then you need to use general relativity.

In general relativity, matter, or all kinds of energy really, affect the geometry of space and time. And so, in the presence of matter the universe indeed gets a preferred direction of expansion. And you can be in rest with the universe. This state of rest is usually called the “co-moving frame”, so that’s the reference frame that moves with the universe. This doesn’t disagree with Einstein at all.

What is the co-moving frame of the universe? It’s normally assumed to be the same as the rest frame of the cosmic microwave background, or at least very similar to it. So what you can do is you measure the radiation of the cosmic microwave background that is coming at us from all directions. If we were in rest with the cosmic microwave background, the energy in that radiation should be the same in all directions. This isn’t the case though, instead we see that the radiation has somewhat more energy in one particular direction and less energy in the exact opposite direction. This can be attributed to our motion through the restframe of the universe.

How fast do we move? Well, we move in many ways, because the earth is spinning and orbiting around the sun which is orbiting around the center of the milky way. So really our direction constantly changes. But the Milky Way itself moves at about 630 kilometers per second relative to the cosmic microwave background. That’s about a million miles per hour. Where are we going? We’re moving towards something called “the great attractor” and no one has any idea what that is or why we’re going there.

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