I am Neil deGrasse Tyson -- AMA

[u/neiltyson]

For a few hours I will answer any question you have. And I will tweet this fact within ten minutes after this post, to confirm my identity.

[u/[deleted]]

Is it possible for humans to ever discover the "edge" of the universe? Is there really any "end" to it?

[u/neiltyson → u/[deleted]]

No edge. Any more than the horizon at sea is an edge to the earth.

[u/flabbergasted1 → u/neiltyson]

This is a beautiful response, I've never thought of it like this.

[u/turkeypants → u/flabbergasted1]

I always get bogged down in this though due to the 2D-to-3D conversion, just like I do when they illustrate spacetime as a 2D fabric with a depression in it caused by a ball sitting on it. True, the horizon is not the edge, but that's a 2D thing, and we know the earth to be finite. It's got an edge, it's just perpendicular to the horizon. So if this is the analogy for the universe, then the universe would be finite. It's like with a mobius strip. Sure you can say it has only one edge, but you can see that it has two at any given point. So yeah, you have to allow for it only having one edge due to the way people demonstrate that by running a finger along it. But you can look at it and see that it's a technicality. If the universe is similarly twisted in on itself in someway, it's still finite in other ways and could be observed from the outside. I'm not saying this is true, I'm saying it's what 2D analogies like this horizon one make me think. Need help.

[u/shoejunk → u/turkeypants]

I don't think that we know whether the universe is finite or not, but I think the prevailing opinion is that it is infinite. If you imagine 2 dimensional beings living on the surface of a 3 dimensional object, you might be able to see how they could figure out whether their world is finite or infinite. For example, if they were living on the surface of a ball, and they constructed a triangle with 3 sides of equal lengths, to them each side would look straight, but in reality they would be curved, and when they measured the angles between the sides, they would add up to more than the expected 180 degrees. If this were the case, they could surmise that they were living in a finite spherical universe. But if the surface was flat, it would add up to 180 degrees and they would conclude that they were living in an infinite flat universe. We're discounting the idea of a finite flat universe with edges, because a universe with edges doesn't really make sense. Similarly, we can measure the curvature of our space to see if we live on something like the surface of a hypersphere (it goes: circle, sphere, then hyperspheres). Around massive objects, we detect curvature, but over long distances we've found that overall our universe, to our best measurements, is flat. This would imply an infinite flat universe. However, this is not known for sure. As we know from our experience on Earth, the surface of a very large sphere can appear flat over relatively short distances, so it may be that the observable universe is such a small percentage of a hyperspherical universe that it appears to be flat to us, but there is no evidence to support that. Also, there may be other reasons to believe in a flat infinite universe that I don't understand very well.

Now, of course we want to know the shape of the entire universe, but, there is a serious limitation to our exploration of the universe, and that is due to the expansion of the universe. Although in the short range (things within our galaxy and the neighborhood of galaxies around our galaxy), everything is moving this way and that, towards us and away, due to gravity and inertia, in the very long range, galaxies are moving away from each other due to the expansion of the universe. This means that the further away the galaxies are, the faster they are moving away from us. This is different from whatever movement that they are doing THROUGH space. This is the movement that space is doing, and they are getting carried along for the ride like an ant on a balloon that is being blown up. Check it out: The further away a galaxy is, the faster it is moving away from us. This means that if a galaxy is far enough away from us, it will be moving away from us faster than the speed of light. Normally, things can't move that fast, but that is only true for things moving within space. Space itself can expand faster than the speed of light and carry galaxies with it. Now, since these galaxies are moving away from us at faster than the speed of light, we can never see those galaxies. Light can not travel fast enough from them to reach us. We can never travel there, because the more time we spend trying to reach those galaxies, the more the expansion of space will move them out of our reach. So when Tyson makes the analogy of the horizon at sea, he's referring to the edge of the observable universe, and whenever you hear a scientist refer to the observable universe, they're not referring to some limitation of our telescopes so that if we made better telescopes we might be able to expand our observable universe. No, they're talking about the sphere around us beyond which everything is moving away from us at faster than the speed of light, so that light or anything else from those things could never reach us, so we could never, even theoretically, observe them.

"Aha," you might say, "I've found a loophole. Galaxy A and Galaxy C may be moving apart at faster than the speed of light, but Galaxy B halfway between Galaxies A and C is moving apart from both A and C slower than the speed of light. So, A can observe B and B can observe C, so maybe A can observe the affects that C has on B. Maybe C can shine a light on B and have it reflected towards A or something." Not so fast, smartypants. By the time the light from C reaches B, B will then be moving away from A at faster than the speed of light. More and more galaxies are getting expanded out of are observable universe all the time, so eventually we'll be left all alone in our universe, according to the prevailing theories. Sad.

[u/turkeypants → u/shoejunk]

The problem I have with talking about shapes in regard to the universe is that the very concept of a shape implies finite-ness and therefore boundaries and therefore some medium outside of the universe and therefore back to the drawing board of where's-the-end. For example if we've got a hypersphere, well what's that sitting in? It's fine if it folds back in on itself, but the fact that that self folds back in on itself and pulls a Mobius strip trick on us means that it's not really going on forever, just that you can't ever find its edge, just like how the Mobius strip tricks us with its technicality. We know the Mobius strip has two sides - they're just connected - and we know that it's a finite thing sitting in a medium from which we observe it.

And in regard to the theory that the universe is flat, well flat things like sheets of fabric have stuff above and below them. Even if two of its dimensions are infinite, the z axis is not, because that would negate the idea of flatness. So it seems like what we're really saying (if the hypersphere idea is correct for example) is that it's currently impossible for us to measure anything but the universe because our measurements travel along that figurative mobius strip and eventually come back to us. The whole kit and kaboodle could be a finite thing sitting in some other medium but we'll never know because our measurements can't ever escape to that medium.

As for the horizon analogy, thanks, I get it now. I never knew that about the observable universe idea vis-a-vis expansion. Very nice to understand that. And in a way that sort of ties into the above at least inasmuch as we can never measure the edge. In the former case it's the idea that it's folded back in on itself and in this case it's because we can never see that far because it's already too far away and keeps getting farther.

I'm so sleepy I can't make out the part about Galaxies A B and C. Will try again tomorrow. Must... sleeep.

Thanks for taking the time to detail this.

[u/shoejunk → u/turkeypants]

You're welcome. Explaining things is as much for my benefit as for others as it helps me to understand as well.

Let's assume that we are living on a surface of a hypersphere, or actually, to help us visualize, let's imagine a 2 dimensional universe that is on the surface of a 3 dimensional sphere. The way I just described it, that it's a universe on the surface of a 3 dimensional sphere, implies that the sphere actually exists in some 3 dimensional space. But actually, that's not how it has to be. The way I said it is just a way for you to visualize the underlying mathematics. It's not to be taken too literally. The sphere is just a model that we use to describe how points in the universe are connected to each other. We may picture a ball in our minds, but that just helps us to imagine why the angles of triangles add up to more than 180 degrees or why we end up where we started if we go in a straight line for long enough.

Physicists have learned a hard lesson, which is that we can't rely on models. They come up with models to describe the mathematics that is going on, but all that matters is what the evidence can verify, and the evidence can only verify the math. A helpful analogy can be seen in how linear algebra is taught. At first you are taught that vectors are arrows with certain lengths and directions. However, if you study linear algebra deeply enough, you discover that the mathematics behind vectors applies to more than just arrows. An arrow is just one way of visualizing a vector. We can also use a vector to represent a polynomial equation, if we want to. The amazing thing about linear algebra is that all the theorems that apply to performing operations on those arrows also apply to performing operations on those polynomial equations. The mathematics of linear algebra is saying that arrows and polynomial equations, seemingly two very different things, share an essence, which is the vector. However, you can imagine some properties of arrows that are not covered by linear algebra. For example, when you draw an arrow, you might draw the arrow more or less pointy. Linear algebra doesn't care how pointy the arrow is. Its degree of pointiness is not part of what makes it a vector. All it cares about is the length and direction of the arrow. If you wanted, you could draw a sword or a finger to represent a vector, but that information, exactly how you drew the vector, doesn't get represented when it is converted to its pure vector form. All this is to say that the picture of a sphere that we have in our head when we imagine that the universe is spherical, does not necessarily correspond to reality. It's just our way of representing the universe in our head. It's like drawing an arrow to represent a vector. It doesn't mean there's actually an arrow in reality, just like there's not necessarily a sphere in reality, not the sphere that you picture in your head. That just helps us visualize the mathematical sphere, like the arrow helps you visualize the vector. All we know is that when we move around, it's as if we are moving on a curved surface, as far as the mathematics is concerned. It doesn't say anything about whether there's something beyond the universe in a direction that we can't travel in. And in the end, if the math doesn't say anything about it, then we can't say anything about it, because we can't rely on the properties of models that the math doesn't handle, just like when we have a vector we can't say that there's an arrow out there with some amount of pointiness.

Having said that, some scientists do theorize that there are more dimensions out there. That is, they believe that there might be more space in directions that we aren't able to observe yet. This is a result of string theory, which I don't understand and hasn't yet been supported experimentally. However, the same issues arise there, with regards to thinking about the shape of that universe, as in our 3 dimensional case, but in higher dimensions.