Is the Isotropic Universe Truly Centerless?

[curioushuman]

In an isotropic universe, every observer sees themself as being at the center. But consider 3 observers, A, B, and C who are 5 billion light years apart and all lined-up in a straight line with B at the center. B knows this to be true because A is in one direction and C is in exactly the opposite direction. This being the case, it is a physical fact that A would have to go through B to get to C. But if the universe is truly isotropic, A and C will also see themselves at the center, and as far as A and C are concerned, it would be a physical fact that A can go directly to C without passing through B. Something is clearly wrong here.

 

[kimbyd]

The universe is only isotropic on average. If it was exactly isotropic, we wouldn't have structures like galaxies.

 

[Ibix]

If the universe were completely isotropic and homogeneous there would be no way to distinguish points A, B and C from each other or any other point. Even if you simply pick points in an isotropic universe, you are imposing an anisotropic structure on it.

So your problem is that you don't have the complete isotropy you think you do.

 

[Orodruin]

The Universe is isotropic. Your assignment of three observers isn’t.

 

[Bandersnatch]

In yet another words - isotropy doesn't mean all observers see the exact same galaxies in their neighbourhood.
In the setup provided in the OP, B sees A to the immediate 'left' on the sky, and C to the immediate 'right'. Isotropy means that C sees B to the left and some other galaxy, let's call it D, to the right. D sees C and E, and so on. On average, every observer will have >a< galaxy to the left and >a< galaxy to the right.
It doesn't mean both A and B see C immediately to their right, and the order of the letters somehow switches around depending on who's looking.

 

[timmdeeg]

But if the universe is truly isotropic, A and C will also see themselves at the center, and as far as A and C are concerned, it would be a physical fact that A can go directly to C without passing through B.

Why do you think that "A can go directly to C without passing through B"?

 

[curioushuman]

Why do you think that "A can go directly to C without passing through B"?

From B's perspective, A and C are at opposite ends of a 10 billion light-year straight line with B at the center (as I set this up). From A's perspective, either: 1) A, B and C are simply not colinear, or 2) A, B and C are colinear with A at the center. The reason A would have to be at the center in (2) is that if A were not between B and C, then A would be at one end of the line and so most of the universe would be in A's direction. Clearly this violates the isotropic premise. In either case (1 or 2), B is not on a straight line between A and C, and so A could go to C without passing through B.

 

[curioushuman]

If the universe were completely isotropic and homogeneous there would be no way to distinguish points A, B and C from each other or any other point. Even if you simply pick points in an isotropic universe, you are imposing an anisotropic structure on it.

So your problem is that you don't have the complete isotropy you think you do.

But we distinguish galaxies at far flung distances and even give them names. We could substitute "galaxies" for "points" if you like. These objects are distinguishable.

 

[curioushuman]

In yet another words - isotropy doesn't mean all observers see the exact same galaxies in their neighbourhood.
In the setup provided in the OP, B sees A to the immediate 'left' on the sky, and C to the immediate 'right'. Isotropy means that C sees B to the left and some other galaxy, let's call it D, to the right. D sees C and E, and so on. On average, every observer will have >a< galaxy to the left and >a< galaxy to the right.
It doesn't mean both A and B see C immediately to their right, and the order of the letters somehow switches around depending on who's looking.

So, in my scenario, C would be unable to see A?

 

[Ibix]

But we distinguish galaxies at far flung distances and even give them names. We could substitute "galaxies" for "points" if you like. These objects are distinguishable.

Yes. The real universe is not completely isotropic.

 

[curioushuman]

Yes. The real universe is not completely isotropic.

I'm working with the premise that the real universe is completely isotropic. To what extent is it non-isotropic?

 

[Ibix]

I'm working with the premise that the real universe is completely isotropic.

Really? You didn't notice that things look different if you look up at the sky from if you look down at the ground?

To what extent is it non-isotropic?

At small scales (the scale of clusters of galaxies and below) the universe is not homogeneous or isotropic.

 

[PeterDonis]

we distinguish galaxies at far flung distances and even give them names. We could substitute "galaxies" for "points" if you like. These objects are distinguishable.

That's because, as has already been pointed out, our actual universe is not completely isotropic, or homogeneous, which is more to the point with this particular observation. ("Isotropic" means "looks the same in all directions". "Homogeneous" means "looks the same at every point". If different points are distinguishable, that, strictly speaking, means the universe is not homogeneous; if the universe looks different in different directions, then it is not isotropic.)

in my scenario, C would be unable to see A?

In your scenario, the universe is not homogeneous (points A, B, and C are distinguishable) and not isotropic (things look different along the direction of the line that A, B, and C lie on, than they do in other directions). Since B is directly between C and A, yes, unless B is transparent, A and C would be unable to see each other.

To make a situation more like the actual universe, and to see what cosmologists actually mean when they say our universe is, to a good approximation on large scales, homogeneous and isotropic, imagine that there are observers in galaxy clusters distributed in all 3 spatial directions, roughly equally spaced (a few billion light years apart), and all looking around them to see what the universe looks like. Suppose A, B, and C are three of these observers, each in their own galaxy cluster (since galaxy clusters are about the scale on which our own universe starts to be homogeneous and isotropic to a good approximation), who happen to lie roughly along a line, in the order given.

Obviously these observers can tell that the universe is not exactly homogeneous and isotropic, since each of them can distinguish their own galaxy cluster from the others, and they can distinguish the direction along the line along which the galaxy clusters of A, B, and C lie from other directions. But they do notice that the spacing of galaxy clusters, on average, is about the same everywhere and in all directions (the direction along which A, B, and C lie does not look any different on average from other directions), and that the overall nature of the galaxy clusters (size, number of galaxies in the cluster, average distribution of galaxies by size, etc.) is about the same everywhere and in all directions. So even though their particular galaxy clusters are distinguishable if you look at fine details, they are all three basically the same kind of galaxy cluster, and they are distributed in space about the same as all the other galaxy clusters. It is in that sense that our own universe is homogeneous and isotropic.

 

[curioushuman]

Really? You didn't notice that things look different if you look up at the sky from if you look down at the ground?

At small scales (the scale of clusters of galaxies and below) the universe is not homogeneous or isotropic.

I might be missing your point, but things look different because the content in my field of view is different. You could say the same about looking left and looking right. I can't draw any inferences about the nature of the universe because the two are different. It's just different content.

If at small scales (clusters of galaxies and below) the universe is not isotropic, is there a distance (some number of light years) at which that threshold occurs?

 

[PeterDonis]

I can't draw any inferences about the nature of the universe because the two are different. It's just different content.

Then why do you think the scenario in your OP is a problem for the universe being isotropic? A, B, and C are just different content, and you can't draw any inferences about the nature of the universe from them. So what's the problem?

 

[curioushuman]

That's because, as has already been pointed out, our actual universe is not completely isotropic, or homogeneous, which is more to the point with this particular observation. ("Isotropic" means "looks the same in all directions". "Homogeneous" means "looks the same at every point". If different points are distinguishable, that, strictly speaking, means the universe is not homogeneous; if the universe looks different in different directions, then it is not isotropic.)
In your scenario, the universe is not homogeneous (points A, B, and C are distinguishable) and not isotropic (things look different along the direction of the line that A, B, and C lie on, than they do in other directions). Since B is directly between C and A, yes, unless B is transparent, A and C would be unable to see each other.

To make a situation more like the actual universe, and to see what cosmologists actually mean when they say our universe is, to a good approximation on large scales, homogeneous and isotropic, imagine that there are observers in galaxy clusters distributed in all 3 spatial directions, roughly equally spaced (a few billion light years apart), and all looking around them to see what the universe looks like. Suppose A, B, and C are three of these observers, each in their own galaxy cluster (since galaxy clusters are about the scale on which our own universe starts to be homogeneous and isotropic to a good approximation), who happen to lie roughly along a line, in the order given.

Obviously these observers can tell that the universe is not exactly homogeneous and isotropic, since each of them can distinguish their own galaxy cluster from the others, and they can distinguish the direction along the line along which the galaxy clusters of A, B, and C lie from other directions. But they do notice that the spacing of galaxy clusters, on average, is about the same everywhere and in all directions (the direction along which A, B, and C lie does not look any different on average from other directions), and that the overall nature of the galaxy clusters (size, number of galaxies in the cluster, average distribution of galaxies by size, etc.) is about the same everywhere and in all directions. So even though their particular galaxy clusters are distinguishable if you look at fine details, they are all three basically the same kind of galaxy cluster, and they are distributed in space about the same as all the other galaxy clusters. It is in that sense that our own universe is homogeneous and isotropic.

Hmm, "not exactly" isotropic. "Not completely" isotropic. Isotrophy either is a feature of the universe or is not a feature of the universe.

Then why do you think the scenario in your OP is a problem for the universe being isotropic? A, B, and C are just different content, and you can't draw any inferences about the nature of the universe from them. So what's the problem?

I think we better drop it. You're missing my whole point.

 

[Bandersnatch]

Can you elaborate a bit more on what you point is? Seems like different people interpret it differently.
To me it doesn't look like anything to do with how perfect the isotropy is in the real world, and more like you've constructed a triangle out of the three points, and wonder why it's not a good representation of the universe. I mean, it can be, if the universe is closed. But it's hard to guess if that's anything related to the issue you're having.

 

[PeterDonis]

Isotrophy either is a feature of the universe or is not a feature of the universe.

By your definition, then, it is not, since it is not exactly isotropic. But nobody in cosmology actually uses that definition. When you see cosmologists say the universe is isotropic, they mean to a good approximation on large enough distance scales (roughly larger than the size of galaxy clusters, 100 million light years or so).

 

[PeterDonis]

you've constructed a triangle out of the three points

The OP scenario had the three points all along a single line, not in a triangle.

 

[PeterDonis]

In an isotropic universe, every observer sees themself as being at the center.

I'm not sure where you're getting this definition from. The usual definition of isotropic is "looks the same in all directions".

 

[Bandersnatch]

The OP scenario had the three points all along a single line, not in a triangle.

A triangle has the property that you can get from each point to any other without getting through the intermediate one, which is what the OP also includes in the setup. And that's the point of confusion as I see it - they find it paradoxical that a line is not a triangle.

 

[curioushuman]

Let me put this in a larger context.

The notion of the universe being isotropic was one of Einstein's premises that led to his discoveries about the nature of the universe. That's a pretty good reason to believe that the universe is isotropic. The fact that galaxies seem to be moving away from US at a speed proportional to their distance from us makes it seem like WE are at the center of it all. This clearly violates the isotropic premise and can, fortunately, be explained in terms of the universe expanding uniformly (the famous raisins in an expanding loaf of bread analogy). But, from this, many cosmologists (including, no less, than Neil DeGrasse Tyson whose talks I thoroughly enjoy) seem to draw the conclusion that there is no "edge" to the universe. "Edge," in their view, is an illusion just like the illusion of seeming to be at the center of the universe since all the galaxies are racing away from us.

I suspect, and I am trying to find out if it is wrong, that there is indeed an edge to the universe. I think we may have over-extended the applicability of the universe's being isotropic based on Einstein's success and on the expanding universe phenomenon. While we are too far from that edge to tell a difference, somebody somewhere probably is, and, as a result, when they look at the universe in one direction they will see something very different than when they look in the other direction. This is just conjecture, of course, but there seems to be a fundamental, logical contradiction in the idea of a robust isotropism of the type most cosmologists believe to be true. I think the ABC straight line thought experiment I laid out gets to the nub of that contradiction.

 

[PeterDonis]

The notion of the universe being isotropic was one of Einstein's premises that led to his discoveries about the nature of the universe.

It wasn't just Einstein, everybody was making that assumption. I'm also not sure which discoveries of Einstein you are referring to. The people who really translated the isotropy assumption (and the homogeneity assumption) into a model of the universe using GR were Friedmann, Lemaitre, Robertson, and Walker (which is why that spacetime geometry is named after them). Einstein's main contribution to cosmological models was his static universe, which turned out to be wrong as a model of our universe.

The fact that galaxies seem to be moving away from US at a speed proportional to their distance from us makes it seem like WE are at the center of it all. This clearly violates the isotropic premise and can, fortunately, be explained in terms of the universe expanding uniformly

Yes, that was the main breakthrough of the FLRW spacetime model.

from this, many cosmologists (including, no less, than Neil DeGrasse Tyson whose talks I thoroughly enjoy) seem to draw the conclusion that there is no "edge" to the universe

That is a feature of the FLRW models, yes--they are all either spatially infinite or have the spatial geometry of a 3-sphere; in either case there is no edge. But that is not a consequence of the isotropy assumption but of the homogeneity assumption--that all points in the universe are the same, at least in terms of spacetime geometry. An "edge" would obviously violate that. But a universe with an "edge" could still be isotropic if you were at the center of it (i.e., at the same distance from the edge in all directions).

"Edge," in their view, is an illusion

I'm not sure why anyone would say this. We have no observational evidence of an "edge" to the universe, so there is nothing that could possibly be an illusion of any such thing.

I suspect, and I am trying to find out if it is wrong, that there is indeed an edge to the universe.

Then this whole thread has been a waste of time, since (a) your original post gave no hint of this and the scenario you posed there has nothing to do with this, and (b) we have neither observational evidence for an edge nor theoretical evidence (nobody has a viable universe model that has an edge), so the simple answer is no, there isn't. Any opinion on your part that there is is personal speculation and is off limits in this forum.

there seems to be a fundamental, logical contradiction in the idea of a robust isotropism of the type most cosmologists believe to be true.

There is no such thing. You simply do not have a correct understanding of the isotropy assumption as it is actually made and used in our cosmological models.

I think the ABC straight line thought experiment I laid out gets to the nub of that contradiction.

Your thought experiment does not say anything whatever about whether or not there is an edge to the universe. Nor does it have anything to do with either isotropy or homogeneity as those assumptions are used in our actual models of the universe. No model used in cosmology assumes either exact homogeneity or exact isotropy, and the approximate homogeneity and isotropy that the models do assume is quite sufficient to ground the conclusions based on those models, including the conclusion that our best current models and evidence indicate that the universe has no edge.

 

[PeterDonis]

This thread is now closed since every substantive point raised has been answered.