A question on the geometry of black holes

[Cerenkov]

No, that's not what I said. What I said is that our observable universe, in the limit as you go to the initial singularity, shrinks to a point. So does any finite-sized region of our universe.

I did not say that that point is somehow a "different" singularity from the initial singularity, or that each different finite region of our universe has its own singularity. Neither of those things are true. There is one initial singularity, and any finite-sized region will shrink to a point as that one initial singularity is approached.

Since the initial singularity is a spacelike line, it can of course also be considered as a continuum of points. If you want a heuristic for what those points "correspond" to in the universe proper, each such point represents a different comoving observer. But that doesn't mean each comoving observer has their own point-sized singularity: it means that each comoving observer corresponds to a point on the one spacelike line that is the one initial singularity.

Ah... now I might be getting it.

Are you saying that any finite volume of our universe will have an initial singularity which is point-like, but the entire volume of the universe (if it were possible to speak in those terms) will possess a spacelike line for the initial singularity?

That a point-like singularity is necessarily generated by the boundary of the finite volume?

Something like that?

 

[PeterDonis]

Are you saying that any finite volume of our universe will have an initial singularity which is point-like, but the entire volume of the universe (if it were possible to speak in those terms) will possess a spacelike line for the initial singularity?

That a point-like singularity is necessarily generated by the boundary of the finite volume?

No. Please read my posts #26 and #30.

 

[Cerenkov]

Better said, any observer can only see a point on the singularity, not the whole extent of it. (Note: it's only possible to see any of the singularity in principle - the universeis opaque that far back.)

Yes, forgive my loose usage of the word 'see'.

I'm aware that 'seeing' through the opaque plasma of the very early universe is not possible.

 

[Ibix]

Yes, forgive my loose usage of the word 'see'.

I'm aware that 'seeing' through the opaque plasma of the very early universe is not possible.

You're still seem to be missing the point, though. In this context there's nothing special about the singularity. The universe is currently infinite, and my observable universe is a patch of it, and yours is a very slightly different patch of it. Some alien trillions of light years away will also have a region of space to call its observable universe now, one which is completely disjoint from ours. The same was true yesterday (although all our observable universes were a bit smaller) and the day before and the day before, all the way back to the singularity. There is one singularity (which is a 3d spacelike surface, or at least the limit of it), we just have different parts of it "behind" us.

 

[Cerenkov]

No. Please read my posts #26 and #30.

Hmmm... to properly understand what you meant in those two posts I'd first have to understand what proper distance and comoving distance are and how they relate to one another.

Which I don't.

So, I'm sorry to say that for all the accuracy of your replies, they are as opaque to me as the plasma-filled early universe.

As I alluded to in post # 17, diagrams are useful for those who cannot do the math. But the Davis & Lineweaver diagrams which are often referred to in discussions like this are just as opaque to me too.

So, perhaps this discussion can go no further?

You can't explain to me what I'd like to know without using terms and diagrams that I can't understand and I can't understand the concepts involved without being able to understand those terms and the diagrams?

Is that a fair summary of where we are?

 

[Cerenkov]

You're still seem to be missing the point, though. In this context there's nothing special about the singularity. The universe is currently infinite, and my observable universe is a patch of it, and yours is a very slightly different patch of it. Some alien trillions of light years away will also have a region of space to call its observable universe now, one which is completely disjoint from ours. The same was true yesterday (although all our observable universes were a but smaller) and the day before and the day before, all the way back to the singularity. There is one singularity (which is a 3d spacelike surface, or at least the limit of it), we just have different parts of it in "behind" us.

That's helpful... I think.

Couldn't the blue line that I placed at the extreme left hand edge of the modified diagram be considered as just such a surface?

Each observer sees their own part of it as a point-like singularity, but it extends infinitely up and down along the vertical axis of the modified diagram.

Doesn't that satisfy the conditions of what you've just written?

 

[Cerenkov]

It's late here and I must log off.

But I thank you both for your patience and perseverance.

Until tomorrow.

 

[Ibix]

Couldn't the blue line that I placed at the extreme left hand edge of the modified diagram be considered as just such a surface?

I think your wording is a bit off if you are meaning the same as what we're saying.

Each observer sees their own part of it as a point-like singularity, but it extends infinitely up and down along the vertical axis of the modified diagram.

I don't think it's a good idea to say they see a point-like singularity, because the case can be made that they see a finite region of it (although it has zero size in some senses - singularities are not well behaved entities by definition). If you dropped "as a point-like singularity" from the bit I've quoted, I'd agree. Note that the big bang singularity is 3d (caveats about not actually being part of spacetime, so formally you need to consider the limits etc, apply), unlike the black hole singularity which is 1d.

It's late here

Likewise,but it's really hot so I'm awake and talking physics. I should try to sleep, I suppose...

 

[PeterDonis]

I'd first have to understand what proper distance and comoving distance are and how they relate to one another.

Which I don't.

The diagrams in Davis & Lineweaver show the difference. In terms of comoving distance, any two comoving observers are a constant distance apart. By convention, that distance is the proper distance between them "now". So a comoving observer that is just at our particle horizon "now" (i.e., at the edge of the funnel in the funnel diagram, if the funnel is centered on us) is about 46 billion light-years away from us in comoving distance. But unlike proper distance, that comoving distance stays constant--so as you move into the past, that comoving observer gets closer to us in terms of proper distance, but stays the same comoving distance away.

So comoving distance can be used as a measure of "distance" along the initial singularity: each point of the singularity corresponds to a different comoving observer. That's what the middle and bottom diagrams of Figure 1 in Davis & Lineweaver show. The comoving observers have worldlines that are vertical in those diagrams: each one stays at "the same point in space" in terms of comoving distance.

 

[PeroK]

It's late here and I must log off.

But I thank you both for your patience and perseverance.

Until tomorrow.

A singularity is where the mathematical model breaks down. The observable universe can't have expanded from a point in a physically meaningful way.

You can, however, mathematically map a finite volume to a point. And that may or may not make sense physically. But, that mapping has no inverse. So, in a sense it's not physically reversible.

Even if you work back to a point, there's no way to work forwards from a point. That's a singularity.