What if dimensions have different sizes and expand at different rates?

[Nacho]

I may look at it wrong, but when I think of a Black Hole, I think of the 3 spatial dimensions we know of compacting to a point, rather than space folding back on itself (I guess it could be just semantics though).

And when you think of a singularity, I think it is inherent in that process you assume that all of the spatial dimensions compact at the same rate, so that it does compact symetrically down to a point.

For what good reason do we assume that? Why can't each of the 3 spatial dimensions be of a different size, and each be expanding at different rates? If they were of different size, even microscopically (on our scale) to where we couldn't tell the difference, they wouldn't necessarily come to a point, or come back to the Planck size at the same point in time.

Can't singularities be avoided that way?

 

[rayjohn01]

I do not know the exact answer but singularities are present in the black hole mathematical solutions in General relativity which is NOT simply 3 dimensional and therefore hard if not impossible to imagine.
I ,like you I think, do not like this and prefer to believe that something is being missed for instance quantum gravity for which at present there is no adequate theory.

 

[Nacho]

rayjohn01,

I only know of quantum gravity by the popular books and articles I read, not much. That's why I brought the question to the big boys here!

But I'd expect GR to have in it's formulas some (a lot of?) ^3 terms. That to me would mean it expects some of its coordinates to be truly spherical. If those terms actually represent dimensions, why do we assume each are of the exact same extent?

You wouldn't so much as need quantum effects to avoid singularities, just that the different dimension don't come together at the same time. But, quantum effects might actually be the reason they wouldn't be of the same extent to begin with (that is, when expansion started)?

 

[Chronos]

There is another way to avoid singularities. Quantum theory places a theoretical density limit of about 10^94 gm/cc. If so, all black holes will have a finite, albeit tiny, physical size. To put this in perspective, a black hole with the mass of the observable universe would occupy a volume of roughly 10^-40 cc.

http://www.astronomycafe.net/qadir/q1502.html

 

[Tom D]

Now that's very interesting idea.

 

[turbo]

What if black holes are not simple one-way mass-dumps? What if they have a characteristic (out of our perceivable universe) that allows their event horizons (in our universe) to shrink under some circumstances? What would they look like? Would they be able to re-emit mass back into our universe? Would they be really luminous?

 

[Nacho]

Chronos,

There is another way to avoid singularities. Quantum theory places a theoretical density limit of about 10^94 gm/cc. If so, all black holes will have a finite, albeit tiny, physical size. To put this in perspective, a black hole with the mass of the observable universe would occupy a volume of roughly 10^-40 cc.

Here's what confuses me in that description. Are they saying it's only a matter of density within space, or that space itself (at least around that object) is compacted down to that size? Or the other small "string" dimensions are compacted down further to that size? Or something entirely different??

 

[Chronos]

Chronos,

Here's what confuses me in that description. Are they saying it's only a matter of density within space, or that space itself (at least around that object) is compacted down to that size? Or the other small "string" dimensions are compacted down further to that size? Or something entirely different??

Yes. There is a limit to how much matter [or energy] will fit into a fixed volume of space. This means a black hole has a non-zero size which avoids the problem of having a mathematical infinity [singularity]. Space in the vicinity of the black hole is greatly curved, but the curvature still finite so long as the size of the black hole is finite.

 

[Stingray]

Nacho,
I think you're asking why a singularity should form in an asymmetrical collapse (?). Intuitively, it would almost seem as though it couldn't, and that's what people thought for a long time. It has now been proven, though, that singularities are unavoidable in a very large range of systems. This is classical GR, and quantum theory is separate issue.

Many people think that quantum gravity will remove the singularities, but this has yet to be seen. There will certainly be some major change in our understanding at the scales Chronos mentioned. That scale does not give a maximum density allowed by quantum theory. Its just a point (arrived at just by dimensional analysis) where we can confidently say we have no idea what's going on anymore.

 

[Chronos]

Nacho,
I think you're asking why a singularity should form in an asymmetrical collapse (?). Intuitively, it would almost seem as though it couldn't, and that's what people thought for a long time. It has now been proven, though, that singularities are unavoidable in a very large range of systems. This is classical GR, and quantum theory is separate issue.

Many people think that quantum gravity will remove the singularities, but this has yet to be seen. There will certainly be some major change in our understanding at the scales Chronos mentioned. That scale does not give a maximum density allowed by quantum theory. Its just a point (arrived at just by dimensional analysis) where we can confidently say we have no idea what's going on anymore.

Agreed.

1. I'm not sure how or if you could distinguish symmetry from asymmetry in the topology of space surrounding black hole. It is so mangled no telling what kind of geometry would be it's equivalent in 'normal' space. I suspect, however, it must be symmetric at some level. It might be necessary to appeal to higher order dimensions to find this supposed symmetry. I find that distasteful, but, possible. I really don't like needing extra and unobservable dimension to explain things. Hard enough to do the math in 4 dimensions.

2. Quantum theory suggests the Planck density may be an actual limiting feature of the universe [which would be a relief to the many who don't know what to do when infinities rear their ugly heads in the equations]. It may also simply be the point where our math breaks down. A workable quantum gravity theory should, but, may not entirely solve the singularity problem. I favor letting the chips fall where they may and assume the physical and mathematical limits of the universe are concordant. It is a simple approach and puts the burden of matching observation with mathematical solutions upon the 'prosecution' [I'm lazy].

 

[Stingray]

1. I'm not sure how or if you could distinguish symmetry from asymmetry in the topology of space surrounding black hole. It is so mangled no telling what kind of geometry would be it's equivalent in 'normal' space. I suspect, however, it must be symmetric at some level. It might be necessary to appeal to higher order dimensions to find this supposed symmetry. I find that distasteful, but, possible. I really don't like needing extra and unobservable dimension to explain things. Hard enough to do the math in 4 dimensions.

Spherical and axial symmetries are both well-defined even in curved spacetime. It can be shown that stars that aren't axisymmetric will still collapse into singularities.

 

[Nacho]

Stingray,

Nacho,
I think you're asking why a singularity should form in an asymmetrical collapse (?). Intuitively, it would almost seem as though it couldn't, and that's what people thought for a long time. It has now been proven, though, that singularities are unavoidable in a very large range of systems. This is classical GR, and quantum theory is separate issue.

No, that is not what I'm asking. I know that stuff, from reading Kip Thorne's book, that an asymetrical mass should collapse to a symetrical BH, GR being the only consideration.

GR predicts singularites, but a lot of persons see that as a failing of GR. And they try to get rid of it by bringing in quantum effects, like what Chronos posted.

That stuff I know -- or at least I've read before, if not fully understood it.

What I'm asking about here is something entirely different, but it still may be a way out of GR predicting singularities.

I'm saying (asking really), that the equations of GR assume that all of our observable 3 spatial dimensions are of equal size, and I think we generally assume that to be the case on all scales of the Universe, from quantum to the very large. That there is no difference in anyone of those 3 spatial dimensions.

I'm asking, "Why do we assume that? Is there a good reason or basis for assuming it?". I don't of any reason. If there is no reason for assuming it, then isn't it equally likely any or all of those 3 spatial dimension are of unequal extent? (and even going a little further, for people who like string theory .. the small curled up dimensions .. is there a reason to believe/assume all of those dimensions are of the same extent, or symetrical?).

Then, if GR could be developed with that in mind, that the spatial dimensions could be of different extent, might that not do away with singularities?

I had a picture in my mind that when a BH forms, that the mass contained in a BH was compressed to very high density, but also that the space containing that mass was compressed. Compressed here meaning the exact opposite of expansion of space. And that when those 3 separate dimensions are compressed down towards the Planck size, that they wouldn't meet together, avoiding a singularity. Note that I not talking about the mass contained in the BH compressing asymetrically, but space itself collapsing asymetrically because it could have been asymetrical to begin with.

Chronos corrected my thinking somewhat by posting that the mass is what collapses, and that space is warped (as apposed to collapsed). But I'm not so sure on that now. If there would have been a singularity, doesn't that suggest matter and space compressed to a point size?

So, my questions are:

1) For what (good) reason does GR assume our spatial dimension are of equal size?

2) And if they are not, would that avoid a singularity when a BH developes?

 

[Stingray]

Chronos corrected my thinking somewhat by posting that the mass is what collapses, and that space is warped (as apposed to collapsed). But I'm not so sure on that now. If there would have been a singularity, doesn't that suggest matter and space compressed to a point size?

So, my questions are:

1) For what (good) reason does GR assume our spatial dimension are of equal size?

2) And if they are not, would that avoid a singularity when a BH developes?

Chronos is right. Space is not compressed to a point size because the rest of the universe still exists. I can't figure out any other meaning for what you said. I don't know what it would mean to say the spatial dimensions are different sizes.

You could talk about some kind of compactification like they do in string theory, but our normal 3 dimensions must not be very compact at all for the world to look like it does. I don't think anything would be affected.

 

[Nacho]

Stingray,

Chronos is right. Space is not compressed to a point size because the rest of the universe still exists. I can't figure out any other meaning for what you said. I don't know what it would mean to say the spatial dimensions are different sizes.

I don't mean "all of space", just space in/around/close to the BH.

I don't know what it would mean to say the spatial dimensions are different sizes.

Imagine an equalateral triangle, then think of the differences if that triangle had all sides unequal. It's hard to extend that to the 3 spatial dimensions of space, because "volume" gets in the way, just like it gets in the way when trying to explain to someone how the Universe has expanded since the BB.


Space was in a sense "compacted" at one time, the BB. It has expanded since, and I'm talking about the opposite of expansion. I guess the question becomes can a portion of space become compacted. I agree though now that that would not be the same as the warping of space around a BH.

 

[Stingray]

What you're describing with compacting space is the right idea for a singularity. But then I think this reduces to what I said before.

Matter and spacetime are completely coupled. An asymmetric collapse (of matter) implies that spacetime is also "collapsing" asymmetrically. You can't separate one from the other. The result is still that it doesn't matter in the end. Enough of the asymmetry gets radiated away.

Sorry if I'm still not getting it.

 

[Nacho]

Stingray,

I'm probably not stating it very well. But I'll try one more time! ;)

Forget about the dimensions and/or matter collapsing to a BH, and instead consider the Universe, very large dimensions. And we're going to assume the Universe is finite and unbounded, so that if you start out in 1 direction and kept going you'd finally come back to the point where you started.

At that point in space take three different directions, all perpendicular to each other, like the x,y,t (or z) axis of a three dimensional coordinate system. Send 3 guys out now, one on each of those 3 axis. When they have traveled around the Universe back to the origin point, would they have traveled the exact same distance, and thus all 3 dimension being the exact same extent?

I think we always assume that the answer is "Yes". My question is "Is there reason to assume it Yes?"

I had said I couldn't think of a reason for it being yes, but I think I remember one now. One of the assumptions the physicists make of the Universe is that "no matter where you are in the Universe and no matter where you look, it all looks the same". That could be taken to say the dimensions of the Universe are symetrical. The question is, is there good reason for that assumption.

[edit -- wrote "bounded" when I meant "unbounded"]

 

[Richard Harris]

one could assume that they assumed it, to make the calculations easy.

one could also assume that from the point of expansion, equal force was applied to each part of matter.

One could also point out, that with such a uniform application of force, all matter should be evenly distributed, in otherwords, there would be no large Groupings of matter in any stage of the universes existence.

 

[Nacho]

Richard Harris,

Well put .. I hadn't considered that the uneven distribution of matter on the scale that we can see could point to an asymetrical expansion of space. If so, wouldn't it have to be asymetrical on all scales greater than the least scale we see it asymetrical (over the asymetries caused by gravitation)?

 

[Chronos]

Under current descriptions of space time, force acts equally in all spatial dimensions. If you add a preferred [unequal] value to any dimension in space time, huge complications arise. GR did away with preferred refence frames and it works well [matches observation]. A simple example: if there was a preferred dimensional frame of direction, would not a free-floating gyroscope tend to move axially to align itself in the direction of least resistance?

 

[Richard Harris]

I'm gona google around a bit, being new here (random link and such) and not even holding highscool qualification worth anything, I have almost no idea of what's being discussed and from what basis or background theorys.

i was semi expecting to be shot down in flames :p

 

[LURCH]

In regard to the original question, I do not think that asymmetrical geometries of different dimensions would prevent a singularity. Is different dimensions collapse at different rates, then perhaps they do not all arrive at the point of singularity simultaneously, but they should still all arrive, eventually. Don't you think?

However, I think the one thing that does (seem to) prevent singularity is that the Center of black hole is, ironically, a prediction arising strictly from general relativity itself. That being the phenomenon of gravitationally-induced time dilation. As time gets slower and slower in the center of a black hole, so the collapse of the original masse must take place more and more slowly. The final moments of collapse should, theoretically, take forever.

 

[Stingray]

The most common models would have all three explorers travel the same distance. There is a lot of astronomical evidence that the universe is nearly homogeneous on large scales, so spacetime must also be homogeneous in an appropriate sense.

Realistically, there are deviations from perfect smoothness, and these can be incorporated into the models without any problems.

There are also models which explicitly allow large asymmetries, although these are pretty much all ruled out by observation now.

In any case, you get a big bang singularity whether there's symmetry or not. I think it was Hawking who first proved that it happens under very general circumstances.