Dimensions: Emergent from the Big Bang?

[Eric Singer]

If we accept the concept that the universe began as a zero-dimensional point, wouldn't that imply that our 3+1 dimensions, or 9+1 / 10+1 dimensions of string theory, emerged at the moment of the Big Bang or some presumably Planck-order time after? Are there any theories on this?

 

[PeterDonis]

If we accept the concept that the universe began as a zero-dimensional point

Then we are contradicting the actual model that cosmologists use, which does not say this. The "initial singularity" is not actually part of spacetime. Every spacelike 3-surface of constant cosmological time in the actual model is just that, a 3-surface, i.e., 3-dimensional.

 

[PeterDonis]

Are there any theories

There are speculations in quantum gravity that spacetime, however many dimensions it has (i.e., whether we're just talking about the 4-dimensional spacetime of standard GR or the 10 or 11-dimensional spacetimes of string theory models), is emergent from some different underlying structure at the Planck scale. However, in these speculative models, the emergence is everywhere; it is not that spacetime "came out of" the Big Bang, but that spacetime everywhere is emergent in this sense.

In any case, these are just speculations, with no way to usefully test them now or in the foreseeable future.

 

[Eric Singer]

Then we are contradicting the actual model that cosmologists use, which does not say this. The "initial singularity" is not actually part of spacetime. Every spacelike 3-surface of constant cosmological time in the actual model is just that, a 3-surface, i.e., 3-dimensional.

Maybe I'm drawing an inference here that doesn't exist - that we started at zero-D and added four. I understand conceptually that the notions of time and space did not exist before the BB. Am I trying to geometrically connect a singularity to a multidimensional space?

Popular descriptions of the Big Bang seem to describe the universe starting as an infinitely dense point "containing" everything, which then exploded or expanded from it. Is that a flawed explanation?

(Sorry if I sound like an amateur at this. I am.)

 

[phinds]

Maybe I'm drawing an inference here that doesn't exist - that we started at zero-D and added four. I understand conceptually that the notions of time and space did not exist before the BB. Am I trying to geometrically connect a singularity to a multidimensional space?

Again, you are using a pop-sci description that does not reflect our understanding of reality

Popular descriptions of the Big Bang seem to describe the universe starting as an infinitely dense point "containing" everything, which then exploded or expanded from it. Is that a flawed explanation?

Deeply, totally flawed to the point of being just silly. You WILL read/see it everywhere in pop-sci but my statement stands.

Pop-sci presentations (books / tv / internet / etc) are ENTERTAINMENT, NOT science. What you learn from pop-sci will be mostly wrong.

 

[PeterDonis]

Maybe I'm drawing an inference here that doesn't exist - that we started at zero-D and added four.

Again, this is not what the actual model that cosmologists use says. In the actual model, spacetime is 4-dimensional everywhere. (I'm not talking about string theory here, which is a whole other issue that belongs in a separate thread in the Beyond the Standard Model forum if you want to discuss it.)

I understand conceptually that the notions of time and space did not exist before the BB.

Then you understand incorrectly. There is no such thing as "before the BB". The spacetime in the model is all that there is; there is nothing "before" it.

Popular descriptions of the Big Bang

Are not good places to learn the actual science. The fact that they incorrectly describe the universe as "starting from a single point" is just one of many, many examples.

 

[PeterDonis]

Is that a flawed explanation?

Yes.

 

[helloplaychess]

Well, I think your understanding of "dimensions" is flawed.

 

[phinds]

Well, I think your understanding of "dimensions" is flawed.

Who are you addressing with this post?

 

[PeroK]

Maybe I'm drawing an inference here that doesn't exist - that we started at zero-D and added four. I understand conceptually that the notions of time and space did not exist before the BB. Am I trying to geometrically connect a singularity to a multidimensional space?

A singularity, technically, is a breakdown of the mathematical model.

Popular descriptions of the Big Bang seem to describe the universe starting as an infinitely dense point "containing" everything, which then exploded or expanded from it. Is that a flawed explanation?

Yes, it's flawed. There is no way to map a single point to anything another than another single point.

(Sorry if I sound like an amateur at this. I am.)

So am I. It's the professionals who write popular science accounts of the Big Bang that should know better! The Big Bang model only goes back so far - and not all the way to time zero - to the point where our current understanding of QM and gravity runs out. That's more accurate, and also more truthful, than pretending we know that the universe started from a single point.

 

[Morbert]

The closest I can think of is the Hartle-Hawking no-bounday proposal, where they sketch the computation of "the amplitude for a given three-geometry to arise from a zero three-geometry i.e. a single point". The zero three-geometry, however, is still a three-geometry, not a "zero-geometry". Nor is it "infinitely dense containing everything". And as far as I can tell it is still just a proposal.

 

[kered rettop]

Yes, it's flawed. There is no way to map a single point to anything another than another single point.

Could you enlarge, please?

 

[PeroK]

Could you enlarge, please?

Let's take the simple example of the real number line. The mapping $f(x) = 0$ (for all $x$) is perfectly valid and maps all real numbers to the number 0. But, the "inverse" mapping $f(0) = \mathbb R$ is not a valid mapping. You can't start with a single point and map it onto the whole number line. Not in any physically meaningful way.

If, however, you have an interval around 0, no matter how small, $(-\epsilon, \epsilon)$, then you can map that to the whole number line. Something like $f(x) = \arctan(\frac{\pi x}{2\epsilon})$ would do.

The popular science authors who state that the beginning of the Big Bang was a single point are wrong for two reasons: 1) the model does not go back to a single point; 2) if you start with a single point, there is no mathematical model that maps that single point to a 4D manifold.

 

[Eric Singer]

Thank you, @PeroK. Combined with @Morbert's answer, I'm inferring that one can have an n-geometric object that happens to have length 0 in all dimensions. Whether this is the case at the moment of the Big Bang has yet to be "decided," though it could have been an object that was zero, infinitesimal or approaching zero in all dimensions.

 

[PeterDonis]

The closest I can think of is the Hartle-Hawking no-bounday proposal, where they sketch the computation of "the amplitude for a given three-geometry to arise from a zero three-geometry i.e. a single point".

This doesn't look like what the no boundary proposal says. It says that there is no boundary at the beginning of the universe; that means no "single point". It means the 4-D geometry of the universe at the beginning is smooth and geodesically complete and the curvature is finite everywhere, instead of the 4-D geometry being geodesically incomplete and the curvature increasing without bound as a past boundary is approached.

The paper you cited is not a paper about the no boundary proposal, but about a different proposal that is part of an attempt to develop a theory of quantum gravity. [Correction--it looks like it is the no boundary paper based on discussion in a separate thread.]

 

[PeterDonis]

Combined with @Morbert's answer, I'm inferring that one can have an n-geometric object that happens to have length 0 in all dimensions.

Your inference is wrong. @PeroK said nothing of the sort. @Morbert may have misdescribed the Hawking "no boundary" proposal, as I have just pointed out in post #15.

 

[Eric Singer]

My apologies, @PeterDonis. Maybe someone with a helpful answer could weigh in.

 

[phinds]

My apologies, @PeterDonis. Maybe someone with a helpful answer could weigh in.

That's very hard to do when you base your statements/questions on invalid models and misunderstanding of the answers you do get. Try to formulate a specific question, taking into consideration all of the answers you have already been given.

 

[PeterDonis]

Maybe someone with a helpful answer could weigh in.

You already have the answer to your original question: your initial premise...

If we accept the concept that the universe began as a zero-dimensional point,

...is wrong. You might not find that "helpful" in the sense that it invalidates the rest of your post. But that just means that there is no answer that would be "helpful" in the sense you are looking for. Sorry.

 

[PeterDonis]

And with that, this thread is closed.