Singularities in General Relativity

[Tio Barnabe]

There are two kind of singularities which are familiar in General Relativity. One of them is the singularity of Black Holes and the other is at the beginning of the universe.

I'm confortable with the former singularity --it seems to make sense. But as with the latter, I'm not so confortable, because I'm going through the following reasoning:

1 - A singularity in General Relativity as far as I know happens when you have enough matter in a region small enough.

2 - Then, talking about a singularity at the moment of the Big Bang is equivalent to saying that there was a plenty of matter together in a small region. This seems to assume that the current galaxies have been existing in the way they are today since the Big Bang, and that at the moment of the Big Bang they were in some sense pilled up. My disconfort comes from the fact that there was no matter at all to form galaxies at the moment of the Big Bang.

My conclusion is then that in this reasoning, we should assume that galaxies have been always existing in the way they are today, with the difference that today they are more far away from each other than they were in the past. Correct?

 

[phinds]

My conclusion is then that in this reasoning, we should assume that galaxies have been always existing in the way they are today, with the difference that today they are more far away from each other than they were in the past. Correct?

No. That would fly COMPLETELY in the face of evidence (such as the CMB)

You are treating "singularity" as though it had physical meaning. I believe it has been pointed out to you before that "singularity" is just a place-holder word so that physicists don't have to keep saying "the place where our math model breaks down and we don't know WHAT is/was going on".

 

[Tio Barnabe]

You are treating "singularity" as though it had physical meaning

"the place where our math model breaks down and we don't know WHAT is/was going on".

Yes. But then you are talking solely of the singularity, whereas I'm considering the context, that is, when the singularity appears in the theory, which in this case is basically when you put enough matter together.

 

[phinds]

Yes. But then you are talking solely of the singularity, whereas I'm considering the context, that is, when the singularity appears in the theory, which in this case is basically when you put enough matter together.

You seem to have posited that galaxies don't form, they just jumped into existence at t=0 but we know that not true. The Hubble telescope shows galaxies in the early stages of formation.

Tio, I don't wish to be rude but your whole theory just seems to be silly. I recommend Weinberg's "The First Three Minutes".

 

[Tio Barnabe]

What you are saying is just the opposite of what I'm saying in the opening post. Please, carefully read it again.

 

[Metmann]

Big Bang is equivalent to saying that there was a plenty of matter together

No, not really. The BB is a subtlety for itself but if we want to stick to your notions I would replace "plenty of matter" by "infinite energy density", where all gauge bosons (e.g. photons $\neq$ matter) + dark energy + dark matter + usual matter (elementary particles) count to the energy density. Galaxies have not existed at the beginning, but elementary particles (what ever are the real elementary particles), gauge bosons, DM and DE have. You should also be aware, that the BB doesn't denote "the beginning of everything", but rather the point where our understanding of the Universe totally breaks down and a quantum theory of gravity is needed. When typical distances approach the Planck length, we cannot describe the Universe any longer using GR alone.

 

[phinds]

What you are saying is just the opposite of what I'm saying in the opening post. Please, carefully read it again.

Gee, I can't imagine how I got the idea that you think galaxies have been around in their currrent state ever since the era of the big bang. OH ... wait, maybe it was because you said EXACTLY that:

My conclusion is then that in this reasoning, we should assume that galaxies have been always existing in the way they are today, with the difference that today they are more far away from each other than they were in the past. Correct?

 

[Tio Barnabe]

@Metmann

"infinite energy density", where all gauge bosons (e.g. photons $\neq$ matter) + dark energy + dark matter + usual matter (elementary particles) count to the energy density

Hmmm, interesting to know. Could this huge amount of energy provoke a singularity in the space time?

@phinds Sounds like a miscommunication between you and me. Perhaps due to my poor knowledge of English.
So I was arguing that for the given claim (singularity at the Big Bang) to be consistent with General Relativity, maybe I am forced to make that conclusion.

 

[phinds]

@phinds Sounds like a miscommunication between you and me. Perhaps due to my poor knowledge of English.
So I was arguing that for the given claim (singularity at the Big Bang) to be consistent with General Relativity, maybe I am forced to make that conclusion.[/QUOTE]I guess I'm not clear on what conclusion you are reaching if it is not that galaxies had to have existed at the time of the big bang. That is what you said and that is what I responded to.

 

[PeterDonis]

A singularity in General Relativity as far as I know happens when you have enough matter in a region small enough.

Heuristically, this is a reasonable way to look at it.

talking about a singularity at the moment of the Big Bang is equivalent to saying that there was a plenty of matter together in a small region. This seems to assume that the current galaxies have been existing in the way they are today since the Big Bang

It assumes no such thing. The matter in the early universe was very different in structure from the matter we see today. For one thing, it was much hotter and denser; for another, its density was much more uniform, since gravitational clumping had not had billions of years to form structures like galaxy clusters and galaxies and stars and planets.

Correct?

No. See above.

 

[PeterDonis]

Could this huge amount of energy provoke a singularity in the space time?

It's worth pointing out here that the singularities that occur in the idealized GR models of black holes and the universe are not considered to be an indication that such things are present in the actual universe. They are considered to be an indication that when energy density/spacetime curvature gets large enough, GR breaks down as a theory and will need to be replaced by a more comprehensive theory that is able to treat such regimes (most physicists think this more comprehensive theory will be whatever theory of quantum gravity turns out to be correct). So thinking of singularities as things that actually happen when enough matter or energy is collected in a small enough space is not really the right way to think about them.

 

[Ibix]

singularities...are considered to be an indication that when energy density/spacetime curvature gets large enough, GR breaks down as a theory and will need to be replaced by a more comprehensive theory

Just to add - GR starts by modelling spacetime as a smooth manifold, then promptly derives the existence of singularities which are pretty much the definition of "not smooth". That kind of self-contradiction is generally regarded as a Bad Thing, but the theory gives accurate predictions where we can test it. So people generally suspect very strongly that there's something wrong about how GR describes situations "near" where it predicts singularities. Unfortunately, it's very difficult to do experiments in such extreme cases to see exactly how the theory goes wrong.

 

[PeterDonis]

GR starts by modelling spacetime as a smooth manifold, then promptly derives the existence of singularities which are pretty much the definition of "not smooth".

It's more subtle than that. The singularities are not part of the manifold, so the manifold is still smooth. In fact this was a major issue during the late 1960s and early 1970s, because the fact I've just stated meant that coming up with a rigorous definition of what it actually means for a spacetime in GR to have a "singularity" was not a simple task. The definition that was finally settled on was geodesic incompleteness, which is not equivalent to "the manifold is not smooth". Geodesic incompleteness, specifically when spacetime curvature/stress-energy density becomes sufficiently large, is what makes physicists think that GR breaks down in this regime.