B Can somebody help me understand singularities better please?

[Cerenkov]

Hello. :)

This is my first post. I'm an amateur astronomer with a interest in cosmology. My understanding of cosmology is entirely derived from reading Hawking's 'A Brief History of Time', Guth's 'The Inflationary Universe' and relevant articles in Scientific American, Sky & Telescope and Astronomy magazines. So, please be gentle with me!

In the above books and magazines I've read about the concepts of a gravitational singularity and of the Big Bang singularity. Up until now I'd (naively?) thought that diagrams like the one below were similar to the contour lines of an ordinary topographical map. That is, they represented what physical reality was doing in a way that the mind could easily grasp.

But now this paper... http://ja-schweitz.se/onewebmedia/BIG BANG METRIC2.pdf ...has confused me. It seems to be saying that such a diagram of the Big Bang singularity is not so much representation as an artifact. (Or artefact.)

Could somebody please explain what's going on here? (Preferably in terms that an enthusiastic amateur can grasp.) Thank you.

Cerenkov.

 

[Nugatory]

You can safely ignore that paper. There's a reason why it's hosted on the author's personal website instead of published in a reputable peer-reviewed journal.

 

[ISamson]

You can safely ignore that paper. There's a reason why it's hosted on the author's personal website instead of published in a reputable peer-reviewed journal.

Is @Cerenkov 's view on singularities and that picture correct?
I don't totally understand singularities as well.

 

[mathman]

Singularities are mathematical artifacts of the theories involved. For example (the one you cited) the equations of general relativity lead to a picture of a black hole as a mathematical point of infinite density (the singularity). However physicists believe that this physically impossible - quantum theory gets in the way. That is a motivation for trying to find a theory uniting these two fundamental theories of modern physics.

 

[windy miller]

A singularity in cosmology is where spacetime curvature, density , pressure etc go infinite. Almost all cosmologists think this represents a breakdown of the theory of relativity and high energy densities. I don't think anyone thinks singularities actually exist. People are trying to make a quantum theory of gravity and expect singularities will be forbidden. This is seen in loop quantum gravity for example.
https://arxiv.org/abs/0812.4703
But no quantum gravity proposal has been tested by experiment so no one really know what's going with any confidence.

 

[PeterDonis]

A singularity in cosmology is where spacetime curvature, density , pressure etc go infinite.

This is a common pop science definition, but it's not actually the one that's used in the literature. The definition that is used in the literature is that a singularity is present in a spacetime if the spacetime is not geodesically complete--i.e., if there are geodesics that cannot be extended to arbitrary values of their affine parameter. This actually is a broader definition than you give, because any spacetime in which spacetime curvature and stress-energy increase without bound along some geodesic is also going to be geodesically incomplete (there are some technical conditions involved here that are out of scope for a "B" level thread), but there are also possible spacetimes (admittedly not ones that are likely to be relevant in a practical sense) that are geodesically incomplete but do not have spacetime curvature or stress-energy increasing without bound anywhere.

 

[newjerseyrunner]

A singularity in cosmology is where spacetime curvature, density , pressure etc go infinite.

No, they're points at which our mathematical descriptions of these places go to infinity (or become nonsensical.) Most scientists believe that these singularities will be resolved when we have a better description of nature.

This is not difficult to imagine. What if you have a round pool and you gave all of the water a push in the direction of the center. That pressure wave would converge on a single point, giving a result of a moment of infinite pressure. That's a singularity. Is it real? Well if all you know how to calculate is the pressure wave, then yeah, but if you understand more about the molecules and how water behaves, you know it's not.

Singularity in water.


Trying to figure out what spacetime is doing at such a scale would be like trying to figure out the physics of water without knowing it's made of molecules.