Why do singularities mean that GR breaks down?

[josephwouk]

Why do singularities mean that GR "breaks down?"

The existence of singularities in the form of black holes as predicted by GR is universally accepted at this point.

The fact that GR calculations don't work inside a black hole means only that we are incapable of penetrating the event horizon with our theories.

Does Heisenberg's uncertainty principle mean quantum mechanics "breaks down?" It is at least as strong a barrier to our knowledge as singularities.

If not, then why can not the presence of singularities be accepted as a truth of nature the same way?

 

[K^2]

GR computations do work under the event horizon. I don't know why you think they do not. If they did not, we wouldn't know about the singularity in the center.

 

[JesseM]

I think it is mostly because of the conflict with quantum mechanics once the energy density reaches the Planck scale, if QM didn't exist we might just accept that infinite-density singularities are physically possible objects (although I think there still might be a problem with indeterminism associated with singularities that could actually emit particles we could see, like naked singularities and white hole singularities...as the 'naked singularity' article puts it, It would also cause foundational problems for general relativity, because in the presence of a naked singularity, general relativity cannot make predictions about the future evolution of spacetime. See also the discussion about toothbrushes on http://books.google.com/books?id=LyVxtGv1RwEC&lpg=PA1&pg=PA247#v=onepage&q&f=false, or the extended discussion starting on p. 65 of the book Bangs, Crunches, Whimpers, and Shrieks) For a basic list of arguments that GR and QM give incompatible predictions at the Planck scale, see the discussion in this paper which starts with the following summary of types of arguments on p. 3:

Lacking real experiments we use thought experiments (Gedankenexperiment) in this note. We give plausible heuristic arguments why the Planck length should be a sort of fundamental minimum - either a minimum physically meaningful length, or the length at which spacetime displays inescapable quantum properties i.e. the classical spacetime continuum concept loses validity. Specifically the six thought experiments involve: (1) viewing a particle with a microscope; (2) measuring a spatial distance with a light pulse; (3) squeezing a system into a very small volume; (4) observing the energy in a small volume; (5) measuring the energy density of the gravitational field; (6) determining the energy at which gravitational forces become comparable to electromagnetic forces. The analyses require a very minimal knowledge of quantum theory and some basic ideas of general relativity and black holes, which we will discuss in section II. Of course some background in elementary classical physics, including special relativity, is also assumed.

 

[Hurkyl]

Inside a black hole, there is an edge in space-time -- everything that passes through the event horizon will eventually reach this edge and vanish from the universe.

The singular nature of this edge implies that it is mathematically impossible to posit the existence of more space-time beyond this edge that obeys the laws of general relativity.

(note that the edge not actually part of space-time -- anything we say about the "shape" of the edge is really a description of the shape of space-time near the edge. e.g. there is no difference between saying the edge is point-like or shaped like a sphere)


So one philosophical aspect of this singularity is that it is aesthetically displeasing for objects to simply vanish off of the face of the universe -- one would prefer a theory that could describe their continued existence.



Another aspect is at the metaphysical level. Physical theories are generally assumed to be approximate, giving (very nearly) correct answers when applied to sufficiently well-behaved systems. It seems quite unlikely that space-time near the singularity is anything resembling well-behaved -- any features of reality overlooked by GR are quite likely to become relevant aspects or even the dominant aspect of how reality behaves.

(and GR is not just assumed to be approximate -- it is known to be approximate because it doesn't explain quantum mechanics)

 

[atyy]

Yes, I have wondered whether MTW are wrong on this point. In this discussion, let's leave aside disproof by experiment. The question is whether the singularities render GR mathematically inconsistent.

Are singularities indications of a mathematical breakdown? Or can in fact the theory be mathematically sound even with singularities?

Is the cosmic censorship conjecture necessary to have GR be a mathematically complete candidate physical theory?

If the cosmic censorship conjecture is necesssary, and GR does have it, will GR be a mathematically complete candidate physical theory?