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I read in Hawking's brief history of time the following:

The final result was a joint paper by Penrose and myself in 1970, which at last proved that there must have been a big bang singularity provided only that general relativity is correct and the universe contains as much matter as we observe. There was a lot of opposition to our work, partly from the Russians because of their Marxist belief in scientific determinism, and partly from people who felt that the whole idea of singularities was repugnant and spoiled the beauty of Einstein’s theory. However, one cannot really argue with a mathematical theorem. So in the end our work became generally accepted and nowadays nearly everyone assumes that the universe started with a big bang singularity. It is perhaps ironic that, having changed my mind, I am now trying to convince other physicists that there was in fact no singularity at the beginning of the universe - as we shall see later, it can disappear once quantum effects are taken into account.

So, according to our current understanding of physics and black holes, what does support the existence of singularities and what does not?

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  • $\begingroup$ Big Bang seed and Black Holes are fully different things despite they both are singularity. $\endgroup$ – Schrödinger's Cat Mar 15 '14 at 14:57
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For obvious reasons we can't measure what happened at the beginning of the universe, nor can we measure what happens at the centre of a black hole. The best we can do is construct a theory that we can test experimentally, then extrapolate that theory back to the beginning of the universe or the centre of a black hole and hope the theory still holds.

Our current best theory for describing the universe is General Relativity, and there are enough experimental tests of GR that we know it gives a good description in the regimes we can test. All our tests are basically weak field tests i.e. the spacetime curvature is small. Part of the interest in studying Sagittarius A$^*$ or trying to detect gravity waves from black hole mergers is that we'll get data from much higher spacetime curvatures and this will provide new tests of GR under more extreme conditions.

Anyhow, what Hawking and Penrose showed is that GR predicts singularities must exist, including the Big Bang Singularity and black holes, provided that (to use Hawking's words) general relativity is correct and the universe contains as much matter as we observe.

But is GR correct? If it isn't then its predictions are not reliable and singularities may not exist. Hawking's current interests lie in studying how quantum effects may modify GR, and what he is saying is that he believes the way QM modifies GR means that the modified theory no longer predicts that singularities will form, and in fact predicts that they cannot form.

All very well, but you ask what does support the existence of singularities and what does not? and the answer is that there is currently no experimental evidence either way, nor is there likely to be for a long time. So in the near future the only evidence is likely to be theoretical. For example if someone comes up with a theory of quantum gravity that looks sensible and predicts things we can measure then we would be inclined to believe that theory and what it predicts about singularities. However at the moment no such theories exist.

I would guess most physicists believe singularities do not exist, mainly because we believe infinities don't occur in the real world (as opposed to the world of mathematics). However this is a gut feel and not a proof.

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I will complement the explanation by John by giving the example of the point charge and the field around it as represented by the electron. The electron is the smallest point charge and its field should go like ${1\over r^2}$. If we only had classical electromagnetic theory, the postulate that the electron is a point particle would point to a singularity at $r=0$, i.e. the field would be large approaching $r_0$ and infinite/indeterminate at $r=0$. What saves the day is the same theory that describes electrons as point particles, quantum mechanics. Within the postulates and the mathematical formulation of the theory is a basic indeterminacy of space and momentum, described by the Heisenberg uncertainty principle that tells us that if we know the momentum of the electron exactly we know nothing about its position, and if we know its position exactly ( $r=0$) we know nothing about its momentum, i.e. we cannot measure it and say "here is an electron with this momentum". Nevertheless, classically we can see the $1/r^2$ behavior of the field until we get to very small dimensions.

In a similar way, the observation that clusters of galaxies are expanding away from each other, like raisins in a rising bread, agrees with the supposition of classical General Relativity that about 14 billion years ago there was a singularity, and we can go fairly back to the few seconds of this classically postulated singularity until we reach dimensions where we know that quantum mechanics should apply and the theory should be quantized, which, as John says, has not been done yet.

Thus I would say that classically it "walks like a duck and it quacks like a duck" so we can say it is a duck, i.e. a singularity, but since we know that the underlying framework of nature is quantum mechanical, and quantum mechanics does not like singularities we, at least I, expect that once general relativity is quantized there will be an indeterminacy at the beginning of the universe that will take care of the classical singularity.

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