I was watching the recent offering from BBC's Horizon - Who's Afraid of a Black Hole - and it got me thinking. It seems, as far as I can see, that far from Einstein's relativity not being able to explain the mathematics of a singularity, they explain it perfectly adequately. It seems, to me, that the scientists involved simply do not accept the idea of infinite density.The word "singularity" doesn't mean "point of infinite density" , though it is often taken to mean that (and popularly used to mean that). The word means a proposed state of a physical system where the mathematical description of the system does not make sense. For a singularity, we can derive a number of contradictory and non-sensical statements. Even in general relativity, there are singularities within the full description of a black hole. Some of them can be removed through a careful description of the objects, but not all of them. This is the real problem.
Am I missing something here? In fact, on a very basic level isn't such a result absolutely obvious? If you are looking to discover the density of a measureless point in space which has mass, the result will clearly be infinite?
Thank you for this response; as I have re-read it I have understood it a little more. However, this still describes what I see as the basic problem for science here, and there are hints of this within some of the responses here.
Surely one of the reasons that science is so interested in black holes is because of the singularities, because of what they can tell us about the big bang. But then, it seems, that science wants to deny what a singularity really is, and indeed must be in order to be considered to describe the 'moment' of creation.
To read that a singularity has zero volume, but that that is not infinitely small..?? This is a notional slight of hand which is as meaningful as using 0 as a real number - and, if true, surely removes any meaning of the concept in terms of the 'moment' of creation.
By the very nature of the 'moment' of creation this singularity must have come into existence within nothing. It is, by definition, a dimensionless point.
And, if we cannot believe in a singularity (in other words, cannot bring ourselves to deal with the dirty concept of infinity) then 'creation' becomes less than creation - and we then have to face the concept of the eternal.