(September 16, 2019 at 4:54 pm)polymath257 Wrote:(September 15, 2019 at 5:14 pm)Darwinian Wrote: How many other people think that when equations produce the answer 'infinity' that they are not deep and profound but actually are simply nonsense and point to the fact that we have no idea what's going on.
For example, the singularity which has infinite mass and density is a product of our ignorance and simply cannot exist.
That depends on the situation. Sometimes it means we don't understand something. Other times it is the 'correct' answer and makes sense in context. Other times it is correct but doesn't 'exist'.
For example, when infinities happen in our calculation of the mass of an electron, we can be pretty sure we are missing something important going on.
But, when water melts, the specific heat goes to infinity. That is just a fancy way of saying that adding heat doesn't lead to an increase of temperature (it leads to more water melting).
Finally, in the Big Bang scenario, the infinities seem to go away when we do quantum gravity. But they also may still be around and signify that our assumptions about space, time, matter, and energy may have to be re-evaluated. In the original BB theory, the singularity means that we cannot even define t=0, let alone t<0. it only makes sense to talk about 'after the Big Bang'.
My impression is that virtually all cosmologists view General Relativity as being incomplete at ultra extremely high energies and densities, namely, right after the Big Bang. But, singularities in GR seem to indicate that a deeper reality needs to be explored, but the mathematics is so far beyond me that I feel embarrassed pontificating any further on any of this.
