# Do Black Holes Exist? Maths & Singularity Explained

• B
• wolram
No, in QM at zero temperature particles still have nonzero energy (because "zero temperature" means "ground state", and the energy of a particle in the ground state is still nonzero).
Energy of particle consists of potential energy plus kinetic energy. But as I understand this there is no certain split between these two energies. So it would mean that kinetic energy does not have specific value. Hmm, then defining pressure using kinetic energy might not work very well.
If the particles are in a potential well, the ground state is most likely going to have zero expectation value of momentum (for example, consider the 1s state of the hydrogen atom) by rotational symmetry.
Average momentum should be zero but it does not seem that this helps with the question.

It seems that my line of argument reached some uncharted territory for me. So I will probably stop there and give it some time to seep in.

Energy of particle consists of potential energy plus kinetic energy.

For some very specific cases, yes.

as I understand this there is no certain split between these two energies

No, in a general spacetime "potential energy" can't even be defined. It can only be defined in stationary spacetimes.

Average momentum should be zero but it does not seem that this helps with the question.

I didn't say "average" momentum. I said the expectation value of momentum. A single electron in the 1s state in a hydrogen atom is not in a momentum eigenstate, so it has no definite value of momentum; but the expectation value of the momentum operator for this state is zero. "Average" momentum, OTOH, is meaningless, since there's only one electron so there's nothing to take the average of.