[reidacdc]

Definitely not my field, but a colleague of mine in grad school who was doing GR stuff was convinced that black holes didn't have singularities.

As I recall (it was a long time ago), it was mostly an aesthetic preference, he felt it was far more likely that at very high curvatures or energies or both, the domain of validity of GR would be exceeded, and Something Else would happen that preserved the theory in the low-curvature regime.

It sounds like that's not even required, if I'm reading this right (did I mention it's not my field?), it sounds like even within GR, singularities are avoidable? Very cool.

[soundarana]

Many physicists believe that no singularity can phisically exist in nature and that they are just our lack of a better theory.

[boxed]

Isn't an electron a singularity in this kind of sense? A mathematical point with some fields, and a certain mass.

[naasking]

That was the old thinking. Turns out it leads to divergences which was one of the difficulties that quantum theory overcame. Baez has a good overview of these kinds of problems:

Struggles with the Continuum, https://arxiv.org/abs/1609.01421

Lots of issues spring from unphysical assumptions like continuous quantities, point-like objects and infinities. Quantum mechanics was the first step towards more discrete formalisms, and I think future physics will take further steps in this direction to eliminate these issues.

[mattsan]

I believe the word you're looking for is quantum - the "point" still has a radius, a singularity does not.

[layer8]

An electron is a fluctuation of the electron field, not a singular point.

[boxed]

It certainly acts like a singular point if you measure it and have it scatter on stuff...

[layer8]

The electron wavelength is around 4 picometers at low energies. The wavelength also imposes a limit on the resolution of electron microscopy, for example. The wavelengths are really small, but they are not zero.

[boxed]

Sure, but when an electron hits a surface (like a detector), it doesn't hit it with a splotch of 4 picometer in size, it hits it as a dot (as far as one can measure, given the uncertainty principle)... right? Same as any photon.