Does cosmic censureship hypothesis avoid incompatibility with QM?

[TGlad]

My understanding of the main problem with adding gravity to quantum theory is that gravity is proportional to 1/distance squared. And so for particles that have no size (like electrons), their gravity is effectively infinite in a collision. Or in quantum terms, the equations don't converge on the interaction of these 'fuzzy' particles.

However, Penrose hypothesises that all singularities will hide behind an event horizon, so we avoid having to deal with them.

Is it not logical that something tiny like an electron should have an event horizon?
Sure, it has a tiny mass, but it has an even tinier radius.

(This is written by a non-expert so it is more just an idle thought)...

 

[mfb]

My understanding of the main problem with adding gravity to quantum theory is that gravity is proportional to 1/distance squared.

The electromagnetic force has the same property. Quantum gravity has no (physical) particles which are at a single point only, therefore this is not an issue.

 

[Finbar]

Ah ha. So in quantum mechanics the mass of an electron is inversely proportional to its mass λ~ 1/m. So the smallness of the electrons mass means it has a large wavelength. It's event horizon radius is proportional to its mass r~ Gm where G is the Newton's constant. This means that an electron has a very large wavelength compared to the radius of it's event horizon. Therefore since we cannot localise the electron to within a smaller distance than its wavelength it has no event horozon.

So an electron won't have an event horizon. Understand?

The mass at which a particle would have an event horizon larger than its wavelength is the Planck mass. This is roughly 1000th of the mass of a flea...many orders of magnitude more than an electron.