Planck Length & Singularity: Point or Sphere?

[jnorman34]

TL;DR Summary

Does the concept of “Planck length” imply that a singularity (or any other “point” particle) is not actually a “point”?

Since Planck length is a distance unit of space-time which cannot be further subdivided, would that not imply that an electron, or singularity, or any other point particle cannot actually be a “point”, but must rather be a spherical volume with a Planck length diameter?
i realize this may well be a naive question based on my poor understanding of so many fundamental concepts. Thank you.

 

[PeterDonis]

Planck length is a distance unit of space-time which cannot be further subdivided

We don't know that this is true. It is a common speculation in quantum gravity, but it's just a speculation. We have no evidence to back it up, and no feasible way of getting any for the foreseeable future, since it would require probing length scales 20 orders of magnitude smaller than the smallest ones we can probe today.

 

[jnorman34]

Thanks Peter - as I understand it, the Planck constant is well established, and Planck length, Planck time, etc are derived directly from the Planck constant. Is there any reason to question the validity of the equations that lead to these Planck units?

 

[Vanadium 50]

Is there any reason to question the validity of the equations that lead to these Planck units?

No, but there is also no reason to think of Planck units as the smallest of anything. The Planck resistance is 30 ohms.

 

[PeterDonis]

Is there any reason to question the validity of the equations that lead to these Planck units?

No, but the Planck units having particular values is not the same as those values being the smallest possible sizes of things.

 

[Ibix]

singularity, or any other point particle

Also worth noting is that a black hole singularity isn't a point in space anyway. A Schwarzschild black hole's singularity is a moment in time (despite a lot of popsci descriptions).

 

[PeroK]

Since Planck length is a distance unit of space-time which cannot be further subdivided, would that not imply that an electron, or singularity, or any other point particle cannot actually be a “point”, but must rather be a spherical volume with a Planck length diameter?

If an electron had a diameter of the Planck length, then its radius would be half the Planck length. Hmm?