-1

I always thought that a point particle would have spherical symmetry. This is the case for the intrinsic electric field from an electron.

However, the intrinsic magnetic field of an electron has cylindrical symmetry. A key property of such field is that is has orientation, the cylinder points in some direction.

I would think that it is mathematically imposible for a point to be oriented. So, this is mathematical proof that an electron is not a point. At least, saying it is a point and that it has an orientation, is mathematically inconsistent.

An I wrong?

(If you claimed that it is an arbitrarily small cylinder, i.e. a short line, that would be consistent, I think) (edit: you could even claim it is a vector, being in a point but also having a direction)

Edit: my question is not a duplicate because I'm not doubting that the electron has intrinsic angular momentum. I'm saying that such property is mathematically incompatible with a point. Unless I am misunderstanding what "point" means, in that case Id change the question to "what is do we mean by point? Can it have an orientation?"

Juan Perez
  • 3,082

1 Answers1

-2

The concept of a point particle, however useful in mathematical constructions, introduces trouble when looking at the particle itself. Tricks like renormalization were invented to swipe infinities under the carpet (even Feynman and Dirac admitted that the renormalization procedure is an contrived one, calling for a more "natural" explanation).

How can a point particle rotate? How can it show "its other side" after one full rotation (spin 1/2 particles). How can it show its other side after a quarter rotation (spin 2 particles)?

An electron can be visualized as having an associated arrow pointing up to rotate one whole round while walking a Möbius strip twice. Or by connecting the rotation to unitary transformations, U(1), for which the identity corresponds to 720 degrees rotation.

Nevertheless, the mystery of rotation remains. Clearly, for an electron, electric charge in motion has to be there because there is a magnetic field around the electron.

Do strings resolve the issue? Strings can rotate around several axes, including their length although this last mode is just as problematic as for the point particle. So you would say that something non-pointy is indeed. Strings offer a nice Ansatz.

MatterGauge
  • 1