# How can a point particle have orientation? [duplicate]

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?"

• This isn't a proof the electron isn't a point particle, this is proof you can't just apply classical thinking to quantum objects. See physics.stackexchange.com/q/234979/50583, physics.stackexchange.com/q/24001/50583, physics.stackexchange.com/q/277565/50583 and their linked questions for extensive discussion of what it means for the electron to be "pointlike". Commented Nov 13, 2021 at 12:24
• I never mention classical intuition. I'm talking about mathematics. A point is a mathematical concept that does not admit orientation. You cannot use it to model an electron. Also, my question is not a duplicate because I'm not doubting that the electron has intrinsic momentum. I'm saying that such property is mathematically incompatible with a point. Commented Nov 13, 2021 at 12:34
• The questions linked in my first comment discuss at length what "the electron is a point" really means. It does not mean "the electron is to be modeled under all circumstances as a single mathematical point" - this is precisely the classical view of a point particle that does not apply here. You're arguing against a straw man. Commented Nov 13, 2021 at 12:36
• You’re last point about an electron being a vector is essentially correct. It is a vector defined at a single point in space. More precisely it’s a spinor which is like a vector (in that it is orientation) but more complicated. Commented Nov 13, 2021 at 13:23
• ACuriousMind is right that you're arguing against a straw man, but to be fair, that straw man is widespread. I even see hints of it in some of the answers to the linked posts. Classical thinking is deeply ingrained because we grew up with it, and words alone cannot describe the nature of an electron in quantum theory because even our language is a product of that deeply-ingrained classical thinking. We can (and often do) repurpose old words to have new meanings, but the only way to appreciate the new meanings is through new experience -- namely with the mathematics of quantum theory. Commented Nov 13, 2021 at 14:42