I think it is only safe to say that that is as much as we know about it at this time. If one is a scientific realist, and takes electrons to be real entities (as opposed to purely theoretical constructs) one cannot rule out the possibility that they might have as yet undiscovered properties. (Such things have happened often enough in the history of science: consider atoms.)
Of course, you are right that if an electron is a purely theoretical construct, then it might be perfectly circular, but that is just because, in that case, itis teh same sort of unreal abstraction as a perfect circle.
Which, I take it you are saying, will be a perfect sphere.
However, even granting your earlier assumptions about the nature of electrons, I doubt that this will be true except in a universe that contains only one electron, and no other electrical charges. Surely the shape of the field centered on an electron will be affected by other fields generated by other particles.
All true. I meant “safe to say” in the semi-scientific sense of “we don’t have any evidence to contradict this yet”.
Also true. This does become a bit of a philosophical exercise–is an electron in an empty universe fundamentally less abstract than a perfect, Platonic circle? I’d like to think so, because electrons really do exist, and because we can come arbitrarily close to creating the flat conditions required for a perfectly spherical electron. But it could be argued either way.
Actually, that’s the photon’s purpose. The electron is the lightest and hence most common charged particle (note that charge is not the same thing as field), but far from the only one, and in no sense the most fundamental one.
And you can actually measure the shape of the rain droplets by measuring the deviation of a rainbow from circular.
I’d say the photon is more a manifestation of the EM field–which is, of course, the same thing, except that with a photon they come in equal proportions, whereas for an electron (or other charged) particle, you only get the electric part (assuming it’s not accelerating, etc.).
And I think the electron (along with its antimatter counterpart, the positron) is special, since it’s elementary, light, and exists free. All other charged particles have substructure, or decay into something else, or can’t exist by themselves.
Is it even determined yet if the mass of an electron comes from anything except for the energy of the field? Last I recall from reading the Feynman Lectures (which are admittedly fairly old), it wasn’t known.
At any rate, I’ll grant that the electron is more a tiny bundle of charge than E field. Whether it’s more than that is… to be determined?
All we can ever say is “this circle is as perfect as our measurements allow”. If that’s not good enough for you, then the answer is “no, there’s no such thing as a perfect circle.”
Well, ok, if you want to be picky this way just amend the question to read “Is there anything that is perfectly circular?” I am fairly confident that that captures the intent, and the answer is still “No”.
What sort of reality or existence, if any, that is remains highly controversial, of course.
:dubious: You might be able to dig up a philosopher or two somewhere who would doubt it, but it really is not very controversial. A rock, for most people (including most philosophers) is pretty much a paradigmatic example of something that exists. It occupies space, and you can see it, feel it, even kick it (as Dr Johnson famously showed).
Mathematical objects are a very different kettle of fish. Nobody has ever seen or felt or smelt the true circle (is there one, or an infinite number of them?), and it does not exist in space-time: maybe in Platonic form-heaven, if there is such a ‘place’ (not many people think so these days - maybe a few philosopher-mathematicians, but thats pretty much it).
And what does that have to do with reality? There are likewise a lot of things you can do to a circle that you can’t do to a rock. Should I assert that a circle is “real” but that the rock isn’t, because I can Fourier transform a circle, or produce a formula that describes it, or precisely define its proportions to arbitrary precision?
Actually I was saying that a rock is real because you can experience it, not because you can do things to it. Can you experience a mathematical circle?
Anyway, I am fairly confident that terms like “real”, “exists” or “is” were applied to things like rocks long before anyone thought of applying them to mathematical abstractions. The issue is whether the extended use of these terms is literal or metaphorical.
And please not that I am not asserting that mathematical objects are not real (I really do not know), just that their reality, or what sort of reality they enjoy, is controversial, whereas the reality of rocks is not very controversial.
