=physics
For the record, I'm writing about this topic because it won a poll.
Even if you're not a physicist, you probably know that electrons are
negatively charged, but their magnetic properties are less well-known.
Electrons have spin,
which is a magnetic field and angular momentum. This magnetic field is very
strong, and in most materials, spins cancel out. An atom of iron is about 10^5
times the
mass of an electron, and the magnetism of a permanent magnet will always be
less than one electron spin per atom; maybe that clarifies how strongly
magnetic electrons are.
I was taught in
school that "iron is ferromagnetic because each atom of iron has an unpaired
electron", but that's not quite right. Only certain crystal structures of
iron are ferromagnetic; alloys that produce austenite crystal structures
aren't ferromagnetic. In those certain crystal structures, some of the
unpaired electrons aligning their spins with a magnetic field allows them to
get closer on average to the protons, and that's where the energy to make a
stronger magnetic field comes from.
In school, I was also taught
that an electron is a point, with no volume. This is probably the most
common view among physicists today.
If an electron is a point, it has
infinite charge density. Apart from the philosophical or aesthetic issues
people may have with infinities, that infinite charge density implies
infinite potential energy, energy is mass, and electron mass isn't infinite.
(Yes, electrons are spread out over a volume, but because an electron
doesn't interact with its own charge, that doesn't solve the issue of
potential energy of a point electron.) The current solution is "renormalization".
That involves treating an electron as a point, getting an infinite value for
its potential energy, and then replacing the infinity with its measured
mass. You can probably see why some physicists consider that unsatisfactory.
How did electrons come to be considered points? If you treat electrons
as having a radius where their electrostatic potential energy equals their
mass (the "classical
electron radius"), then calculate how fast a ball that big would have to
spin to have the magnetic field of an electron, the result is faster than
the speed of light. As a result, Wolfgang Pauli successfully argued that
spin doesn't involve actual rotation, and is instead a non-geometric
attribute of electrons that happens to contain angular momentum.
That
argument is
wrong: as
Belinfante noted, if you don't simplify electrons to a ball of charge,
spin can be considered a rotation of charge and energy in the field around
an electron. This isn't a fringe view among theoretical physicists, just an
alternative interpretation that's generally considered not to be very
useful, but it's not generally taught by physics teachers.
It would be aesthetically pleasing to explain electrons as an emergent
property of some extended space-time field, where they consist of some flows
or vibrations of the fabric of reality. Photons are
fairly easy
to explain with such a system, so what about other particles?
This is
basically the motivation of string theory, but there are some differences:
string theory assumes that fundamental particles are 1-dimensional strings
that take a path through a bunch of dimensions but are points in normal
space. The "string" for an electron is a point in real space because that's
Pauli's dogma, and it's one-dimensional because the math is easier that way.
You may have heard that, for some reason, string theory hasn't been very
successful.
Let's suppose that electrons consist, at least partly, of a ring of spinning charged space-time. There are some obvious issues with that model:
A) Why doesn't the negatively charged fabric of space fly apart?
B) Why
does the spin of an electron have twice the
magnetism per
angular momentum of electrons moving in a circle?
C) Why is an
electron stable only at a particular mass and charge?
Saying that an electron is a
point has a converse problem to (A): when a gamma ray becomes an
electron-positron pair, how does the energy of a (space-occupying) photon
coalesce into a point? The usual answer is "it just does, shut up and
calculate" - but you could say the same thing with a different model. On the
other hand, if you have spinning rings of charged space-time, it's easy to
imagine how electrons and positrons could annihilate to produce gamma rays.
A possible resolution to (A) and (B) is to say that an electron contains
4/3e of negative charge rotating one direction, and 1/3e of positive charge
rotating the opposite direction, with the positive charge inside the
negative charge and holding it together. (Quarks have charge in multiples of
1/3e, so 1/3e being the actual fundamental unit of charge seems reasonable.)
But then, why does the positive charge stay inside? This certainly isn't a
complete explanation of anything, but maybe it's a start.
Why is a
helium atom so large? Why is there so much space between the electrons and
the nucleus? That's because electron orbitals must be an integer multiple of
the electrons' de
Broglie wavelength; that simple rule results in the complexity of
chemistry. Current physics doesn't have a force that pushes
electrons into that state when they diverge from it; it simply says that
electrons are forbidden from having other orbitals. Another possible
analogy is the
quantum vortices in superfluids and superconductors, which are somewhat
similar to electron orbitals.
Since we're at the point of inventing
axioms here, we could postulate that spinning charged space-time must have
an integer wavelength of some sort, which results in quantization of charge
and causes electrons to be stable.