All electrons are fundamentally the same. They may be in different orbitals around nuclei, or, if free, may have different kinetic energies, but if you look at any free electron in its own frame of reference it is identical to all others as I understand it.
So what about photons? Its impossible to view photons in their own inertial frame to say they are identical. Blue photons have more energy than red photons. You could travel towards the red photon and make it seem more energetic so it looks the same as the blue photon.
But suppose you have a red and a blue photon traveling towards you on parallel paths. Any velocity you now take with a component towards the pair will increase the energy of both, but the blue photon will always appear more energetic to you regardless of your velocity. Ditto for any velocity with a component away from the pair. So it seems that two photons traveling in parallel paths can never look identical to any observer. In what sense can the two be said to be identical?
They are identical in that they both exist. That’s not really identical, though. ? Does every single characteristic have to be shared, in order to be identical?
In quantum mechanics there is a concept called ‘identical particles’ and it refers to particles which it is impossible to distinguish between even in principle. For example this could be a Fermi gas consisting of electrons.
This description though doesn’t really lend itself to photons, not because they are more distinguishable than electrons, but because normal quantum mechanics is non-relativistic and can’t be used to describe relativistic particles like photons. However when you move over to relativistic quantum field theory, when describing the electromagnetic field, there’s a hidden assumption that photons can be described as identical particles in the same ways that electrons can be described as identical particles.
This was exactly what I was referring to. But for any two “nonparallel” photons there is a frame of reference in which they are identical except for their direction of movement (and possibly polarization I guess) so their differences are extrinsic, but for two two photons traveling on parallel trajectories, there is no frame of reference for which they are identical. So it wold seem there has to be an intrinsic difference between them.
Or perhaps under general relativity in a non-empty universe, there are no Euclidean parallel paths?
Equally though for two electrons travelling along parallel paths there is no frame where they have the same energy either. Identical particles are a bit different as in that situation the two particles both have precise trajectories which are known, but quantum particles don’t have precise trajectories, so when you measure the two electrons/photons how do you know they haven’t swapped over? The idea of identical particles is that any labeling of the particles (e.g. electron 1, electron 2, etc) is arbitrary and if you swap the labels around there’s no alteration of the physics.
That’s not true is it? They’d only have different energies if they had different speeds. So if I used the frame of reference with the “average”* velocity, they’d have equal speeds though opposite velocities and have the same energies.
In any case, my original point was electrons are all identical when measured in their own rest frame, which photons have not. But I guess the point about the uncertainty principle is what’s driving things here rather than my guess about non-Euclidean geometry.
I’ve said “average” up there as I’m thinking we’d have to compute it differently from usual if the velocities were relativistic.