# Why are electrons alike but photons not?

Perhaps this is a misconception, but why are electrons alike and photons not? Given two photons, they may differ by having different frequencies (energies). Given two electrons, there are just two indistinguishable electrons?

It's a good question, and one that puzzled me for a while as well. However the answer is very simple.

For a massive particle like an electron the total energy is given by:

$$E^2 = p^2c^2 + m^2 c^4$$

where $p$ is the momentum and $m$ is the rest mass of the electron. Electrons can obviously have any momentum you want, so the total energy can be any value greater than $mc^2$. The de Broglie wavelength of the electron is $\lambda = h/p$, so the electron can have any wavelength you want.

If we now consider a photon, the key difference is that the rest mass is zero, so the equation for the energy becomes:

$$E^2 = p^2c^2$$

Just like the electron, the photon can have any momentum you want, so the total energy can be any value greater than zero. The wavelength of the photon is again $\lambda = h/p$.

So there isn't any difference between the electron and photon except that the non-zero rest mass of the electron means the energy can't be zero. Both electrons and photons can have different energies and wavelengths.

Why are electrons alike but photons not?

Because it takes a given amount of an energy to make an electron: 511keV. That's the energy of an electron at rest. A fast-moving electron comprises more energy than an electron just sitting there in front of you, but if you were to stop it by removing the kinetic energy, its rest-energy is 511keV, and its mass is 511keV/c². Check out Compton scattering and the inverse Compton for adding and removing kinetic energy.

Perhaps this is a misconception, but why are electrons alike and photons not?

Because the electron is a "standing wave field structure". We make electrons (and positrons) in pair production, see Wikipedia. We start with a field-variation, and we end up with a standing field. Also see the Wikipedia atomic orbitals article where you can read that "electrons exist as standing waves". When it comes to standing waves, you can't have just any old wavelength. It's got to be a particular wavelength, which for the electron is 2.426 × 10$^{-12}$ m.

As for exactly how and why, there's nothing definitive in the literature, but I expect it's got something to do with Planck's constant h, the reduced Planck's constant ħ, and the nature of spinors.