Why don't currents in Superconductors lose energy as light? We are told that in superconductors, there is no internal resistance. So if a current is induced in a superconducting material (like an Eddie Current), it should theoretically flow forever (or until the material heats up). However, in atoms, we know the electron could not be rotating around the protons because the constant acceleration inwards produces light which radiates away energy. I was wondering why superconductors don't also radiate away their energy as light as the electrons loop around the circuit.
If the electron's wavefunction is localized, then even though the charge distribution appears smooth macroscopically, the microscopic changes should still add up and radiate light. If it's similar to atoms and the electrons don't radiate light because the wavefunction is distributed around the circuit in discrete states, then does that mean currents in superconductors can only exist in loops whose lengths are an integer multiple of the electron's wavelength (so not all radii of Eddie currents are possible)?
 A: A superconducting current is constant in time and produces a static magnetic field. A radiative field requires a current that varies in time.
A: That is good reasoning.  See lecture for a detailed discussion.  The magnetic flux through a superconducting loop, and thus the current in a superconducting loop (carrying a DC current), is quantized.
A: 
However, in atoms, we know the electron could not be rotating around the protons because the constant acceleration inwards produces light which radiates away energy

Close.
The electron will lose energy until it gets to the lowest possible energy state. That might be the ground state, or it might be some higher-energy state if the lower states are occupied by other electrons. Once they reach that state, they stop radiating.
Superconductors work the same way. Once everyone is in a stable state, there's no lower-energy level to move to, and the radiation stops.
A: Supercurrents are a flow of the Bose-Einstein-Condensate (BEC), where each boson is an electron pair. BEC-bosons have a minimum and quantized kinetic energy and, thus, cannot emit their energy by arbitrarily small portions. So below BEC temperature the pairs don't lose any energy.
