Re: Hard Science Help
Presumably, but we're on slippery ground here. If we're talking about a black hole, and the photon is inside the black hole, then (1) the photon had to "borrow" its initial energy from the energy of the black hole in order to exist in the first place and (2) strictly speaking, you shouldn't ask questions about what goes on inside a black holes, because you can't learn the answers (no information can escape the event horizon). In fact, you can't be certain whether the same laws of physics operate inside a black hole as outside, because no information escapes to let you know.
Virtual particles (of which photons are certainly included) come into existence and are destroyed all the time. This situation probably fits into that process, modulo the problems of discussing the inside of black holes already mentioned.
Actually, I never considered that before. There's no fundamental limit on the minimum energy in a photon, but you have practical problems making very low energy photons. The black-body spectrum goes to zero as energy/frequency goes to zero/wavelength goes toward infinity. Also, in a non-vacuum, photons interact with the particles around them, which tends to increase the photon energies, though I forget the dependencies of the strengths of the interactions as a function of photon energy (it's a constant value at low energy, though).
Remember, you're changing frames of reference. Not only do the clocks slow down as your speed increases, but your meter sticks contract, also. With photons, the total photon energy is conserved as you change reference frames ... it was arguments about electromagnetic waves and energy conservation that make the entirety of "On the electrodynamics of moving bodies" which was Einstein's initial paper on special relativity.