- If photon will travel for million years without collisions, what subtle effects can be accumulated ?
- Gravity fields affect trajectory, but is energy completely intact after fly by ?
- Photon has its own equivalent mass of energy, does it affect itself over long long period of time and integrate into frequency shift ?
- Is uncertainty principles applicable for speed of free flying photon ?
- What if uncertainty of time/location of photon violates speed of light (exceeding it with very small amount of violation) or this violation only occures in lag just a little bit below hard speed limit ?
- What if there is photon-to-photon interaction when they travel in packs or cross each other individually with some tiny losses scattered ?
- As photons and mass affect each other, can it be that photons in packs are affecting each other as well ? Can it cause some lens, scatter, frequency change effects ?
- If some of this effects exist, can it be accumulated over enourmous age and be percepted falsely as doppler red-shift of very distant objects ?
Well, if the mode is speed-questioning, I'll attempt speed-answering:
The wave packet keeps expanding (or your uncertainty about location, take your pick), and the frequency drops due to space expansion. Nothing else that anyone knows about.
Depends. Just as with NASA probe launches, a moving gravitational body can increase, leave unchanged, or decrease photon energy depending on how the trajectory is done. That is, you can slingshot photons just like spaceships, only less effectively, and of course they stay at c (only energy/frequency/momentum changes).
No. Mass/energy is simply conserved, whether for photons or fermions.
Yes! But only at very, very small ranges. You have to accommodate superluminal photons in QED to get correct answers, in fact. For the situation you just described, the opposite applies: Long times mean very, very certain velocities.
All photons do just that, all the time. It's part of how they propagate, another aspect of how they "explore" alternate paths (the "integral of all possible histories"). They try to explore different velocities also, but conservation rules force that kind of "virtual" behavior to smooth out very, very quickly at the classical level.
Photons can interact, but it's not a terribly large effect at ordinary intensities, and is quite negligible at the scales and low intensities you are describing. If they interact at all it's via virtual particle pairs. My absolute favorite has been tested in the lab and demonstrated to be real: The right frequency of gamma rays colliding head on with green laser light will occasionally produce a high-velocity (gamma ray momentum dominates) electron-positron pair. Can't recall who did that, but it's been done and papers have been written, fairly recently (last few years).
For most of the above, the effects are virtual, which means that when you settle accounts all conservation laws must be met, and met fully. So for those, no. The one case you mentioned where you could get a false Doppler shift is via a negative gravitational slingshot. That's an interesting possibility, and I'm not aware of anyone ever having looked for it (near a black hole maybe?), but it's certainly not generic enough to account for the Doppler shifts seen in all directions.