This is kind of an exploration on an idea I posted in the another thread - that the force produced by a field should be affected according to time dilation. If gravity is 'emitted' by massive objects then less of it should be emitted by objects which experience time dilation. However, this is counteracted exactly by relativistic mass increase since both are governed by the lorentz factor. Coincidence? It makes me wonder if all fields will behave in this way. The mass of an electron will increase if it is moving at relativistic speeds and it will accordingly experience time dilation. Will the electron then emit a smaller electric field since it is 'emitting' em field particles more slowly? Or will the field somehow become strengthened? The problem here is that charge would be related to mass of the electron. Its only normal to assume that gravity is affected by mass, but charge would imply that there is something inherently charged in the makeup of the electron, so that when the electron got heavier its charge also increased. This would however be undetectable and therefore nonexistent according to the tenets of logical positivism. The question really boils down to whether the electric field of an electron can be measured to decrease when that electron is moving at a relativistic speed. But this would lead to violations of momentum and conservation of energy. So, it is probably the case that the electric field does not change. Working with this you have to assume that the field is not emitted but rather an indentation of electric space (or whatever) or that the emitter is somehow strengthened in direct proportion to time dilation. This by definition cannot be tested. Please Register or Log in to view the hidden image!
Coincidence that a theory which has a postulate that physics is frame invariant ends up making a prediction that some physics is frame invariant? No, not really. This is not how quantum, field theory works. You don't have some rate at which charged objects emit bosons, you calculate probability amplitudes for given processes. When you calculate the differential cross section of a process you calculate the contribution from one, two, three etc exchanged particles and you aren't interested in how quickly they are exchanged. Everything is done statistically because you can't give a precise statement about "In this second an electron will emit 30 photons", you can only sum over all possibilities and you get statistical results.
This certainly does not add credence to the fundamental laws. If the theory was made to be intact with these laws then there is no way this same theory can break them - and if the theory can in fact be turned on itself it is more a mistake by the author than it is a proof against the basic laws, innit? So suppose that instead of a single electron you test hundreds - the average of the 'field profiles' (or something like that) of many relativistic electrons vs newtonian electrons. This way you can get a statistically significant result. So, does the charge in fact 'emit' bosons? If it does, wouldn't you agree that it should do this at a slower rate when time is dilated?
Fields certainly look different to different observers. This happens even in classical electromagnetism, which also happens to have the Lorentz transformations built into it, despite the fact that special relativity hadn't been discovered yet. Electric fields look like they have magnetic components when viewed by moving observers, things like that. In QFT it gets worse, even particle number can change from observer to observer. I can't quite envisage your scenario but there is probably something interesting to be said about it. Probably nothing not already known though.
