I am not sure whether this belongs here or not, but I'll try this topic insteed of SR+GR I was wondering, since everytime I came across elementary particle equations, such as Dirac or Klein-Gordon, they all consider a metric in the process of a Minkowski space. I am not sure but I feel uneasiness when I extract results out of a Minkowski metric. Of course these results might be true,for let's say regions where gravity is absent. But what about regions where it's not? For an example, I can think of the solar neutrinos. Why do we want to think that neutrinos are generated and propagating from the sun according to a flat space's metric, whereas we accept that photons can indeed be bend by the sun's gravitation? Also, what's the problem of using in particle physics a general metric [itex]g^{\mu\nu}(x^{ρ})[/itex] instead of the constant [itex]g^{\mu\nu}=diag(+---)[/itex]?
The rule is (As Einstein once said) to make a problem as simple as possible but not simpler. If you don't need general coordinates to solve a problem than use the simpler Minkowsky coordinates.
For example, wouldn't the Schwarchild's metric (instead of Minkowski) be a better description of how the geometry around and near the sun is?
Yes, it is a better description. The question is what problem are you solving and do you need to use Schwartzchild's metric in order to solve it accurately?
For example? The solar neutrinos I mentioned above... By -for example- weak interactions we can predict the number of neutrinos reaching the earth from the sun. Of course the number we measure here is by far less than the one predicted (and that's a reason we speak about neutrino oscillations). On the other hand, I'm asking...don't weak interactions behave differently to a curved spacetime than they do in the flat minkowski space? so that there will be also a contribution in the rates we predict by that? Someone would also say that gravitation of the sun (or better put the curvature of spacetime around the sun) does not affect neutrinos or elementary particles in general...However we can observe the gravitational lensing happening by the sun onto the photons.... The same example I could also use for a more extreme limit- for example when we study the behavior of particles in the early universe times... (eg leptogenesis, baryongenesis, etc- of course some of them are consequences of symmetries so it's not exactly that I'm asking about). More specifically that even if on Earth we can study energies ~14TeV of the early universe, these studies are "closed" into the region of a by far "uncurved" spacetime in contrast to what should be the case when universe was still some seconds old.
Quantum field theory in curved spacetimes is ... tricky. You don't need it for solar neutrinos. Spacetime curvature everywhere in the solar system is tiny, and locally you always have a good approximation to a flat minkowski space (and weak interactions are very locally!). There are many independent oscillation measurements now, and they are well in agreement with each other. The solar neutrino problem is solved. Who said this? There is some influence - the neutrinos lose a tiny bit of energy. So tiny that it is way below the sensitivity of our detectors. Photon detection methods are much more sensitive, so there the effect has been observed.
There is an effect on observed rate due to time dilation but it is too small to be relevant to the solar neutrino problem.
Yeah I am not trying to solve the solar neutrino problem (I accept neutrino oscillations ). But I guess physicists before introducing that phenomenon, would also try to do some corrections? But I guess that the corrections should be totally negligible... One more motivation for asking that, is that in general when we define fields, we ask for them to have a spacelike separation...in order for us to define spacelike separations we need a metric before... am I wrong? But before dealing with the metric as a dynamical variable-solution of Einstein's equation (since I don't want to get into Quantum Gravity)- I would ask for a given -not flat metric- would things change dramatically or not?