In quantum mechanics, the position and momentum of a particle cannot be known simultaneously. In special relativity, the idea of simultaneity loses its meaning. Would it be possible to measure first the position of a particle and then the momentum of a particle, and do a Lorentz transformation into a frame where those two measurements are made simultaneously? If not, why not? If that is possible, does this violate the Heisenberg uncertainty principle?
Furthermore, would it be possible for an observer who makes those two measurements at different points in time to transmit that information into a Lorentz frame in which those two measurements are made simultaneously?