Hi folks, In his seminal work of 1937, Wigner showed that the rest mass and (absolute) spin of a particle are the same for all observers related by Lorentz transformation. Does anyone know whether these quantities are also preserved under transformations to relatively accelerated observers (including those rotating w/r/t each other)? Many thanks!
For point particles, we can use general covariance and the properties of a manifold to define mass and spin. Basically, in a small enough neighborhood of a point, we can introduce flat coordinates. So we have local Poincare invariance to allow us to define mass and spin. Since the flat coordinates have to map nicely on intersections of neighborhoods, when we extend this to the rest of the manifold we will find that all observers must agree on the mass and spin of the particle. For extended particles like the proton, in any experiment that we could actually do, the curvature is constant over the microscopic size of the particle, so we can treat them like point particles. For extended systems (size comparable to the distances over which the curvature is varying), it can be very complicated to define mass and angular momentum. See this wiki for an extensive discussion and references.
Thanks for that! But can I ask how the situation looks even in flat spacetime? I appreciate that observers related by Poincare transformations will always agree on the proper mass and absolute spin of a particle, but what about observers accelerating w/r/t each other, even in Minkowski spacetime? Any thoughts much appreciated!