On May 19, 2016, at 10:27 AM, Warren D Smith <warren.wds@gmail.com> wrote:
You've heard of the "principle of least time" in optics... light follows a path which minimizes the time it takes to get there... in quantum field theory there is a more general action principle, which is that the integral, over all paths followed by all particles, of exp(i*T*m*c^2/hbar) dT is stationarized, where T is the proper time consumed by that particle (of rest mass m) in following its trajectory. (Actually things a bit trickier for spinor particles, and there are certain constant factors inserted whenever two particles merge or bifurcate, but I will ignore that here.)
Taking seriously -- in quantum mechanics -- the sum over all paths, one has to include particle world-lines parts of which are not time-like and over which T is pure imaginary. With the right choice of sign, “tachyonic” propagation is thereby suppressed in a direct way. If the Hilbert action formulation is the right way to think about classical GR, i.e. the Einstein equations are just a consequence, then it seems reasonable that action-stationarity in that setting is also the hbar->0 asymptotics of a sum-over-whatever (e.g. metrics) principle. Nobody has yet made sense of that sum. Are there real-exponentially suppressed configurations? -Veit