I understand that it is more common in GR for the metric to be given a $(-,+,+,+)$ signature and more common in particle physics (or field theory, as Peskin & Schroeder tells me) to use the $(+,-,-,-)$ metric signature. I'm wondering why. Is there any advantage in these disciplines in terms of actual physics to using one over the other, or it simply an entrenched arbitrary convention?
In the theory of geometry of space-time, it makes much more sense to use $-+++$ because geometric view comes from intuition about 3D space, where we have metric $+++$. Time requires opposite sign, so we end up naturally with $-+++$ (or $+++-$ in some books).
In other areas where geometry and space distances are not that important but particles and their proper time is, and four-momenta appear a lot, using $+---$ makes the expression $p^\mu p_\mu$ proportional to rest mass squared, and $dx^\mu dx_\mu$ on the trajectory of particle turns out positive, which is more convenient if we want it to be differential of proper time squared. I hear also that in the theory of spinors, $+---$ is much more convenient.