A Note on Metrics in General Relativity

Space Time Distances

There are two Minkowski metrics: the “right one” and the “wrong one”. The right one, g^μ_ν=(-1,1,1,1), is right because it has positive spatial distances (time distances are already less intuitive than space distances, so there is no real obstacle to making them be negative). The wrong one (which is perfectly fine to use, as long as you are consistent) has negative spatial distances and positive temporal distances. This metric, g^μ_ν=(1,-1,-1,-1), is commonly used by people from a particle physics background, whereas the right one is typically used by people from a relativity background.