Recently I've been trying to learn General and Special Relativity by myself. There is an specific thing I do not understand perfectly, proper time in the metric of the space-time. Take the case of an empty space-time: $$-c^2 \mathrm d \tau^2 = -c^2 \mathrm d t^2 + \mathrm d x^2 + \mathrm d y^2 +...