What is proper time? Is it a part of Minkowski space (that is a mere spacetime interval)? Or is it an intrinsic characteristic of massive particles (a sort of "aging")? Example: In the following Minkowski diagram,
A is the worldline of a particle moving with the observer's reference frame.
B is the worldline of another particle with proper time between two events = 4 (space distance x= 3, time interval t = 5, proper time τ = 4, according to the equation $$ \tau^2 = \delta t^2 - \delta x^2 $$)
C is just 2 events without any worldline between, and if a particle would travel through both events, its proper time would be 4
Is there proper time in C even if no particle is travelling there? Or is in C only hypothetic proper time in case a particle is travelling this path?