This in fact applies to any time-like curve in spacetime, whether or not it is a geodesic. If one also notes that with a metric of signature +,-,-,- that geodesics actually maximize arc length (quite different from the Riemannian case) one has a quick resolution of the "twin paradox" (the "non-traveling twin" has a world line that is a geodesic while the traveling twin has a non-geodesic world line, so the non-traveling twin's world line has the greater proper time)

 

Vaguely, the application of "rocket thrusters", by the traveling twin, somehow "drives them against the grain of space-time", so that they are "shoved along a short-cut" through space-time ?? Somehow the artificial force "cut corners off" the would-have-been geodesic arc-length-path ??

 

Vaguely, I intuit "maximizing arc-length" as "maximizing proper time" as implying that, in the absence of artificial forces, particles "lackadaisically take their time" through space-time ??

Edited February 6, 201213 yr by Widdekind

I'm not really good in physics, but when you said that "photons are timeless"

 

.. feels like "From the moment a photon was born, it traveled observing everything else halt"

Edited February 6, 201213 yr by khaled