# General theory of relativity

# Equivalence principle

Einstein’s **equivalence principle** has to do with the equivalence of the inertial mass and graviational mass of an object. That is, the mass of an object measured by exerting a known force and observing its acceleration (using Newton’s second law to solve for the obejct’s mass) *is the same as* the object’s mass as derived from the gravitational force it exerts on another object with known mass (allowing us to solve for the object’s mass using Newton’s universal gravitation formula). While these two definitions of mass are conceptually different, experiments have long shown that the two are the same, yielding measured values of mass in many different scenarios.

While their equivalence was assumed, it was never understood why this was the case until Einstein. Einstein stated that one could not tell the difference between resting in a gravitational field (e.g. standing on Earth) and being inside a non-inertial, or accelerating, reference frame. This hypothetical comparison of course assumes that the acceleration of the reference frame is the same as the acceleration due to gravity in the corresponding gravitational field. The equivalence here is the due to the fact that an observer would feel the exact same “force” in both scenarios; fall to earth due to gravity or the floor of a reference frame’s acceleration toward you (e.g. a rocket ship in deep space) due to its outward acceleration while you would otherwise be floating.

A similar statement can be said about weightlessness. There is no discernible difference between freely floating in deep space and free falling in a gravitational field (Einstein’s “happiest thought”). In both cases the observer would be unable to feel their own weight. While the observer may be situated in a gravitational field and is subject to gravity pulling them back to earth (while in free fall), there is no floor for them to be pushed into, to “realize” the effects of gravity for the observer.

# One way speed of light

The measurement of the speed of light has only ever involved measuring the “two way speed of light”. That is, the only way to accurately measure the speed of light involves the travel of light away from and back to a single clock (or the equivalent of this; some experiments involving multiple clocks can be reduced to this situation). The common assumption is then that light travels the same speed to and from the source, but experimentally this hasn’t been proven. In theory, light could travel at different speeds in different directions, at the most extreme $c/2$ in one direction and instantaneously in the other. So long as the round trip time results in an average speed of $c$, we have no way to experimentally determine if there were varying speeds along the journey. As a result, physical laws seems to be indifferent on whether or not the symmetry holds, but it’s nevertheless an interesting thought experiment (namely the idea of seeing the across the galaxy in real-time, with light reaching across massive distances instantly). Great video from Veritasium here.