Question

I've heard three seemingly contradictory facts, so apparently I'm not understanding at least one of them correctly.

Proper time along a path is the time elapsed for a clock that travels along that path.

Proper time along a null path is zero.

There are no preferred inertial reference frames, so if I travel at the speed of light, my own clock that I take with me will tick like normal for me.

So how can it tick like normal but then not tick at all? Which of these three statements is incorrect?

Answer 1

Time dilation in special relativity explains the seemingly contradictory statements.

Step-by-step explanation:

The seemingly contradictory statements can be resolved with an understanding of time dilation in special relativity. Time dilation in special relativity explains the seemingly contradictory statements.

Proper time is the time elapsed for a clock that travels along a path. Along a null path, where the object is not moving, the proper time is indeed zero.

However, when an object is moving at the speed of light, according to the Earth-bound observer, time slows down in the moving frame. This means that the clock carried by the object would appear to tick slower or not tick at all, depending on the relative velocity between the two frames of reference.