This post was inspired by Chandru Iyer’s post *here*.

Consider a light ray sent a certain *distance* *s* that is immediately reflected back. According to Newtonian mechanics if a light ray travels at speed *c*, then for a body moving at speed *v *relative to the stationary frame, the light ray should travel at the speed *c − v* one way and at speed *c + v* the other way.

The *total distance* of the light ray is 2*s*. The *total time* of the light ray is

Then the mean speed is

However, according to Einstein’s relativity theory, the mean speed of light is a constant, *c*. So the above speed needs to be multiplied by the gamma factor squared, *γ*². As Iyer notes, this is accomplished by contracting the moving rulers by the factor (1/*γ*) and dilating the moving clocks by the factor *γ*.

**But that is not the correct approach.**

Consider a light ray sent a certain *distance* *s* that is immediately reflected back, for a total distance of 2*s*. Since distance is the independent variable, time is a dependent variable and pace instead of speed is the proper rate of motion. The pace for speed *c* is 1/*c* and the pace for speed *v* is 1/*v*. Then for a body moving at pace 1/*v *relative to the stationary frame, the light ray should travel at the pace 1/*c − 1/v* one way and at pace 1/*c + 1*/*v* the other way. Then the total time is

This is the same as that observed from the rest frame. The mean pace is

If time *is* the independent variable, the result is similar:

Consider a light ray sent a certain *time interval* *t* that is immediately reflected back, for a total time of 2*t*. According to Newtonian mechanics if a light ray travels at speed *c*, then for a body moving at speed *v *relative to the stationary frame, the light ray should travel at the speed *c − v* one way and at speed *c + v* the other way.

The *total time* of the light ray is 2*t*. The *total distance* of the light ray is

Again, this is the same as that observed from the rest frame. The mean speed is