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In an intro level college physics class, we were taught about the thought experiment showing how light would be bent in an accelerating reference frame (see this YouTube video for a visual), and by the principle of equivalence, gravity bends light (and space-time). The way the thought experiment was explained, however, seems to suggest that the light would also be bent in a reference frame moving with constant velocity. Is this the case? Or would light not be bent because it also has constant velocity in the same direction as the reference frame? If that was the case, wouldn't light be moving faster than c?

Srihari P
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1 Answers1

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There is no bending - light always travels in straight lines in an inertial frame - but the observed direction of the path is different, because from the point of view of a frame moving relative to a sequence of events, the sequence of events don't occur in the same place. Because the speed of light is the same for all observers, a change in the measured time makes up the difference.

Suppose you have a laser emitter, a mirror, and a detector. You point the laser straight up towards the mirror. It goes in a straight line for $\Delta t$, bounces off of the mirror, goes in a straight line, and hits the detector at $2 \Delta t$.

I zip past you at some relative velocity $v$. I, too, see the laser leave your emitter, travel in a straight line, strike the mirror, bounce off, travel in a straight line, and strike the detector.

However, in my frame, the emitter is at $x=0$, the mirror's x-coordinate when the laser hits it is at $x=v\Delta t'$, and the detector is at $x=2v \Delta t'$ when the laser hits it.

Our Lorentz factor for shifting between my frame and yours, $\gamma = 1/\sqrt{1-v^2/c^2}$ such that $\Delta t' = \gamma \Delta t$, coordinates between our frames such that light can travel at $c$ along the shorter path in your frame (floor to ceiling to floor), while in my frame, it travels at $c$ along the longer path, but I measure a commensurately longer time between the same events.

See wikipedia for an explanation with pictures.

g s
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