In Greene's video: https://www.youtube.com/watch?v=2pV20KuDucs

In the video Greene describes a fairly well-known thought experiment. A person is in a rectangular box floating in space with a laser mounted on middle of one wall. The light beam hits the middle of wall opposite.

Then the box is imagined in free fall where the person in the box notices no difference but the outside observe sees the beam follow a curved path.

It seems that whether in free fall or floating in space the light looks the same to the person in the box but to an observer outside the box in free fall the light beam traverses a greater distance but arrives in the same time. That seems like it is moving faster than light -- how can this be?

Neglecting what the person in the box observes, the time it takes the beam to follow the curved, hence longer, path is exactly the same for the outside observer which to me implies the light is moving faster.

EDIT: It sounds like the guy in the box, moving with respect to the observer, has time moving more slowly so this is as I understand it just plain special relativity and is sort of like the mirror experiment.

  • $\begingroup$ yes. Time dilation $\endgroup$
    – Kosm
    Sep 14 '20 at 21:28

Light moves at $c$ with respect to local inertial coordinates. It doesn't move at $c$ with respect to arbitrary coordinates, even in special relativity. (For example, with respect to Rindler coordinates in special relativity, the speed of light isn't $c$.)

In general relativity, there are no global inertial coordinates in general. Light just doesn't travel at $c$, except locally in a certain sense.

In this particular problem, you can use inertial coordinates where light travels at $c$ (the freefall/box coordinates), but you don't have to.


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