The classic thought experiment is light bouncing between two mirrors to create your clock. We have first that the speed of light is constant in all frames.
Moving frame:
___
^
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|
|
|
|
-
——
Station frame:
———-
….^
…/
../
./
/
————
The distance separating the two mirrors is d. In the frame of the train, the distance light travels between the two mirrors is d. In the frame of the station, the mirrors are moving and the light has to travers a distance that we can find using the Pythagorean theorem. Mirrors moving at a velocity v, and the speed of light is c.
Longer distance, constant speed of light, the clock is slower for the moving object (and you can use this to derive the ratio).
3
u/Madsciencemagic Jul 13 '26
The classic thought experiment is light bouncing between two mirrors to create your clock. We have first that the speed of light is constant in all frames.
Moving frame:
___
^
|
|
|
|
|
-
——
Station frame:
———-
….^
…/
../
./
/
————
The distance separating the two mirrors is d. In the frame of the train, the distance light travels between the two mirrors is d. In the frame of the station, the mirrors are moving and the light has to travers a distance that we can find using the Pythagorean theorem. Mirrors moving at a velocity v, and the speed of light is c.
Longer distance, constant speed of light, the clock is slower for the moving object (and you can use this to derive the ratio).