# Time dilation textbook

my textbook shows me an example where an astronaut is in a spaceship beside 2 parallel mirrors with a beam of light coming from the bottom, reflecting off the top and coming back to the bottom. It says that the light has to travel farther if the spaceship is moving because it must travel the hypotenuse of the triangle where y is mirror to mirror and x is the distance the ship travels. and therefore the light takes more time from an observer on earth's frame of reference than the astronaut's (where it only travels the y component). what i don't get is why, in the case of the moving ship, if the beam is shot from the middle of the bottom mirror does it not hit the top mirror a little bit off center and come back to the bottom one in not exactly the same position..

so basically.. if the ship is moving near the speed of light (or if the mirrors are incredibly small), couldn't the beam of light coming from the bottom mirror miss the top mirror, because by the time it reached the top it had moved with the spaceship?

Janus
Staff Emeritus
Gold Member
so basically.. if the ship is moving near the speed of light (or if the mirrors are incredibly small), couldn't the beam of light coming from the bottom mirror miss the top mirror, because by the time it reached the top it had moved with the spaceship?

That would violate the postulate that the speed of light is the same in all inertial frames. If the light "drifted" like this in the view of the Astronaut, then what happens if he fires the light in the same direction as he is traveling? It would, for him, take more time to reach the mirror than it does to return from the mirror. Meaning, relative to himself, the speed of the light would change depending on what direction it was moving.

robphy
Homework Helper
Gold Member
so basically.. if the ship is moving near the speed of light (or if the mirrors are incredibly small), couldn't the beam of light coming from the bottom mirror miss the top mirror, because by the time it reached the top it had moved with the spaceship?

In response to a question like this [that seems to come up every now and then], I developed the following explanation:
that beam of light is the particular beam (among a family of beams from the emission event) that reaches the mirror (at the reception event).

Here's an animation from my webpage:
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.avi [Broken] (AVI, 5 Mb)
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.rm [Broken] (Real, 0.3 Mb)

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In response to a question like this [that seems to come up every now and then], I developed the following explanation:
that beam of light is the particular beam (among a family of beams from the emission event) that reaches the mirror (at the reception event).

Here's an animation from my webpage:
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.avi [Broken] (AVI, 5 Mb)
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.rm [Broken] (Real, 0.3 Mb)

that's exactly what's happening in this example... i didn't realize the second beam was shot on an angle like that, i thought they were both shot up in straight lines. but then, shouldn't it take longer for the second beam to hit the mirror even if the ship weren't moving since its vertical velocity is less than the one travelling straight up? =/

Last edited by a moderator:
JesseM