Time Dilation: Astronaut in Moving Spaceship

[apope]

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]

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]

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 (AVI, 5 Mb)
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.rm (Real, 0.3 Mb)

Does that address your question?

 

[apope]

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 (AVI, 5 Mb)
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.rm (Real, 0.3 Mb)

Does that address your question?

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 traveling straight up? =/

 

[JesseM]

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..

If the flashlight or laser or whatever is moving along with the mirrors, the beam will shoot straight up in the rest frame of the flashlight, not in the frame where the mirrors are moving. If this wasn't true, it would violate the postulate that the laws of physics are the same in every frame, i.e. that no experiment you can do in a windowless room in deep space will tell you whether you at rest relative to a given object (the galaxy, say) or moving at high velocity relative to it. If the beam went straight up in our frame when the flashlight was moving to the right, this would mean that in the flashlight's own rest frame the beam is being emitted at an angle rather than parallel to the orientation of the flashlight, so a person in a windowless room would be able to tell whether they were at rest relative to us or moving relative to us by turning on a flashlight and seeing whether the beam was parallel to its orientation in their own rest frame, a definite violation of that postulate of relativity.

 

[JesseM]

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.

They are both shot up in straight lines, in the rest frame of the mirrors and beam-emitter (the 'flashlight' in my post above). But this means that if you are moving relative to the mirrors and beam-emitter, in your frame the light must move at an angle.

 

[apope]

im beginning to understand.. but can someone give me another example of time dilation that could help me out.

 

[apope]

so basically... the time it takes for the light to reach the mirror and come back relative to the astronaut in the ship is shorter than the time i observe it to happen? does this not mean that the event occurs twice? sorry if it's a stupid question