Time dilation, mirror question

[ucsdhopeful]

I only know time dilation in it's basic form and it was explained to me beautifully using mirrors in a spacecraft . The light would go vertically, taking longer if you were at a stationary frame looking into the spacecraft . This all made sense to me; however, what would happen if the mirrors were horizontally placed, and light traveled horizontally? I know this is the basis of length contraction, but wouldn't light take less time to go from one mirror to another?

 

[ghwellsjr]

Maybe this will help: consider a spacecraft traveling very close to the speed of light. For the vertical orientation of the mirrors, the path of the light will be very close to a straight line as viewed from the stationary frame. Now if you consider the horizontal orientation of the mirrors, they have to be very close together in order for the light path to be the same distance and therefore to take the same amount of time as the vertical orientation.

Just think if they were no closer together, it would take a very long time for the light to catch up to one of the mirrors in the horizontal orientation.

 

[Janus]

I only know time dilation in it's basic form and it was explained to me beautifully using mirrors in a spacecraft . The light would go vertically, taking longer if you were at a stationary frame looking into the spacecraft . This all made sense to me; however, what would happen if the mirrors were horizontally placed, and light traveled horizontally? I know this is the basis of length contraction, but wouldn't light take less time to go from one mirror to another?

If you mean that according to the stationary frame, the light will take less time to between the mirrors going one way than when going the other, then yes. This is an effect known as the Relativity of Simultaneity. For instance, let's say that you are halfway between two mirrors and you sent a pulse of light to both. According to you, the pulses will reach the mirrors at the same time. However, from a frame which considers you as moving, the pulse will arrive at the mirrors at different times. Event that are simultaneous for you are not simultaneous for them.

You will both agree that the light pulse will return to you at the same time . For you, each pulse took the same time going out and coming back, and for the other frame one pulse took less time going out and more coming back while the other pulse took more time going out and less time coming back.