Time Dilation Explained: What About Light Speed?

[richardparsons]

Many explanations of time dilation use light sent from mirror to mirror on moving spaceships to explain that since the distance the light travels increases then time must increase in order to keep the speed of light the same . . . however, in order for the light to leave one spaceship and hit the other one, the light must have a horizontal velocity equal to the speed of the spaceship . . . if it has c as its speed toward the other ship and it has a horizontal velocity . . . then, in fact, its speed is greater than c . . which is not allowed. How does this work?

 

[Doc Al]

Many explanations of time dilation use light sent from mirror to mirror on moving spaceships to explain that since the distance the light travels increases then time must increase in order to keep the speed of light the same

Yes, the standard "light clock" thought experiment.

. . . however, in order for the light to leave one spaceship and hit the other one,

The light just bounces back and forth between two mirrors inside the one spaceship.

the light must have a horizontal velocity equal to the speed of the spaceship . . . if it has c as its speed toward the other ship and it has a horizontal velocity . . . then, in fact, its speed is greater than c . . which is not allowed. How does this work?

When the moving light clock is viewed from another frame it is certainly true that the light pulses must have a horizontal component of velocity equal to that of the spaceship. But from that frame, the light moves at an angle with speed c.

In the moving spaceship's own frame, the light just moves vertically. Also at speed c.

 

[ghwellsjr]

Here's an animation I made that might help you:

https://www.youtube.com/watch?v=dEhvU31YaCw

If you want detailed explanation, see this thread.