How Does Light Speed Change in Relativity?

[thought]

if a ship is going at half the speed of of light (just imagine okay) and there is a light in the center of the ship then how fast would the light appear to go to somebody at the back of the ship?

first it would look like it was going at the speed of light to an outsider so to the person in the ship it would look like it was going at 1.5c. then time would dialate (to one half speed?) and the speed would increase even more (to 3c). however light appears to go at the same speed for all observers so how does this work?

 

[HallsofIvy]

No, a basic premise of relativity, based on experimental evidence, is that the speed of light is the same in every frame of reference. If a rocket, going at 1/2 the speed of light, relative to an observer on an asteroid it is passing, shines a light toward its front, that observer would see the light leaving the ship at c, the speed of light, a person on the ship would see it leaving at c, indeed a person going the opposite direction at 99% the speed of light would see it leaving the ship at c. Nor would any of those observer's notice anything peculiar about that. The observer on the asteroid, seeing the ship go past at c/2 and seeing the light moving at c, having studied relativity, would calculate that a person in the ship would see the light leaving at
$$\frac{c- c/2}{1-\frac{c(c/2)}{c^2}}= \frac{c/2}{1- 1/2}= \frac{c/2}{1/2}= c$$. He would calculate that the person on the ship going the opposite direction at 99% the speed of light would see the light going from the first ship at $$\frac{.99c+ c/2}{1+\frac{.99c(c/2)}{c^2}}= \frac{1.49c}{1+ 0.49}= c$$.

 

[thought]

but

but how fast does the light going towards the back of the ship look like its going?

 

[jackle]

but how fast does the light going towards the back of the ship look like its going?

Light always goes at c

 

[Jimmy Snyder]

but how fast does the light going towards the back of the ship look like its going?

As HallsOfIvy wrote, a basic premise of relativity, based on experimental evidence, is that the speed of light is the same in every frame of reference.
What that means is that when any observer measures the speed of light, they always get the same value, no matter how fast the emitter is traveling with respect to the observer.

This is by no means a trivial statement. Compare this to tossing a baseball while on a train. Different observers see the ball traveling at different speeds depending upon how fast they see the train travelling.

Because of this consistency in the speed of light, concepts of space and time need to be adjusted.

 

[thought]

Yes but time dilates to accommodate for the light moving forwards (half speed) however when the light moves towards the back the speed would look like 1.5/.5 or 3, the light would look like it was moving at three times the speed of light. I know it is based on experimental evidence and I'm asking how that works. I know it is time dilation but how exactly does that time dilation work?

 

[JesseM]

Yes but time dilates to accommodate for the light moving forwards (half speed) however when the light moves towards the back the speed would look like 1.5/.5 or 3, the light would look like it was moving at three times the speed of light. I know it is based on experimental evidence and I'm asking how that works. I know it is time dilation but how exactly does that time dilation work?

No, the speed of light is the same for an inertial observer no matter which direction it goes. One thing to keep in mind is that it's not just time dilation that explains this, it's also the fact that different frames define simultaneity differently--two events that happen at the same time-coordinate in one frame happen at different time-coordinates in another. You might find the example I gave on this thread helpful in understanding how this ensures that different observers measure the same speed of light.

 

[franznietzsche]

Yes but time dilates to accommodate for the light moving forwards (half speed) however when the light moves towards the back the speed would look like 1.5/.5 or 3, the light would look like it was moving at three times the speed of light. I know it is based on experimental evidence and I'm asking how that works. I know it is time dilation but how exactly does that time dilation work?

No, the speed of light is always c, for all observers, no matter how they are moving. This is a postulate (and one well supported by experiment). Time dilation is a necessary consequence of this.