i already posted a homework question in the homework forum. i'm asking this question so i can finish my homework but its not just for one particular question so i'm just gonna ask it here.(adsbygoogle = window.adsbygoogle || []).push({});

i'm not 100% sure about how the speed of light stays constant in all reference frames. say i'm driving on the surface of earth and there is a beam of light at the very back end of my car traveling towards the front of my car. so in my reference frame, relative to me, the light beam is moving at the speed of light right? and relative to say a tree on earths surface, it is still moving at the speed of light.

so say i want to know how long the beam of light will take to go from the back of my car to the front of it, relative to my reference frame. the beam of light will take t' = d'/c where d is the proper length of my car relative to my reference frame, to travel all across it. so say my car is 10m long, then it will take the light 10m/c to travel from the back to the front of my car?

i think that is correct. so if i want to know how long it will take the light to travel from the back to the front of my car relative to the tree's reference frame it it will be t = y*t = sqrt(1 - v^2/c^2) * 10m/c where v is the velocity of the car? which will end up being slightly smaller than t' am i right?

so basically in the tree's reference frame it will measure fewer seconds for the light to go from the back to the front of the car, and in the car's reference frame it will measure more seconds for the light to go from the back to the front? can someone please just tell me if i'm correct about this. i'm in my first modern physics course and learning about relativity for my first time.

edit:

so lets say light is moving in the opposite direction of the car. lets say the car is going 10m/s in the +x direction and the light is going at speed c in the -x direction. does that mean the light relative to the car is still going at c? And not (c + 10m/s)?

would it take light the same amount of time to travel from the front to the back of my car while im driving straight as it would to travel from the back to the front if im moving straight?

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# Question about how the speed of light is constant

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