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I posted a simple thread regarding Lorentz transforms, but it has been locked for "staff review". May be because I used some "Net-Speak" conventions while writing some responses (which has earned me infraction points, never mind, my mistake). However, one of my questions remained unanswered there, and so this post...

Let's say, there are two mirrors in a train (mirrors A & B, separated by a distance of c/2 km, perpendicular to the motion of the train) so that they are arranged as "Last Bogy - A - B - Engine", and the speed of the train is v km/s.

So for an observer in the train, the distance traveled for light (with speed c km/s in the direction of the train for A-B-A path) will be 2*c/2=c. For an out side observer, the distance traveled would be,

(c/2) + a + (c/2) - a = c.

(c/2) + a for distance A to B; (c/2) - a for distance B to A

(this is not velocity addition; c is just a number ca. equal to 300000)

Note that, without considering the principle of relativity (or LR or SR for that matter), the distance traveled by light for both the observers is c (no length contraction). The time taken is also c/c=1s (no time dilation). the laws of physics are same for both the observers. Then why would we need the Lorentz transforms? Do correct me if I'm missing something?

For more clarification, for an outside observer, when the light starts traveling from mirror A to B, it will travel in the same direction as the train itself, so the mirror B (which is first destination of the light ray) will also move away from the light with the speed v (speed of the train), and hence, the light will have to travel more distance then just distance between the mirrors, which will amount to c/2 + a. however, when the ray reflects back from B to A, the mirror B will be approaching the wave of light (as the light is traveling in opposite direction from the motion of the train), so the wave will travel the distance c/2 - a.

Let's say, there are two mirrors in a train (mirrors A & B, separated by a distance of c/2 km, perpendicular to the motion of the train) so that they are arranged as "Last Bogy - A - B - Engine", and the speed of the train is v km/s.

So for an observer in the train, the distance traveled for light (with speed c km/s in the direction of the train for A-B-A path) will be 2*c/2=c. For an out side observer, the distance traveled would be,

(c/2) + a + (c/2) - a = c.

(c/2) + a for distance A to B; (c/2) - a for distance B to A

(this is not velocity addition; c is just a number ca. equal to 300000)

Note that, without considering the principle of relativity (or LR or SR for that matter), the distance traveled by light for both the observers is c (no length contraction). The time taken is also c/c=1s (no time dilation). the laws of physics are same for both the observers. Then why would we need the Lorentz transforms? Do correct me if I'm missing something?

For more clarification, for an outside observer, when the light starts traveling from mirror A to B, it will travel in the same direction as the train itself, so the mirror B (which is first destination of the light ray) will also move away from the light with the speed v (speed of the train), and hence, the light will have to travel more distance then just distance between the mirrors, which will amount to c/2 + a. however, when the ray reflects back from B to A, the mirror B will be approaching the wave of light (as the light is traveling in opposite direction from the motion of the train), so the wave will travel the distance c/2 - a.

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