Light Beam Opposite Motion: Einstein Special Theory

[MZaeemQ]

Hello Everyone. I recently studied the Einstein special theory of relativity. I studied the thought experiment where a beam of light is thrown from a moving spaceship in the direction of its motion and the distance after a certain time interval was different from perspective of a man on spaceship from a man on Earth (I understand this). the conclusion was that time on spaceship passed at a slower rate than on earth.
My Question is that what if the light beam is thrown from back window of the spaceship opposite to its direction of motion? because in this case the result may be that time on Earth passes slowly than that on spaceship. reversed effect from same experiment ??

 

[Ibix]

No. That would be self-contradictory. Clocks will always tick slower as observed by someone who sees them moving.

Typically the derivation of the Lorentz transforms involves light moving both forwards and backwards in a moving vehicle. It may be possible to derive them with light traveling in only one direction, but I haven't seen it done.

 

[MZaeemQ]

let me elaborate my question. suppose there are two spaceships A and B. A is moving with very high speed (say 1 m/s) in x-axis and B is at rest. A throws a beam of light where distance on x-axis of the beam is 0 w.r.t both A and B. now beam travels with constant speed of light (assume 2 m/s). after 2 seconds the distance on x-axis of beam from B is 4m while distance from A is 2m because A is already in motion. as speed of light is constant, so something must give way for distance to be reduced for A. that thing is Time. so we can deduce that time on spaceship A passed slowly compared to that on B. right ?
Now same experiment but this time throw light beam in opposite direction to motion of A. this time we get reversed results. why ?

 

[Ibix]

1m/s is 3.6kph - a slow walking pace. The speed of light is 3x10⁸m/s.

There are three effects of special relativity. Time dilation and length contraction are the famous ones, but the notion of "simultaneous" is also something that changes between frames. Between the three things it's possible to produce a coherent explanation of your scenario.

The end-points of both your scenarios happen four seconds after the light was emitted, which is to say that they end simultaneously - according to B. However, things that are simultaneous according to B are not simultaneous according to A. A has no problem with the fact that the pulses are different distances away from him because, from A's perspective, the measurements of their location were not made simultaneously. The light had different amounts of time to travel, so it traveled different distances.

Einstein used very nearly this exact example to derive the Lorentz transforms. Google for Einstein's train thought experiment.