Let say the Earth is not moving through space...Then a beam splitter that refracts the beam into 2 new created beams at an angle of 90° towards reflectors which will reflect the beams at 180° again to the splitter will be eventually touched by these reflected beams. But in the case the Earth is moving, and we know it is moving just to not fall into the Sun for example...then the reflected beams will not end their journeys into the splitter but a little bit away from it due to a bit of path traveled by the Earth during the time the 2 reflected beams reach again the splitter. So as we know the speed of light and the geometry of the setup of that virtual experiment we should figure out the absolute speed of Earth?
2$\begingroup$ Absolute motion doesn't exist. $\endgroup$– David WhiteFeb 21 at 20:45
$\begingroup$ @DavidWhite Please, suggest an edit but not to change the aim of the question... $\endgroup$– jbradvi9Feb 21 at 20:48
2$\begingroup$ My whole point is that the question cannot be answered as stated. Only relative motion can be measured, and there is no unique stationary reference point from which to make the measurement that you allude to. $\endgroup$– David WhiteFeb 21 at 20:59
$\begingroup$ How is this different from en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment ? $\endgroup$– BowlOfRedFeb 21 at 22:59
$\begingroup$ Are you reinventing the Michaelson interferometer? If you weren't aware of it and came up with this experiment from first principles, that's impressive. $\endgroup$– RC_23Apr 26 at 5:05
The problem here is that the source (laser) is stationary relative to the prism and so they are in the same inertial reference frame. There is no shift in position because the whole set-up is (in effect) stationary.
If you allow the prism to move relative to the laser, this doesn't improve anything because at best all you measure is the relative speed of the prism and laser.
It's probably worth mentioning the Michelson-Morley experiment in this regard which attempted to do determine is there was an ether (which performed the role of an absolute reference frame). What it found was that there was no ether - no absolute reference frame.
$\begingroup$ Please answer.. if we point a laser in direction of a wall from a moving train perpendicular to the motion of the train would the reflected beam end on the point where it was emitted or the motion of the train would cause the beam missing the starting point? $\endgroup$– jbradvi9Feb 22 at 10:29
In addition the Stephen's answer consider this. Each of your light paths travels in the same direction. They just do it in a different order. The top path goes up then goes down. The bottom path goes down and then up. So any gain or loss in any direction would be realized by both arms.
$\begingroup$ comment-question...If the Earth was moving down so paralel to the beams should we detect no deflection of the beam i.e. the beam would end its journey onto the splitter? $\endgroup$– jbradvi9Feb 22 at 10:21