reply to post by Arbitrageur
All right, let's see.
Before I start, please remember that in this thread, I am NOT attempting to falsify Einstein's Relativity of simultaneity. I am simply discussing the
fact that Relativity of Simultaneity naturally implies Relativity of Speed of Light, which is not a bad thing but nevertheless still is in
contradiction with our current understanding of light.
Okay. My maths are VERY rusty, but I'll give it a try:
Let us imagine that the train is 4 x 299,792,458 meters long.
The observer is in the center of the moving train. There is 2 x 299,792,458 meters between him and each ends of the train.
Let us also imagine that the train moves at the speed of 1/2 c.
As the train rushes at 1/2 c, the two lightning bolts simultaneously strike both ends of the train, generating Event A (on the rear) and Event B (on
the front).
Because of the train's velocity, it doesn't take 2 seconds for the light from Event B to reach the observer, but in fact 1.3 second (d/(c+v) =
2/(1+0.5) = 1.3). This creates the illusion that Event B happened
before Event A.
Because of the train's velocity, it doesn't take 2 seconds for the light from Event A to reach the observer, but in fact 4 seconds (d/(c+v) =
2/(1+-0.5) = 4). This creates the illusion that Event A happened
after Event B.
This shows that for Relativity of Simultaneity to occur, Relativity of Speed of Light must exist.
Since this seems in contradiction with current understanding of light, one may invoke length contraction and/or time dilation as a solution. But
again, this only resolves one Event out of two, never both:
If length contraction occurs at relativistic speed, to the point of transforming 3 x 299,792,458 meters into 2 x 299,792,458 meters, then this may
indeed solve the Event B's anomalous light speed:
3/(1+0.5) = 2 seconds for 2 x 299,792,458 meters (as perceived by the observer inside the train) = normal speed of light
But such contraction does not solve the Event A light speed anomaly:
3/(1+-0.5) = 6 seconds for 2 x 299,792,458 meters (as perceived by the observer inside the train) = abnormal speed of light
In fact, such length contraction renders the Event A speed anomaly even more at odds with the Michelson-Morley experiment.
If time dilation occurs at relativistic speed, to the point of slowing 1.3 seconds to 2 seconds (transformation ratio: 0.65), then this may indeed
solve the Event B's anomalous light speed:
(2/(1+0.5))/0.65 = 2 seconds for 299,792,458 meters (as perceived by the observer inside the train) = normal speed of light
But such dilation does not solve the Event A ligth speed anomaly:
(2/(1+-0.5))/0.65 = 6.153 seconds for 299,792,458 meters (as perceived by the observer inside the train) = abnormal speed of light
In fact, such time dilation renders the Event A speed anomaly even more at odds with the Michelson-Morley experiment.
So... there is it. Something keeps on showing up, and that's the apparent relativity of the speed of light.
Is it possible that the Michelson-Morley device was not capable if detecting evidences of relative speed of light for an observer moving below 0.0001
c?
Regards,
Swan