I assume here, Billy T, that the clocks on the embankment frame are synchronized wrt each other. Meaning that instantaneously the embankment clocks read the same time.
Here is some physics that the statement above ignores. When the flash of lights occur the source of the flash has no effect on the speed of the flashes of light. As the frame is moving wrt the embankment, the "vacua", the light will surely reach the on coming light from the rear of the train before the forward moving light will arrive at the forward clock.
One cannot use a relative motion for measuring the absolute motion of light. The light knows not of the moving bombs and clocks, one approaching, the other receding both wrt the motion of the lights.
The clocks on the moving frame are also synchronized within the moving frame. There is no rational manipulation of the independence postulate that will allow the lights to arrive at the two clocks simultaneously in the moving frame.
Whatever is the perception of an observer at the midpoint of the two clocks, the light is moving at a speed c wrt to the vacua, and seen from the embankment, Vce - Vte = Vlt, which say the speed of light wrt to the embankment, minus the speed of the train, also wrt the embankment, provides the realtive velocity of frame aand photon, as seen from the embankment.
The expression above was that derived by Einstein in "Relativity", Section 7. However, AE took the expression for the relative motion of frame and photon and intended the reader to believe that this expression was using the train as the inertial coordniate system, and then he complained that this measured the speed of light less than c.
It could not be clearer that the expression is merely describing the measured relative motion of frame and photon, and is not an expression for a " measured speed of light". The speed of light is always c wrt the vacua.
Billy T said:
Do you not use the clocks of your own frame to judge simultaneity?
The clocks on the embankment will measure sequential explosions that occur due to the arrival of the two light pulses at the points the bombs are located on the moving frame, as will the clocks on the moving frame.
Billy T, the lights do not move in some special manner to satisfy notions of the SRT observers. When the flashes arew emitted, it is the same as if the lights were emitted in the stationary frame as the speed of light is independent of the speed of the source of the lights. If there is mome time dilation and/or Lorentz contraction in the sapce covereed by the foprward moving nphoton,m then what kind of time/space manipulation occurs in the space traveled by the rear moving light?
When you impose the independence postulate on the moving lights all becomes crystal clear.
When the rearward moving photon has covered a distance ct,m the frame has moved a distance vt toward the rear moving photon. The forward moving photon has also moved ct, and is locted a distance 2vt from the forward clock. This photon covers the 2vt distance plus the small distance the frame moves in the interim, vt', in time t',or ct' = 2vt + vt', or t' = t(2v)/(c - v), the time the two lights would be moving in the same direction had the left photon reflected at the left clock. In any event, t' is time difference in the explosions measured on the moving frame, by the moving frame clocks.
Billy T said:
Recall that there is some frame in which my birth is simultaneous with that of Christ. (I think Christ's birth proceded mine by about 2000 years - but I stupidly compare simultaneity using only my clocks,
without computation for all other frames.)
Thus, to consider other frames when judging if two events are simultaneous (for you) or not is ridiculess.
Billy T, We need not compare clocks in this experiment. We need only determine if the clocks on the moving frame receive the flashes simultaneously or sequentially. (See above, the lights arrived sequentially on the moving frame).
Billy T said:
I designed this scenario to avoid using any theory.* Only use your mind and fact speed of light is independent of direction of travel. (I do not even require that it is the same in all frames!) It could be 3x10^8 on train and 2x10^8 on the ground and my thought experiment still shows:
Events Simultaneous in one frame are NOT Simultaneous in any other.
You assumed that the explosions would occur simultaneously on the moving frame, which I showed the oppisite. That the explosions were sequential will be reflected by the clock reading in the stationary frame as well as the moving frame. It is only in the condition where the frame is actually stationary wrt the vacua that "at rest physics is allowed".
I refer you to those rationalizations of the Twin Paradox (Feynman, Bohm et al) where only in the space ship frame, that actuially accelerated and moved, was the age rate lowered, the earth frame being considered at rest wrt the spwace ship throughout. This is the same as saying only in the accelerated frames do SRT effects occur, which means all the train embankment gedanken must be edited to demand that only the train accelerates, not the embankment, but then there goes the equivalence of intertial frames postulates. The self-slaying cycle of this result is cruel, I know.
Geistkiesel