rbwinn wrote:
[...]
All you have is a clock running at a different rate than the clock in
the frame of reference of the track. Other than that, the train,
bolts of lightning, and motion of the train happen the same as shown
by these equations.

x'=x-vt
y'=y
z'=z
t'=t

The bolts of lightning strike simultaneously in both frames of
reference. The flashes of lightning are seen at the same time by the
observer by the track. The flashes of lightning are seen at the same
time by the observer on the train.

Doesn't work. Consider two events: light from the front flash
reaching the observer on the train, and light from the rear
flash reaching that same observer. According to your last
sentence above, Robert, the observer on the train finds that
those two events coincide; they happen at the same point in
space and time.

Both the Galilean transform and the Lorentz transform are
1-to-1. A single point in the space and time coordinates
of one frame maps to just one point in the other. Therefore
in the coordinate system in which the track is stationary,
the two events must likewise occur at the same point in
space and time.

When we work out the results from the track-bound observer's
frame of reference, either the two light fronts moves at
different speeds in that frame, or the two events happen at
different places and different times. Robert, if I understood
correctly, your theory accepts that the speed of light is the
same in all frames that are in Galilean motion. If so, your
theory is self-contradictory.


--
--Bryan