On May 8, 8:45�pm, Bryan Olson wrote:
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.

--
Thank you for your input, Bryan. As a matter of fact, we can work out
this little difficulty that you have envisioning what happens. We
have two observers, one by the track and one on the train. As far as
the coordinates of space are concerned, the Galilean transformation
equations have no distance contraction, no relativity of simultaneity,
no other shell games. The light is where it is in both frames of
reference. The difference is in the time in each frame of reference
at any given x and x'.
The lightning strikes in both frames of reference at t'=t=0. The
two observers are both at the middle of the train. A photon starts
toward the observers from the front of the train toward both
observers, a photon starts from the back of the train toward both
observers. The train moves in the +x direction at a velocity of v.
When the photon from the front of the train reaches the observer on
the train, it has traveled a distance of .5L in the frame of reference
of the train, where L is the length of the train. In the frame of
reference of the track, it has traveled a shorter distance. The point
it is traveling from in the frame of reference of the track is the
mark left by the lightning on the track. The point where it is
traveling from in the frame of reference of the train is the mark left
by the lightning on the front of the train. Since the photon is
traveling at a speed of c in both frames of reference, when it reaches
the observer on the train, it has traveled a time of .5L/c, but in the
frame of reference of the track, it has only traveled (.5L minus the
distance the train has traveled)/c, so time at that event is less in
the frame of reference of the track. The photon passes the observer
on the train and continues on to the observer by the track, reaching
him in a time of .5L/c in the frame of reference of the track.
The flash of light from the rear of the train proceeds from the
point where it was emitted in the frame of reference of the track, the
mark left by the lightning on the track, to the observer by the track,
reaching him in a time of .5L/c. When the light reaches the observer
by the track, the train has moved forward, so in the frame of
reference of the train, it hs prosceeded from the point where it was
emitted in the frame of reference of the train, the mark on the
caboose of the train, to the observer by the track, a shorter distance
because the distance between the caboose of the train and the observer
by the track has decreased. Therefore in the frame of reference of
the train, the light reaches the observer by the track in a time of (.
5L minus the distance the train has traveled) divided by c. The light
then continues on to the observer at the middle of the train, reaching
him in a time of .5L/c.
The time the observer on the ground sees the two flashes of light
is .5L/c as measured by a cesium clock in S, the frame of reference of
the track, and the time the observer on the train sees the two flashes
of light is .5L/c as measured by a cesium clock on the train. Time on
the cesium clock in S is t in the Galilean transformation equations.
Time on the cesium clock in S' is given by

n'=t(1-v/w)
w= velocity of light.

All that is necessary is relativity of time, which can be determined
in each frame of reference by the distance a photon has traveled in
that frame of reference from the time it is emitted until the time it
is observed.
Robert B. Winn