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From: DSeppala on 6 Mar 2010 20:24
Please help with the SR physics explanation of the following
probability problem.

Let there be two inertial reference frames with a relative velocity V
along the x-axis. Let there be two pulses traveling along the x-axis
from the left (negative) direction toward the right direction
(positive direction). I'll label these two pulses AL and BL. Let
these two pulses have identical pulse widths. In one frame they each
have a pulse length equal to L and in the other reference frame they
each have a pulse length equal to L'. Let the pulses travel a great
distance along the x-axis. At some random time after the pulses have
started traveling, a photon (or any point object) is emitted and
travels across the x-axis at some random x position far removed from
the starting points of the two pulses. Don't observers in both frames
conclude that the likelihood of this photon crossing the x-axis and
hitting pulse AL is equal to the likelihood of this photon crossing
the x-axis and hitting pulse BL since both observers agree that the
pulse width of AL equals BL?
If that is not correct please explain which pulse has a higher
likelihood of being hit by this photon as it crosses the x-axis.
If it is correct that both pulses have the same probability of
being hit by the photon as it crosses the x-axis, then what happens if
pulse AL is reflected off a mirror that has zero velocity in the non-
primed frame, and pulse BL is reflected off a mirror that has zero
velocity relative to the primed frame. I'll call these reflected
pulses AR and BR to indicate they are coming from the right and going
to the left. If a pulse is reflected off a mirror that is stationary
in its reference frame, the pulse width remains constant (per SR). If
a pulse is reflected off a mirror that is moving relative to a frame
along the same axis as the pulse, the observers in that frame measure
that the pulse width changes (per SR). Therefore the two frames now
measure that the pulse width of AR does not equal the pulse width of
BR.
One frame measures pulses AL and BL and AR to all have the
identical pulse width, while the other frame measures pulses AL and BL
and BR to have the identical pulse width. Now if a photon is emitted
that crosses the x-axis at some random time and position far removed
from where these two mirrors reflected pulses AL and BL, then one
frame measures the likelihood of the photon hitting pulse AR is equal
to the probability of hitting AL and BL, while the other frame
measures the likelihood of the photon hitting pulse BR is equal to the
probability of the photon hitting AL and BL. Yet because neither
frame measures AR and BR to be the same pulse width, they do not
measure the likelihood of the photon hitting pulse AR to equal the
proability of hitting BR. I don't see how this is mathematically
possible if the experiment is repeated N times with N being an
extremely large number.
Thanks,
David Seppala, Bastrop, TX

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