A funny kind of rectilinearity
- From: msadkins04@xxxxxxxxx
- Date: 30 Jul 2005 15:25:01 -0700
In SR, light propagates in a vacuum in a straight line and does not
share the velocity of the source (i.e., additive velocities do not
apply to c regardless of the motion of the source). But clearly it
does share the velocity -- at least, the directional component of the
velocity vector. And the angle of this "straight line" is something
different for every frame.
For example, consider a frame S', which has a pulse-laser at A and a
detector at B, and the path of the light defines a straight line from A
to B. This straight line is at a right angle to an axis we can call
y'. Now, consider a frame S which views S' as moving with a velocity
whose directional component is along the axis y'. From the perspective
of S', who considers his own frame at rest, at time t'1 the laser fires
a pulse at A, which is received by B at time t'2, and B has not moved
between time t'1 and time t'2. However, from the perspective of S, B
*has* moved between the time t1 that the laser fires, and the time t2
that it is detected, and therefore the light travels not from A at time
t1 to where B *is* at time t1, but rather from A at time t1 to where B
*will be* at time t2; and this is not a right-angle to the axis y'.
The only way that the light could take this path is if the light shares
the direction component of the velocity vector of S' -- despite not
sharing the scalar component!
Since the path of the light as assumed by S is longer than the path
assumed by S', then assuming (as both do) that the scalar component of
c is absolute regardless of the velocity of the source, light must take
longer to cover the path assumed by S than to cover the path assumed by
S'. Hence the time light takes to cross this path will be asserted by
S' to have a value less than that asserted by S.
However, each frame's assumptions about the path light takes (and they
are just that, assumptions) have already been incorporated into the
clock synchronization procedures. That is, S', in synchronizing his
clocks, assumes himself at rest; whereas S assumes that the clocks in
S' are in motion; and since light (having an assumed absolute velocity)
is used in SR to conduct the synchronization procedure, S and S' will
have different assumptions about the length of the path light travels
during that synchronization. Thus, it can be seen that the "dilation"
is really an artifact of different assumptions about the length of the
path light takes when S' synchronizes his clocks.
If the principle of the relativity of simultaneity were applied
universally in SR, S would have to conclude that S' mis-synchronized
his clocks, because he incorporated wrong assumptions about the length
of the path that light took from one clock to another during his clock
synchronization procedures. If he did that, the "dilations" would
disappear because they no longer have any mathematical basis. But, in
constrast to every other "observation" by S, in which S is free to deem
his observations correct (even when they disagree with those of S'),
here S, instead of quite properly insisting that S' has
mis-synchronized his clocks, accepts the clock synchronization
procedures of S' as valid!
When I brought this fact out in a previous Usenet post some time ago,
one respondent sneered, "Well, of course S assumes that S' knows how to
properly synchronize his clocks". In fact, however, it isn't the
mechanical prowess of S' that is at issue, but his *assumptions* about
the length of the path taken by light traveling between his clocks
during his synchronization procedure. Why S should be free to insist
on the validity of his own observations with respect to every other
event other than the clock synchronization procedure of S', but not in
the latter case, is a mystery whose answer is not to be found in the
literature of SR.
Mark Adkins
msadkins04@xxxxxxxxx
.
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