Re: What Exactly Happens to TIME in GPS Orbit?


Sorceror

http://www.androcles01.pwp.blueyonder.co.uk/Sagnac/Sagnac.htm

Merry Xmas ;-)

http://www.mathpages.com/rr/s2-07/2-07.htm

"Despite the ease and clarity with which special relativity accounts
for the Sagnac effect, one occasionally sees claims that this effect
entails a conflict with the principles of special relativity. The usual
claim is that the Sagnac effect somehow falsifies the invariance of
light speed with respect to all inertial coordinate systems. Of course,
it does no such thing, as is obvious from the fact that the simple
description of an arbitrary Sagnac device given above is based on
isotropic light speed with respect to one particular system of inertial
coordinates, and all other inertial coordinate systems are related to
this one by Lorentz transformations, which are defined as the
transformations that preserve light speed. Hence no description of a
Sagnac device in terms of any system of inertial coordinates can
possibly entail non-isotropic light speed, nor can any such description
yield physically observable results different from those derived above
(which are known to agree with experiment).



Nevertheless, it remains a seminal tenet of anti-relativityism (for
lack of a better term) that the trivial Sagnac effect somehow
"disproves relativity". Those who espouse this view sometimes claim
that the expressions "c+v" and "c-v" appearing in the derivation of the
phase shift are prima facie proof that the speed of light is not c with
respect to some inertial coordinate system. When it is pointed out that
those quantities do not refer to the speed of light, but rather to the
sum and difference of the speed of light and the speed of some other
object, both with respect to a single inertial coordinate system, which
can be as great as 2c according to special relativity, the
anti-relativityists are undaunted, and merely proceed to construct
progressively more convoluted and specious "objections". For example,
they sometimes argue that each point on the perimeter of a rotating
circular Sagnac device is always instantaneously at rest in some
inertial coordinate system, and according to special relativity the
speed of light is precisely c in all directions with respect to any
inertial system of coordinates, so (they argue) the speed of light must
be isotropic at every point around the entire circumference of the
loop, and hence the light pulses must take an equal amount of time to
traverse the loop in either direction. Needless to say, this
"reasoning" is invalid, because the pulses of light are never (let
alone always) at the same point in the loop at the same time during
their respective trips around the loop in opposite directions. At any
given instant the point of the loop where one pulse is located is
necessarily accelerating with respect to the instantaneous inertial
rest frame of the point on the loop where the other pulse is located
(and vice versa). As noted above, it¹s self-evident that since the
speed of light is isotropic with respect to at least one particular
frame of reference, and since every other frame is related to that
frame by a transformation that explicitly preserves light speed, no
inconsistency with the invariance of the speed of light can arise.



Having accepted that the observable effects predicted by special
relativity for a Sagnac device are correct and entail no logical
inconsistency, the dedicated opponents of special relativity sometimes
resort to claims that there is nevertheless an inconsistency in the
relativistic interpretation of what's really happening locally around
the device in certain extreme circumstances. The fundamental fallacy
underlying such claims is the idea that the beams of light are
traveling the same, or at least congruent, inertial paths through space
and time as they proceed from the source to the detector. If this were
true, their inertial speeds would indeed need to differ in order for
their arrival times at the detector to differ. However, the two pulses
do not traverse congruent paths from emission to detector (assuming the
device is absolutely rotating). The co-rotating beam is traveling
slightly farther than the counter-rotating beam in the inertial sense,
because the detector is moving away from the former and toward the
latter while they are in transit. Naturally the ratio of optical path
lengths is the same with respect to any fixed system of inertial
coordinates."

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