On 8/12/16 8/12/16 9:19 PM,
danco...@gmail.com wrote:
> [...]
> The only first-order effect that is present in your apparatus is the Sagnac effect.
Not true. There are two effects that are first-order in v/c: Sagnac and SR's
RoS. By varying the fiber configuration and turning the optical processing on
and off I can measure them separately.
Here are the three setups that convinced me that I can cancel the Sagnac effect
and measure RoS. They show unequivocally that I can separate Sagnac from RoS.
These are all the idealized calculation using light pulses, using idealized fibers.
In all figures I do not draw the moving rod or its supports, I draw only light
paths in fibers, and components: PD=photodetector, M1,M2=50% mirrors, X=optical
processing; the source sends simultaneous light pulses into two fibers and is at
rest in the lab. In all cases when two paths are together, consider them right
on top of each other, not separated as my ASCII art shows. At the right are
frame labels bracketed by "!". View in a fixed-width font.
================================ Setup A ================================
The fibers are bent 180 degrees at the ends of the rod, infinitesimally outside
the mirrors. At the center of the rod (below PD) and at the optical processing
(X) the fibers hinge without changing length (at *). The rod frame moves
left-right, here shown at its center-of-motion moving right.
M1 M2 !
|---------------------------->PD<----------------------------| ! Rod
-----------------------------* *------------------------------ ! Frame
| |
| |
| |
| | (Fibers don't
| | flex, they
| | hinge at *)
| |
| |
* * !
X X ! Lab
Source ! Frame
With the optical processing off there is NO delay between pulses at the PD.
There is no Sagnac effect, because A=0. A more careful analysis of light speed
in the rod frame shows that the pulses in the two fibers arrive simultaneously
at the center of the rod, move to M1 and M2 over equal distances with equal
speeds, and also from M1 and M2 to PD, hence no time offset at PD. Note the
pulses do NOT arrive at M1 and M2 simultaneously in the lab frame: in the lab
frame the pulses arrive simultaneously at the center of the rod, move to M1 and
M2 at different speeds over different distances (so they don't arrive
simultaneously at M1 and M2), but those differences are exactly canceled in the
paths from M1 and M2 to PD, hence no time offset at PD.
With the optical processing on there IS delay between pulses at the PD,
displaying SR's relativity of simultaneity. (Remember the optical processing
keeps the pulses simultaneous in the lab at M1 and M2 by changing the individual
fiber lengths at each X.)
================================ Setup B ================================
The fibers are bent 90 degrees at the ends of the rod, infinitesimally outside
the mirrors. At the ends of the rod and in the lab below them the fibers hinge
without changing length (at *). The rod frame moves left-right, here shown at
its center-of-motion moving right.
M1 M2 !
|---------------------------->PD<----------------------------| ! Rod
* * ! Frame
| |
| |
| |
| |
| (Fibers don't flex, |
| they hinge at *) |
| |
| |
* * !
----------------------------- ----------------------------- !
X X ! Lab
Source ! Frame
With the optical processing off there IS delay between pulses at the PD. By
construction the pulses arrive at M1 and M2 simultaneously in the lab, so there
is delay between them at PD which can be attributed to either the Sagnac effect
or to SR's RoS.
With the optical processing on there IS delay between pulses at the PD, as this
is the same as with it off.
================================ Setup C ================================
The fibers are bent 90 degrees at the ends of the rod, far outside the mirrors
which are moved toward the center of the rod. At the ends of the rod and in the
lab below them the fibers hinge without changing length (at *). The rod frame
moves left-right, here shown at its center-of-motion moving right.
M1 M2 !
--------------|-------------->PD<--------------|-------------- ! Rod
* * ! Frame
| |
| |
| |
| |
| (Fibers don't flex, |
| they hinge at *) |
| |
| |
* * !
----------------------------- ----------------------------- !
X X ! Lab
Source ! Frame
With the optical processing off there IS delay between pulses at the PD. By
construction the pulses arrive at the ends of the rod simultaneously in the lab,
so there is delay between them at PD which can be attributed to either the
Sagnac effect or to SR's RoS. Note the pulses do NOT arrive simultaneously in
the lab at M1 and M2.
With the optical processing on there IS delay between pulses at the PD, but it
is DIFFERENT from that with the processing off. This demonstrates SR's RoS, and
the processing has cancelled the additional effect of Sagnac.
Tom Roberts