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L1 Length (m)
angle
d
L1 arm (deg.)
Path L1 Lorentz contraction (
a
LC )
velocity of local frame (m/s)
a
=SQRT(1-v^2/(c^2))
L2 Length (m)
angle
d
L2 arm (deg.)
Refractive index (n) of arms
Path L2 Lorentz contraction (
a
LC )
X
L1 Arm
L2 Arm
L1p
L2p
Source
Detector
Stationary light speed C (m/s)
Avg Time Dilation factor in v frame
(
a
t )
a
=SQRT(1-v^2/(c^2))
l
in vacuum (m)
Optical Path L1:
C': 1/(n/c+v/c^2 * cos
d
+v^2n/2c^3(1+cos^2
d
))
Total Newtonian Time t
Local time Dilated
t'
F (sec)
t'R
(sec)
t' average (sec)
t' average (sec) *
a
t
C'
F (m/s)
C'
R (m/s)
C' average (m/s)
C' average (m/s) /
a
t
Optical Path L2:
C': 1/(n/c+v/c^2 * cosd +v^2n/2c^3(1+cos^2d))
Total Newtonian Time t
Local time Dilated
t'
F (sec)
t'R
(sec)
t' average (sec)
t' average (sec) *
a
t
C'
F (m/s)
C'
R (m/s)
C' average (m/s)
C' average (m/s) /
a
t
Local time dilation at position L1p along the optical path
time difference at detector (sec)
distance L1p (m)
Newtonian time at L1p (sec)
local time in v frame at L1p (sec)
"0"
c/n
L1p/(c/n)
L1
F
*
a
LC
/ C'
F
+ L1
R
*
a
LC
/ C'
R
Forward Trip (m)
Fringe Shift at Detector (
l
)
L1 Length (m)
L2 Length (m)
Newtonian time *
a
t
at L1p (sec)
time dilation Newtonian - local (sec)
"0"
Reverse trip (m)
L1p*
a
t
/(c/n)
L1/(c/n)-(L1
F
*
a
LC
/C'
F
+L1
R
*
a
LC
/C'
R
)
Local Time Dilation at Position L1p
Local time dilation at position L2p along the optical path
[L1/(c/n)-(L1F*
a
LC/C'F+L1R*
a
LC/C'R)]/[L1*
a
t/(c/n)-L1/(c/n)]
Clock position L1p (m)
Clock Position L2p (m)
distance L2p (m)
Newtonian time at L2p (sec)
local time in v frame at L2p
(sec)
L2p/(c/n)
L2
F
*
a
LC
/ C'
F
+ L2
R
*
a
LC
/ C'
R
*
a
t
Forward Trip (m)
Local Time Dilation at Position L2p
Newtonian time *
a
t
at L1p (sec)
time dilation Newtonian - local (sec)
[L2/(c/n)-(L2F*
a
LC/C'F+L2R*
a
LC/C'R)]/[L2*
a
t/(c/n)-L2/(c/n)]
L1 Path Angle (deg.)
L2 Path Angle (deg.)
Reverse trip (m)
L2p*
a
t
/(c/n)
L2/(c/n)-(L2
F
*
a
LC
/C'
F
+L2
R
*
a
LC
/C'
R
)
*
a
t
This spreadsheet is a simulation of a Michelson interferometer similar to the Shamir and Fox Experiment of 1969. In this simulation using Lorentz Ether Theory (LET) the source and detector are at the origin (0,0) and the interferometer is moving to the left at the velocity of the local frame (adjustable above). The refractive index along the optical arms is adjustable, as well as the length of each arm and its angle to the motion. This simulation demonstrates that in the transformation from the stationary to moving state the speed of light will appear to be C no matter how the interferometer is adjusted - it demonstrates that if a preferred frame for light speed exists, it is undetectable by this method. The average time dilation when the beams arrive back at the moving detector is
a
t = SQRT(v^2/c^2). Less time has elapsed in the moving frame, 1 second of apparent time in the moving frame is
g
*t longer than in the stationary frame.
However, the implied time dilation at any other point during the light trip along the interferometer arms can be calculated by moving the clock position on each arm with the sliders. The local time dilation at these points is found to rise to a maximum at the forward end of each arm before averaging out to 1
a
when the beams meet back at the detector. This suggests time dilation is not a real change in time but rather a synchronization error between moving clocks. In fact, the discrepency increases as the velocity decreases, since the synchronization error arises from the first order velocity difference, whereas the average time dilation is a second order effect.
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