Position 1: 
angle d L1A arm (deg.) 
Path L1B/L2B Lorentz contraction ( gLC ) 
Path L1A/L2A Lorentz contraction ( gLC ) 
velocity of local frame (m/s) 


Rotating Triangle Interferometer: 



L1
Length (m) 

SQRT(1v^2/(c^2)) 
SQRT(1v^2/(c^2)) 









angle d L1 arm (deg.) 


Refractive index (n) of arms 







L2
Length (m) 

Avg Time Dilation factor in v frame ( gt
) 
Path L1/L2 Lorentz contraction ( gLC ) 

X 

X 

Source 
Detector 


angle d L1B arm (deg.) 
SQRT(1v^2/(c^2)) 
SQRT(1v^2/(c^2)) 
1 



















Path
L1A Parallel: 
Path
L1B Parallel: 
L1
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) radial
path 
t'F (sec) radial path 
t'F (sec) circumference path 
t'
average (sec) 
t'
average (sec) 































C'F (m/s) 
C'F (m/s) 
C'R (m/s) 
C'
average (m/s) 
C'
average (m/s) 







Path L2A Parallel:

Path L2B Parallel:

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'F (sec) 
t'F (sec) 
t'
average (sec) 
t'
average (sec) 































C'F (m/s) 
C'F (m/s) 
C'R (m/s) 
C'
average (m/s) 
C'
average (m/s) 







Position 2: 
angle d L1A arm (deg.) 
Path L1B/L2B Lorentz contraction ( gLC ) 
Path L1A/L2A Lorentz contraction ( gLC ) 
velocity of local frame (m/s) 


Position 1 Length 
c/n 


L1
Length (m) 

SQRT(1v^2/(c^2)) 
SQRT(1v^2/(c^2)) 


m 





angle d L1 arm (deg.) 


Refractive index (n) of arms 




L2
Length (m) 

Avg Time Dilation factor in v frame ( gt
) 
Path L1/L2 Lorentz contraction ( gLC ) 


Position 2 Length 




angle d L1B arm (deg.) 
SQRT(1v^2/(c^2)) 
SQRT(1v^2/(c^2)) 
Light speed C (m/s) 

m 














Path
L1 Parallel: 
Path
L1 Parallel: 
C': 1/(n/c+v/c^2 * cosd
+v^2n/2c^3(1+cos^2d)) 
Total Newtonian Time t 
Local time Dilated 


Rotation velocity 

t'F (sec) radial path 
t'F (sec) radial path 
t'F (sec) circumference path 
t'
average (sec) 
t'
average (sec) 

m/s 





















Angle Position 1 



C'F (m/s) 
C'F (m/s) 
C'R (m/s) 
C'
average (m/s) 
C'
average (m/s) 

^{o}





Path L2 Parallel:

Path L2 Parallel:

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'F (sec) 
t'F (sec) 
t'
average (sec) 
t'
average (sec) 


Angle Position 2 









^{o}











C'F (m/s) 
C'F (m/s) 
C'R (m/s) 
C'
average (m/s) 
C'
average (m/s) 

Time Diff. Position 1 vs 2: 
Fringe Shift at Det. Pos. 1 vs 2 

Angular velocity 
Length overall (m): 
time difference (Sagnac Effect) 
time difference Position 1 (sec) 
time difference at Position 2 (sec) 










Note: The source and detector are at the origin
(0,0) on the graph. Motion is right to left. 


Radius 
Area 
fringe shift (Sagnac Effect) 
Fringe Diff forward/Rev. (l)

Fringe Diff Forward/Rev. (l) 

Light emitted by the source travels
clockwise/counterclockwise around the triangle.









The returning beams interfere at the detector
forming a fringe pattern. 





