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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) |
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Rotating Triangle Interferometer: |
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| L1
Length (m) |
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SQRT(1-v^2/(c^2)) |
SQRT(1-v^2/(c^2)) |
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angle d L1 arm (deg.) |
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Refractive index (n) of arms |
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| L2
Length (m) |
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Avg Time Dilation factor in v frame ( gt
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Path L1/L2 Lorentz contraction ( gLC ) |
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Source |
Detector |
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angle d L1B arm (deg.) |
SQRT(1-v^2/(c^2)) |
SQRT(1-v^2/(c^2)) |
1 |
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| Path
L1A Parallel: |
Path
L1B Parallel: |
L1
C': 1/(n/c+v/c^2 * cosd +v^2n/2c^3(1+cos^2d))
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Total Newtonian Time t |
Local time Dilated |
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| t'F (sec) radial
path |
t'F (sec) radial path |
t'F (sec) circumference path |
t'
average (sec) |
t'
average (sec) |
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| C'F (m/s) |
C'F (m/s) |
C'R (m/s) |
C'
average (m/s) |
C'
average (m/s) |
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Path L2A Parallel:
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Path L2B Parallel:
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L2
C': 1/(n/c+v/c^2 * cosd +v^2n/2c^3(1+cos^2d)) |
Total Newtonian Time t |
Local time Dilated |
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| t'F (sec) |
t'F (sec) |
t'F (sec) |
t'
average (sec) |
t'
average (sec) |
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| C'F (m/s) |
C'F (m/s) |
C'R (m/s) |
C'
average (m/s) |
C'
average (m/s) |
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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) |
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Position 1 Length |
c/n |
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| L1
Length (m) |
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SQRT(1-v^2/(c^2)) |
SQRT(1-v^2/(c^2)) |
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m |
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angle d L1 arm (deg.) |
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Refractive index (n) of arms |
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| L2
Length (m) |
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Avg Time Dilation factor in v frame ( gt
) |
Path L1/L2 Lorentz contraction ( gLC ) |
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Position 2 Length |
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angle d L1B arm (deg.) |
SQRT(1-v^2/(c^2)) |
SQRT(1-v^2/(c^2)) |
Light speed C (m/s) |
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m |
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| 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 |
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Rotation velocity |
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| t'F (sec) radial path |
t'F (sec) radial path |
t'F (sec) circumference path |
t'
average (sec) |
t'
average (sec) |
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m/s |
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Angle Position 1 |
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| C'F (m/s) |
C'F (m/s) |
C'R (m/s) |
C'
average (m/s) |
C'
average (m/s) |
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Path L2 Parallel:
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Path L2 Parallel:
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C': 1/(n/c+v/c^2 * cosd +v^2n/2c^3(1+cos^2d)) |
Total Newtonian Time t |
Local time Dilated |
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| t'F (sec) |
t'F (sec) |
t'F (sec) |
t'
average (sec) |
t'
average (sec) |
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Angle Position 2 |
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o
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| C'F (m/s) |
C'F (m/s) |
C'R (m/s) |
C'
average (m/s) |
C'
average (m/s) |
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Time Diff. Position 1 vs 2: |
Fringe Shift at Det. Pos. 1 vs 2 |
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Angular velocity |
Length overall (m): |
time difference (Sagnac Effect) |
time difference Position 1 (sec) |
time difference at Position 2 (sec) |
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Note: The source and detector are at the origin
(0,0) on the graph. Motion is right to left. |
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Radius |
Area |
fringe shift (Sagnac Effect) |
Fringe Diff forward/Rev. (l)
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Fringe Diff Forward/Rev. (l) |
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Light emitted by the source travels
clockwise/counterclockwise around the triangle.
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The returning beams interfere at the detector
forming a fringe pattern. |
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