By Bruce W. Macdonald
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Extra info for China, Space Weapons, and U.S. Security (Csr)
Where ϕ was the angle separating the rod and the x0-axis when the rod was at rest in frame S0.
The body moves along a long rod O′′x2 which is at rest with respect to the S2 frame. At time t0 (for S0), the body has covered a distance A in S2, which is equal to the real length of O′′A measured from reference frame S0, with a non-contracted meter stick. We will use the subscript “r” for real and “app” for apparent. 13) SO S1 S2 rod A O O' O'' x0 x1x2 Figure 10. At instant t0 the body has covered the distance O′′A in reference frame S2. From Galileo to Lorentz… and Beyond 45 where v01 and v02 are, respectively, the real speeds of S1 and S2 with respect to S0.
4) we obtain: = ∆= v01 A 0 C2 2 1 − v02 / C 2 V − v01 . 1)). = 0 V − v01 V − v02 24 Joseph Lévy This time is the universal time measured with clocks attached to frame S0, in which there is no speed of light anisotropy and no clock retardation. However, in frame S1 we must take the synchronism discrepancy effect and clock retardation into account, so that the experimental ‘apparent’ time obtained when we use the Poincaré-Einstein method is: 2 T1app = T1r 1 − v01 / C2 − ∆ = A0 2 2 1 − v02 / C 2 (1 − v01V / C ) 2 1 − v01 / C2 V − v02 .