Idealized Determination of Absolute Velocity of an Inertial Frame Coordinate System

Take an arbitrary inertially moving point as the origin. Synchronize seven clocks at the origin. Use one clock at the origin to mediate the symmetrical deployment of the other six clocks to points equal lengths from the origin on each of three orthogonal axes. If there is no effect of movement on clocks, all clocks will remain synchronized with each other, this is assumed to be so. Because the system is not at rest, light signals sent between moved clocks may not take the same time in each direction. After timing light in each direction for each axis, the clocks are returned to the origin to verify synchroneity. If the velocity of this coordinate system in the rest system, β = 〈βx, βy, βz〉, is an unknown, and if one way light time in the positive x direction is Tx1 and in the opposite direction Tx2, then `*`(rho, `*`(x)) = `/`(`*`(`+`(T[x1], `-`(T[x2]))), `*`(`+`(T[x1], T[x2]))) has the sign of βx, and we can take as a first approximation βx = ρx, (and similarly for the other axes.) We can refine our approximation of β by aligning our x-axis with the direction of β and repeating entire procedure until ρy and ρz vanish.

With the positive x-axis parallel to known β if a light signal is sent from a clock at (x1, y1, z1, t1) to a synchronized clock at (x2, y2, z2, t2), then `+`(t[2], `-`(t[1])) = `/`(`*`(sqrt(`+`(`*`(`^`(`+`((`+`(x[2], `-`(x[1])))(`+`(1, `-`(`*`(`^`(beta, 2))))), `-`(`cβ`(`+`(t[2], `-`(t[1]))))), 2)), (`+`(1, `-`(`*`(`^`(beta, 2)))))(`+`(`*`(`^`(`+`.... Solving, `+`(t[2], `-`(t[1])) = `+`(`/`(`*`(beta, `*`(`+`(x[2], `-`(x[1])))), `*`(c)), `&+-`(sqrt(`+`(`*`(`^`(beta(`+`(x[2], `-`(x[1]))), 4)), `*`(`^`(`+`(y[2], `-`(y[1])), 2)), `*`(`^`(`+`(z[2], `-`(z[1])), 2..., using the sign of (x2 - x1).

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