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Half-duplex relativity

Galilean relativity requires the speed of light to be instantaneous (i.e., zero pace). Because the one-way speed of light is not known, it may be instantaneous as long as the mean speed of light is finite. Such a situation is possible if light is conceived as in half-duplex telecommunications: one direction at a time is observed or transmitted, but never both simultaneously.

Consider a light clock in this context:

light at restSaw-tooth light path

Let Δt be the time for one cycle of light at rest (top diagram). Let Δt’ be the time for one cycle of light traveling at relative velocity v (bottom diagram). The mean speed of light is c. Then

Δt = h/c or h = cΔt,

Δt’ = d/c, or d = cΔt’, and

b = vΔt’.

So that

d² = b² + h² = (cΔt’)² = (vΔt’)² + (cΔt)².Δt)

The result is

Δt’ = Δt/√(1 – v²/c²),

which is the time dilation of the Lorentz transform.

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