Half-duplex relativity

Galilean relativity requires the speed of light to be infinite (i.e., zero pace). Because the one-way speed of light is not known, it may be infinite as long as the two-way 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:Saw-tooth light pathLet 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.