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:
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.