Synchrony conventions

Reichenbach and Grünbaum noted that “the relation of simultaneity within each inertial reference frame contains an ineradicable element of convention which reveals itself in our ability to select (within certain limits) the value to be assigned to the one-way speed of light in that inertial frame.” (John A. Winnie, “Special Relativity without One-Way Velocity Assumptions: Part I,” Philosophy of Science, Vol. 37, No. 1, Mar., 1970, p. 81.)

Because the speed of light is measured as a round-trip speed, the one-way speed of light is unknown. It is a convention. This thesis is called the conventionality of simultaneity. Winnie writes (p. 82):

At time t1, by the clock at A, a light beam is sent to B and reflected back to A. Suppose that the return beam arrives at A at time t3 by the A-clock. The question now arises: at what time t2 (by the A-clock) did the beam arrive at B? Were we to “postulate” that the back and forth travel-times of the light beam were equal, clearly the answer is:

(1-1 ) t2 = t1 + (t3 – t1)/2

But should we fail to postulate the equality of the back-and-forth travel times, the best that we could do in this case would be to maintain that t2 is some timepoint between t1 and t3. Thus (using Reichenbach’s notation) we have the claim:

(1-2) t2 = t1 + ε(t3 – t1), (0 < ε < 1).

The simplest convention is one in which ε = ½, which is what Einstein suggested, by synchronizing clocks this way and slowly transporting them to other locations. It is called Einstein synchronization or synchrony convention (ESC). That way, the speed of light has the same value going and coming; it is a constant, c.

What would Galileo do? To preserve the Galilean transformation as much as possible, the speed of light either outgoing or incoming could be made effectively infinite. That would require a value of ε that is 0 (infinite speed outgoing) or 1 (infinite speed incoming). Such a Galilean synchrony convention (GSC) would need the speed of light in the other direction to equal c/2, that is, half of the ESC speed of light. That is because the harmonic mean of infinity and c/2 equals c (sequential speeds are averaged by the harmonic mean, not the arithmetic mean). Jason Lisle proposed such an anisotropic synchrony convention (ASC).

Synchrony is also required for those who use the diurnal movement of the sun and stars to tell time, i.e., the apparent or mean solar time. This applies to travel on or near the surface of the earth. The round trip time should not be affected by latitude or longitude, but without a correction for longitude, the travel time east or west would not match the return trip because of the direction of the sun’s motion. If one did not correct for latitude, travel north or south could also not match the return trip. It would be possible for a airplane to fly west with the sun or stars in the same position, so that no time elapsed in this sense.