Anisotropy and reality

This follows posts on synchrony conventions such as here.

Astronomers say things like this: “it takes sunlight an average of 8 minutes and 20 seconds to travel from the Sun to the Earth.”

The statement above assumes the Einstein convention that the one-way speed of light is isotropic and so equal to one-half of the two-way speed of light. However, it is possible that the one-way speed of light could be anywhere in the range of c/2 to infinity as long as the two-way speed of light equals c. So, the speed of light could be c/2 one direction and infinity in the opposite direction.

The possibility seems strange until we consider how we ordinarily speak. We see the sun in the sky and its position now is taken as the position where it appears to be. It turns out there is nothing wrong with that manner of thinking and speaking. It is the same as saying the incoming speed of light is infinite, which is perfectly acceptable as long as the outgoing speed of light is c/2.

And so it is with all the comets, moons, planets, and stars: where they appear to be now is where we ordinarily speak of them as being. If there were something wrong with this manner of speaking, we should correct it, but there is nothing wrong with it.

There is something similar happening down on Earth with measurements of the travel time of commuters. The time and location of multiple travelers may be compiled by a traffic data office from electronic communications or from recordings made at the time of measurement. Travel times are then presented with tables and maps such as this isochrone map:

The travel times are taken as they were at one instant, as if vehicles all arrived at the isochrone lines simultaneously. That is how we think and speak about it, whether or not it is exactly true.

Effectively this says that the speed of each commuter or signal they transmit is infinite in one direction – the direction to the traffic data office – and a finite measured value in the travel direction. In this case the round-trip speed is finite but irrelevant.

Anisotropy is more common than we realize.