Axioms

Ultimately, science is about predicting the outcomes of experiments and observations. If you can't observe it, directly or indirectly, it is beyond the realm of scientific inquiry. The one-way speed of light falls into this hole. Speed is normally defined as distance divided by time, but when we're talking about relativistic speeds, we need to be clear about which time we mean.

So, let's imagine a specific setup. We'll send a pulse of light from point A to point B. So, what is the one-way velocity of the light? It is the distance between A and B, divided by the time it takes for the signal to arrive. But whose time?

It turns out that, not only is there no reasonable way for the scientists at A and B to communicate the fact that the pulse has arrived (short of sending a second pulse and thereby measuring the round-trip time instead), it is actually not meaningful for an event at A and an event at B to happen "simultaneously." There will always be an observer who thinks that A's event happened first, and an observer who thinks that B's event happened first, unless the events are in each others' light cones, in which case everyone will agree that one comes before the other. But you can't get everyone to agree that both events happen simultaneously.

This creates a problem, because no matter where you put the clock, it has to be synchronized with respect to two distant events:

1. The pulse being sent from A.
2. The pulse arriving at B.

You cannot synchronize a clock with respect to an event unless the clock is physically present at that event, because simultaneity is otherwise relative to one's choice of reference frame. So the clock has to be at both A and B. You could imagine two clocks, synchronized with each other, but then you have to decide what you mean by "synchronized," because simultaneity is still relative. There is always a reference frame in which the clocks are not synchronized.

If the pulse were traveling slower than light, then you could move the clock with the pulse. This would give you a metric called the "proper time," and that actually does have some useful properties in this context. In particular, it is independent of reference frame or choice of coordinates, so that the one-way velocity of any slower-than-light object is perfectly well-defined and even measurable. But you can't do that with a pulse of light, because the pulse is traveling at the speed of light, and the clock can't go that fast if it has any mass. If the clock doesn't have any mass, then it cannot function as a clock in the first place, because massless particles do not experience the passage of time.

As a result, there is no operational definition of the one-way speed of light that is compatible with the laws of physics. This is why Einstein, for example, describes it as a "convention" in his special relativity paper, rather than asserting it as fact. It's not fact, it's just a convenient way of labeling the diagram.

Having said all that, there is one thing we can experimentally verify (and have done so): The time it takes for light to travel along a closed inertial path of length L is L/c, as measured at the start/endpoint of the path, regardless of what the path looks like or how it is shaped. So, if there are any variations in the one-way speed of light that depend on angle, they *always* cancel each other out. As a result, if you simply assume that the one-way speed of light is a constant, then you can use that assumption to "synchronize" distant clocks by sending light pulses between them and adjusting for the speed of light delay. Although this "synchronization" is ultimately just a convention, it behaves a lot like you would expect "true" synchronization to behave (at least with respect to the clocks' reference frames, anyway). Einstein describes how this works in his paper, and others have elaborated on the details (in short, the clocks should be in inertial reference frames and not in relative motion).