Using Special relativity theory, of course. Can Lorentz transformations to "tell" something about it? "Wikipedia's" article: http://en.wikipedia.org/wiki/One-way_speed_of_light .
Answer
The big misunderstanding about this "one-way speed of light" thing is that there is something to be proven experimentally. While it is just a matter of convention about
how to synchronize the clocks at the source and the detector
Let me explain with an example. Consider a following experimental setup:
- We have three observers $O$,$A$ and $B$ at rest in our reference frame.
Their positions are $x_O=0, x_A=-1$ and $x_B=1$. - First they synchronize their clocks following the standard procedure:
- The $O$ observer sends a signal at $t_O=-2$ both to $A$ and $B$.
- At the moment of the signal arrival, $A$ and $B$ set their clocks to $t_{A,B}=-1$
- $A$ and $B$ return those signals and $O$ receives them back at $t_O=0$
- Clocks are synchronized.
- Now this guys measure something. For example there are two light flashes -- red and green, passing by. And observers are fixing the times of their passage.
Here is the space-time diagram for the process with the "standard" speed of light:
Such a diagram is drawn by the observers when they gather together at a meeting after the experiment was performed. Every observer has a list of events that locally happened at his place. And altogether they recreate "the big picture" of the experiment.
But now the observers have some doubts -- why do they presuppose that the speed of light is the same in both directions? So they agreed to change that and see what happens. Say that right-speed is three times as fast as the left-speed:
The description has changed. But it is just a change in the coordinates. It couldn't possibly affect any experimental predictions by any theory that observers have.
So it is just a convention. And there is nothing to be "proven" experimentally.
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