Perhaps I should explain a bit more how gravitational wave detection relates to Lisle’s scheme.
Detectable gravitational waves require colossal accelerations such as black hole or neutron star mergers to set into motion. Waves are generally a propagating disturbance in some substance such as water, but massless waves such as gravitational waves move through space at the speed of light. In the case of gravitational waves, space itself is compressed and stretched, which is somewhat counterintuitive to the idea of space as just so much emptiness between objects.
Gravitational wave (GW) detectors use every trick in the book to measure distance much more precisely than your old wooden ruler, employing interference from lasers along perpendicular arms which are kilometers long. The technology is expensive and fascinating, but relevant to the discussion here is that the few detectors that are operational are connected, comparing precision synchronized clocks in an attempt to locate the source of a wave in order to coordinate light spectrum observations.
But it is exactly the relativistic impossibility of synchronizing separated clocks which is at the heart of the difficulty measuring the one way speed of light. A couple of points in regards to the time synchronization of gravitational wave detectors: 1) they are in the same inertial frame aside from the known rotation, and 2) their clocks are synchronized assuming the one way speed of light is the same as the two way speed. By these assumptions, as a GW propagates at the speed of light through the planet in a quarter of a tenth of a second, this time of flight is easily registered as different times of detection between the three or more observatories. The differences between event timestamps with a bit of trigonometry yields an area of sky being the direction of the incoming wave.
None of this in itself proves that the speed of the wave matched the average speed of light, or “c”. Bear in mind that the clocks were synchronized assuming a constant speed of light, and as Lisle points out, if that assumption was wrong the time of flight differences would still register the same, because the clock calibration and the event measurement would be following the same coordinates. But that is not the issue.
Let us assume Lisle is right, and that light is instantaneous with respect to the observer. That would mean that each observatory directly sees the wave immediately in the same instant. That is what Lisle’s equation states, and as he correctly says himself, stipulating instant propagation is equivalent to a coordinate system. So however the clock in each station was set, there would be a pattern of timestamps, offsets between stations A, B, …n, that are used to triangulate the source of the wave.
Herein lies the crux. For the pattern of timestamps, it does not matter if the station clocks were synchronized by time of flight or slowly moving clocks, or even if the clocks are synchronized at all. Say one gravitational wave observatory’s clock was set using a timex watch from walmart, the next observatory is set by a fake street vendor Rolex, and the other by the shift start whistle at the local mill. They are all wrong, but still the same pattern of timestamp offsets will always present for every event, no matter where in the sky the GW is from. By Lisle’s formula, THE DIRECTION MAKES NO DIFFERENCE TO THE TIMESTAMP PATTERN, BECAUSE EACH OBSERVING STATION DIRECTLY AND INSTANTLY DETECTS THE WAVE IN ALL CASES. Conversely, given infinite speed it would follow that you could not use the pattern of timestamps to infer the direction of travel for the GW. The reality, of course, is that times of detection are routinely used to triangulate the direction of the GW, so Lisle is wrong.
The ability to triangulate GW sources is consistent with light traveling at the same or different speeds by direction in space, or frames of reference, but that is not Lisle’s formulation. He discards direction in space for direction to the observer, and that is incompatible with GW triangulation and special relativity.
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