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This page contains:

"If you are in a closed room on a ship sailing at a constant speed and the ride is perfectly smooth...[t]here’s no physical experiment you could conduct to tell whether you’re moving or stationary (assuming you’re not peeking out of a porthole)."

If am in the room mentioned above and I send an electromagnetic signal via wire of minimum length from the center of the room to detectors centered at each of its six surfaces and I also send an EM signal to those same detectors wirelessly at the same time, will all detectors always indicate receipt of the signal simultaneously, controlling for any reduction in signal propagation speed due to the wire medium -or- can motion alter such results?

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On the page you are referring to titled 'Understanding gravity—warps and ripples in space and time' the quote that you give tells the story out of order.

Before the introduction of relativity the assumption was that that the relativity of inertial motion was exclusively valid for mechanics, that is, for the motion of objects with mass.

The fundamental step that was introduced by Einstein's relativity was the supposition that for propagation of electromagnetic waves and for the motion of objects with mass the same relativity of inertial motion applies. Among the clues that led Einstein to that supposition were the observations of stellar aberration, and the experiments by Fizeau that compared the speed of light through water that was stationary to the speed of light through water that was moving. (Fizeau's experiments were interferometry experiments. Fizeau could vary the flow rate of the water, and see whether that produced a shift in interference pattern.)

So that is what is out of order on that web page.

What is described in section that you quoted is what the physics community accepted as part of the overall accceptence of special relativity.

I recommend that you look for another source of information about relativity than that web page. Presumably their goal was to simplify the story, but it seems they ended up writing gibberish.

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You have invented the Michelson-Morley experiment, conducted for the first time in 1887. The result was that you cannot detect constant motion through the transmission of electromagnetic waves.

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