Is there anything preventing the following experiment from being done right now?
Imagine that a human ran from point 'a' to point 'b' while light particles that reflected off a clock moved through a special medium from point 'a' to point 'b' as well. Could a human arrive at point 'b' before light? (As for the special medium, I'm imagining something like a complex maze of mirrors submerged in a very dense material.)
If so, if the human waited at the finish line to view light arriving in second place, would they see the time that the race began on the clock?
Answer
No physical laws are being broken in this thought experiment. If you are concerned with the relativistic requirement "nothing can go faster than the speed of light", that only applies to the speed light goes in a vacuum: $c = 3 \times 10^8$ m/s. The reference to light in that relativity postulate makes it sound like if you could only find a situation where you slowed light down, you could break the laws of physics; not so. A better statement of the postulate would be "nothing can go faster than $3 \times 10^8$ m/s, which happens to also be the speed light travels at in a vacuum." I don't see anyone going faster than $3 \times 10^8$ m/s in this thought experiment, so no physics violations.
As for what the human at the end of the race sees:
He sees a blinding blue light from the all the Cherenkov Radiation from even the slightest charged particle passing through the medium. And perhaps the time at the start of the race. It's exactly what you would imagine since we are talking non-relativistic speeds. What an anti-climactic answer, eh?
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