>> If we shine a light on a detector, we can measure the time the light takes to reach the detector. Are you saying that the light hits the detector instantly, and then goes back to the source, or that the detector is the source and the light comes back to it after hitting the source instantly?

> If you shine a light on a detector, you measure the time it takes to travel both legs.

reflector, surely, rather than detector? Your director can record a timestamp locally while you and your flashlight are across the room. You don't need two legs.

The main objection upthread is that while your flashlight's "on" switch can also record a timestamp within the flashlight, synchronizing the flashlight's time to the detector's time so that one can compare the timestamps after the experiment is done (or days later, or weeks later, again and again) is not feasible within the framework of Special Relativity. Therefore if one has confidence in one's local timestamps, one can compare them when measuring the round trip of the flashlight beam reflected off a mirror across the room back onto a detector mounted right beside the flashlight's bulb, inside the flashlight.

However, nature provides several gravitationally-driven systems which can provide a "preferred foliation", or a naturally-produced easily-compared timestamp. Examples include fancy sundials (including observations of millisecond pulsars), lunisolar tides, and the cosmological scale factor. These can be recovered independently in a (probably pretty large) flashlight and the detector looking for the light from the flashlight. Timestamps can then be compared with greater precision than available via Special Relativity synchronization methods.

Indeed, this is something that has been worked on in lunar-ranging experiments over the past decades. Can we use detailed knowledge of the solar system to predict a signal aimed Earthward by a 21st century space probe on or very near the moon as well as a signal launched from Earth to a reflector on the moon that is picked up by a detector on Earth? It turns out we can, to good precision!

> Final note

"c" is the free parameter of the Lorentz group, which is the fundamental isometry group of Special Relativity (and quantum electrodynamics and the Standard Model of particle physics). "c" is also a constant in the Einstein Field Equations of General Relativity, and there is a mathematical connection between that and Special Relativity.

In both theories, unless interfered with by interaction with matter, massless objects are constrained to move, obligatorily, from one spacetime point to another point from a restricted set of neighbours. These points are on the surface of a null cone.

Light is experimentally massless, so null curves are often called lightlike curves, null cones are usually called light cones, and so on. However, electromagnetic radiation is not the only massless species in the cosmos.

> very specific environment

An excellent approximation of vacuum (very long mean free paths for electromagnetic radiation at all frequencies) dominates the observable universe, so the permeability and permittivity of free space is a good choice except in very specific environments (planet-bound electrical engineering laboratories and copper wires are out-volumed by intergalactic, or even interplanetary, space by a lot). In those matter-rich environments, the mean free path of light is low. The constant c remains the same in such matter-rich environments, but electromagnetic radiation passing through them does not propagate at c.

> the value that we put as c

is exactly 1. <https://en.wikipedia.org/wiki/Geometrized_unit_system>