This question assumes light motion or time is a fourth dimension added to three spatial dimensions, Should the time dimension be distinguished from the three spatial dimensions? If so, on what basis?
I think mundane time is already distinguished from space by the (-,+,+,+) signature of the metric. Classically mundane time was a parameter of motion. Locally away from singularities 3+1 formulation is ok. Are you asking whether both time and motion are illusion? Or you want to keep one? In the simple case of the exterior Kerr spacetime, space coordinate theta measures time. Some people think that time must be real because gravitational waves exist. Complex extension of the Kerr spacetime also has colliding gravitational waves. I think one can build a philosophical theory that that the spacetime is static and the sense of time is felt only when people (say children of shaitan) try to understand what they are not supposed to understand. If however we need to believe the reality of motion, time could be a thermodynamic concept like temperature.
Too much mystery surrounds the concept of "time" as a "dimension". Time is but one of four orthogonal components that include the three "static" space "dimensions" that allow objects to be located in space (relative to a suitable coordinate or reference system) and "time" as the "dynamic" component that allows objects to undergo change (with time as parameter) and, thus, to evolve. Without time there could be no change (and, thus, no evolution) and without change ther is no need for time. (See my RG preprint Pondering the Imponderables).
The answer on this thread’s question see the last SS posts in the thread
https://www.researchgate.net/post/What_is_Spacetime_how_does_space_time_work
and in https://www.researchgate.net/post/Is_time_particulate
Cheers
The SS post in
https://www.researchgate.net/post/Does_dimension_relate_to_cosmogenesis
is relevant/useful for this thread.
Cheers
Physics Today, February 2019 edition, page 60, has a book review written by Anthony Aguirre of the U. of California of a book by Carlo Rovelli called The Order of Time. The review says the book is divided into four sections. The third of the four sections: 'block-universe view of time holds that all events are laid out through spacetime with "equal reality".... This might bear on the question above.
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