Special&general relativity, one the pillars and one of the 3 more successful physical theories, gives a prime or hierarchically high role to the properties of light, which are the startingbpoint or "effective cause" in Aristotelian linga, tonits inspection.
However, as these theories, despite continuing confirmational success, show resistance to be compstible with a big portion of other physics (exceptions such as Dirac relativistic Quantum mechanics exist).
Therefore one gets to think that maybe the tact that their physical motivational mothering was more peripheral than required to deserve such a prime role in unification (a discipline level definitional trait) than currently ascribed.
It's not the light speed which is the fundamental velocity but, the signal speed i.e., the velocity an electromagnetic signal have in vacuum.
This signal is fundamental for any understanding of physics.
JES
No. As is, always, the case, it's much easier to start from symmetries and then find all patterns that break them, than the opposite.
Once invariance under global Lorentz transformations was identified as one of the properties that define electromagnetism (the other being gauge invariance, which can be understood as local charge conservation), it's straightforward to describe all possible ways that global Lorentz invariance can be broken and use these to define backgrounds for experiments. This is has been done here: https://lorentz.sitehost.iu.edu/kostelecky/faq.htm in the broader framework of the Standard Model, since electromagnetism is but one property of matter and the other non-gravitational interactions are known.
Gravity, which is described by general relativity, shows how global Lorentz invariance can be understood as a special case of invariance under general coordinate transformations. The description provided by general relativity relies on the assumption that only the metric describes the spacetime geometry; it is known that the most general description of spacetime geometry is provided by supergravity.
When gravity is relevant, the speed of light isn't the most useful quantity to study, because, in a curved spacetime, relative velocity can't be globally defined. Light, in any spacetime, propagates along null geodesics, these are the relevant notions. All this is known and nothing ``modern'' anymore.
Before entering in any mathematical discussion; you should know that the relativity theories are wrong.
I've given a very simple demonstration in my profile. What results of that is that the postulates of Einstein should be change from "any inertial reference system" to "the local reference system".
This explains why the experimental data corresponds to the relativity theory, in all measurements in the laboratory , since the laboratory reference is identical for both theories. It's only when you choose a different system of reference that the difference becomes evident.
JES
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