Just musing:
I disagree that all physics is continuous; there is presently no indication universally of that. Though I suspect that it is true. If the systems chosen to be considered have continuous properties, but this does not mean all physics is continuous.
Consider quantum entanglement as it relates to duality. The fringe patterns appear to exist despite individual photons being used. There is an un-modeled coupling between fringe patterns and photon emissions.
Nothing can be said concretely that determines why one photon travels differently than another; discretely differently.
Observable photons only exist at a terminus. En-route in any media a photon is not detected nor observable. Only when the photon finds a pathway to our eye/detector does it become observable. Yet experimentation repeatedly shows that remote influence by things like quantum entanglement are natural and pervasive. This is non-linear because it is inconsistent actions not accounted for in known physics.
Almost all physics modeling is only consistent within tight constraints. Therefore, the models are not linear outside of those constraints.
Two photons from the same source in a distant galaxy can be detected at varying incremental lateral spacings and have different energies; undisturbed until a terminus is reached, even when passing through billions of light-years of varying gravity fields. Yet for other photons there is observable gravitational lensing. Why one set of photons, and not others?
Based upon gravitational lensing, the observable sky should be a blotchy grey from gravity induced scatter.
I happen to support the concept of quantum causality and the related physics to consider time separately from space (warping space/time relationships). The instantaneous processes associated with the decoherence of quantum entanglement supporting the systems of causality involved with a single entanglement.
I find it troubling that the speed of light can change over time (would have to look up reference). That means physics is non-linear and physics constants evolve. At what point does physics constants evolve (entropy) to the point of becoming a different dimensional state?
Do we flux out of our dimensional state and become the source of a Big Bang into a dominantly different dimensional state?
If so, what are the other systems of quantum causality that we cannot observe that we are influencing, and influenced by, as the dimensional states evolve as indicated by entropy.
Measurements mostly seem to be different recursions of meters/second, i.e. space/time. So what is different in the foundations of speed, energy, power, ....? What controls the ratios and recursions to create different observable artifacts?
This is why building relativity from quantum causality is attractive to me. There is no requirement for linearity related to relativity, yet can have a linear foundation.