Alex,
You start off by pointing out mathematical approaches have led us into this dead end and then propose another mathematical approach. ?
Math is very good for description, but not always so good for explanation. Epicycles were brilliant math, as a description of the cosmos, but the crystalline spheres were lousy physics, as an explanation.
Consider the relationship between energy and form. Energy is what drives waves. Frequency and amplitude are the information expressed by the form of their fluctuations.
As biological entities, we have the digestive, respiratory and circulatory systems processing the energy driving us on, while the central nervous system sorts through and further coalesces the forms/information precipitating out. Motor and steering.
Heck, even galaxies are energy radiating out, as form/mass coalesces in.
Yet this math based physics tries to explain everything in terms of the information it can extract. Might it be missing the elephant in the room?
Consider time; As mobile creatures with a sequential process of perception and a narrative based culture, we think of time as the point of the present moving past to future, which physics codifies as measures of duration. The reality though, is that change turns future to past. Tomorrow becomes yesterday, because the earth turns.
There is no literal dimension of time, because the past is consumed by the present, to inform and drive it, aka, causality and conservation of energy. Cause becomes effect.
Time is asymmetric, because what is actually measured, action, is inertial. The earth only turns one direction. Entropy isn’t what’s measured and is a second order effect of change, due to the convective process of energy pushing out, as the forms coalesce in.
Different clocks can run at different rates simply because they are separate actions. Think metabolism.
So time is an effect, like temperature, pressure, color, sound, etc. Think frequencies and amplitudes. Ideal gas laws correlate volume with temperature and pressure, but we don’t refer to them as the 5th and 6th dimensions of space, because they are only foundational to our emotions, bodily functions and environment, not the sequence of thought.
Basically the energy, being conserved, is always and only present, so it’s changing configuration creates time. The process goes past to future, while the patterns generated go future to past. As consciousness goes past to future, while thoughts go future to past.
Energy and form go opposite directions of time!!!!!
I could go on, but I’ve banged my head on this wall enough to know it’s pretty futile, because, surprise, the sociology trumps the logic. Eventually the geniuses will have to just go outside their ivied towers and smell the flowers. Some generation of theorists will rebel against orthodoxy.