Thank you both for these profound insights.

To the second point: I completely agree that mathematical proofs are the bedrock of any serious theory. My goal isn't to bypass the math, but to find if there's a physical interpretation that remains consistent with it while addressing the 'double-counting' paradox from a logical standpoint. I take to heart the advice about studying statistical mechanics to demystify QM—it’s a bridge I intend to cross.

To the first point: The Feynman quote is humbling. I realize that 'common sense' is often just a collection of prejudices acquired by age eighteen. However, my 'engineering bias' isn't a rejection of modern physics, but rather a drive to find the mechanical 'why' behind the abstract 'how'. If the rules of this universe are counterintuitive, the challenge is to refine our intuition, not to ignore the rules.

I am curious: if we treat spacetime not just as a coordinate system but as a dynamic participant in energy conservation, does the 'mathematical vs. physical' gap start to close?

3 hours ago, Mordred said:

Examples being superposition, correlation functions the list goes on. It does help pull a lot of the mystery out of QM.

Have been following online lectures on QM so that I can appropriately incorporate it to a theory have been developing...when I start thinking about the link btn what am doing and QM ...I just feel... abnormally heavy sleep...when I transition from GR to what am doing to QM back to what am doing...episodes of mental freeze occurs 😂, it seems fundamental science is a form of intoxication.

41 minutes ago, Time Traveler said:

However, my 'engineering bias' isn't a rejection of modern physics, but rather a drive to find the mechanical 'why' behind the abstract 'how'. I

Here's an interesting trick for you then take the equation of motion for a mechanical spring. If you compare the equation for the quantum harmonic oscillator you will find the precise same relations albeit a change in variables applied. The ratios of change are identical.

If you study deep enough you will find a great deal of similarities between the seemingly complex equations have similar relations to many classical physics formulas commonly used in engineering.

48 minutes ago, Time Traveler said:

I am curious: if we treat spacetime not just as a coordinate system but as a dynamic participant in energy conservation, does the 'mathematical vs. physical' gap start to close?

This is quite a bit more complex first and foremost the conservation rules require a closed system or a closed group. To go into greater detail would be more suitable to a seperate thread and such a discussion can get extensively lengthy.

In some treatments involving spacetime one can define a conserved system usually ties into innvariance of a quantity. This is often done under local geometry in some mathematical space or manifolds.

Anyways best left for a different thread

1 hour ago, Mordred said:

This is quite a bit more complex first and foremost the conservation rules require a closed system or a closed group.

It is worth pointing out that there is a big difference between the meaning of closed in mathematics and in engineering physics.

2 hours ago, Time Traveler said:

However, my 'engineering bias' isn't a rejection of modern physics, but rather a drive to find the mechanical 'why' behind the abstract 'how'. If the rules of this universe are counterintuitive, the challenge is to refine our intuition, not to ignore the rules.

How much quantum mechanics and relativity have you used in your career as an engineer?