Can Operator Theory Help Unify Quantum Mechanics and General Relativity?

[Physics4Funn]

TL;DR

The mathematical operator view might be extended.
Maybe expand the number of operators to phenomena that haven't been considered.

What do you think about using operator theory to model spacetime?

1. In Newtonian physics, F = ma describes exactly describes mass m at an exact point x, a force F, and acceleration a by absolute and independent x and time t.

2. In quantum mechanics, physics moved to an energy description including a trade off between time and energy. There is uncertainty in the state and a tradeoff between location and movement.
Instead of just solving a differential equation, mathematics changed to an operator view and a Hilbert space for solutions.

3. Quantum Electrodynamics introduced special relativity so mass and energy, time and space are related. The operator view increased and was named Quantum Field Theory. Now operators also described charge, mass, rotation, and others.

4. General Relativity replaced force with spacetime geometry. But quantum field theory continued using the idea of gravitational force through mass and energy.

The newest concepts have been quantized. There are still some concepts that have not been quantized. Quantum states can be discrete and continuous.

The mathematical operator view might be extended.
Maybe expand the number of operators to phenomena that haven't been considered.

What do you think about using operator theory to model spacetime?

 

[jedishrfu]

It looks like someone has beat you to the punch:

https://arxiv.org/pdf/1606.00701.pdf

 

[Physics4Funn]

This paper is new to me, but I know that this idea not new. Another scientist has been working along these lines since 2000. I can usually talk to grad students about new techniques for work beyond the standard model, but I have not found many working physicists willing to even discuss these approaches. The last time that I posted about this subject on Physics Forums I received no replies.

So what do think about the prospect quantizing more physics concepts? The math gets complex for all of the ideas about bringing theories together. I'm just wondering if this approach might be less weird than 11 dimensions or multiverses. Not that I am against other approaches. I'll accept any model that is verified in the lab.