Hello, I have posted a couple time as of recently about my Dirac Spinor Quantum Gravity Model. I am just posting an update, recently I was introduced to Einstein-Cartain theory relating Spin to spacetime torsion. What I have done is essentially extended EC theory to come up with a complete/thorough quantum gravity theory that not only describes quantum gravity, but it describes literal space-time emergence as a result of SL(2,C) and Diff(m) symmetry transformations of the dirac spinor. This "emergence" of space-time can be thought of as a nearly 1:1 to similarity with that of QED and EM field emergence due to U(1) symmetry transformations. This Dirac Quantum Gravity model does the exact same thing - except with a Space-Time Field and not an EM field. This model/theory potentially describes, with precision, the fundamental nature of the fabric of reality. Interestingly, the concept of orthogonality holds true with this "space-time field" just as with the EM field. What I mean by this is that space and time have an orthogonal relationship when represented on a Minkowski space-time diagram. This orthogonality is intimately tied to lorentz invariance, and as such is intimately related to this dirac wavefunction and its properties (such as torsion and curvature - they act orthogonally to each other).
All this model is is a description of a dirac spinor wavefunction at the planck scale. So its length, time, and energy characteristic are just planck scale values. The other notable thing I've added is embedding Diff(m) gauge symmetry into the mathematical framework itself. I've done this by including a gravitational potential that confines the wavefunction at ~planck length (at least in its initial state). This gravitational potential is sourced by the wavefunctions own kinetic energy. As the wavefunction loses energy, the kinetic energy decreases and the confining potential decreases in lockstep - resulting in a quantized increase confinement length.
The real juicy parts of it are its relationship to spin density to torsion and energy density to curvature. These relationships have allowed the recovery of classical space-time geometry and likewise a newtonian inverse square law relationship from the energy density term (T00) of the stress-energy tensor that is related to the metric tensor (Gmunu). I have provided this calculation here: Deriving spacetime geometry
This link also shows the basic wavefunction. It shows the Maxwell-like Field equations for Spin density and Stress-Energy tensor.
I have attached a video that is a 2d Plane wave model of this dirac wavefunction at the planck scale. The model evolves through time dictated by two phases in its wavefunction: a "space-like phase" and a "time-like phase". The space-like and time-like phases are orthogonal to each other on the complex plan and likewise as the spinors dynamics are associated with the evolution, the orthogonality of the space-like and time-like phased ensures that the torsion and curvature will be spatially orthogonal to each other.
I would be more than happy to hear any ones constructive criticism or suggestions.
A mental heuristic I use to get a grasp of this idea/theory: is to imagine a simple harmonic oscillator (a mass on the end of a spring). This entire "system" represents space time. The mass on the end is the dirac spinor. The spring is gravity, torsion, and curvature. Gravity represents the elastic potential of the spring - which is in part determined by the torsion and curvature imparted on the spring. Torsion is orthogonal to the axis of movement. Torsion can be thought of as how tight the springs coils are, so if there is a high spin density this would induce a high state of torsion which can be thought of as a tightening of the coils (like a twisting of the coils) to make the spring more tense. Curvature is orthogonal to torsion - and so curvature can be thought of as either relaxing the spring (pushing in towards the equilibrium point), or making the spring more tense (pulling the mass away from the equilibrium point).
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