Quantum Relativity: an essay

TL;DR

This paper proposes a novel approach to unify gravity and electromagnetism through deformation theory, quantum groups, and quantum information dynamics, suggesting gravity emerges from quantum discrete structures.

Contribution

It introduces a deformation-based quantum gauge theory linking gravity and electromagnetism via quantum groups and complex couplings, proposing a new framework for quantum gravity.

Findings

Quantum deformation parameter linked to 1/c and h.

Complex coupling constant (m,q) relates to interaction strength.

Gravity may emerge from quantum discrete structures.

Abstract

Is "Gravity" a deformation of "Electromagnetism"? Deformation theory suggests quantizing Special Relativity: formulate Quantum Information Dynamics $SL(2,C)_h$-gauge theory of dynamical lattices, with unifying gauge ``group'' the quantum bundle obtained from the Hopf monopole bundle underlying the quaternionic algebra and Dirac-Weyl spinors. The deformation parameter is the inverse of light speed 1/c, in duality with Planck's constant h. Then mass and electric charge form a complex coupling constant (m,q), for which the quantum determinant of the quantum group $SL(2,C)_h$ expresses the interaction strength as a linking number 2-form. There is room for both Coulomb constant $k_C$ and Newton's gravitational constant $G_N$, exponentially weaker then the reciprocal of the fine structure constant $\alpha$. Thus "Gravity" emerges already "quantum", in the discrete framework of QID, based on the quantized complex harmonic oscillator: the quantized qubit. All looks promising, but will the details backup this "grand design scheme"?