Modified Relativity for Emergent Quantum Mechanics

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq +3 more

Jeffrey Alloy Q. Abanto

A new model of Deformed Special Relativity (DSR) was proposed to derive a modified General Relativity at the sub-quantum level towards the Planck scale. This was used as a basis for a new approach to Emergent Quantum Mechanics from which the standard mathematical formalism of Relativistic Quantum Mechanics was derived. Lastly, a new interpretation for the so-called quantum wave was suggested.

Pericles Rodrigues Silva

MOED II: Geometric Oscillations and the Emergence of Effective Quantum Dynamics This work presents the second theoretical development of the Modified Einstein Dynamics (MOED) framework, exploring the hypothesis that quantum-mechanical behavior may emerge as an effective statistical description of underlying geometric oscillations of the conformal-vierbein sector. Within the MOED formalism, the coupled dynamics of the conformal factor sigma, the complex vierbein structure, and the torsional invariant I_t generate oscillatory geometric modes in the near-critical regime I_t → 0. In the harmonic approximation, these modes naturally reproduce equations structurally analogous to damped quantum harmonic oscillators. The paper does not propose a replacement for quantum mechanics, nor an ontological reinterpretation of established quantum theory. Instead, it investigates the possibility that the quantum formalism emerges operationally as the most effective statistical language for describing non-rigid geometric reference frames and conformal-torsional fluctuations. A kinetic renormalization factor Z(sigma, I_t) is introduced to characterize the stability and propagation of geometric fluctuations, leading to modified effective sound speeds and emergent uncertainty relations associated with dynamically oscillating measurement frames. The work is intentionally exploratory and speculative, aimed at stimulating mathematical verification, theoretical criticism, and further investigation into possible geometric origins of effective quantum behavior.

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq +3 more

Gláuber C. Dorsch

Although gravity could not be quantized yet, there are good theoretical evidences that the unification of General Relativity and Quantum Mechanics should lead to the existence of a minimal observable length, a length scale below which the very notion of length looses meaning. Such effect proves to be worth some further analysis, for it acts as a natural regulator parameter, thus avoiding the divergences that plague Quantum Field Theories. In order to investigate some of the physical consequences of the existence of this peculiar effect, we propose to include it in the framework of Quantum Mechanics by modifying the Heisenberg algebra (i.e., the commutation relation of position and momentum operators, Xˆ and Pˆ), so that a minimum non-zero value for the uncertainty ?x emerges, which, being a limitation to the localizability of particles, acts as a minimal length. The Hilbert space of the theory must be modified accordingly. As we will see, the changes are not merely quantitative. On the contrary, our main result is that the familiar concept of “position measurement” must be reformulated, as well as other concepts related to it. We present a proposal for such reformulation.

Joginder Singh Galsin