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A Five-Dimensional Spacetime-Energy Framework: a Geometric Unification of Quantum Mechanics and Gravity

Author:

Peled, Aaron

Category:

Research Papers

Sub-Category:

Cosmology

Language:

English

Date Published:

April 12, 2026

File:

/Research Papers-Cosmology/Download/10513

Downloads:

118

Keywords:

General Relativity, Quantum Mechanics, 5D Spacetime-Energy, null geodesics, Compton wavelength, Zitterbewegung, Planck Scale, Gravitational Constant

Abstract:

We propose a five-dimensional geometric framework in which energy is elevated to the status of a geometric coordinate, analogous to the role time plays in special relativity. By defining a new 5th coordinate x ₅ = ħc/E, as the reduced Compton wavelength associated with energy E, we construct a 5D spacetime-energy interval and impose a null geodesic condition. Without any quantization postulates, field equations, or tensorial machinery, this condition yields: the energy-time uncertainty principle, the Compton wavelength as a natural length scale, the Zitterbewegung frequency of massive particles, and the quantum phase evolution of wavefunctions. Furthermore, the Planck length emerges as the natural minimum of x ₅ , and Newton’s gravitational constant G is shown to be derivable from the geometry of the fifth dimension rather than being a fundamental input. We propose that quantum mechanics and gravity are therefore projections of a single 5D geometric structure governed entirely by the two fundamental constants c and ħ.

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