The Equivalence Postulate of Quantum Mechanics, Dark Energy and The Intrinsic Curvature of Elementary Particles

TL;DR

This paper presents an axiomatic approach to quantum mechanics via the equivalence postulate, linking quantum potential to intrinsic curvature and dark energy, with implications for quantum gravity and elementary particles.

Contribution

It introduces a novel formalism connecting quantum potential with intrinsic curvature and dark energy, extending the Hamilton-Jacobi approach to quantum mechanics.

Findings

Quantum potential interpreted as intrinsic curvature and dark energy.

Solutions of Schrödinger equation used to solve nonlinear quantum Hamilton-Jacobi equation.

Quantum potential magnitude is extremely suppressed, with cumulative effects in multi-particle systems.

Abstract

The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underly the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant under $D$--dimensional Mobius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of the D-dimensional quantum Hamilton--Jacobi equation. In this approach, the solutions of the associated Schrodinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrodinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. I propose that the quantum potential, which is always non-trivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multi--particle case the quantum potential, as well as the mass, are cumulative.