Hamilton-Jacobi Many-Worlds Theory and the Heisenberg Uncertainty Principle

TL;DR

This paper demonstrates that quantum mechanics can be viewed as classical Hamilton-Jacobi theory constrained by a global determinism condition, leading to a multiverse interpretation and deriving the uncertainty principle from universe interference.

Contribution

It introduces a novel interpretation of quantum mechanics based on Hamilton-Jacobi theory, linking it to a multiverse and deriving the uncertainty principle without intrinsic indeterminism.

Findings

Quantum mechanics is equivalent to constrained classical Hamilton-Jacobi theory.

The wave function's magnitude measures universe density in a multiverse.

Uncertainty arises from multiverse interference, not intrinsic randomness.

Abstract

I show that the classical Hamilton-Jacobi (H-J) equation can be used as a technique to study quantum mechanical problems. I first show that the the Schr\"odinger equation is just the classical H-J equation, constrained by a condition that forces the solutions of the H-J equation to be everywhere $C^2$. That is, quantum mechanics is just classical mechanics constrained to ensure that ``God does not play dice with the universe.'' I show that this condition, which imposes global determinism, strongly suggests that $\psi^*\psi$ measures the density of universes in a multiverse. I show that this interpretation implies the Born Interpretation, and that the function space for $\psi$ is larger than a Hilbert space, with plane waves automatically included. Finally, I use H-J theory to derive the momentum-position uncertainty relation, thus proving that in quantum mechanics, uncertainty arises from the interference of the other universes of the multiverse, not from some intrinsic indeterminism in nature.