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

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 Schrödinger 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 ${\psi }^{\ast }\psi$ 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.

References in corpus (1)

• Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything

Cited by in corpus (1)

• Gravitation and cosmology with York time