Quantum Mechanics Based on an Extended Least Action Principle and Information Metrics of Vacuum Fluctuations

Abstract

We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle extends the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a physical system needs to exhibit during its dynamics in order to be observable. Second, there is constant vacuum fluctuation along a classical trajectory. A novel method is introduced to define the information metrics to measure additional observability due to vacuum fluctuations, which is then converted to an additional action through the first assumption. Applying the variational principle to minimize the total actions allows us to recover the basic quantum formulations including the uncertainty relation and the Schrödinger equation in the position representation. The extended least action principle brings in new results on two fronts. At the conceptual level, we find that the information metrics for vacuum fluctuations are responsible for the origin of the Bohm quantum potential. Even though the Bohm potential for a bipartite system is inseparable, the underlying vacuum fluctuations are local. Thus, inseparability of the Bohm potential does not justify a non-local causal relation between the two subsystems. At the mathematical level, quantifying the information metrics for vacuum fluctuations using more general definitions of relative entropy results in a generalized Schrödinger equation that depends on the order of relative entropy. The extended least action principle is a new mathematical tool that can be applied to derive other quantum formalisms such as quantum scalar field theory

18 pages. Closely match the version that is published in Foundations of Physics

References in corpus (22)

• In defense of the epistemic view of quantum states: a toy theory
• Informational derivation of Quantum Theory
• Operationally Invariant Information in Quantum Measurements
• A derivation of quantum theory from physical requirements
• Relational EPR
• Schrodinger equation from an exact uncertainty principle
• Existence of an information unit as a postulate of quantum theory
• Quantum theory from questions
• Information Invariance and Quantum Probabilities
• A closed-form expression for the Sharma-Mittal entropy of exponential families
• On Rényi and Tsallis entropies and divergences for exponential families
• Entropic Dynamics, Time and Quantum Theory
• From Information Geometry to Quantum Theory
• Toolbox for reconstructing quantum theory from rules on information acquisition
• Young's experiment and the finiteness of information
• The Entropic Dynamics approach to Quantum Mechanics
• Three-dimensionality of space and the quantum bit: an information-theoretic approach
• Quantum mechanics from a Heisenberg-type equality
• Information geometry, dynamics and discrete quantum mechanics
• The Relativity Principle at the Foundation of Quantum Mechanics
• Quantum mechanics from two physical postulates
• Quantum Scalar Field Theory Based on the Extended Least Action Principle

Cited by in corpus (2)

• Spin Theory Based on the Extended Least Action Principle and Information Metrics: Quantization, Entanglement, and Bell Test With Time Delay
• Alternative Framework to Quantize Fermionic Fields