Schrodinger equation from an exact uncertainty principle

Abstract

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation. Thus there is an exact formulation of the uncertainty principle which precisely captures the essence of what is "quantum" about quantum mechanics.

Latex, 18pp, nature of fluctuations & differences from stochastic mechanics clarified

References in corpus (1)

• Exact uncertainty relations: physical significance

Cited by in corpus (55)

• Interacting classical and quantum ensembles
• Quantum phenomena modelled by interactions between many classical worlds
• Origin of Complex Quantum Amplitudes and Feynman's Rules
• The Vacuum Fluctuation Theorem: Exact Schroedinger Equation via Nonequilibrium Thermodynamics
• On two recent proposals for witnessing nonclassical gravity
• Entropic Dynamics
• Entropic Dynamics, Time and Quantum Theory
• Consistent classical and quantum mixed dynamics
• Imprints of the Quantum World in Classical Mechanics
• Exact uncertainty approach in quantum mechanics and quantum gravity
• An Information-Theoretic Link Between Spacetime Symmetries and Quantum Linearity
• Spreading lengths of Hermite polynomials
• Bosonic field equations from an exact uncertainty principle
• Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction
• From Classical Hamiltonian Flow to Quantum Theory: Derivation of the Schroedinger Equation
• Information Measures for Inferring Quantum Mechanics
• Entropic Dynamics: an Inference Approach to Quantum Theory, Time and Measurement
• Weakly nonlocal fluid mechanics - the Schrodinger equation
• Quantum-classical correspondence via a deformed kinetic operator
• Incompleteness of trajectory-based interpretations of quantum mechanics
• Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class
• Entropic Dynamics: Reconstructing Quantum Field Theory in Curved Space-time
• Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
• Superselection from canonical constraints
• Variational approach to dequantization
• Another look through Heisenberg's microscope
• Quantum mechanics is a calculus for estimation under epistemic restriction
• Is quantum mechanics based on an invariance principle?
• Quantization from an exponential distribution of infinitesimal action
• Thermodynamic Gravity and the Schrodinger Equation
• A framework for nonrelativistic isotropic models based on generalized uncertainty principles
• From probabilistic mechanics to quantum theory
• Black Hole Information Problem and Wave Bursts
• Unique additive information measures - Boltzmann-Gibbs-Shannon, Fisher and beyond
• "Systemic Nonlocality" from Changing Constraints on Sub-Quantum Kinematics
• Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable
• A Physical Axiomatic Approach to Schrodinger's Equation
• Schroedingers equation with gauge coupling derived from a continuity equation
• Estimation independence as an axiom for quantum uncertainty
• Nonlinear Schrödinger equation from generalized exact uncertainty principle
• Quantum Mechanics Based on an Extended Least Action Principle and Information Metrics of Vacuum Fluctuations
• The identification of mean quantum potential with Fisher information leads to a strong uncertainty relation
• Quantum Scalar Field Theory Based on the Extended Least Action Principle
• Modeling double slit interference via anomalous diffusion: independently variable slit widths
• Mean Value of the Quantum Potential and Uncertainty Relations
• Galilean relativity and wave-particle duality imply the Schrödinger equation
• Remarks on osmosis, quantum mechanics, and gravity
• The Physical Origin of Schrödinger Equation
• The Klein-Gordon equation in Machian model
• Solitons, chaos, and quantum phenomena: a deterministic approach to the Schrödinger equation
• Spin Theory Based on the Extended Least Action Principle and Information Metrics: Quantization, Entanglement, and Bell Test With Time Delay
• Understanding quantization: a hidden variable model
• Epistemic uncertainty from an averaged Hamilton-Jacobi formalism
• Alternative Framework to Quantize Fermionic Fields
• Irrotational Momentum Fluctuations Conditioning the Quantum Nature of Physical Processes