ENTROPIC DYNAMICS: QUANTUM MECHANICS
The pragmatic idea that physics consists of models designed for the purpose of making probabilistic inferences about reality extends to the laws of quantum mechanics, quantum field theory, and general relativity. We have developed an alternative approach to the derivation and interpretation of quantum mechanics as an entropic dynamics of probabilities that has led to new insights into the entropic nature of time including the arrow of time.
The deeply geometrical (both metric and symplectic) nature of QM explains the linearity of QM, the need for complex numbers, and the role of Hilbert spaces, all in a language that brings the theories of quantum mechanics and general relativity closer together. The commitment to ontological clarity—a clear distinction of the ontic or epistemic nature of the various observables, beables, and inferables that pervade QM—has allowed a resolution of the puzzles associated to the quantum measurement problem. Most of this material is presented in the (still unfinished) book "Entropic Physics: Probability, Entropy, and the Foundations of Physics.”
Click here to go to My Book page. Last modified 06/26/2026. This version contains new chapters: Ch. 14 "The Entropic Dynamics of Spin" and Ch. 16 "Entropic Quantum Electrodynamics".
This paper develops the Entropic Dynamics of a local gauge theory.
“Entropic Dynamics approach to Quantum Electrodynamics,” invited paper for the special volume in honor of Prof. S. Amari, ed. by A.M. Scarfone and T. Wada, Entropy 27, 1247 (2025); https://doi.org:10.3390/e27121247; arXiv.org:2511.19238.
The ontic electromagnetic field is redundantly represented by a vector potential, which accounts for the local gauge symmetry. After deriving the functional Schrodinger equation, as a test that despite its unorthodox foundation the ED approach is empirically successful, we derive Maxwell's equations.
The relational approach (in the Machian sense of Barbour) is formulated here:
“Entropic Dynamics Approach to Relational Quantum Mechanics”, (with H. Saleem) Entropy 27, 797 (2025); https://doi.org:10.3390/e27080797; arXiv.org:2506.07921.
Here the ED framework is extended to account for spin.
“What is Ontic and What is Epistemic in the Quantum Mechanics of Spin?”, invited paper for the special volume on Maximum Entropy Principle and Applications, ed. by P. Macedo, M. C. Costa, and A. Dionisio, Entropy 27, 315 (2025); https://doi.org:10.3390/e27030315; arXiv.org:2502.21214.
The result is a realist ψ-epistemic model in which the ontology consists of a particle described by a definite position plus a discrete variable that describes Pauli’s peculiar two-valuedness. As expected, the resulting dynamics of probabilities is described by the Pauli equation. What may be unexpected is that the generators of transformations—the Hamiltonian, linear and angular momenta, including spin, are all granted clear epistemic status.
The Problem of Quantum Measurement is addressed here.
“Entropic Dynamics and Quantum Measurement”, Phys. Sci. Forum 1, 36 (2022); arXiv:2208.02156.
The ED approach to QM is ideally suited to address the problem of measurement because it is based on entropic and Bayesian methods of inference that have been designed to process information and data. The approach succeeds because ED achieves a clear-cut separation between ontic and epistemic elements: the positions of particles are ontic, while probabilities and wave functions are epistemic. Thus, ED leads to a viable realist ψ-epistemic model. Such models are widely assumed to be ruled out by various no-go theorems. We show that ED evades those theorems by adopting purely epistemic dynamics and denying the existence of an ontic dynamics at the subquantum level.
The following is a derivation of the mathematical formalism of quantum mechanics based on its symplectic and information geometry.
“Quantum mechanics as Hamilton-Killing flows on a statistical manifold” Phys. Sci. Forum 3, 12 (2021); arXiv:2107.08502.
The strategy is to seek flows that preserve (in the sense of vanishing Lie derivatives) both the symplectic structure (a Hamilton flow) and the information metric structure (a Killing flow). The result is a formalism in which the Fubini–Study metric, the linearity of the Schrödinger equation, the emergence of complex numbers, Hilbert spaces and the Born rule are derived rather than postulated.
The following paper is a review of entropic dynamics.
“The Entropic Dynamics approach to Quantum Mechanics” Entropy 21, 943 (2019); arXiv:1908.04693.
For a more comprehensive and up to date review click here to visit My Book page.
The first derivation of the Schrödinger equation from entropic principles is in the paper below. A central feature is that associated to a dynamics based on entropy there is a relational notion of time in which the update from a prior to a posterior translates into a natural arrow from the past to the future. As might be expected, this early piece inevitably contained some ad-hoc assumptions and other rough spots; most of these blemishes were eliminated in later work.
“Entropic Dynamics, Time, and Quantum Theory” J. Phys. A.: Math. Theor. 44, 225303 (2011); arXiv:1005.2357.
Over the years various topics in quantum mechanics (spin, quantum measurement, classical limit, Brownian vs. Bohmian trajectories, QM on curved spaces, relational QM, entropic time, etc.) were developed in the papers below.
A Geometric Algebra/Entropic Dynamics approach to spin:
“The Entropic Dynamics of Spin” (with N. Carrara) arXiv:2007.15719.
“Quantum measurement and weak values in entropic quantum dynamics” (with K. Vanslette) Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2016), ed. by G. Verdoolaege, AIP Conf. Proc. 1853, 090003 (2017); arXiv.org:1701.00781.
“The classical limit of entropic quantum dynamics” (with A. Demme) Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2016), ed. by G. Verdoolaege, AIP Conf. Proc. 1853, 090001 (2017); arXiv.org:1612.01905.
“Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class” (with D. Bartolomeo) EmQM15: Emergent Quantum Mechanics 2015, J. Phys: Conf. Series 701, 012009 (2016); arXiv.org:1603.08469.
“Relational entropic dynamics of particles” (with S. Ipek) in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by A.Giffin and K. Knuth, AIP Conf. Proc. 1757, 030003 (2016); arXiv.org:1601.01901.
“Entropic dynamics on curved spaces” (with S. Nawaz and M. Abedi) in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by A.Giffin and K. Knuth, AIP Conf. Proc. 1757, 030004 (2016); arXiv.org:1601.01708.
“Entropic dynamics and the quantum measurement problem” (with D. T. Johnson) in Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2011), ed. by P. Goyal et al., AIP Conf. Proc. 1443, 104 (2012); arXiv:1108.2550.
“Non-relativistic gravity in entropic quantum dynamics” (with D. T. Johnson) in Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2010), ed. by A. Mohammad-Djafari, et al., AIP Conf. Proc. 1305, 971 (2010); arXiv:1010.1467.
“Entropic time” in Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2010), ed. by A. Mohammad-Djafari, et al., AIP Conf. Proc. 1305, 200 (2010); arXiv:1011.0746.
“From Entropic Dynamics to Quantum Theory” in Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2009), ed. by P. Goggans et al., AIP Conf. Proc. 1193, 48 (2009); arXiv:0907.4335.
Here are two early versions of a dynamics and a notion of time that are purely derived from entropy and information geometry. This work has been superseded but at the time they were personally important to me because they demonstrated that on the basis of inference one could construct models that resembled dynamical laws of physics.
“Entropic dynamics” in Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2001), ed. by R. L. Fry, A.I.P. Vol. 617, 302 (2002); arXiv.org/abs/gr-qc/0109068.
“Change, time, and information geometry” in Maximum Entropy and Bayesian Methods in Science and Engineering (MaxEnt 2000), ed. by A. Mohammad-Djafari, A.I.P. Vol. 568, 72 (2001); arXiv.org/abs/math-ph/0008018.