The Entropic Dynamics of Relativistic Quantum Fields∗

The formulation of quantum mechanics within the framework of entropic dynamics is extended to the domain of relativistic quantum fields. The result is a non-dissipative relativistic diffusion in the infinite dimensional space of field configurations. On extending the notion of entropic time to the relativistic regime we find that the field fluctuations provide the clock that sets the scale of duration. We also find that the usual divergences that affect all quantum field theories do not refer to the real values of physical quantities but rather to epistemic quantities invariably associated to unphysical probability distributions such as variances and other measures of uncertainty.The formulation of quantum mechanics within the framework of entropic dynamics is extended to the domain of relativistic quantum fields. The result is a non-dissipative relativistic diffusion in the infinite dimensional space of field configurations. On extending the notion of entropic time to the relativistic regime we find that the field fluctuations provide the clock that sets the scale of duration. We also find that the usual divergences that affect all quantum field theories do not refer to the real values of physical quantities but rather to epistemic quantities invariably associated to unphysical probability distributions such as variances and other measures of uncertainty.

arXiv:1212.6946AIP conference proceedingsJan 1, 20132 citations

Entropic dynamics: reconstructing quantum field theory in curved space-time

Selman Ipek, Mohammad Abedi, Ariel Caticha

Abstract The Entropic Dynamics reconstruction of quantum mechanics is extended to the quantum theory of scalar fields in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kuchař, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory.Abstract The Entropic Dynamics reconstruction of quantum mechanics is extended to the quantum theory of scalar fields in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kuchař, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory.

arXiv:1803.07493Classical and Quantum GravitySep 11, 201919 citations

From Entropic Dynamics to Quantum Theory ∗

Ariel Caticha

Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the configuration space is a statistical manifold. The dynamics then follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. The resulting formalism is close to Nelson’s stochastic mechanics. The statistical manifold is a dynamical entity: its (information) geometry determines the evolution of the probability distribution which, in its turn, reacts back and determines the evolution of the geometry. As in General Relativity there is a kind of equivalence principle in that “fictitious ” forces – in this case diffusive “osmotic ” forces – turn out to be “real”. This equivalence of quantum and statistical fluctuations – or of quantum and classical probabilities – leads to a natural explanation of the equality of inertial and “osmotic ” masses and allows explaining quantum theory as a sophisticated example of entropic inference. Mass and the phase of the wave function are explained as features of purely statistical origin.Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the configuration space is a statistical manifold. The dynamics then follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. The resulting formalism is close to Nelson’s stochastic mechanics. The statistical manifold is a dynamical entity: its (information) geometry determines the evolution of the probability distribution which, in its turn, reacts back and determines the evolution of the geometry. As in General Relativity there is a kind of equivalence principle in that “fictitious ” forces – in this case diffusive “osmotic ” forces – turn out to be “real”. This equivalence of quantum and statistical fluctuations – or of quantum and classical probabilities – leads to a natural explanation of the equality of inertial and “osmotic ” masses and allows explaining quantum theory as a sophisticated example of entropic inference. Mass and the phase of the wave function are explained as features of purely statistical origin.

Aug 4, 201310 citations

Quantum fields from real-time ensemble dynamics

Yong Zhang

Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we formulate quantum fields in a real-time Schrödinger-picture framework, in which fields evolve as probability ensembles on the space of field configurations. Within this formulation, the wavefunctional $Ψ[φ,t]$ encodes a first-order, causal ensemble dynamics on configuration space. Interactions appear as couplings between configuration-space directions, while propagators arise as derived correlation structures rather than as fundamental postulates. Entanglement, scattering amplitudes, and conformal field theory correlators emerge as distinct projections of the same underlying ensemble evolution, corresponding to equal-time, asymptotic, and symmetry-organized observables. Standard operator, diagrammatic, and path-integral formulations are recovered as computational representations of this single real-time dynamics. This organization makes explicit the distinction between fundamental dynamical structure and representational tools in QFT, and clarifies the scope within which ensemble-averaged correlators account for quantum fluctuations, while also delineating the level at which questions associated with individual realizations and randomness would arise beyond the correlator-based field-theoretic description.Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we formulate quantum fields in a real-time Schrödinger-picture framework, in which fields evolve as probability ensembles on the space of field configurations. Within this formulation, the wavefunctional $Ψ[φ,t]$ encodes a first-order, causal ensemble dynamics on configuration space. Interactions appear as couplings between configuration-space directions, while propagators arise as derived correlation structures rather than as fundamental postulates. Entanglement, scattering amplitudes, and conformal field theory correlators emerge as distinct projections of the same underlying ensemble evolution, corresponding to equal-time, asymptotic, and symmetry-organized observables. Standard operator, diagrammatic, and path-integral formulations are recovered as computational representations of this single real-time dynamics. This organization makes explicit the distinction between fundamental dynamical structure and representational tools in QFT, and clarifies the scope within which ensemble-averaged correlators account for quantum fluctuations, while also delineating the level at which questions associated with individual realizations and randomness would arise beyond the correlator-based field-theoretic description.

hep-thCross-listedarXiv:2602.04229Feb 5, 20260 citations

Entropic Dynamics of Quantum Scalar Fields in Curved Spacetime

Selman Ipek, Mohammad Abedi, Ariel Caticha

In the Entropic Dynamics framework quantum theory is derived as an application of the method of maximum entropy. In previous work the entropic dynamics of relativistic quantum scalar fields was formulated in the Schroedinger functional representation in which the Lorentz symmetry is not manifest. Here the formalism is extended to curved spacetimes. We develop a manifestly covariant approach inspired by the Hamiltonian methods of Dirac, Kuchar, and Teitelboim. The key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces.In the Entropic Dynamics framework quantum theory is derived as an application of the method of maximum entropy. In previous work the entropic dynamics of relativistic quantum scalar fields was formulated in the Schroedinger functional representation in which the Lorentz symmetry is not manifest. Here the formalism is extended to curved spacetimes. We develop a manifestly covariant approach inspired by the Hamiltonian methods of Dirac, Kuchar, and Teitelboim. The key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces.

Mar 20, 20180 citations

The entropic dynamics of relativistic quantum fields in curved space-time

Selman Ipek

It has often been the case in history that the laws of physics have been used as the framework for understanding and implementing information processing. The tacit assumption is that the laws of physics are fundamental and that the notion of information is derived from these laws. Here we take the opposite view: the laws of physics are an application of the rules for processing information. The inferential framework of entropic dynamics (ED) has previously been developed by A. Caticha for the purposes of understanding and deriving quantum theory, in much the same way that E.T. Jaynes used the MaxEnt approach to derive the formalism of statistical mechanics. In this thesis we apply the ED framework to construct a quantum dynamics for scalar fields in space-time.It has often been the case in history that the laws of physics have been used as the framework for understanding and implementing information processing. The tacit assumption is that the laws of physics are fundamental and that the notion of information is derived from these laws. Here we take the opposite view: the laws of physics are an application of the rules for processing information. The inferential framework of entropic dynamics (ED) has previously been developed by A. Caticha for the purposes of understanding and deriving quantum theory, in much the same way that E.T. Jaynes used the MaxEnt approach to derive the formalism of statistical mechanics. In this thesis we apply the ED framework to construct a quantum dynamics for scalar fields in space-time.

arXiv:2105.07042Jan 1, 20210 citations

Ψ[φ,t]

encodes a first-order, causal ensemble dynamics on configuration space. Interactions appear as couplings between configuration-space directions, while propagators arise as derived correlation structures rather than as fundamental postulates. Entanglement, scattering amplitudes, and conformal field theory correlators emerge as distinct projections of the same underlying ensemble evolution, corresponding to equal-time, asymptotic, and symmetry-organized observables. Standard operator, diagrammatic, and path-integral formulations are recovered as computational representations of this single real-time dynamics. This organization makes explicit the distinction between fundamental dynamical structure and representational tools in QFT, and clarifies the scope within which ensemble-averaged correlators account for quantum fluctuations, while also delineating the level at which questions associated with individual realizations and randomness would arise beyond the correlator-based field-theoretic description.