The Information Geometry of Space-Time

Caticha, Ariel

doi:10.3390/proceedings2019033015

Cited by 11 publications

(16 citation statements)

References 37 publications

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“…Or, in the spirit of an entropic dynamics, shall we search for an appropriately constrained dynamics of probabilities and information geometries? First steps towards formulating a first-principles theory along these lines are given in [ 114 , 115 ].…”

Section: Some Final Remarksmentioning

confidence: 99%

The Entropic Dynamics Approach to Quantum Mechanics

Caticha

2019

Entropy

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Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures -which is a Hamilton-Killing flow in phase space -is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations.4 There exist many different Bayesian interpretations of probability. In section 13 we comment on how ED differs from the frameworks known as Quantum Bayesianism [16]-[18] and its closely related descendant QBism [19][20].5 In both the ES and the OU processes, which were originally meant to model the actual physical Brownian motion, friction and dissipation play essential roles. In contrast, ED is non-dissipative. ED formally resembles Nelson's stochastic mechanics [23] but the conceptual differences are significant. Nelson's mechanics attempted an ontic interpretation of QM as an ES process driven by real stochastic classical forces while ED is a purely epistemic model that does not appeal to an underlying classical mechanics.

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Section: Some Final Remarksmentioning

confidence: 99%

The Entropic Dynamics Approach to Quantum Mechanics

Caticha

2019

Entropy

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“…The structure of Equation (11) is highly suggestive: if we interpret ρ σ [χ] as being an initial state, then we can interpret ρ σ [χ ] as being posterior to it in the sense that it has taken into account the new information captured by the transition probability P [χ |χ]. Here we take this hint seriously and adopt Equation (11) as the equation that we seek for updating probabilities.…”

Section: Ordered Instantsmentioning

confidence: 99%

“…The dynamics expressed in integral form by (11) and (12) can be rewritten in differential form. The result is [28,29],…”

Section: The Local-time Diffusion Equationsmentioning

confidence: 99%

“…Canonical approaches to QG, such as LQG, have wagered, with varying degrees of success, as to whether the former is true. But there are various clues (see, e.g., [7][8][9][10][11]) suggesting that gravity is an emergent, statistical phenomenon, not unlike temperature and pressure in statistical physics. Would any physicist quantize a temperature field?…”

Section: Introductionmentioning

confidence: 99%

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The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

Ipek

Caticha

2020

Symmetry

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Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

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“…Information geometry is a very effective branch of science, being regarded as a combination of differential geometry and statistics. Its applications can be found in various fields of research, like (see [1,3,4,6,7,17]): image processing, physics, computer science and machine learning. It merges fundamental differential geometry tools like metric, curvature and geodesics, to statistical models, and makes it possible to illustrate statistical objects as geometric ones.…”

Section: Introductionmentioning

confidence: 99%

Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric

Balan¹,

Peyghan²,

Sharahi³

2019

HJMS

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The first part of the paper is devoted to the classification of the statistical structures which live on the tangent bundle of a statistical manifold endowed with a Sasaki metric. Further, considering a Kähler structure on the base statistical manifold, we introduce a family of almost complex structures on the tangent bundle equipped with the Sasaki metric, and find equivalent conditions for which this family induces a Kähler structure. Finally, we derive equivalent conditions for existence of holomorphic structures on the tangent bundle equipped with the Sasaki metric in the presence of a statistical structure. Several illustrative examples are provided, as well.

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The Information Geometry of Space-Time

Cited by 11 publications

References 37 publications

The Entropic Dynamics Approach to Quantum Mechanics

The Entropic Dynamics Approach to Quantum Mechanics

The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric

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