Resonant cavity for the stimulated emission of x rays

Caticha, Ariel; Caticha, Nestor; Caticha‐Ellis, S.

doi:10.1063/1.100799

Cited by 47 publications

(34 citation statements)

References 17 publications

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“…The evidence supporting it is already considerable. Indeed, most of the formal structure of statistical mechanics [1] and of quantum theory [2] can already be derived from principles of inference (consistency, probabilities, entropy, etc. ).…”

Section: Introductionmentioning

confidence: 99%

From Information Geometry to Newtonian Dynamics

Caticha¹,

Cafaro²

2007

AIP Conference Proceedings

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Newtonian dynamics is derived from prior 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 state of a particle is defined by a probability distribution. The corresponding configuration space is a statistical manifold the geometry of which is defined by the information metric. The trajectory follows from a principle of inference, the method of Maximum Entropy. No additional "physical" postulates such as an equation of motion, or an action principle, nor the concepts of momentum and of phase space, not even the notion of time, need to be postulated. The resulting entropic dynamics reproduces the Newtonian dynamics of any number of particles interacting among themselves and with external fields. Both the mass of the particles and their interactions are explained as a consequence of the underlying statistical manifold.

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Section: Introductionmentioning

confidence: 99%

From Information Geometry to Newtonian Dynamics

Caticha¹,

Cafaro²

2007

AIP Conference Proceedings

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“…This paper is a continuation of previous work [7] [8] in which quantum theory is formulated as the only consistent way to manipulate amplitudes. In this consistent-amplitude quantum theory (CAQT) amplitudes have a clear interpretation: they are tools for reasoning that encode information about how complicated experimental setups are related to those more elementary setups from which they were built.…”

Section: Introductionmentioning

confidence: 92%

“…which is equivalent to a linear Schrödinger equation as can easily be seen [7][8] by differentiating with respect to t f and evaluating at t f = t. Thus, a quantum theory formulated in terms of consistently assigned amplitudes must be linear; nonlinear modifications of quantum mechanics must violate assumptions A1 or A2 else be internally inconsistent [19]. The question of how amplitudes or wave functions are used to predict the outcomes of experiments is addressed through the time evolution equation (4).…”

Section: Introductionmentioning

confidence: 99%

“…Once one finds that time evolution must be linear [7] the obvious next question is whether it must also be unitary. These two issues of linearity and unitarity are usually considered together (for a short review see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…What problem is quantum mechanics trying to solve? We choose a pragmatic, operational approach: statements about a system are identified with those experimental setups designed to test them [7][8]. Our strategy is to establish a network of relations among setups in the hope that information about some setups might be helpful in making predictions about others.…”

Section: Introductionmentioning

confidence: 99%

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Caticha

2000

Foundations of Physics

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The objective of the consistent-amplitude approach to quantum theory has been to justify the mathematical formalism on the basis of three main assumptions: the first defines the subject matter, the second introduces amplitudes as the tools for quantitative reasoning, and the third is an interpretative rule that provides the link to the prediction of experimental outcomes. In this work we introduce a natural and compelling fourth assumption: if there is no reason to prefer one region of the configuration space over another then they should be 'weighted' equally. This is the last ingredient necessary to introduce a unique inner product in the linear space of wave functions. Thus, a form of the principle of insufficient reason is implicit in the Hilbert inner product. Armed with the inner product we obtain two results. First, we elaborate on an earlier proof of the Born probability rule. The implicit appeal to insufficient reason shows that quantum probabilities are not more objective than classical probabilities. Previously we had argued that the consistent manipulation of amplitudes leads to a linear time evolution; our second result is that time evolution must also be unitary. The argument is straightforward and hinges on the conservation of entropy. The only subtlety consists of defining the correct entropy; it is the array entropy, not von Neumann's. After unitary evolution has been established we proceed to introduce the useful notion of observables and we explore how von Neumann's entropy can be linked to Shannon's information theory. Finally, we discuss how various connections among the postulates of quantum theory are made explicit within this approach.

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Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

Caticha

2018

Annalen der Physik

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Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single-valuedness of wave functions.

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Resonant cavity for the stimulated emission of x rays

Cited by 47 publications

References 17 publications

From Information Geometry to Newtonian Dynamics

From Information Geometry to Newtonian Dynamics

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Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

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