Interfering Quantum Trajectories Without Which-Way Information

Mathew, Kiran; John, Moncy V.

doi:10.1007/s10701-017-0088-1

Cited by 4 publications

(5 citation statements)

References 28 publications

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“…An example is the Bohmian explanation of the two-slit experiment (Sect. 5.1) [268, § 6.1.1] [434]. In some versions, the state (or guiding field) features in a physical law, rather than as part of independent reality [239,428], although making this distinction is not necessarily straightforward [219].…”

Section: De Broglie and Bohmian Theories: More Descriptive But No Les...mentioning

confidence: 99%

Understanding quantum mechanics: a review and synthesis in precise language

Drummond¹

2019

Open Physics

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This review, of the understanding of quantum mechanics, is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject. To enhance clarity, the main findings are presented in the form of a coherent synthesis of the reviewed sources. The review highlights core characteristics of quantum mechanics. One is statistical balance in the collective response of an ensemble of identically prepared systems, to differing measurement types. Another is that states are mathematical terms prescribing probability aspects of future events, relating to an ensemble of systems, in various situations. These characteristics then yield helpful insights on entanglement, measurement, and widely-discussed experiments and analyses. The review concludes by considering how these insights are supported, illustrated and developed by some specific approaches to understanding quantum mechanics. The review uses non-mathematical language precisely (terms defined) and rigorously (consistent meanings), and uses only such language. A theory more descriptive of independent reality than is quantum mechanics may yet be possible. One step in the pursuit of such a theory is to reach greater consensus on how to understand quantum mechanics. This review aims to contribute to achieving that greater consensus, and so to that pursuit.

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Section: De Broglie and Bohmian Theories: More Descriptive But No Les...mentioning

confidence: 99%

Understanding quantum mechanics: a review and synthesis in precise language

Drummond¹

2019

Open Physics

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“…The formulation ( 17) ensures that the state ψ ∆z z is automatically normalized to 1. Substituting ( 16) into (17) and expressing the p.d.f., we find:…”

Section: B Projection Of the Initial State Position Filteringmentioning

confidence: 99%

“…Since F 0 L (z) = δ(z), the square root in the right-hand side of ( 16) is not defined and consequently ( 16) and (17) are not applicable when ∆z = 0. The passage to the limit can only be done for the p.d.f., by using (18) 2 .…”

Section: B Projection Of the Initial State Position Filteringmentioning

confidence: 99%

“…The first theory of this type dates back to the beginnings of the history of quantum mechanics and treats the Fraunhofer diffraction by a grating by combining the concept of light quantum with Bohr's principle of correspondence [10]. Then, models involving quantum mechanics to calculate diffraction are mostly those based on the formalism of path integrals [11][12][13][14] and those predicting quantum trajectories in the framework of hidden variables theories [15][16][17]. Other models combine the resolution of the Schrödinger equation (or of the wave equation for photons) with the Huygens-Fresnel principle [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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On the quantum theory of diffraction by an aperture and the Fraunhofer diffraction at large angles

Fabbro¹

2017

Preprint

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A theoretical model of diffraction based on the concept of quantum measurement is presented. It provides a general expression of the state vector of a particle after its passage through an aperture of any shape in a plane screen (diaphragm). This model meets the double requirement of compatibility with the Huygens-Fresnel principle and with the kinematics of the particle-diaphragm interaction. This led to assume that the diaphragm is a device for measuring the three spatial coordinates of the particle and that the transition from the initial state (incident wave) to the final state (diffracted wave) consists of two specific projections which occur successively in a sequence involving a transitional state. In the case of the diffraction at infinity (Fraunhofer diffraction), the model predicts the intensity of the diffracted wave over the whole angular range of diffraction (0 • -90 • ). The predictions of the quantum model and of the theories of Fresnel-Kirchhoff (FK) and Rayleigh-Sommerfeld (RS1 and RS2) are close at small diffraction angles but significantly different at large angles, a region for which specific experimental studies are lacking. A measurement of the particle flow intensity in this region should make it possible to test the FK and RS1-2 theories and the suggested quantum model.

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“…In [12], using the 'quantum trajectories' approach, we checked whether the coasting evolution of a universe that starts from singularity [4] will have exact quantum-classical correspondence and obtained a positive result. In that case, we have used the de Broglie-Bohm (dBB) [13,14] and modified de Broglie-Bohm (MdBB) [15][16][17][18][19][20] trajectory formulations of quantum mechanics. In the present paper, instead of writing the WD equation, we employ the operator method in canonical quantisation and show that the quantum cosmological wave function can be obtained as an exact solution to the corresponding wave equation for the universe.…”

Section: Introductionmentioning

confidence: 99%

Bouncing and Coasting Universe with Exact Quantum-Classical Correspondence

John¹

2021

Int J Theor Phys

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When the scale factor of expansion of the universe is written as a(t) ≡ Ae α (t) , with A as some real constant and α(t) a real function, the gravitational action I G appears in the same form as the matter action I M for a homogeneous and isotropic scalar field with a specific scale factor-dependent potential. We observe that by making analytic continuation of the Lagrangian function in this I G to the complex plane of α, one can obtain terms corresponding to both parts of a total action that describes a viable cosmological model. The solution gives a bouncing and coasting universe, which first contracts and then expands linearly, with a smooth bounce in between them. Such a bounce, called a Tolman wormhole, is due to a Casimir-like negative energy that appears naturally in the solution. In a novel approach to quantum cosmology, we perform canonical quantization of the above model using the operator method and show that it can circumvent the operator ordering ambiguity in the conventional formalism. It leads to a quantum wave equation for the universe, solving which we get the interesting result that the universe is in a ground state with nonzero energy. This solution is different from the Wheeler-DeWitt wave function and possesses exact quantum-classical correspondence during all epochs.

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Interfering Quantum Trajectories Without Which-Way Information

Cited by 4 publications

References 28 publications

Understanding quantum mechanics: a review and synthesis in precise language

Understanding quantum mechanics: a review and synthesis in precise language

On the quantum theory of diffraction by an aperture and the Fraunhofer diffraction at large angles

Bouncing and Coasting Universe with Exact Quantum-Classical Correspondence

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