The Causal Formulation of Quantum Mechanics of Particles (the Theory of De Broglie, Bohm and Takabayasi)

Freistadt, Hans

doi:10.1007/bf02744313

Cited by 56 publications

(14 citation statements)

References 40 publications

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“…In the second reformulation, we show how the first-order ('Aristotelian' [3]) law of postulate 2 may be expressed equivalently as a second-order ('Newtonian') equation, which brings out the fundamental role played by force in the causal explanation. In the context of the second-order equation the status of the first-order law is that it constrains the initial velocity of the particle, the constraint being preserved by the second-order equation.…”

Section: The Postulatesmentioning

confidence: 97%

“…Moreover, conclusions drawn from the particle law beyond its remit of conserving the quantum probability may be suspect. For example, if we wish to dispense with postulate 3 and attempt to derive it using an argument based on the guidance law, as first suggested by Bohm [3], we risk circularity if that postulate has already been invoked to justify the law. Another example is the use of the trajectory law to compute quantities that go beyond the standard quantum formalism, such as transit time [8].…”

Section: Limitationsmentioning

confidence: 99%

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Uniting the wave and the particle in quantum mechanics

Holland

2019

Quantum Stud.: Math. Found.

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We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie-Bohm theory: its reliance on the quantum probability formula to justify the particle guidance equation; its insouciance regarding the absence of reciprocal action of the particle on the guiding wavefunction; and its lack of a unified model to represent its inseparable components. Following the author's previous work, these problems are examined within an analytical framework by requiring that the wave-particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, energy and momentum) with their Schrödinger counterparts. In conjunction with the condition of time reversal covariance this implies the de Broglie-Bohm law for the particle where the quantum potential mediates the wave-particle interaction (we also show how the time reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the composite's mass, and its energy and momentum conservation laws. Our principal result is the unification of the Schrödinger equation and the de Broglie-Bohm law in a single inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes via the quantum potential. The theory is extended to many-body systems. We review de Broglie's objections to the pilot-wave theory and suggest that our field-theoretic description provides a realization of his hitherto unfulfilled 'double solution' programme. A revised set of postulates for the de Broglie-Bohm theory is proposed in which the unified field is taken as the basic descriptive element of a physical system....our model in which wave and particle are regarded as basically different entities, which interact in a way that is not essential to their modes of being, does not seem very plausible. The fact that wave and particle are never found separately suggests that they are both different aspects of some fundamentally new kind of entity... David Bohm [1]⎡ ⎣ ⎤ ⎦ .

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Section: The Postulatesmentioning

confidence: 97%

Section: Limitationsmentioning

confidence: 99%

Uniting the wave and the particle in quantum mechanics

Holland

2019

Quantum Stud.: Math. Found.

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“…41 Vigier brought momentum to the causal interpretation. For Freistadt's works, see Freistadt (1953Freistadt ( , 1955Freistadt ( , 1957. With de Broglie and Vigier, the Institut Henri Poincaré became the world headquarters of the causal interpretation.…”

Section: Supportersmentioning

confidence: 99%

The Quantum Dissidents

Freire¹

2015

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“…Eq. (8) with its adjoint are equivalent to the pair of equations of hydrodynamic representation 34, 47–54: where the density ρ and mean four‐velocity, 〈 u μ 〉, are connected with amplitude χ and phase S by the relations 55 …”

Section: Hydrodynamic Representation Of Wave Mechanicmentioning

confidence: 99%

Deduction of the Klein–Fock–Gordon equation from a non‐Markovian stochastic equation for real pure‐jump process

Скоробогатов

2002

Int J of Quantum Chemistry

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ABSTRACT:From the Madelung's work in 1926, it became clear that the pair of adjoint Schrödinger equations is equivalent to two equations of hydrodynamic representation for probability density w(x ជ, t) ϭ ͉(x ជ, t)͉ 2 and mean momentum p ជ(x ជ, t) ϭ i (ٌ x ជ * Ϫ *ٌ x ជ )/2w. Both these equations can be derived from the quantum transport equation (QTE) for a probability density P( p ជ, x ជ, t) as two equations for the two first moments w(Then, QTE can be obtained from a non-Markovian stochastic Kolmogorov-Gikhman-Skorokhod equation for a real pure-jump process. Similarly, the Klein-Fock-Gordon equation follows from non-Markovian relativistic QTE (RQTE). Thus, all quantum mechanics as mathematical theory is a topic of the theory of real pure-jump non-Markovian stochastic processes.

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The Causal Formulation of Quantum Mechanics of Particles (the Theory of De Broglie, Bohm and Takabayasi)

Cited by 56 publications

References 40 publications

Uniting the wave and the particle in quantum mechanics

Uniting the wave and the particle in quantum mechanics

The Quantum Dissidents

Deduction of the Klein–Fock–Gordon equation from a non‐Markovian stochastic equation for real pure‐jump process

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