Fisher Information Perspective of Pauli’s Electron

Yahalom, Asher

doi:10.3390/e24121721

Cited by 10 publications

(17 citation statements)

References 36 publications

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“…T α0 denotes the temperature of the "fluid element" in the rest frame, and P α0 is the pressure of the same. The rest of the thermodynamic analysis follows the same analysis in equation A29-A34 of [1] in which attention should be paid to the fact that it is only correct in the rest frame.…”

Section: Variational Analysismentioning

confidence: 99%

“…The variation of internal energy is the only new calculation with respect to the calculation done for a system of particles described previously [8], thus the rest of the analysis is trivial. Varying equation (1) we thus obtain:…”

Section: Variational Analysismentioning

confidence: 99%

“…The electromagnetic interaction variation terms are not different than in the low speed (nonrelativistic) case, see for example equations A47 and A48 of [1], and their derivation will not be repeated here:…”

Section: Variational Analysismentioning

confidence: 99%

“…A comprehensive introduction to the subject of the variational formalism of non-relativistic fluid dynamics and quantum mechanics and their deep interconnections is given in [1,2] and will not be repeated here.…”

Section: Introductionmentioning

confidence: 99%

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Variational Approach to Relativistic Fluid and Quantum Mechanics

Yahalom

2023

J. Phys.: Conf. Ser.

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In previous papers we have shown how Schrödinger’s equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour was derived from Fisher information terms which were added to the classical Lagrangian. It was thus shown that a quantum mechanical system is drived by information and not only electromagnetic fields. This program was applied also to Pauli’s equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful there were still terms that did not admit interpretation, some of them can be easily traced to the relativistic Dirac theory. Here we repeat the analysis for a relativistic flow, pointing to a new approach for deriving relativistic quantum mechanics.

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Section: Variational Analysismentioning

confidence: 99%

Section: Variational Analysismentioning

confidence: 99%

Section: Variational Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational Approach to Relativistic Fluid and Quantum Mechanics

Yahalom

2023

J. Phys.: Conf. Ser.

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“…It was also suggested that one may define comoving scalar fields as in ideal fluid mechanics, however, this was only demonstrated implicitly but not explicitly. A common feature of previous work on the fluid & Fisher information interpretation of quantum mechanics, is the negligence of electromagnetic interaction thus setting the vector potential to zero, this was recently corrected in [30].…”

Section: Introductionmentioning

confidence: 99%

Pauli’s Electron in Ehrenfest and Bohm Theories, a Comparative Study

Yahalom¹

2023

Preprint

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Electrons moving at slow speeds much lower that the speed of light are described by a wave function which is a solution of Pauli’s equation. This is a low velocity limit of the relativistic Dirac equation. Here we compare two approaches, one which is the more conservative Copenhagen’s interpretation denying a trajectory of the electron but allowing a trajectory to the electron expectation value through Ehrenfest theorem. The said expectation value is of course calculated using a solution of Pauli’s equation. A less orthodox approach is championed by Bohm, and attributes a velocity field to the electron also derived from the Pauli wave function. It is thus interesting to compare the trajectory followed by the electron according to Bohm and its expectation value according to Ehrenfest. Both similarities and differences will be considered.

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Dirac Theory, Relativistic Fluid Dynamics & Fisher Information

Yahalom

2024

J. Phys.: Conf. Ser.

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In previous papers we have shown how Schrödinger equations which include an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour was derived from Fisher information terms which were added to the classical Lagrangian. It was thus shown that a quantum mechanical system is drived by information and not only electromagnetic fields. This program was applied also to Pauli’s equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful there were still terms that did not admit interpretation, some of them can be easily traced to the relativistic Dirac theory. It is thus suggested to repeat the analysis for a relativistic flow, relating it to the Dirac theory by adding invariant four dimensional Fisher information terms. It is shown that while the classical parts of a classical fluid and a Dirac fluid can be mapped, the Fisher information term of Dirac theory is non-trivial. L Quantum = L Classical Fluid + L Fisher Information

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Fisher Information Perspective of Pauli’s Electron

Cited by 10 publications

References 36 publications

Variational Approach to Relativistic Fluid and Quantum Mechanics

Variational Approach to Relativistic Fluid and Quantum Mechanics

Pauli’s Electron in Ehrenfest and Bohm Theories, a Comparative Study

Dirac Theory, Relativistic Fluid Dynamics & Fisher Information

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