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de Broglie–Bohm, Delayed-Choice, Double-Slit Experiment, and Density Matrix

James S. Bell

WORLD SCIENTIFIC eBooksAug 1, 20017 citations

de Broglie–Bohm, delayed-choice double-slit experiment, and density matrix

James S. Bell

I will try to interest you in the de Broglie–Bohm version of non-relativistic quantum mechanics. It is, in my opinion, very instructive. It is experimentally equivalent to the usual version insofar as the latter is unambiguous. But it does not require, in its very formulation, a vague division of the world into ‘system’ and ‘apparatus,’ nor of history into ‘measurement’ and ‘nonmeasurement.’ So it applies to the world at large, and not just to idealized laboratory procedures. Indeed the de Broglie–Bohm theory is sharp where the usual one is fuzzy, and general where the usual one is special. This is not a systematic exposition, but only an illustration of the ideas with a particularly nice example, and then some remarks on the role of the density matrix – in tribute to the title of this conference. No one more eloquently than John A. Wheeler has presented the delayed-choice double slit experiment. A pulsed particle source S (see Fig. 1) is so feeble that not more than one particle is emitted per pulse. The associated wave pulse B falls on a screen with slits 1 and 2. The transmitted pulses B′ are focussed by off-centred lenses into intersecting plane wave trains which fall finally on particle counters C 1 and C 2 – unless a photographic plate P is pushed into the region where the two wave trains interpenetrate. The decision, to interpose the plate or not, is made only after the pulse has passed the slits.I will try to interest you in the de Broglie–Bohm version of non-relativistic quantum mechanics. It is, in my opinion, very instructive. It is experimentally equivalent to the usual version insofar as the latter is unambiguous. But it does not require, in its very formulation, a vague division of the world into ‘system’ and ‘apparatus,’ nor of history into ‘measurement’ and ‘nonmeasurement.’ So it applies to the world at large, and not just to idealized laboratory procedures. Indeed the de Broglie–Bohm theory is sharp where the usual one is fuzzy, and general where the usual one is special. This is not a systematic exposition, but only an illustration of the ideas with a particularly nice example, and then some remarks on the role of the density matrix – in tribute to the title of this conference. No one more eloquently than John A. Wheeler has presented the delayed-choice double slit experiment. A pulsed particle source S (see Fig. 1) is so feeble that not more than one particle is emitted per pulse. The associated wave pulse B falls on a screen with slits 1 and 2. The transmitted pulses B′ are focussed by off-centred lenses into intersecting plane wave trains which fall finally on particle counters C 1 and C 2 – unless a photographic plate P is pushed into the region where the two wave trains interpenetrate. The decision, to interpose the plate or not, is made only after the pulse has passed the slits.

Cambridge University Press eBooksJun 3, 200411 citations

de Broglie–Bohm, Delayed-Choice, Double-Slit Experiment, and Density Matrix

James S. Bell

World Scientific series in 20th century physicsSep 1, 199513 citations

The density matrix in the de Broglie-Bohm approach

Maroney, O J E

If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie-Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which Bell appears to suggest that such an interpretation is not possible. Bell's argument is shown to be based upon a different understanding of the density matrix to that proposed here.If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie-Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which Bell appears to suggest that such an interpretation is not possible. Bell's argument is shown to be based upon a different understanding of the density matrix to that proposed here.

Nov 21, 200322 citations

Random Thoughts on Quantum Mechanics

Partha Ghose

Here are a few random thoughts on the interpretations of the quantum double slit experiment, the Mach Zehnder experiment, the delayed-choice experiment and the measurement problem.

arXiv:2204.02262Apr 3, 20220 citations

Interpretation of Double-Slit Experiment by Space-Time Ladder Theory—Essence of Delayed Choice Quantum Eraser Experiment

炳功常

Modern PhysicsJan 1, 20191 citation

De Broglie-Bohm, delayed-choice, double-slit experiment, and density matrix

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De Broglie-Bohm, delayed-choice, double-slit experiment, and density matrix

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