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Springer eBooks

Some Basic Differences Between the Copenhagen and de Broglie Interpretation of Quantum Mechanics Leading to Practical Experiments

J. R. Croca

Published Jan 1, 1989• 1 citation
Publisher
DOI
10.1007/978-94-009-1175-8_15

Related papers

Reflections on the Foundations of Quantum Mechanics

Alireza Jamali

In this paper the quantised version of Newton Second Law is derived assuming merely the existence of de Broglie matter-waves and their basic properties. At the same time we keep an eye towards interpretations of quantum mechanics and will realise that the two most different interpretations (Copenhagen interpretation and the de Broglie-Bohm theory) owe their difference to two fundamentally different approaches to `Harmonisation'. In this regard we shall see that the guiding equation of the de Broglie-Bohm theory currently found in literature is not the most complete equation possible; as a result we answer one of the important questions in interpreting quantum mechanics, namely that `when does the concept of classical path (trajectory) makes sense in quantum mechanics?' Moreover, in light of special-relativistic considerations we shall easily see that in the Number-Division approach, i.e. that of de Broglie-Bohm, the wave operator no longer appears, making it in turn impossible the application of Clifford algebras (Dirac's `square root' of the wave operator).

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The Bohm-de Broglie quantum mechanics has made possible to calculate the trajectories of electrons in a typical double-slit experiment[C. Philippidis et al., Il Nuovo Cimento, 52 B, 15-28 (1979)]. The trajectories do not correspond to an uniform movement but to an accelerated one. The acceleration is caused by the quantum potential. From the quantum theoretical point of view, the accelerated electrons should, with a certain probabil-ity, emit photons during its movement from the slits to the screen. According to the Copenhagen interpretation we found that this quantity is strictly zero because the electron moves as a free particle along its path after it leaves the slit and before reach the screen. Then, there is no emission of photons. On the other hand, by using the Bohm-de Broglie (BdB) approach we calculate the emission power, giving a general formula and which results, for a concrete real experiment, in a very tiny but not a vanishing value. We give an idea of the type of spectrum that could be measured. Therefore we have shown that the theoretical predictions of the usual quan-tum mechanics and that of Bohm-de Broglie’s interpretation are different. An experiment could determine the correct prediction.

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Implications of a deeper level explanation of the deBroglie–Bohm version of quantum mechanics

Gerhard Grössing, Siegfried Fussy, J Mesa Pascasio +1 more

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In this paper the quantised version of Newton Second Law is derived assuming merely the existence of de Broglie matter-waves and their basic properties. At the same time we keep an eye towards interpretations of quantum mechanics and will realise that the two most different interpretations (Copenhagen interpretation and the de Broglie-Bohm theory) owe their difference to two fundamentally different approaches to `Harmonisation'. In this regard we shall see that the guiding equation of the de Broglie-Bohm theory currently found in literature is not the most complete equation possible; as a result we answer one of the important questions in interpreting quantum mechanics, namely that `when does the concept of classical path (trajectory) makes sense in quantum mechanics?' Moreover, in light of special-relativistic considerations we shall easily see that in the Number-Division approach, i.e. that of de Broglie-Bohm, the wave operator no longer appears, making it in turn impossible the application of Clifford algebras (Dirac's `square root' of the wave operator).
The Bohm-de Broglie quantum mechanics has made possible to calculate the trajectories of electrons in a typical double-slit experiment[C. Philippidis et al., Il Nuovo Cimento, 52 B, 15-28 (1979)]. The trajectories do not correspond to an uniform movement but to an accelerated one. The acceleration is caused by the quantum potential. From the quantum theoretical point of view, the accelerated electrons should, with a certain probabil-ity, emit photons during its movement from the slits to the screen. According to the Copenhagen interpretation we found that this quantity is strictly zero because the electron moves as a free particle along its path after it leaves the slit and before reach the screen. Then, there is no emission of photons. On the other hand, by using the Bohm-de Broglie (BdB) approach we calculate the emission power, giving a general formula and which results, for a concrete real experiment, in a very tiny but not a vanishing value. We give an idea of the type of spectrum that could be measured. Therefore we have shown that the theoretical predictions of the usual quan-tum mechanics and that of Bohm-de Broglie’s interpretation are different. An experiment could determine the correct prediction.
The non-relativistic quantum theory has been interpreted causally by de Broglie, David Bohm, and others, where a quantum entity is viewed as a particle with a definite position and momentum. This interpretation contrasts with the Copenhagen orthodox interpretation, which conveys uncertainty through the commutator relationship between position and momentum operators. This is further exacerbated by the de Broglie-Bohm interpretation, which uses no operators corresponding to these observables. We reconcile these opposing viewpoints by introducing mathematical nonlinear transforms in Bohmian mechanics for the momentum observable. While these nonlinear operator-like transforms cannot be easily represented as matrices in the Hilbert space, we show that they can be utilized in the de Broglie-Bohm interpretations of quantum theory.