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Macroscopic realism, wave-particle duality and the superposition principle for entangled states

Nikolay Leonidovich Chuprikov

Published Oct 5, 2006• 0 citations
OpenAlex

Abstract

On the basis of our model of a one-dimensional (1D) completed scattering (Russian Physics, 49, p.119 and p.314 (2006)) we argue that the linear formalism of quantum mechanics (QM) respects the principles of the macroscopic realism (J. Phys.: Condens. Matter, 14, R415-R451 (2002)). In QM one has to distinguish two kinds of pure ensembles: pure unentangled ensembles to be macroscopically inseparable, and pure entangled ones to be macroscopically separable. A pure entangled ensemble is an intermediate link between a pure unentangled ensemble and classical mixture. Like the former it strictly respects the linear formalism of QM. Like the latter it is decomposable into macroscopically distinct subensembles, in spite of interference between them; our new model exemplifies how to perform such a decomposition in the case of a 1D completed scattering. To respect macroscopic realism, the superposition principle must be reformulated: it must forbid introducing observables for entangled states.

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On the basis of our model of a one-dimensional (1D) completed scattering (Russian Physics, 49, p.119 and p.314 (2006)) we argue that the linear formalism of quantum mechanics (QM) respects the principles of the macroscopic realism (J. Phys.: Condens. Matter, 14, R415-R451 (2002)). In QM one has to distinguish two kinds of pure ensembles: pure unentangled ensembles to be macroscopically inseparable, and pure entangled ones to be macroscopically separable. A pure entangled ensemble is an intermediate link between a pure unentangled ensemble and classical mixture. Like the former it strictly respects the linear formalism of QM. Like the latter it is decomposable into macroscopically distinct subensembles, in spite of interference between them; our new model exemplifies how to perform such a decomposition in the case of a 1D completed scattering. To respect macroscopic realism, the superposition principle must be reformulated: it must forbid introducing observables for entangled states.
On the basis of our recent model of a one-dimensional (1D) completed scattering we argue that Leggett's principles of macroscopic realism must and can be extended onto the level of single electrons and atoms. These principles need three quite feasible innovations in quantum mechanics (QM): (1) at the conceptual level, QM must treat a pure time-dependent one-particle state to involve two or more macroscopically distinct alternatives for a particle as a pure {\it combined} one - the intermediate link between a pure {\it elementary} state (indecomposable into macroscopically distinct parts) and statistical mixture; (2) at the mathematical level, QM must provide the presentation of the pure time-dependent combined state as a coherent superposition of macroscopically distinct elementary states (MDESs); (3) at the experimental level, QM must provide for such states two types of measurements - those for observing the interference pattern resulting from the joint action of MDESs, and non-demolishing 'which-way' measurements for scanning the individual properties of MDESs.
The origin of nonlocality in quantum mechanics (QM) is analyzed from the viewpoint of our new model of a one-dimensional (1D) completed scattering. Our study of quantum nonlocality complements those carried out by Volovich and Khrennikov. They pointed to an unphysical character of nonlocality in Bell's theorem whose context does not contain the very structure of the space-time. However, there is another reason leading to nonlocality in QM. The existing model of a 1D completed scattering evidences that QM, as it stands, even with a proper space-time context, contradicts special relativity. By our model this scattering process represents an entanglement of two coherently evolved alternative sub-processes, transmission and reflection; whose characteristics are measured well after the scattering event. Quantum nonlocality appears in this problem due to the inconsistency of the superposition principle with the corpuscular properties of a particle. It can take part only in one of the sub-processes. However the superposition principle allows introducing observables common for them. In the fresh wording, this principle must forbid introducing observables for entangled states.
We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states. The same concerns the entangled states of compound quantum systems. In the {\it existing} quantum mechanics, introducing Bell's inequalities is fully legal. However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation. Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm. They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.
Macroscopic realism is a classical worldview that a macroscopic system is always determinately in one of the two or more macroscopically distinguishable states available to it and so is never in a superposition of these states. The question of whether there is a fundamental limitation on the possibility to observe quantum phenomena at the macroscopic scale remains unclear. Here we implement a strict and simple protocol to test macroscopic realism in a light-matter-interfaced system. We create a micro-macro entanglement with two macroscopically distinguishable solid-state components and rule out those theories which would deny coherent superpositions of up to 76 atomic excitations shared by 1010{10}^{10}1010 ions in two separated solids. These results provide a general method to enhance the size of superposition states of atoms by utilizing quantum memory techniques and to push the envelope of macroscopicity at higher levels.
Entanglement is usually associated with compound systems. We first show that a one-dimensional (1D) completed scattering of a particle on a static potential barrier represents an entanglement of two alternative one-particle sub-processes, transmission and reflection, macroscopically distinct at the final stage of scattering. The wave function for the whole ensemble of scattering particles can be uniquely presented as the sum of two isometrically evolved wave packets to describe the (to-be-)transmitted and (to-be-)reflected subensembles of particles at all stages of scattering. A noninvasive Larmor-clock timing procedure adapted to either subensemble shows that namely the dwell time gives the time spent, on the average, by a particle in the barrier region, and it denies the Hartman effect. As regards the group time, it cannot be measured and hence it cannot be accepted as a measure of the tunneling time. We argue that nonlocality of entangled states appears in quantum mechanics due to inconsistency of its superposition principle with the corpuscular properties of a particle. For example, this principle associates a 1D completed scattering with a single (one-way) process, while a particle, as an indivisible object, cannot take part in transmission and reflection, simultaneously.
As contrasted with physicists to idolize Bell's theorem and quantum nonlocality, we argue that quantum mechanics (QM), in reality, respects the principles of a macroscopic realism (PMRs). The current QM to tell us that "... the state of a system can be instantaneously changed by a distant measurement >..." cannot be treated as a physical theory. Its key statements - that the EPR-Bell experiments to violate Bell's inequality verify nonlocality, and nonlocal correlations respect special relativity - are false. Both the EPR-Bell experiments and theorems to support the "non-signalling principle" are based on the implicit assumption that all quantum postulates and, in particular, Born's averaging rule are fully applicable to Cat states. However, this is not the case. Introducing observables (e.g., correlations) for Cat states violates the correspondence principle. Pure (macro- and micro-)Cat states must be governed both by the PMRs and superposition principle. Our (macrorealistic) model of a one-dimensional completed scattering shows how these principles coexist with each other, in the case of a one-electron micro-Cat state.