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arXiv:0908.0957

A new interpretation of superposition, entanglement, and measurement in quantum mechanics

Rajendra Kumar Bera, Menon, Vikram

Published Aug 7, 2009• 5 citations
arXivHTMLPDF

Abstract

We present a new interpretation of the terms superposition, entanglement, and measurement that appear in quantum mechanics. We hypothesize that the structure of the wave function for a quantum system at the sub-Planck scale has a deterministic cyclic structure. Each cycle comprises a sequential succession of the eigenstates that comprise a given wave function. Between unitary operations or measurements on the wave function, the sequential arrangement of the current eigenstates chosen by the system is immaterial, but once chosen it remains fixed until another unitary operation or measurement changes the wave function. The probabilistic aspect of quantum mechanics is interpreted by hypothesizing a measurement mechanism which acts instantaneously but the instant of measurement is chosen randomly by the classical measuring apparatus over a small but finite interval from the time the measurement apparatus is activated. At the instant the measurement is made, the wave function irrevocably collapses to a new state (erasing some of the past quantum information) and continues from thereon in that state till changed by a unitary operation or a new measurement.

DOI
10.48550/arxiv.0908.0957

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We present a new interpretation of the terms superposition, entanglement, and measurement that appear in quantum mechanics. We hypothesize that the structure of the wave function for a quantum system at the sub-Planck scale has a deterministic cyclic structure. Each cycle comprises a sequential succession of the eigenstates that comprise a given wave function. Between unitary operations or measurements on the wave function, the sequential arrangement of the current eigenstates chosen by the system is immaterial, but once chosen it remains fixed until another unitary operation or measurement changes the wave function. The probabilistic aspect of quantum mechanics is interpreted by hypothesizing a measurement mechanism which acts instantaneously but the instant of measurement is chosen randomly by the classical measuring apparatus over a small but finite interval from the time the measurement apparatus is activated. At the instant the measurement is made, the wave function irrevocably collapses to a new state (erasing some of the past quantum information) and continues from thereon in that state till changed by a unitary operation or a new measurement.
We propose an information-centric interpretation of quantum mechanics. According to this interpretation, a quantum mechanical system, AAA, can always choose a basis in which its own state is an eigenstate; it never sees itself in a superposition. This holds true even if, from the perspective of another system BBB, AAA is entangled with system SSS. In this case, AAA and SSS are in eigenstates (in their own systems) with their counterpart subsystem wave functions collapsed in the entangled degrees of freedom, but they are entangled according to BBB. This interpretation does not introduce new physics, and is consistent with the experimental predictions of quantum mechanics. At the same time, it avoids many ambiguities and potential inconsistencies associated with other interpretations. We further clarify concepts of measurement, macroscopic superposition, entanglement, and the dichotomy between the classical and quantum realms, in accordance with our interpretation.
We will give a new model for measurements of a quantum system, expressed as the compact operators on a Hilbert space, such that the measuring apparatuses are described by a unital separable non-type I nuclear simple C∗^*∗-algebra equipped with certain unital endomorphisms and pure states. An interaction between the quantum system and the apparatus is specified by a unitary associated with the combined system as before. Magnifying to the classical level some aspects of the quantum system so captured in the apparatus is explicitly done by applying the endomorphism; then the resulting state is the superposition of {\em phases} with weights. Nature will then choose each phase according to the probability prescribed by the weights just as does one when multiple phases appear as in phase transition. Thus in our model state-reduction (or collapse of the wave function) is a primary event; whether this corresponds to the measurement of an observable or which one if it does is another matter.
Theory of measurement is presented which is based on the statistical interpretation of quantum mechanics. The reduction of wave packet is ascribed to undue comparison of the state of an ensemble before measurement and the state of an individual system after measurement. By studying the evolution of statistical operators for subsystems and composite systems comprising an object, a measuring apparatus and an observer, one can definitely locate where the measurement is done, thus negating the principle of psycho-physical parallelism due to von Neumann. Time needed for measurement is also discussed. The Einstein-Podolsky-Rosen state is described as an eigenstate of correlation. The argument lends support to the standpoint that the physical state of a system is to be represented by the statistical operator, not by the wave function, in the conceptual foundation of quantum mechanics.
We will give a new model for measurements of a quantum system such that the measuring apparatuses are described by a unital separable non-type I nuclear simple C∗^*∗-algebra equipped with certain unital endomorphisms and pure states. An interaction between the quantum system and the apparatus is specified by a unitary associated with the combined system as before. Magnifying to the classical level some aspects of the quantum system so captured in the apparatus is explicitly done by applying the endomorphism; then the resulting state is the superposition of {\em phases} with weights. Nature will then choose each phase according to the probability prescribed by the weights just as does one when multiple phases appear as in phase transition. Thus in our model state-reduction (or collapse of the wave function) is a primary event; whether this corresponds to the measurement of an observable or which one if it does is another matter.
Theory of measurement is presented which is based on the statistical interpretation of quantum mechanics. The reduction of wave packet is ascribed to undue comparison of the state of an ensemble before measurement and the state of an individual system after measurement. By studying the evolution of statistical operators for subsystems and composite systems comprising an object, a measuring apparatus and an observer, one can definitely locate where the measurement is done, thus negating the principle of psycho-physical parallelism due to von Neumann. Time needed for measurement is also discussed. The Einstein-Podolsky-Rosen state is described as an eigenstate of correlation. The argument lends support to the standpoint that the physical state of a system is to be represented by the statistical operator, not by the wave function, in the conceptual foundation of quantum mechanics.
This paper proposes a timeless interpretation of quantum mechanics in which fundamental reality is configurational rather than temporal. What we perceive as the temporal evolution of a particle is reinterpreted as our sequential perspective on a static structure of spatial correlations. Quantum superposition reveals this nature: all possible spatial configurations coexist in a timeless reality, and only when we—bound by time—observe the system, do we project this multiplicity into a temporal sequence. When we measure a quantum system, we do not collapse a wave function but rather synchronize our clock-system with a specific section of the timeless structure. This interpretation connects naturally with existing timeless approaches such as the Page-Wootters mechanism and Wheeler-DeWitt equation, while offering a distinctive perspective on the nature of the wave function, measurement, and the emergence of time from correlations within an atemporal quantum reality.