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arXiv:1312.1589

The Generation of Quantum Hamiltonian Evolution from A Pseudo-Measurement Process

Brown, Matthew F.

Published Dec 5, 2013• 0 citations
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Abstract

Here we shall consider the idea that the Hamiltonian evolution of a quantum system is generated by sequential observations of the system by a `pseudo-apparatus'. This representation of Hamiltonian dynamics, originally discovered by Belavkin, is a canonical dilation of the Schroedinger equation that reveals a Minkowski space structure outside of the context of Special Relativity. In particular, this formalism gives rise to the notion of a Boosted Schroedinger equation referred to a dilated time increment which is the manifestation of a Lorentz transform in the Minkowski space of the apparatus.

DOI
10.48550/arxiv.1312.1589

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Here we shall consider the idea that the Hamiltonian evolution of a quantum system is generated by sequential observations of the system by a `pseudo-apparatus'. This representation of Hamiltonian dynamics, originally discovered by Belavkin, is a canonical dilation of the Schroedinger equation that reveals a Minkowski space structure outside of the context of Special Relativity. In particular, this formalism gives rise to the notion of a Boosted Schroedinger equation referred to a dilated time increment which is the manifestation of a Lorentz transform in the Minkowski space of the apparatus.
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The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection rule. In order to avoid the subjective nuance, I emphasis that the notion of "measurement" here, is nothing but the covariant differentiation procedure in the functional quantum phase space CP(N−1)CP(N-1)CP(N−1), having pure objective sense of evolution. Transition to the local moving quantum reference frame leads to some particle-like solutions of quasi-linear field PDE in the dynamical space-time. Thereby, the functionally covariant quantum dynamics gives the perspective to unify the Einstein relativity and quantum principles which are obviously contradictable under the standard approaches.
On the level of quantum phenomena, there is no precise possibility of separating an examined physical system from a measuring instrument. This fact lends support to the assertion that the evolution of a quantum system ceases to be rigorously causal from the moment when the system is subjected to investigation. A quantum measurement is special in that it always causes a jump in the system under study to an eigenstate of the considered variable. Possible interactions between the measuring and measured objects will be neglected, so that a given quantum system, which is free from any disturbances, e.g. measurements or other perturbations, will evolve in a rigorously predictable manner. Globally speaking, a quantum-mechanical scheme of description of physical phenomena can be summarized by introducing the so-called Schrödinger picture. A physical field is obtained when a given physical feature is attributed to each point of a space in which the process under study is developing.