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- TL;DR Summary
- A new, elementary, and self-contained deductive approach to quantum mechanics
I just finished a new paper,
Starting from first principles inspired by quantum tomography rather
than Born's rule, this paper gives a new, elementary, and self-contained
deductive approach to quantum mechanics. A suggestive notion
for what constitutes a quantum detector and for the behavior of its
responses leads to a logically impeccable definition of measurement.
Applications to measurement schemes for optical states, position
measurements and particle tracks demonstrate that this definition is
applicable without any idealization to complex realistic experiments.
The various forms of quantum tomography for quantum states, quantum
detectors, quantum processes, and quantum instruments are discussed.
The traditional dynamical and spectral properties of quantum mechanics
are derived from a continuum limit of quantum processes. In particular,
the Schrödinger equation for the state vector of a pure, nonmixing
quantum system and the Lindblad equation for the density operator of
a mixing quantum system are shown to be consequences of the new
approach. A slight idealization of the measurement process leads to the
notion of quantum fields, whose smeared quantum expectations emerge as
reproducible properties of regions of space accessible to measurements.
The paper may be viewed as a derivation of my thermal interpretation of quantum physics from first principles.
Now there is a related Insight article, Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics, with a more extensive overview of the new approach.
- A. Neumaier, Quantum mechanics via quantum tomography, arXiv:2110.05294.
- A. Neumaier, Quantum tomography explains quantum mechanics, arXiv:2110.05294.
Starting from first principles inspired by quantum tomography rather
than Born's rule, this paper gives a new, elementary, and self-contained
deductive approach to quantum mechanics. A suggestive notion
for what constitutes a quantum detector and for the behavior of its
responses leads to a logically impeccable definition of measurement.
Applications to measurement schemes for optical states, position
measurements and particle tracks demonstrate that this definition is
applicable without any idealization to complex realistic experiments.
The various forms of quantum tomography for quantum states, quantum
detectors, quantum processes, and quantum instruments are discussed.
The traditional dynamical and spectral properties of quantum mechanics
are derived from a continuum limit of quantum processes. In particular,
the Schrödinger equation for the state vector of a pure, nonmixing
quantum system and the Lindblad equation for the density operator of
a mixing quantum system are shown to be consequences of the new
approach. A slight idealization of the measurement process leads to the
notion of quantum fields, whose smeared quantum expectations emerge as
reproducible properties of regions of space accessible to measurements.
The paper may be viewed as a derivation of my thermal interpretation of quantum physics from first principles.
Now there is a related Insight article, Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics, with a more extensive overview of the new approach.
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