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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.

**Abstract:**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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