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Modern Physics Letters B

Entanglement, inelastic scattering of particles and measurement problem in quantum mechanics

Alexey V. Melkikh

Published May 20, 2022• 0 citations
Publisher

Abstract

In this paper, a constructive definition of entanglement for nonidentical particles is given. It is shown that particles arising in the process of inelastic scattering are entangled with each other. This property is a consequence of the symmetry of fundamental interactions. Considering detectors of elementary particles, it was concluded that only inelastic scattering can be the basis of a measuring instrument. In the process of inelastic scattering, the measuring instrument can acquire information about the particle (system), while in the case of elastic scattering, it cannot. The nonlinearity of inelastic scattering naturally solves the measurement problem in quantum mechanics.

DOI
10.1142/s0217984922500488

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In this paper, a constructive definition of entanglement for nonidentical particles is given. It is shown that particles arising in the process of inelastic scattering are entangled with each other. This property is a consequence of the symmetry of fundamental interactions. Considering detectors of elementary particles, it was concluded that only inelastic scattering can be the basis of a measuring instrument. In the process of inelastic scattering, the measuring instrument can acquire information about the particle (system), while in the case of elastic scattering, it cannot. The nonlinearity of inelastic scattering naturally solves the measurement problem in quantum mechanics.
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Abstract The problem of the wave function collapse (a problem of measurement in quantum mechanics) is considered. It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation (annihilation) of a particle, an additional uncertainty arises, which “smears” the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term “collapse of the wave function” becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.
In order to assess inelastic effects on two fermion entanglement production, we address an exactly solvable two-particle scattering problem where the target is an excitable scatterer. Useful entanglement, as measured by the two particle concurrence, is obtained from post-selection of oppositely scattered particle states. The SSS matrix formalism is generalized in order to address nonunitary evolution in the propagating channels. We find the striking result that inelasticity can actually increase concurrence as compared to the elastic case by increasing the uncertainty of the single particle subspace. Concurrence zeros are controlled by either single particle resonance energies or total reflection conditions that ascertain precisely one of the electron states. Concurrence minima also occur and are controlled by entangled resonance situations where the electron becomes entangled with the scatterer, and thus does not give up full information of its state. In this model, exciting the scatterer can never fully destroy phase coherence due to an intrinsic limit to the probability of inelastic events.
The thesis of this paper is that quantum measurement can be analyzed and understood within quantum mechanics itself. The statistics of the measurement process comes from the unknown details of the macroscopic measurement device. Quantum measurement is analyzed within the framework of scattering theory of quantum field theory with the aim of finding a physical rather than a metaphysical understanding. The measurement interaction is treated together with the quantum process to be measured. The evaluation of a Feynman diagram for the total process leads to one factor from the measurement interaction for each channel multiplying the basic scattering amplitudes. With increasing entanglement taken into account, these factors compete for dominance. They depend on unknown details of the measurement apparatus. The statistics of this competition is studied under the assumption that the measurement interaction does not introduce any bias. A binary quantum system is analyzed and after that the n-channel case. As a background, a couple of classical examples are shown, leading to the same selective mechanisms. The result of this analysis is that the quantum measurement process can be understood, whether a single measurement or an ensemble of measurements, as a result of an ordinary unitary time development, based on the interaction beteen the system subjet to measurement and the measurement apparatus. This result makes it possible to view the quantum-mechanical state as describing reality rather than merely a potentiality. This opens again for an ontology of physics, and hence for science in general.
The measurement problem of quantum mechanics concerns the question as to under which circumstances coherent wave evolution becomes disrupted to produce eigenstates of observables, instead of evolving superpositions of eigenstates. The problem already needs to be addressed within wave mechanics, before second quantization, because low-energy interactions can be dominated by particle-preserving potential interactions. We discuss a scattering array of harmonic oscillators, which can detect particles penetrating the array through interaction with a short-range potential. Evolution of the wave function of scattered particles, combined with Heisenberg’s assertion that quantum jumps persist in wave mechanics, indicates that the wave function will collapse around single oscillator sites if the scattering is inelastic, while it will not collapse around single sites for elastic scattering. The Born rule for position observation is then equivalent to the statement that the wave function for inelastic scattering amounts to an epistemic superposition of possible scattering states, in the sense that it describes a sum of probability amplitudes for inelastic scattering off different scattering centers, whereas, at most, one inelastic scattering event can happen at any moment in time. Within this epistemic interpretation of the wave function, the actual underlying inelastic scattering event corresponds to a quantum jump, whereas the continuously evolving wave function only describes the continuous evolution of probability amplitudes for scattering off different sites. Quantum jumps then yield definite position observations, as defined by the spatial resolution of the oscillator array.