A small quantum scattering system (the microsystem) is studied in interaction with a large quantum system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem in a certain basis, and it leads to an imprint on the macrosystem. Moreover, the interaction is assumed to involve only small transfers of energy and momentum between the two systems (as compared to typical energies/momenta within the microsystem). This makes it suitable to carry out the analysis in scattering theory, where the transition amplitude for the whole system factorizes. The interaction taking place within the macrosystem is assumed to depend on the stochastic variables in such a way that, on the average, no particular channel is favoured. The result is then, in the thermodynamic limit of the macrosystem, that the whole system bifurcates and the microsystem ends up in a state described by one of the basis vectors (in the mentioned basis). The macrosystem ends up in an entangled state tied to this basis vector. For the ensemble of macrosystems, the interaction with the microsystem leads, on the average, to the usual decoherence and diagonal density matrix for the microsystem. The macrosystem can be interpreted as representing a measurement device for performing a measurement on the microsystem. The whole discussion is carried out within quantum mechanics itself without any modification or generalization.
A small quantum scattering system (the microsystem) is studied in interaction with a large quantum system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem in a certain basis, and it leads to an imprint on the macrosystem. Moreover, the interaction is assumed to involve only small transfers of energy and momentum between the two systems (as compared to typical energies/momenta within the microsystem). This makes it suitable to carry out the analysis in scattering theory, where the transition amplitude for the whole system factorizes. The interaction taking place within the macrosystem is assumed to depend on the stochastic variables in such a way that, on the average, no particular channel is favoured. The result is then, in the thermodynamic limit of the macrosystem, that the whole system bifurcates and the microsystem ends up in a state described by one of the basis vectors (in the mentioned basis). The macrosystem ends up in an entangled state tied to this basis vector. For the ensemble of macrosystems, the interaction with the microsystem leads, on the average, to the usual decoherence and diagonal density matrix for the microsystem. The macrosystem can be interpreted as representing a measurement device for performing a measurement on the microsystem. The whole discussion is carried out within quantum mechanics itself without any modification or generalization.
A small quantum scattering system (the microsystem) is studied in interaction with a large system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem in a certain orthonormal basis, and the interaction gives an imprint on the macrosystem. Moreover, the interaction is assumed to involve only small transfers of energy and momentum between the two systems (as compared to typical energies/momenta within the microsystem). The analysis is carried out within scattering theory. Calculated in the conventional way, the transition amplitude for the whole system factorizes. The interaction taking place within the macrosystem is assumed to depend on the stochastic variables in such a way that, on the average, no particular basis vector state of the microsystem is favoured. The density matrix is studied in a formalism which includes generation of the ingoing state and absorption of the final state. Then the dependence of the final state on the conventional scattering amplitude for the microsystem is highly non-linear. In the thermodynamic limit of the macrosystem, the density matrix of the ensemble (of microsystem plus macrosystem) develops into a final state which involves a set of macroscopically distinguishable states, each with the microsystem in one of the basis vector states and the macrosystem in an entangled state. For an element of the ensemble, i.e., for a single measurement, the result is instead a random walk, where the microsystem ends up in one of the basis vector states (reduction of the wave packet).
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 process of quantum mechanics is analysed in the scattering theory of quantum field theory. A matrix of bilinear forms of the scattering amplitudes (the R-matrix) is used as the basic descriptive tool. The measurement process is viewed as a final-state interaction described through a series of linear stochastic mappings of the R-matrix, not changing the observable to be measured. The unknown details of the measurement apparatus enter through the stochasticity of the mappings. Although linear in terms of the R-matrix, the mappings are nonlinear in the density matrix, which is obtainable from the R-matrix through normalization. The eigenstates of the observable are the attractors of the mapping process. This result, known from previous generalizations of quantum mechanics, is obtained here within linear quantum mechanics. The conclusion is that the measurement process can be understood within relativistic quantum field theory itself without any generalization or metatheory.
Abstract The so-called quantum measurement problems are solved from a new perspective. One of the main observations is that the basic entities of our world are particles, elementary or composite. It follows that each elementary process, hence each measurement process at its core, is a spacetime, pointlike, event. Another key idea is that, when a microsystem ψ gets into contact with the experimental device, factorization of ψ rapidly fails and entangled mixed states appear. The wave functions for the microsystem-apparatus coupled system for different measurement outcomes then lack overlapping spacetime support. It means that the aftermath of each measurement is a single term in the sum: a “wave-function collapse”. Our discussion leading to a diagonal density matrix, ρ = diag(|c 1|2,…,|cn |2,…) shows how the information encoded in the wave function <?CDATA $|\psi \rangle =\displaystyle {\sum }_{n}{c}_{n}|n\rangle $?> | ψ 〉 = ∑ n c n | n 〉 gets transcribed, via entanglement with the experimental device and environment, into the relative frequencies Pn = |cn |2 for various experimental outcomes F = fn . Our discussion represents the first, significant steps towards filling in the logical gaps in the conventional interpretation based on Born’s rule, replacing it with a clearer understanding of quantum mechanics. Accepting objective reality of quantum fluctuations, independent of any experiments, and independently of human presence, one renounces the idea that in a fundamental, complete theory of Nature the result of each single experiment must necessarily be predictable.
A dynamical model for the collapse of the wave function in a quantum measurement process is proposed by considering the interaction of a quantum system (spin-1/2) with a macroscopic quantum apparatus interacting with an environment in a dissipative manner. The dissipative interaction leads to decoherence in the superposition states of the apparatus, making its behaviour classical in the sense that the density matrix becomes diagonal with time. Since the apparatus is also interacting with the system, the probabilities of the diagonal density matrix are determined by the state vector of the system. We consider a Stern-Gerlach type model, where a spin- 1/2 particle is in an inhomogeneous magnetic field, the whole set up being in contact with a large environment. Here we find that the density matrix of the combined system and apparatus becomes diagonal and the momentum of the particle becomes correlated with a spin operator, selected by the choice of the system-apparatus interaction. This allows for a measurement of spin via a momentum measurement on the particle with associated probabilities in accordance with quantum principles.
The quantum measurement problems are discussed from a new perspective.
One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that each elementary process, hence each measurement process at its core, is a spacetime, pointlike, event. Another key idea is that, when a microsystem ψ gets into contact with the experimental device, factorization of ψ rapidly fails and entangled mixed states appear. The wave functions for the microsystem-apparatus coupled systems for different measurement outcomes then lack overlapping spacetime support. It means that the aftermath of each measurement is a single term in the sum: a ``wave-function collapse.
Our discussion leading to a diagonal density matrix, ρ=diag(∣c1∣2,…,∣cn∣2,…) shows how the information encoded in the wave function ∣ψ⟩=∑ncn∣n⟩ gets transcribed, via entanglement with the experimental device and environment, into the relative frequencies Pn=∣cn∣2 for various experimental results F=fn.
These results represent the first, significant steps towards filling in the logical gaps in the standard interpretation based on Born's rule, and replacing it with a more natural one. Accepting objective reality of quantum fluctuations, independent of any experiments, and independently of human presence, one renounces the idea that in a fundamental, complete theory of Nature the result of each single experiment must necessarily be predictable.
A few well-known puzzles such as the Schr\odinger cat conundrum and the EPR paradox are briefly reviewed: they can all be naturally explained away.