arXiv subjects
Publications and source records attributed to Karl-Erik Eriksson.
Quantum diffusion, as developed in the 1990s, could explain how a system, subject to measurement, goes into an eigenstate of the measured observable. Here it is shown that quantum diffusion theory can be interpreted as a result within linear relativistic quantum mechanics. Thus, in contrast to what is widely believed, quantum measurement can be analyzed within the theory of quantum mechanics itself.
At the time of publication of H. Everett's Relative-State Formulation (1957) and DeWitt's Many-Worlds Interpretation (1970), quantum mechanics was available in a more modern and adequate version than the one used by these authors. We show that with the more modern quantum theory, quantum measurement could have been analyzed along more conventional lines in a one-world cosmology. Bell criticized the Everett-DeWitt theory quite sharply in 1987 but this seems not to have affected the acceptance of the old quantum mechanics as the framework for analysis of measurement.
We model quantum measurement of a two-level system $μ$. Previous obstacles for understanding the measurement process are removed by basing the analysis of the interaction between $μ$ and the measurement device on quantum field theory. We show how microscopic details of the measurement device can influence the transition to a final state. A statistical analysis of the ensemble of initial states reveals that those initial states that are efficient in leading to a transition to a final state, result in either of the expected eigenstates for $μ$, with probabilities that agree with the Born rule.
In an exact quantum-mechanical framework, we show that expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge, and in the presence of classical sources, automatically lead to causal and retarded electro-magnetic field strengths. The classical $\hbar$-independent Maxwell's equations naturally emerge from this fundamental quantum-mechanical approach in terms of expectation values of quantum fields, and are therefore also consistent with the special theory of relativity. The fundamental difference between interference phenomena due to the linear nature of the classical Maxwell theory as, e.g., in classical optics, and interference effects of quantum states is clarified. The framework outlined also provides for a simple approach to, e.g., spontaneous photon emission and/or absorption processes as well as to the classical Vavilov-Cherenkov radiation. The inherent and necessary quantum fluctuations, limiting a precise space-time knowledge of expectation values of the quantum fields considered, are, finally, recalled.
In a previous work and in terms of an exact quantum-mechanical framework, $\hbar$-independent causal and retarded expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge were derived in the presence of a conserved classical electric current. The classical $\hbar$-independent Maxwell's equations then naturally emerged. In the present work, we extend these considerations to linear gravitational quantum deviations around a flat Minkowski space-time in a Coulomb-like gauge. The emergence of the classical causal and properly retarded linearized classical theory of general relativity with a conserved classical energy-momentum tensor is then outlined. The quantum-mechanical framework also provides for a simple approach to classical quadrupole gravitational radiation of Einstein and microscopic spontaneous graviton emission and/or absorption processes.
We present a generic model of (non-destructive) quantum measurement. Being formulated within reversible quantum mechanics, the model illustrates a mechanism of a measurement process --- a transition of the measured system to an eigenstate of the measured observable. The model consists of a two-level system $μ$ interacting with a larger system $A$, consisting of smaller subsystems. The interaction is modelled as a scattering process. Restricting the states of $A$ to product states leads to a bifurcation process: In the limit of a large system $A$, the initial states of $A$ that are efficient in leading to a final state are divided into two separated subsets. For each of these subsets, $μ$ ends up in one of the eigenstates of the measured observable. The probabilities obtained in this branching confirm the Born rule.
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.