The Observational Problem in Quantum Theory

和泰 重本

Masahiro Hotta, Masanao Ozawa

Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable is available for experimenters. Here, we generalize the theory to problems in which the experimenter can use only locally accessible observables. For such problems, we establish a Cram\'er-Rao-type inequality by obtaining an explicit form of the Fisher information as a reciprocal lower bound for the mean-square errors of estimations by locally accessible observables. Furthermore, we explore various local quantum estimation problems for composite systems, where nontrivial combinatorics is needed for obtaining the Fisher information.

Alfred Landé

和泰 重本

Joop M. Houtkooper

Abstract—The problem of devising a theory for paranormal phenomena (psi) may be separated into, first, the basic physical mechanism and second, the psychological aspects of how and when people are able to elicit psi. Observational theory addresses primarily the first aspect, the basic physical mechanism of psi. A problem is that the known types of physical interaction do not fit the existing data. The measurement problem in quantum mechanics can be used to hypothe-size an observer who adds information at the collapse of the wave function. For each random event one of the possible outcomes becomes realized as the event is being observed. The basic tenet of observational theory is: the statis-tics of single events become biased if the observer is motivated and prefers one of the possible outcomes over the other. Features of observational theory are: its predictive power, proven with re-gard to retroactive psychokinesis (PK); parsimony: the same mechanism ex-plains ESP as well as PK; fruitfulness, as there is a direct relationship with quantum mechanics; and openness to crucial experiments. The falsifiability criterion poses some problems: these are discussed in relation to Lakatos’ methodology of research programmes. Observational theory is a solution to the problem of the mediation of psi, thus providing a framework for the psychological problem of the manifesta-tion of psi. Henceforth, the observation of the outcome should be regarded as formal part of parapsychological experiments. There is reason for cautious, patient optimism about the acceptance of observational theory.

Daniel M. Greenberger, Anton Zelinger