Fundamental Statistical Theories

Andrei Yu. Khrennikov

We propose the principle, the law of statistical balance for basic physical observables, which specifies quantum statistical theory among all other statistical theories of measurements. It seems that this principle might play in quantum theory the role that is similar to the role of Einstein's relativity principle.

Shigeji Fujita, Kei Ito, Salvador Godoy

M. D. Srinivas

Relativistic quantum theory is formulated as a theory of successive local observations, consistent with all the fundamental requirements of relativistic invariance. Based on the causal structure of the space–time of special relativity, it is argued that the nonrelativistic notion of a ’’time-ordered sequence of instantaneous observations’’should be replaced in a relativistic theory by the notion of a ’’causally ordered sequence of local observations.’’ The fundamental statistical law of relativistic quantum theory is then formulated such that it provides an unambigous prescription for the statistical correlations between the outcomes of any causally ordered sequence of local observations. It is also shown that the fundamental statistical law of the theory is consistent with the so-called ’’principle of local causes’’ which essentially states that the probability connections between a set of local events do not depend on local observations carried out in space–time regions which lie outside of their causal past. Finally, an equivalent formulation of the theory in terms of a relativistically covariant generalization of the collapse postulate is presented.

Watanabe, Shinzo, Prokhorov, Jurii

R. Collins

The formulation of quantum theory on the basis of the statistical definition of a duplicated experiment, as initiated in a recent paper, is used to reexamine the embedding formalism introduced in earlier papers. It is shown that the familiar relations between momentum and coordinate representations are given a statistical basis by the embedding theory. It is also shown that a complete quantum theory includes three fundamental sets of operators and that one of these seems to represent an operator formalism for thermodynamics.