Frieden wave-function representations via an Einstein-Podolsky-Rosen-Bohm experiment

Abstract

The appearance of the spin-1 2 and spin-1 representations in the Frieden-Soffer extreme physical information (EPI) statistical approach to the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment is shown. In order to obtain the EPR-Bohm result, in addition to the observed structural and variational information principles of the EPI method, the condition of the regularity of the probability distribution is used. The observed structural information principle is obtained from the analyticity of the logarithm of the likelihood function. It is suggested that, due to the self-consistent analysis of both information principles, quantum mechanics is covered by the statistical information theory. The estimation of the angle between the analyzers in the EPR-Bohm experiment is discussed.

Generalization of the Aoki–Yoshikawa sectoral productivity model based on extreme physical information principle

“…Previous attempt to solve the Aoki-Yoshikawa productivity problem by the EPI method was based on the Frieden-Soffer approach [4]. However, this paper implements only the analytical form of the (modified) observed structural information principle [14].…”

“…The sample of the EPI method (so-called inner sample [12,14]) for the AY model is N = 1-dimensional 4 . Thus, both the sample space B and the base space of events are in AY case equivalent to Y a [14]. 4 In [3,4] the condition of the minimal value of the information (kinematical) channel capacity I → min is postulated as the one that fixes the value of N in a unique way.…”

“…However, sometimes the non-minimal values of I are also discussed as they lead to the EPI method's models, which are of a physical significance [3,4]. Some discussion on this topic can be also found in [14]. For example, from the analogy with the EPI model of momentum distribution presented in [4], for N > 1 the nonequilibrium, stationary solutions for the square flow (where the flow is proportional to the root productivity) might be obtained instead.…”

“…For N = 1 the information channel capacity I reduces to the Fisher information I F (θ 1 ) = I F (θ A ) for θ 1 ≡ θ A , the only parameter. The necessary steps leading from the general form of the Fisher information to the one used in this paper are similar as in [14].…”

“…As θ A is the scalar parameter and the dimension of the sample is equal to N = 1 the information channel capacity I(θ A ) of the measurement channel (θ A ) [12] is equal to the Fisher information I F (θ A ) of the parameter θ A [14]:…”