Multidimensional theories still remain attractive from the point of view of better understanding fundamental interactions. In this paper a six-dimensional Kaluza-Klein type model at the classical, Einsteins gravity formulation is considered. The stat
ic spherically symmetric solution of the six-dimensional Einstein equations coupled to the Klein-Gordon equation with the massless dilatonic field is presented. As it is horizon free, it is fundamentally different from the four-dimensional Schwarzschild solution. The motion of test particles in such a spherically symmetric configuration is then analyzed. The presence of the dilatonic field has a similar dynamical effect as the existence of additional massive matter. The emphasis is put on some observable quantities like redshifts. It has been suggested that strange features of emission lines from galactic nuclei as well as quasar-galaxy associations may in fact be manifestations of the multidimensionality of the world.
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 add
ition 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.
The self-consistent model of classical field interactions formulated as the counterpart of the quantum electroweak model leads to homogeneous boson ground state solutions in presence of non-zero extended fermionic charge density fluctuations. Two dif
ferent types of electroweak configurations of fields are analyzed. The first one has non-zero electric and weak charge fluctuations. The second one is electrically uncharged but weakly charged. Both types of configurations have two physically interesting solutions which possess masses equal to 126.67 GeV at the value of the scalar fluctuation potential parameter $lambda$ equal to ~ 0.0652. The spin zero electrically uncharged droplet formed as a result of the decay of the charged one is interpreted as the ~ 126.5 GeV state found in the Large Hadron Collider (LHC) experiment. (The other two configurations correspond to solutions with masses equal to 123.7 GeV and $lambda$ equal to ~ 0.0498 and thus the algebraic mean of the masses of two central solutions, i.e., 126.67 GeV and 123.7 GeV, is equal to 125.185 GeV.) The problem of a mass of this kind of droplets will be considered on the basis of the phenomenon of the screening of the fluctuation of charges. Their masses are found in the thin wall approximation.
Three steps in the development of the maximum likelihood (ML) method are presented. At first, the application of the ML method and Fisher information notion in the model selection analysis is described (Chapter 1). The fundamentals of differential ge
ometry in the construction of the statistical space are introduced, illustrated also by examples of the estimation of the exponential models. At second, the notions of the relative entropy and the information channel capacity are introduced (Chapter 2). The observed and expected structural information principle (IP) and the variational IP of the modified extremal physical information (EPI) method of Frieden and Soffer are presented and discussed (Chapter 3). The derivation of the structural IP based on the analyticity of the logarithm of the likelihood function and on the metricity of the statistical space of the system is given. At third, the use of the EPI method is developed (Chapters 4-5). The information channel capacity is used for the field theory models classification. Next, the modified Frieden and Soffer EPI method, which is a nonparametric estimation that enables the statistical selection of the equation of motions of various field theory models (Chapter 4) or the distribution generating equations of statistical physics models (Chapter 5) is discussed. The connection between entanglement of the momentum degrees of freedom and the mass of a particle is analyzed. The connection between the Rao-Cramer inequality, the causality property of the processes in the Minkowski space-time and the nonexistence of tachions is shown. The generalization of the Aoki-Yoshikawa sectoral productivity econophysical model is also presented (Chapter 5). Finally, the Frieden EPI method of the analysis of the EPR-Bhom experiment is presented. It differs from the Frieden approach by the use of the information geometry methods.
The paper examines the geometrical properties of a six-dimensional Kaluza-Klein type model. They may have an impact on the model of the structure of a neutron and its excited states in the realm of one particle physics. The statistical reason for the
six-dimensionality and the stability of the solution is given. The derivation of the weak limit approximation of the general wave mechanical (quantum mechanical) approach, defined in the context of losing its self-consistency (here gravitational), is presented. The non self-consistent case for the Klein-Gordon equation is defined. The derivation of the energy of states and the analysis of the spin origin of the analyzed fields configuration is presented as the manifestation of both the geometry of the internal two-dimensional space and kinematics of fields inside it. The problem of the departure from the (gravitational) self-consistent calculations of the metric tensor and of other fields of the configuration is discussed. The implementation of the model for the description of a neutron and its excited states, including their spins and energies, is given. The informational reason for the existence of the internal extra space dimensions is proposed.
