An Essay on the Double Nature of the Probability

Classical statistics and Bayesian statistics refer to the frequentist and subjective theories of probability respectively. Von Mises and De Finetti, who authored those conceptualizations, provide interpretations of the probability that appear incompatible. This discrepancy raises ample debates and the foundations of the probability calculus emerge as a tricky, open issue so far. Instead of developing philosophical discussion, this research resorts to analytical and mathematical methods. We present two theorems that sustain the validity of both the frequentist and the subjective views on the probability. Secondly we show how the double facets of the probability turn out to be consistent within the present logical frame

Probabilistic Events and Physical Reality: A Complete Algebra of Probability

This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We conclude that the argument of probability is the critical knot of the probability foundations and put forward the structure of levels for the partially determinate event. The structural model enables us to define the prabability and to attune its subjective and objective interpretations

Strong CP problem and mirror world: the Weinberg Wilczek axion revisited

A new possibility for solving the strong CP-problem is suggested,which assumes that apart of the ordinary world of observable particles described by standard model, there exits a mirror sector of particles and two sectors share the same Peccei-Quinn symmetry realized {\it a l\`a} Weinberg-Wilczek model. The mirror gauge group is completely analogous to that of the standard model for ordinary particles but having somewhat larger electroweak scale,which in turn implies the infrared scale $\Lambda'$ of the mirror strong interactions has to be larger than the ordinary QCD scale $\Lambda$. In this way, the axion mass and interaction constants are actually determined by mirror sector scales $v'$ and $\Lambda'$, while the $\theta$ terms are simultaneously cancelled in both sectors due to mirror symmetry. The experimental and astrophysical limits on such an axion is discussed. An interesting parameter window is found where $f_a \sim {\rm few}\times 10^4$ GeV whereas the axion mass is $\sim 1$ MeV.Comment: 13 LaTex pages, 3 Postscript figure