By Sisir Roy (auth.)

Recent effects from high-energy scattering and theoretical advancements of string thought require a transformation in our realizing of the elemental constitution of space-time. This ebook is set the development of rules at the stochastic nature of space-time from the Nineteen Thirties onward. particularly, the writer promotes the concept that of area as a collection of hazy lumps, first brought through Karl Menger, and constructs a singular framework for statistical behaviour on the microlevel. some of the chapters deal with themes similar to space-time fluctuation and random strength, non-local fields, and the beginning of stochasticity. Implications in astro-particle physics and cosmology also are explored. *Audience:* This quantity can be of curiosity to physicists, chemists and mathematicians keen on particle physics, astrophysics and cosmology.

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**Extra resources for Statistical Geometry and Applications to Microphysics and Cosmology**

**Example text**

This time like vector can be attached to a fixed frame of reference like aether in older time. In that case, the scattering matrix or S- matrix operator would depend on the parameters of one fixed frame and would immediately violate the equivalence of all Lorentz frames. Therefore, the time-like vectors n must be allowed to vary over the whole set of Lorentz frames. It immediately raises the question regarding the physical meaning of frame dependence. Ingraham put forward a hypothesis regarding this frame dependence.

The increasing degree of fuzziness of the topology so that in the limit W2 can be written globally and we have the corresponding HamiltonJacobi equation for where p = exp[2R]. 28) It should be mentioned that Kramosil and Michalek [Kramosil 1975] have already established that the concepts of statistical metric and fuzzy metric are equivalent in certain sense. So the above procedure can be thoroughly considered in fuzzy metric spaces which might have greater impact in other branches of physical science.

6) I, I, and 9ij52 being the metric tensors when the slit one is open only and slit two open only respectively. It is also assumed that the screen in the experiment is placed far from the slits so that the individual probabilities ( _g51) 1/2 and (_g52) 1/2 can be considered as constants over the screen. ". ". " - 1 0 0 0 1 0 0 0 s 0 0 0 0 0 0 -t Irl ",,1 = -st sand t are yet unspecified function of position. 8) = exp(ia), where a g81 ~v = 1 0 0 0 is some unspecified function, we get 0 1 0 0 0 0 eia 0 0 0 0 _e- ia and, -82 9 where, ~v = 1 0 0 0 0100 0 0 eiß o 0 0 _e-iß ß is another unspecified function.