By Sisir Roy (auth.)
Recent effects from high-energy scattering and theoretical advancements of string concept require a transformation in our knowing of the elemental constitution of space-time. This ebook is ready the development of principles at the stochastic nature of space-time from the Thirties onward. specifically, the writer promotes the idea that of area as a suite of hazy lumps, first brought through Karl Menger, and constructs a unique framework for statistical behaviour on the microlevel. some of the chapters deal with themes corresponding to space-time fluctuation and random power, non-local fields, and the starting place of stochasticity. Implications in astro-particle physics and cosmology also are explored.
Audience: This quantity should be of curiosity to physicists, chemists and mathematicians focused on particle physics, astrophysics and cosmology.
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Additional info for Statistical Geometry and Applications to Microphysics and Cosmology
Here lies the deeper connection of non-Iocal fields and the stochastic space-time which we shall discuss in latter chapter. 18) is implicit in the assumption that the probability depends on these variables. Therefore, it is natural to consider the variable as the intern al variable. A stochastic space-time then be constructed with the line element defined by e e. 19) Here, the metric tensor G 1'11 is function of both x and This is popularly known as Finsler metric [Asanov 1985]. We shall show in latter chapter that Finsler metric is inherently probabilistic in nature.
59) 2 4>(i, t), T denoting the correlation time. It is assumed with V(i, t) that T is much sm aller than the relevant quantum time of the system. For example, a typical colloid grain is of the order of 10- 5 cm. Let us take L = 10-4 cm, then T = 3 X 10- 15 s. The corresponding quantum time is = which becomes (for proton) ~ 10-9 s. Hence our above assumption mf, STATISTICAL GEOMETRY, MICROPHYSICS AND COSMOLOGY 41 holds. We can calculate the function 9 considering the correlation function for 4>(i, t).
4) Within this framework, it is possible to establish the following uncertainty principle for position and momentum observables q and p respectively. 5) In quantum mechanics, the wave function contains more information rather than the probability density. The wave function contains the phase which is very important in describing the interference phenomena. But here, in the frame of stochastic space-time we are dealing directly with P(z, t). So, it appears to be problematic to explain the interference phenomena within this framework.