hadronic mathematics, mechanics and chemistry - Institute for Basic ...

HADRONIC MATHEMATICS, MECHANICS AND CHEMISTRY 4036.1.4 Rudiments of Santilli IsorelativityFor minimal self-sufficiency of this volume, let us recall that special relativityand relativistic quantum mechanics are based on the ”universal constancy of thespeed of light” c o that is achieved via the invariance of the line element in theMinkowskian spacetime M(x, η, R) (Section I.3.5.3)x 2 = (x µ × η µν × x ν ) × I == (x 1 × x 1 + x 2 × x 2 + x 3 × x 3 − x 4 × x 4 ) × I ∈ R,x 4 = c o × t, I = Diag.(1, 1, 1, 1), (6.1.1)under the celebrated Lorentz symmetry O(3.1) characterized by the Lorentz transformationshere expressed for simplicity in the (3, 4) coordinatesx 1 ′= x 1 , x 2 ′= x 2 , (6.1.2a)x 3 ′= γ × (x 3 − β × x 4 ), x 4 ′= γ × (x 4 − β × x 3 ),(6.1.2b)γ = (1 − β 2 ) −1/2 , β = v 2 /c 2 o, (6.1.2c)where: × is the conventional associative product; + is the conventional sum;I = Diag.(1, 1, 1, 1) is the fundamental unit of the Lorentz symmetry O(3.1);for consistency, I is assumed as the unit of the base field of real numbers R =R(n, +, ×); and the multiplication of the line element by I is then necessary forx 2 to be an element of the assumed base field.However, the ”universal constancy of the speed of light” is a manipulation ofscientific reality, particularly when ventured by experts, whenever said statementis proffered without the crucial addition ”in vacuum.” The ”universal constancyof the speed of light in vacuum” (namely, in exterior conditions), has been experimentallyestablished beyond scientific or otherwise useful doubt. When thisstatement is contracted into ”universal constancy of the speed of light” it isreferred to all possible conditions existing in the universe, including interior conditions.In the latter case, not only we have no experimental evidence at all,but have robust evidence on the lack of constancy of the speed of light. Hence,when experts venture the statement of the ”universal constancy of the speed oflight” without the crucial specification ”in vacuum” they perpetrate a manipulationof science intended to extend the validity of special relativity to all possibleconditions existing in the universe.For all cases of interior dynamical problems within a physical medium, experimentalevidence establishes that the speed of light c is a local variable dependingon the density d, temperature τ, frequency ω, and other characteristics of themedium considered, c = c(d, τ, ω, ...), as expressed by the historical form studiedin high schoolc = c(d, τ, ω, ...) = c on =c on(d, τ, ω, ...) . (6.1.3)