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

HADRONIC MATHEMATICS, MECHANICS AND CHEMISTRY 409As we shall see, and as expected for any new invariance in our spacetime, the novelinvariance (6.1.10) carries fundamental implications at all levels of study, fromparticle physics to cosmology, including far reaching advances such as the firstknown axiomatically consistent grand unification of electroweak and gravitationalinteractions studied in Chapter 14.The fact that the new isoinvariance (6.1.10) remained un-noticed throughoutthe 20-th century until identified in Ref. [5] should not be surprising because itsidentification required the prior discovery of new numbers, Santilli’s isonumberswith arbitrary positive-definite unit Î.From now on we shall use the following terminology: the use of conventionalterms, such as speed, mass, energy, etc., eill denote conventional quantities definedon the conventional Minkowski space over the conventional field of realnumbers. Terms such as isospeed, isomass, isoenergy, etc. will denote quantitiesdefined on the Minkowski-Santilli isospace over the isofield of real numbers.Santilli isorelativity (see Volume I as well as monographs [6] (as well as EHM-II and HM-I) and original references quoted therein) is based on the Poincaré-Santilli isosymmetry and the following isoaxioms (see Section I.3.5 for details):ISOAXIOM I. The projection in our spacetime of the maximal causal invariantspeed is given by:V max = c o × b 4b 3= c o × n 3n 4= c= c × n 3 = c o × g1/2 44b 3g 1/233. (6.1.11)ISOAXIOM II. The projection in our spacetime of the isorelativistic additionof speeds within physical media is given by:v tot = v 1 + v 2=1 + v 1×b 2 3 ×v 2c o×b 2 4 ×cov 1 + v 2=1 + v 1×n 2 4 ×v 2c o×n 2 3 ×cov 1 + v 21 + v 1×g 33×v2. (6.1.12)c o×g 44 ×c oISOAXIOM III. The projection in our spacetime of the isorelativistic laws ofdilation of time t ◦ , contraction of length l ◦ and variation of mass m ◦ with speedare given respectively by:t = ˆγ × t ◦ ,(6.1.13a)l = ˆγ −1 × l ◦ ,m = ˆγ × m ◦ .(6.1.13b)(6.1.13c)ISOAXIOM IV. The projection in our spacetime of the Doppler-Santilli isolawis given by the law (here formulated for simplicity for 90 ◦ angle of aberration):ω = ω o × 1 − ˆβ × ˆ cosˆθ√1 − hatbeta 2 , (6.1.14)