Authors: Markos Georgallides
Primary Dipole dš = ĀB =[a ± b.i] as complex number, and z̄o =[ s, v̄n.i] = [λ ,±Λ .i ] = [λ , Λ] as quaternion in [PNS] is the ENTITY with the embodied LAW [A , B - PA , PB ],is composed of the two only elements λ , Λ which are created from points A and B , |AB| = λ = wavelength (dipoles ) and from work W = ∫A-B [ P.ds ] = 0 = (dP.r̄) = r̄xp = I.w = [λ.p] = λ.Λ = k2 , the momentum Λ = p = k2/ λ. and Forces dP = P B –P A) ,which are the sources of Space field . Forces dP parallel to the parallel of Space Anti-Space lines [S]≡ [AS], create a Static force field E in (dP, λ) plane , and Forces dP perpendicular to the parallel of Space Anti-Space lines [S]≡[AS] , create a Static force field B which is perpendicular to E and to ( dP,λ) plane . Motion occurs from the moving charges exerted as velocity v ,created from dipole momentum ± Λ when is mapped in force field B as v E|| dP and v B dP with the generalized mass m (the reaction to the motion) which creates the component forces FE = (λm).E , FB = (λm) .v̄ x B. Velocity vector v\ (v\ E , v\ B) is in [ v \. B \ ] plane forming an angle θ < 180° to the field B , and total force F= FE + F B = (λm). E + (λm). v̄ x B which combination of the two types result in a helical motion, with the stability demand → E = - (v̄xB) = - (v̄.B) which is the alternative conservation of momentum [ k 2 = Λ²/2λm ] in the two perpendicular fields E , B and in case (λm) = q then force F = FE + FB = q.E + q.v̄ xB = q.[ E + v̄ x B ] → which is Lorentz force . Since Spin ( vortices) Λ , - Λ , are in inverted order of rotation and vice-versa , then even function f(Λ) = f(-Λ) and odd function is - f(Λ) = f(-Λ) and their sum f(Λ)+f(-Λ)=0 and so, Mapping (graph) of Even function f(Λ),is always symmetrical about Λ axis or a mirror and of Odd symmetrical about the origin and is the interpretation of the Wave nature of spaces i.e. The Physical Universe behaves as a simple harmonic oscillator . Conjugating quaternion of the differential time operator and 3D angular speed vector w̄ with negation truth eo = [- λ,xΛ] = 0 then ( ∂/∂t ,
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