Mathematical Physics

   

The Wave Nature of the Geometry Primary Dipole

Authors: Marcos Georgallides

In prior articles , the position of points in Spaces creates Momentum [Λ] which is bounded in the three constant Energy Layer States k1,2,3 [10] . This rotating energy E = Λ λ is transformed into the Acceleration al and Rotational Ellipsoid , and radiated away ,by loosing angular momentum E = r.m.vr and conserved as momentum E = M.v where emission of linear momentum creates vector v of generalized mass M . When vector v = 0 , this rotating Energy is generalized mass M which is mapped on the perpendicular to Λ plane as velocity v̄r which creates Newton smallest equilibrium accelerations (a f + a p = 0) from Centrifugal (Ff) and Centripetal (Fp) forces . On the infinite points of [PNS] and on the infinite dipole AiBi this acceleration vectors create the Wave motion of the infinite dipole AiBi which dipole are composed of the wavelength λ and the rotating Energy Λ . From this Position , Time enters in equations of motion as the meter of changes only .This rotating Energy is interchanged on dipole A  B = (λ , Λ= mv) in the Configuration of co variants λ , m , v̄ as ellipsoid in the two perpendicular fields E = [(/x) + (/dy) + (/z)] . Λ and B = [(/x) + (/dy) + (/z)] xΛ following conservation laws only. Classical theories are confined in Space -Time and Planck-time (which are not assessing the outer reality of Spaces ) , with Time , which is only a meter of changes , and not existing differently . Spaces are composed of infinite points which are related each other with a quantum of Work ( Energy ) .The Norm is the Equation of Total Energy State of Monads equal to → ET = •[(k/ λv) .vE ²] ² + [Λ.vB +ΛxvB ] ² = • [(k/λv) .vE.² ]² + T ² ← which is completely refining Time and leaving only λ Λ = k which indicates a Space Energy Universe . Energy in a Vibrating system is either dissipated into Heat (temperature) which is another type of energy { Energy E as momentum vector Λλ is damped on the perpendicular to Λ plane , as it is like a < Spring-mass System with viscous dumping > , on the basic three co-variants of , Energy E , Lagranges generalized mass M = m , and velocity v̄ with Norm the wavelength λ , and secondly on the rotating Energy Λ= r̄.M.ūr } or radiated away. Newton's laws have a Universal application in all Configuration Systems instead of the referred as the Inertial ones . Even also to the smallest circular motion , ( anywhere that exists momentum ) , exists also Centrifugal and Centripetal forces which create acceleration and the Oscillatory motion . Since also velocity v maybe equal to 0 → c → ∞ then the velocity of light is not the faster in universe . In Black Holes Configuration a new Type of light is needed with a greater velocity than that of light to see what is happening . Light which is a quaternion is travelling either as wave ( photon Λ) either as particle (E =Mv̄= r.m.v̄r ) and in both cases as , a travelling Energy λ.Λ = k interchanged in the two perpendicular forced fields E = . Λ and B =  x Λ ( Electromagnetic fields ) following conservation laws . Gauss laws spring from this property. Oscillatory motion is the simplest case of Energy dissipation of Work embodied in dipole . In the vibratory system , Energy k = λΛ is Spin of Dipole , dissipated on ⊥ to Λ plane and damped as momentum vector λ.mv̄ . Monad ĀB is the ENTITY and [ A ,B – PA  , P B  ] is the LAW , so Entities are embodied with the Laws . Entity is quaternion A B , and law |AB| = length of points A,B and imaginary part forces PA , P B  . Dipole A  B = [ λ , Λ ] in [PNS] are composed of the two elements λ , Λ which are created from points A ,B only where Real part |AB| = λ = wavelength (dipoles ) and from the embodied work , λ Λ , the Imaginary part W = ∫ P.ds =(r.dP) = r̄xp = I.w = [λ.p] = λ.Λ = k2 , where momentum Λ = p= m.v and Forces dP = P B –P A are the stationary sources of the Space Energy field . The moving charges is velocity v created from the rotating Energy momentum vector [ Ω = (λ.P) = ± Spin ] which creates the Centrifugal force (Ff) , the equal and opposite to it Centripetal force (Fp) and the acceleration ā mapped (damped ) on the perpendicular to Λ plane as → v E||dP and v B  dP. F = q.E + q.v̄ x B = q.[ E + v̄ x B ] is Lorentz force in Electromagnetic crossed fields E and B . Since (dP  ± Λ ) the work occurring from momentum p = mv = Λ acting on force dP is zero so when v E =0 , momentum Λ  = mv only , is exerting the velocity vector v B to the dipole , , λ , and the generalized mass M ( the reaction to the change of velocity v̄ ) which creates the component forces , FE || dP .v and FB  dP x v .

Comments: 13 Pages.

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[v1] 2014-04-03 09:19:10

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