Mathematical Physics

   

The Outside Relativity Space Energy Universe

Authors: Markos Georgallides

The position of points in Spaces presupposes Energy [22] → Point , which is nothing and has not any Position may be anywhere in Space , therefore , the Primary point A being nothing also in no Space , is the only Point and nowhere i.e. Primary Point is the only Space and from this all the others which have Position , therefore is the only Space and to exist point A at a second point B somewhere else , point A must move at point B , where then A ≡ B ← Point B is the Primary Anti-Space which Equilibrium point A in [PNS]=[A≡ B] . The position of points in [PNS] creates the infinite dipole and all quantum quantities which acquire the Potential difference and the Intrinsic moment Λ in the three Spatial dimensions (x , y , z) and on the infinite points of the ( i ) Layers at these points , which exist from the other Layers of the Primary Space Anti-Space and Sub-Space , and this because Spaces = monads = quaternion = Wave [24] . Since Primary point A is the only Space , then exists the Principle of Virtual Displacements W = ∫P.ds = 0 or [ds .(PA + P B) = 0] i.e. for any ds > 0 Impulse P = ( PA + P B ) = 0 . All points may exist with P = 0 and also with P ≠ 0 , ( P A + P B = 0 ) in ( PNS) , for all points in Spaces and Anti – Spaces , therefore [PNS] is self created , and because at each point may exist also P ≠ 0, then [PNS] is a (perfectly elastic) Field with infinite points which have a ± Charge with P = 0 → P = Λ → ∞ . Beyond Planck scale , Energy is dissipated as Temperature in this , Perfect Elastic , Configuration in individual particles with 0 < ds < 10 - 35 m as monads the units AiBi = ds- , which equilibrium by the Primary Anti–Space by an Inner Impulse (P) at edges A,B where P i A + P i B ≠ 0 , and ds = 0 → N → ∞ following the ideal Gas equation [Λ= nRT/V] of Entropy in Thermodynamics (perfectly elastic) . Monad A-B is the ENTITY and [A,B – P –A , P -B ] is the LAW , so Entities are embodied with the Laws and is quaternion A- B , and law |AB| = length of points A , B and imaginary part forces P –A , P –B . Monads = Quantum = ds = AB / ( n= ∞ → 0) = [a ± b.i] = 0 → ∞ create Spaces (S) , Anti-Spaces ( A-S) and Sub-Spaces (S-S) of AB , which Sub-Spaces are Bounded Spaces , Anti-Spaces and Sub Spaces in it and are not purely spatial because are Complex numbers which exist for all Spaces since dsn is Complex number also , in a specific number of independent moles called , Fermions and Bosons , with F = qE+qv- xB = q[ E+v- xB ] the Lorentz force in Electromagnetic crossed fields E ,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 the Imaginary part W=∫P.ds = (r.dP) = r–x p- = I.w = [λ.p] = λΛ = k2 , where momentum Λ= p and Forces dP = P –A ,P -B are the stationary sources of the Space Energy field [22-25] . EulerÁs rotation in 3D space is represented by an axis (vector) and an angle of rotation , which is a property of complex numbers and defined as z = [ s ± v-.i ] where s , |v-| are real numbers and i the imaginary part such that i² = -1. Extending imaginary part of dipole to the three dimensions v-1 i , v-2 j , v-3 k → v-.Ñi then becomes quaternion . In [24] monad [ 0,Λ ] = Energy is dissipated on points and on quantized spaces smaller < and > greater to Planck scale . The moving charges is velocity v- created from the rotating Energy momentum vector [Λ = Ω = (λ.P) = ± Spin] which creates on monads the Centrifugal force (Ff) , the equal and opposite to it Centripetal force (Fp) and acceleration ā is mapped [and because of the viscous (semi-elastic) is damped] on the ⊥ to Λ plane as → v- E||dP and v- B ^ dP ← following Kirchhoff 's circuit R ,L,C rules with circuits , the Sub-spaces of the tiny monads . The kinetic rotated energy in the viscously damped configuration ( as a Lagrange's Ray light viscously damped system ) is dissipated as Electromagnetism and when v-E- = 0 , momentum Λ- = m v- only , is exerting the velocity vector v-B to the dipole vector , λ , and the generalized mass M (the reaction to the change of velocity v-) creating component forces FE||dP -.v- and FB ^ dP – xv- in the non-viscous damped monads ( the solids ) . Energy in a vibrating System is either damped (or dissipated) into Heat which is another type of energy [Energy ,momentum vector Λ.λ is then damped on the perpendicular to Λ plane , as this is a Spring-mass System , with viscous dumping , on co variants Energy E , mass M , velocity v- or radiated away . Spin =Λ= r-.m.u- r is the rotating energy of the oscillatory system . Oscillatory motion is the simplest case of Energy dissipation of Work embodied in dipole . In any vibratory system , Energy k = λΛ is Spin of Dipole λ , and is dissipated in the three quantized Planck Spaces 0 < λ < 10 \34, (10 \ 34 < λ < 10 34 ) , λ > 10 34 m and damped as the linear momentum vector Λ = M.v̄ in them , i.e The only < Space - Energy Configuration > is a constant Sinusoidal Potential System . [28]

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[v1] 2014-05-10 11:29:35

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