Mathematical Physics

   

Quantization of Points and Energy on Dipole Vectors and on Spin

Authors: Markos Georgallides

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 , so then this primary point A to exist at a second point B somewhere else , point A must move at point B , where then A ≡ B . Presupposition for Unit AB = ds means an Impulse P removes point A to B and since in each Restrained System (S) the Work done ( W ) by Impulse P on a Virtual displacement ( ds > 0) is zero , and then W = ∫ A-B [ P.ds ] = 0 → [ ds .( PA+P B ) = 0 ] and Point A is in Space [S] and point B is in Anti-Space [aS] which are self created and are Property and Essence from the same Unit AB, therefore these are also a Restrained System(S). Since the only two Elements of Universe are ds and P and are connected by Virtual Work Principle and since Unit AB = ds is a quantized dimension,so Impulse is also quantized.Quantization of Points becomes through Vector Unit dš = ÃB which is the first dimensional Unit [ Zenon Paradox 13]and this because Vector has Position and Direction .Quantization of Energy is done in bound States ( loops ) because bound states [11-16] withhold diffusion ( flow ) .The two fundamental dimensions ( quanta of Points (ds) and quanta of Energy (dP) , are connected on Primary dipole and on any dipole AiBi . [PNS] is self created and consists a space (x,y,z) Scalar field Sp which constructs a vector field Sa = Ñ.Sp . The position of dipole in the equilibrium Space Anti-Space keeps charge = momentum ( Energy→ the difference of primary Work which is bounded on edge points ) and Angular momentum ( Spin → angular momentum is the intrinsic twist of Space , Anti-Space ) which inextricably unify geometry of Space and motion . On any Dipole AB of [PNS] with dš = ( [J,E,B] and content © ) ,where motion occurs only as (+) → (-) Source (+) → Drain (-) ,Conservation State of Work exists on magnitude |dš| = √ J² + E² + B² of vector ř ( J,E, B ) ( which is the Sub-Space of AB ) and on the two perpendicular Fields Ê = Ñx J , B = Ñx Ê ( which are the two diffused equilibrium Spaces and Anti -Spaces of AB , Ñx Ê = 0 , Ñ x B = 0 ) . Since,Source (+) →Drain (-) , in [PNS] is the equilibrium of Space [S] and Anti-Space [aS] , therefore the only magnitude for motion is J , while E and B are produced , as this happens in the Magnetic fields where lines ( loops ) close in themselves and this because no sources exist ↑→ ® for magnetic fields B and so the two models [ the B-field Pole and Amperian loop ] are explained. Solving equation ds.( PA+ PB ) = 0 then ds.PA = - ds.PB and since , dš , is constant for Primary dipole , so the Work conserved on every point in Spaces is constant and equal to [ dš .Impulse P = constant ] . i.e. The applied Work [ Wi → 1 → ∞ ] = ( charge ± P ) on every point of the three , Spaces , Anti–Spaces and Sub–Spaces , which coexist in [PNS] is conserved on Points , meaning that every point of [PNS] consist the fundamental ± Scalar Field with variables the Constraint Forces and Angular momentum [ Spin = Wij →1→ ∞] , and is conserved always in [PS] , [ PaS] or, The two elements [Vector dš = AB (matter) , ± dP ,Work p , Spin = momentum ] of the Infinite Dipole Vectors [AB] = [ ĀB – PA , PB ] build Particles with Identity Card , the Constant Product → dš . p = constant …(k) ← so , the Possible Energy Range (m) Scales , of the two fundamental and quantized dimensions [ ds , - P , + P ] are the three Layers , (- i ) ↔ (0 ) = - P → [ ds , - P , ] → Black Holes Scale = k 1 → ds 1. dP 1 = k 1 (-i ) ↔ (+i) = 7 P → [ ds , - P , + P ] → Planck Scale Matter = k 2 → ds 2. dP 2 = k 2 (+i ) ↔ (0 ) = + P → [ ds , + P , ] → Dark Matter Scale = k 3 → ds 3. dP 3 = k 3 For any single particle of wavelength λ = ds and dP = Charge → momentum ( p ) exists : dš.dP = λ . p = constant = h → is the reduced Planck constant in Planck Scale Matter . For ds near zero and P = ∞ , is needed a new Type of Light to see what is happening below Planck length Level , Layer 10¯35 m .Primary Vector monad and Vector monads are , either Static ( equilibrium ) or Dynamic ( are moving ) , and keep their Conservation of State ( The Total work is equal to zero ) in the three equilibrium and perpendicular monads [ J , E , B ] which are in Subspaces , Spaces , Anti-Spaces ( and thus , not turn to non-existence ) and are interchanged by Pythagoras conservation law of Volume. The geometric concepts of [PNS] as two dimensional field is that , the third dimension represents the amplitude of the potential S . Considering x-y Plane as the base and the vertical (z) is the potential S , then contours of constant potential altitudes of [PNS] are Cylindrical or Solenoidal and for Position 0 ( which is the equilibrium Horizon of Space and anti-Space) is Sphere , therefore [PNS] with the included Space [S] and Anti-Space [aS] may be Sphere and Solenoidal simultaneously.

Comments: 22 Pages.

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Submission history

[v1] 2013-03-21 04:22:55

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