Τρίτη, 11 Ιουνίου 2019

Spacetime-Odyssey - A-08b

Spacetime Odyssey
(Οδύσσεια του Χωρόχρονου)

Ευκλείδειος Χώρος & Χρόνος
(Πίνακες)

Σχετική εικόνα


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Εδώ βρίσκουμε τα περιεχόμενα της σειράς: Spacetime-Odyssey
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Ακολουθούν Ανακεφαλαιωτικοί Πίνακες

Evolutional Correspondence
between
Spacetime & Geometry
α/αPhysical Space
(Position vector)
Geometry
(Transformation Symmetry)
Euclidean Spaces
1.one-dimensional (1D)
Euclidean Space

 r⃗  =[x]
1D-Space Rotation
R(θ)=[θ]
2.two-dimensional (2D)
Euclidean Space

 r⃗  =[xy]
&
 r⃗  =[xy]
2D-Space Rotation
R(θ)=[0+θθ0]
3.three-dimensional (3D)
Euclidean Space

 r⃗  =xyz
&
 r⃗ =[xyz]
3D-Space Rotation
R(θ)=0+θzθyθz0+θz+θyθx0
Minkowskian Times
1.one-dimensional (1D)
Minkowski Time

rt=[t]
1D-Time Rotation
R(ϕ)=[0]
2.two-dimensional (2D)
Minkowski Time

 r⃗ t=[0t]
&
 r⃗ t=[0t]
2D-Time Rotation
R(ϕ)=[0+ϕϕ0]
3.three-dimensional (3D)
Minkowski Time

 r⃗ t=00t
&
 r⃗ t=[00t]
3D-Time Rotation
R(ϕ)=00ϕy00+ϕz+ϕyϕz0


Evolutional Correspondence
between
Geometry & Mechanics
α/αGeometry
(Transformation Symmetry)
Mechanics
(Invariant Quantities)
Euclidean Spaces
1.1D-Space Rotation
R(θ)=[0]
1D-Angular momentum
L=[0]
2.2D-Space Rotation
R(θ)=[0+θθ0]
2D-Angular momentum
L=[0+LzLz0]
3.3D-Space Rotation
R(θ)=0+θzθyθz0+θz+θyθx0
3D-Angular momentum
 L⃗  =0+LzLyLz0+Lx+LyLx0
Minkowskian Times
1.1D-Time Rotation
R(ϕ)=[0]
1D-mass-Center position
C=[0]
2.2D-Time Rotation
R(ϕ)=[0+ϕϕ0]
2D-mass-Center position
C=[0+CzCz0]
3.3D-Time Rotation
R(ϕ)=00ϕy00+ϕz+ϕyϕz0
3D-mass-Center position
 C⃗  =00Cy00+Cz+CyCz0



Evolutional Correspondence
between
Geometry & Electrodynamics
α/αGeometry
(Transformation Symmetry)
Electrodynamics
(Invariant Quantities)
Euclidean Spaces
1.1D-Space Rotation
R(θ)=[0]
1D-Magnetic Strength
B=[0]
2.2D-Space Rotation
R(θ)=[0+θθ0]
2D-Magnetic Strength
B=[0+BzBz0]
3.3D-Space Rotation
R(θ)=0+θzθyθz0+θz+θyθx0
1D-Magnetic Strength
 B⃗  =0+BzByBz0+Bx+ByBx0
Minkowskian Times
1.1D-Time Rotation
R(ϕ)=[0]
1D-Electric Strength
E=[0]
2.2D-Time Rotation
R(ϕ)=[0+ϕϕ0]
2D-Electric Strength
E=[0+EzEz0]
3.3D-Time Rotation
R(ϕ)=00ϕy00+ϕz+ϕyϕz0
3D-Electric Strength
 E⃗  =00Ey00+Ez+EyEz0


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Εδώ βρίσκουμε τα περιεχόμενα της σειράς: Spacetime-Odyssey
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