Spacetime-Odyssey - A-08a

Spacetime Odyssey
(Οδύσσεια του Χωρόχρονου)

Αγχίγραμμος Χώρος & Χρόνος
(Πίνακες)

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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/α	Physical Space (Position vector)	Geometry (Transformation Symmetry)
Affine Spaces
1.	one-dimensional (1D) Affine Space  r⃗  =[x]	1D-Space Translation T(l)=[lx]
2.	two-dimensional (2D) Affine Space  r⃗  =[xy]	2D-Space Translation T(l)=[lxlx]
3.	three-dimensional (3D) Affine Space  r⃗  =⎡⎣xyz⎤⎦	3D-Space Translation T(l)=⎡⎣⎢lxlylz⎤⎦⎥
Affine Times
1.	one-dimensional (1D) Affine Time rt=[t]	1D-Time Translation T(lt)=[lt]
2.	two-dimensional (2D) Affine Time r⃗ t=[0t]	2D-Time Translation T(lt)=[0lt]
3.	three-dimensional (3D) Affine Time r⃗ t=⎡⎣00t⎤⎦	3D-Time Translation T(lt)=⎡⎣00lt⎤⎦

Evolutional Correspondence between Geometry & Mechanics
α/α	Geometry (Transformation Symmetry)	Mechanics (Invariant Quantities)
Affine Spaces
1.	1D-Space Translation T(l)=[lx]	1D-Linear Momentum P=[Px]
2.	2D-Space Translation T(l)=[lxly]	2D-Linear Momentum  P⃗  =[PxPy]
3.	3D-Space Translation T(l)=⎡⎣⎢lxlylz⎤⎦⎥	3D-Linear Momentum  P⃗  =⎡⎣⎢PxPyPz⎤⎦⎥
Affine Times
1.	1D-Time Translation T(lt)=[lt]	1D-energy E=[E]
2.	2D-Time Translation T(lt)=[0lt]	2D-energy  E⃗  =[0E]
3.	3D-Time Translation T(lt)=⎡⎣00lt⎤⎦	3D-energy  E⃗  =⎡⎣00E⎤⎦

Evolutional Correspondence between Geometry & Electrodynamics
α/α	Geometry (Transformation Symmetry)	Electrodynamics (Invariant Quantities)
Affine Spaces
1.	1D-Space Translation T(l)=[lx]	1D-Current Density J=[Jx]
2.	2D-Space Translation T(l)=[lxly]	2D-Current Density  J⃗  =[JxJy]
3.	3D-Space Translation T(l)=⎡⎣⎢lxlylz⎤⎦⎥	3D-Current Density  J⃗  =⎡⎣⎢JxJyJz⎤⎦⎥
Affine Times
1.	1D-Time Translation T(lt)=[lt]	1D-Charge Density Q=[Q]
2.	2D-Time Translation T(lt)=[0lt]	2D-Charge Density  Q⃗  =[0Q]
3.	3D-Time Translation T(lt)=⎡⎣00lt⎤⎦	3D-Charge Density  Q⃗  =⎡⎣00Q⎤⎦

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Εδώ βρίσκουμε τα περιεχόμενα της σειράς: Spacetime-Odyssey

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