Ενιαία Μήτρα Απειροστής Στροφής
Infinitesimal Rotation
Μετασχηματισμός Χωρική Στροφή
Ενιαία Μήτρα Απειροστής Στροφής Βαρυτομαγνητικό Πεδίο Gravitomagnetism 11x11 Lie algebra matrix (generator) 5D-Spacetime (complex) --- real part (red) imaginary part (blue) theta (θ) = elliptic rotation angle phi (φ) = hyperbolic rotation angle chi (χ)= parabolic "rotation angle" (charge) psi (ψ) = spin electromagnetism & rotation (left part) gravity & torsion (right part)
- Μία μήτρα ενός μετασχηματισμού .
Η ονομασία "Απειροστός" σχετίζεται ετυμολογικά με την λέξη "άπειρο " .
Η Ενιαία Μήτρα Απειροστής Στροφής
αναπαριστά τον μετασχηματισμό της απειροστής στροφής στον Ενιαίο 11-διάσταστο Χωρόχρονο.
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{\displaystyle {\mathcal {R}}={\begin{bmatrix}0&\color {Orange}{-\chi _{x}}&\color {Orange}{-\chi _{y}}&\color {Orange}{-\chi _{z}}&\color {Orange}{+\psi }&0&\color {Cyan}{{\tilde {\psi }}^{-1}}&\color {Cyan}{{\tilde {\chi }}_{z}^{+1}}&\color {Cyan}{{\tilde {\chi }}_{y}^{+1}}&\color {Cyan}{{\tilde {\chi }}_{x}^{+1}}&1\\\color {Orange}{+\chi _{x}}&0&\color {Red}{-\theta _{z}}&\color {Red}{+\theta _{y}}&\color {Orange}{-\phi _{x}}&0&\color {Cyan}{{\tilde {\phi }}_{x}^{+1}}&\color {Blue}{{\tilde {\theta }}_{y}^{-1}}&\color {Blue}{{\tilde {\theta }}_{z}^{+1}}&1&\color {Cyan}{{\tilde {\chi }}_{x}^{-1}}\\\color {Orange}{+\chi _{y}}&\color {Red}{+\theta _{z}}&0&\color {Red}{-\theta _{x}}&\color {Orange}{-\phi _{y}}&0&\color {Cyan}{{\tilde {\phi }}_{y}^{+1}}&\color {Blue}{{\tilde {\theta }}_{x}^{+1}}&1&\color {Blue}{{\tilde {\theta }}_{z}^{-1}}&\color {Cyan}{{\tilde {\chi }}_{y}^{-1}}\\\color {Orange}{+\chi _{x}}&\color {Red}{-\theta _{y}}&\color {Red}{+\theta _{x}}&0&\color {Orange}{-\phi _{z}}&0&\color {Cyan}{{\tilde {\phi }}_{z}^{+1}}&1&\color {Blue}{{\tilde {\theta }}_{x}^{-1}}&\color {Blue}{{\tilde {\theta }}_{y}^{+1}}&\color {Cyan}{{\tilde {\chi }}_{z}^{-1}}\\\color {Orange}{-\psi }&\color {Orange}{+\phi _{x}}&\color {Orange}{+\phi _{y}}&\color {Orange}{+\phi _{z}}&0&0&1&\color {Cyan}{{\tilde {\phi }}_{z}^{-1}}&\color {Cyan}{{\tilde {\phi }}_{y}^{-1}}&\color {Cyan}{{\tilde {\phi }}_{x}^{-1}}&\color {Cyan}{{\tilde {\psi }}^{+1}}\\0&0&0&0&0&-5&1&1&1&1&1\\\color {Cyan}{+\psi }&\color {Cyan}{-\phi _{x}}&\color {Cyan}{-\phi _{y}}&\color {Cyan}{-\phi _{z}}&0&1&1&\color {Orange}{{\tilde {\phi }}_{z}^{+1}}&\color {Orange}{{\tilde {\phi }}_{y}^{+1}}&\color {Orange}{{\tilde {\phi }}_{x}^{+1}}&\color {Orange}{{\tilde {\psi }}^{-1}}\\\color {Cyan}{-\chi _{z}}&\color {Blue}{+\theta _{y}}&\color {Blue}{-\theta _{x}}&0&\color {Cyan}{+\phi _{z}}&1&\color {Orange}{{\tilde {\phi }}_{z}^{-1}}&1&\color {Red}{{\tilde {\theta }}_{x}^{+1}}&\color {Red}{{\tilde {\theta }}_{y}^{-1}}&\color {Orange}{{\tilde {\chi }}_{z}^{+1}}\\\color {Cyan}{-\chi _{y}}&\color {Blue}{-\theta _{z}}&0&\color {Blue}{+\theta _{x}}&\color {Cyan}{+\phi _{y}}&1&\color {Orange}{{\tilde {\phi }}_{y}^{-1}}&\color {Red}{{\tilde {\theta }}_{x}^{-1}}&1&\color {Red}{{\tilde {\theta }}_{z}^{+1}}&\color {Orange}{{\tilde {\chi }}_{y}^{+1}}\\\color {Cyan}{-\chi _{x}}&0&\color {Blue}{+\theta _{z}}&\color {Blue}{-\theta _{y}}&\color {Cyan}{+\phi _{x}}&1&\color {Orange}{{\tilde {\phi }}_{x}^{-1}}&\color {Red}{{\tilde {\theta }}_{y}^{+1}}&\color {Red}{{\tilde {\theta }}_{z}^{-1}}&1&\color {Orange}{{\tilde {\chi }}_{x}^{+1}}\\0&\color {Cyan}{+\chi _{x}}&\color {Cyan}{+\chi _{y}}&\color {Cyan}{+\chi _{z}}&\color {Cyan}{-\psi }&1&\color {Orange}{{\tilde {\psi }}^{+1}}&\color {Orange}{{\tilde {\chi }}_{z}^{-1}}&\color {Orange}{{\tilde {\chi }}_{y}^{-1}}&\color {Orange}{{\tilde {\chi }}_{x}^{-1}}&1\end{bmatrix}}}
Συνοπτικά, η μήτρα αυτή μπορεί να γραφεί:
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{\displaystyle {\mathcal {R}}={\begin{bmatrix}0&\color {Orange}{-{\mathit {\mathrm {X} }}}&\color {Orange}{+{\mathit {\Psi }}}&0&\color {Cyan}{\mathit {\tilde {\Psi }}}^{-1}&\color {Cyan}{\mathit {\tilde {\mathrm {X} }}}^{+1}&0\\\color {Orange}{+{\mathit {\mathrm {X} }}}&\color {Red}{\mathit {\Theta }}&\color {Orange}{-{\mathit {\Phi }}}&0&\color {Cyan}{\mathit {\tilde {\Phi }}}^{+1}&\color {Blue}{\mathit {\tilde {\Theta }}}&\color {Cyan}{\mathit {\tilde {\mathrm {X} }}}^{-1}\\\color {Orange}{-{\mathit {\Psi }}}&\color {Orange}{+{\mathit {\Phi }}}&0&0&0&\color {Cyan}{\mathit {\tilde {\Phi }}}^{-1}&\color {Cyan}{\mathit {\tilde {\Psi }}}^{+1}\\0&0&0&-5&1&3&1\\\color {Cyan}{+{\mathit {\Psi }}}&\color {Cyan}{-{\mathit {\Phi }}}&0&1&1&\color {Orange}{\mathit {\tilde {\Phi }}}^{+1}&\color {Orange}{\mathit {\tilde {\Psi }}}^{-1}\\\color {Cyan}{-{\mathit {\mathrm {X} }}}&\color {Blue}{\mathit {\Theta }}&\color {Cyan}{+{\mathit {\Phi }}}&3&\color {Orange}{\mathit {\tilde {\Phi }}}^{-1}&\color {Red}{\mathit {\tilde {\Theta }}}&\color {Orange}{\mathit {\tilde {\mathrm {X} }}}^{+1}\\0&\color {Cyan}{+{\mathit {\mathrm {X} }}}&\color {Cyan}{-{\mathit {\Psi }}}&1&\color {Orange}{\mathit {\tilde {\Psi }}}^{+1}&\color {Orange}{\mathit {\tilde {\mathrm {X} }}}^{-1}&1\end{bmatrix}}}
Χωρικό Μέρος [ ]
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{\displaystyle {\mathcal {R}}_{space}={\begin{bmatrix}0&\color {Magenta}{-\chi _{x}}&\color {Magenta}{-\chi _{y}}&\color {Magenta}{-\chi _{z}}&\color {Cyan}{\cdot }&\cdot &\color {Cyan}{\cdot }&\color {Magenta}i{\tilde {\chi }}_{z}^{+1}&\color {Magenta}i{\tilde {\chi }}_{y}^{+1}&{\color {Magenta}i{\tilde {\chi }}_{x}^{+1}}\;\;\;0\\\color {Magenta}{+\chi _{x}}&0&\color {Red}{+\theta _{z}}&\color {Red}{-\theta _{y}}&\color {Blue}{\cdot }&\cdot &\color {Green}{\cdot }&\color {Brown}{i{\tilde {\theta }}}_{y}^{-1}&\color {Brown}{i{\tilde {\theta }}}_{z}^{+1}&0\;\;\;\;\color {Magenta}i{\tilde {\chi }}_{x}^{-1}\\\color {Magenta}{+\chi _{y}}&\color {Red}{-\theta _{z}}&0&\color {Red}{+\theta _{x}}&\color {Blue}{\cdot }&\cdot &\color {Green}{\cdot }&\color {Brown}{i{\tilde {\theta }}}_{x}^{+1}&0&\color {Brown}{i{\tilde {\theta }}}_{z}^{-1}\;\;\;\;\color {Magenta}i{\tilde {\chi }}_{y}^{-1}\\\color {Magenta}{+\chi _{z}}&\color {Red}{+\theta _{y}}&\color {Red}{-\theta _{x}}&0&\color {Blue}{\cdot }&\cdot &\color {Green}{\cdot }&0&\color {Brown}{i{\tilde {\theta }}}_{x}^{-1}&\color {Brown}{i{\tilde {\theta }}}_{y}^{+1}\;\;\;\color {Magenta}i{\tilde {\chi }}_{z}^{-1}\\\color {Cyan}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }&\cdot &\cdot &\cdot &\color {Green}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }\;\;\;\;\;\;\;\;\color {Cyan}{\cdot }\\\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot \;\;\;\;\;\;\;\;\cdot \\\color {Cyan}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }&\cdot &\cdot &\cdot &\color {Blue}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }\;\;\;\;\;\;\;\;\color {Cyan}{\cdot }\\\color {Magenta}{-i\chi _{z}}&\color {Brown}{+i\theta _{y}}&\color {Brown}{-i\theta _{x}}&0&\color {Green}{\cdot }&\cdot &\color {Blue}{\cdot }&0&\color {Red}{\tilde {\theta }}_{x}^{-1}&\color {Red}{\tilde {\theta }}_{y}^{+1}\;\;\;\color {Magenta}{\tilde {\chi }}_{z}^{+1}\\\color {Magenta}{-i\chi _{y}}&\color {Brown}{-i\theta _{z}}&0&\color {Brown}{+i\theta _{x}}&\color {Green}{\cdot }&\cdot &\color {Blue}{\cdot }&\color {Red}{\tilde {\theta }}_{x}^{+1}&0&\color {Red}{\tilde {\theta }}_{z}^{-1}\;\;\;\color {Magenta}{\tilde {\chi }}_{y}^{+1}\\\color {Magenta}{-i\chi _{x}}&0&\color {Brown}{+i\theta _{z}}&\color {Brown}{-i\theta _{y}}&\color {Green}{\cdot }&\cdot &\color {Blue}{\cdot }&\color {Red}{\tilde {\theta }}_{y}^{-1}&\color {Red}{\tilde {\theta }}_{z}^{+1}&0\;\;\;\;\;\color {Magenta}{\tilde {\chi }}_{x}^{+1}\\0&\color {Magenta}{+i\chi _{x}}&\color {Magenta}{+i\chi _{y}}&\color {Magenta}{+i\chi _{z}}&\color {Cyan}{\cdot }&\cdot &\color {Cyan}{\cdot }&\color {Magenta}{\tilde {\chi }}_{z}^{-1}&\color {Magenta}{\tilde {\chi }}_{y}^{-1}&{\color {Magenta}{\tilde {\chi }}_{x}^{-1}}\;\;\;\;0\\\end{bmatrix}}}
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{\displaystyle {\mathcal {R}}_{Space}={\begin{bmatrix}0&\color {Magenta}{-\mathrm {X} }&\color {Cyan}{\cdot }&\cdot &\color {Cyan}{\cdot }&\color {Magenta}i{\tilde {\mathrm {X} }}^{+1}&0\\\color {Magenta}{+\mathrm {X} }&\color {Red}{\Theta }&\color {Blue}{\cdot }&\cdot &\color {Green}{\cdot }&\color {Brown}i{\tilde {\Theta }}&\color {Magenta}i{\tilde {\mathrm {X} }}^{-1}\\\color {Cyan}{\cdot }&\color {Blue}{\cdot }&\cdot &\cdot &\cdot &\color {Green}{\cdot }&\color {Cyan}{\cdot }\\\cdot &\cdot &\cdot &\cdot &\cdot &\cdot &\cdot \\\color {Cyan}{\cdot }&\color {Green}{\cdot }&\cdot &\cdot &\cdot &\color {Blue}{\cdot }&\color {Cyan}{\cdot }\\\color {Magenta}{-i\mathrm {X} }&\color {Brown}{i\Theta }&\color {Green}{\cdot }&\cdot &\color {Blue}{\cdot }&\color {Red}{\tilde {\Theta }}&\color {Magenta}{\tilde {\mathrm {X} }}^{+1}\\0&\color {Magenta}{+i\mathrm {X} }&\color {Cyan}{\cdot }&\cdot &\color {Cyan}{\cdot }&\color {Magenta}{\tilde {\mathrm {X} }}^{-1}&0\end{bmatrix}}}
Χρονικό Μέρος [ ]
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{\displaystyle {\mathcal {R}}_{time}={\begin{bmatrix}\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{+\psi }&0&\color {Cyan}i{\tilde {\psi }}^{-1}&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\;\;\;\;\;\cdot \\\color {Magenta}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }&\color {Blue}{+\phi _{x}}&0&\color {Green}i{\tilde {\phi }}_{x}^{-1}&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot \;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Blue}{+\phi _{y}}&0&\color {Green}i{\tilde {\phi }}_{y}^{-1}&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }\;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Blue}{+\phi _{z}}&0&\color {Green}i{\tilde {\phi }}_{z}^{-1}&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }\;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Cyan}{-\psi }&\color {Blue}{-\phi _{x}}&\color {Blue}{-\phi _{y}}&\color {Blue}{-\phi _{z}}&0&0&0&\color {Green}i{\tilde {\phi }}_{z}^{+1}&\color {Green}i{\tilde {\phi }}_{y}^{+1}&\color {Green}i{\tilde {\phi }}_{x}^{+1}\;\;\;\color {Cyan}i{\tilde {\psi }}^{+1}\\0&0&0&0&0&0&0&0&0&0\;\;\;\;\;\;\;0\\\color {Cyan}{+i\psi }&\color {Green}{+i\phi _{x}}&\color {Green}{+i\phi _{y}}&\color {Green}{+i\phi _{z}}&0&0&0&\color {Blue}{\tilde {\phi }}_{z}^{-1}&\color {Blue}{\tilde {\phi }}_{y}^{-1}&\color {Blue}{\tilde {\phi }}_{z}^{-1}\;\;\;\color {Cyan}{\tilde {\psi }}^{-1}\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Green}{-i\phi _{z}}&0&\color {Blue}{\tilde {\phi }}_{z}^{+1}&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }\;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Green}{-i\phi _{y}}&0&\color {Blue}{\tilde {\phi }}_{y}^{+1}&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }\;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }&\color {Green}{-i\phi _{x}}&0&\color {Blue}{\tilde {\phi }}_{x}^{+1}&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot \;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{-i\psi }&0&\color {Cyan}{\tilde {\psi }}^{+1}&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\;\;\;\;\;\cdot \\\end{bmatrix}}}
Συνοπτικά, η μήτρα αυτή μπορεί να γραφεί:
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{\displaystyle {\mathcal {R}}={\begin{bmatrix}\cdot &\color {Magenta}{\cdot }&\color {Cyan}{+\psi }&0&\color {Cyan}i{\tilde {\psi }}^{-1}&\color {Magenta}{\cdot }&\cdot \\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\color {Blue}{+\Phi }&0&\color {Green}i{\tilde {\Phi }}^{-1}&\color {Brown}{\cdot }&\color {Magenta}{\cdot }\\\color {Cyan}{-\psi }&\color {Blue}{-\Phi }&0&0&0&\color {Green}i{\tilde {\Phi }}^{+1}&\color {Cyan}i{\tilde {\psi }}^{+1}\\0&0&0&0&0&0&0\\\color {Cyan}{+i\psi }&\color {Green}{+i\Phi }&0&0&0&\color {Blue}{\tilde {\Phi }}^{-1}&\color {Cyan}{\tilde {\psi }}^{-1}\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\color {Green}{-i\Phi }&0&\color {Blue}{\tilde {\Phi }}^{+1}&\color {Red}{\cdot }&\color {Magenta}{\cdot }\\\cdot &\color {Magenta}{\cdot }&\color {Cyan}{-i\psi }&0&\color {Cyan}{\tilde {\psi }}^{+1}&\color {Magenta}{\cdot }&\cdot \end{bmatrix}}}
Χωρίς το "μηδενικό πυρήνα" η Μήτρα γράφεται
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{\displaystyle {\mathcal {R}}_{time}={\begin{bmatrix}\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{+\psi }&0&\color {Cyan}i{\tilde {\psi }}^{-1}&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\;\;\;\;\;\cdot \\\color {Magenta}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }&\color {Blue}{+\phi _{x}}&0&\color {Green}i{\tilde {\phi }}_{x}^{-1}&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot \;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Blue}{+\phi _{y}}&0&\color {Green}i{\tilde {\phi }}_{y}^{-1}&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }\;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Blue}{+\phi _{z}}&0&\color {Green}i{\tilde {\phi }}_{z}^{-1}&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }\;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Cyan}{-\psi }&\color {Blue}{-\phi _{x}}&\color {Blue}{-\phi _{y}}&\color {Blue}{-\phi _{z}}&\cdot &\cdot &\cdot &\color {Green}i{\tilde {\phi }}_{z}^{+1}&\color {Green}i{\tilde {\phi }}_{y}^{+1}&\color {Green}i{\tilde {\phi }}_{x}^{+1}\;\;\;\color {Cyan}i{\tilde {\psi }}^{+1}\\0&0&0&0&\cdot &\cdot &\cdot &0&0&0\;\;\;\;\;\;\;0\\\color {Cyan}{+i\psi }&\color {Green}{+i\phi _{x}}&\color {Green}{+i\phi _{y}}&\color {Green}{+i\phi _{z}}&\cdot &\cdot &\cdot &\color {Blue}{\tilde {\phi }}_{z}^{-1}&\color {Blue}{\tilde {\phi }}_{y}^{-1}&\color {Blue}{\tilde {\phi }}_{z}^{-1}\;\;\;\color {Cyan}{\tilde {\psi }}^{-1}\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Green}{-i\phi _{z}}&0&\color {Blue}{\tilde {\phi }}_{z}^{+1}&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }\;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Green}{-i\phi _{y}}&0&\color {Blue}{\tilde {\phi }}_{y}^{+1}&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }\;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }&\color {Green}{-i\phi _{x}}&0&\color {Blue}{\tilde {\phi }}_{x}^{+1}&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot \;\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{-i\psi }&0&\color {Cyan}{\tilde {\psi }}^{+1}&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\;\;\;\;\;\cdot \\\end{bmatrix}}}
Οι 4 πεντα-διάστατοι Χωρόχρονοι [ ]
Πραγματικός [ ]
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{\displaystyle {\mathcal {R}}_{real}={\begin{bmatrix}0&\color {Magenta}{-\chi _{x}}&\color {Magenta}{-\chi _{y}}&\color {Magenta}{-\chi _{z}}&\color {Cyan}{+\psi }&0&\color {Cyan}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\cdot \\\color {Magenta}{+\chi _{x}}&0&\color {Red}{+\theta _{z}}&\color {Red}{-\theta _{y}}&\color {Blue}{+\phi _{x}}&0&\color {Green}{\cdot }&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot \;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{+\chi _{y}}&\color {Red}{-\theta _{z}}&0&\color {Red}{+\theta _{x}}&\color {Blue}{+\phi _{y}}&0&\color {Green}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{+\chi _{z}}&\color {Red}{+\theta _{y}}&\color {Red}{-\theta _{x}}&0&\color {Blue}{+\phi _{z}}&0&\color {Green}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }\;\;\;\color {Magenta}{\cdot }\\\color {Cyan}{-\psi }&\color {Blue}{-\phi _{x}}&\color {Blue}{-\phi _{y}}&\color {Blue}{-\phi _{z}}&0&0&\cdot &\color {Green}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }\;\;\;\color {Cyan}{\cdot }\\0&0&0&0&0&0&0&0&0&0\;\;\;0\\\color {Cyan}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }&\cdot &0&\cdot &\color {Blue}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }\;\;\;\color {Cyan}{\cdot }\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Green}{\cdot }&0&\color {Blue}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Green}{\cdot }&0&\color {Blue}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }&\color {Green}{\cdot }&0&\color {Blue}{\cdot }&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot \;\;\;\;\color {Magenta}{\cdot }\\\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{\cdot }&0&\color {Cyan}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\cdot \\\end{bmatrix}}}
Φανταστικός [ ]
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{\displaystyle {\mathcal {R}}_{imag}={\begin{bmatrix}\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{\cdot }&0&\color {Cyan}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\cdot \\\color {Magenta}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }&\color {Blue}{\cdot }&0&\color {Green}{\cdot }&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot \;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Blue}{\cdot }&0&\color {Green}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Blue}{\cdot }&0&\color {Green}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }\;\;\;\color {Magenta}{\cdot }\\\color {Cyan}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }&\cdot &0&\cdot &\color {Green}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }\;\;\;\color {Cyan}{\cdot }\\0&0&0&0&0&0&0&0&0&0\;\;\;0\\\color {Cyan}{+i\psi }&\color {Green}{+i\phi _{x}}&\color {Green}{+i\phi _{y}}&\color {Green}{+i\phi _{z}}&0&0&\cdot &\color {Blue}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }\;\;\;\color {Cyan}{\cdot }\\\color {Magenta}{-i\chi _{z}}&\color {Brown}{+i\theta _{y}}&\color {Brown}{-i\theta _{x}}&0&\color {Green}{-i\phi _{z}}&0&\color {Blue}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{-i\chi _{y}}&\color {Brown}{-i\theta _{z}}&\cdot &\color {Brown}{+i\theta _{x}}&\color {Green}{-i\phi _{y}}&0&\color {Blue}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{-i\chi _{x}}&0&\color {Brown}{+i\theta _{z}}&\color {Brown}{-i\theta _{y}}&\color {Green}{-i\phi _{x}}&0&\color {Blue}{\cdot }&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot \;\;\;\color {Magenta}{\cdot }\\0&\color {Magenta}{+i\chi _{x}}&\color {Magenta}{+i\chi _{y}}&\color {Magenta}{+i\chi _{z}}&\color {Cyan}{-i\psi }&0&\color {Cyan}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\cdot \\\end{bmatrix}}}
Συμπραγματικός [ ]
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{\displaystyle {\mathcal {R}}_{co-real}={\begin{bmatrix}\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{\cdot }&0&\color {Cyan}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\;\;\;\;\cdot \\\color {Magenta}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }&\color {Blue}{\cdot }&0&\color {Green}{\cdot }&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot \;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Blue}{\cdot }&0&\color {Green}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Blue}{\cdot }&0&\color {Green}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Cyan}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }&\cdot &0&\cdot &\color {Green}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }\;\;\;\;\;\;\;\color {Cyan}{\cdot }\\0&0&0&0&0&0&0&0&0&0\;\;\;\;\;\;\;0\\\color {Cyan}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }&\cdot &0&0&\color {Blue}{\tilde {\phi }}_{z}^{-1}&\color {Blue}{\tilde {\phi }}_{y}^{-1}&\color {Blue}{\tilde {\phi }}_{z}^{-1}\;\;\;\color {Cyan}{\tilde {\psi }}^{-1}\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Green}{\cdot }&0&\color {Blue}{\tilde {\phi }}_{z}^{+1}&0&\color {Red}{\tilde {\theta }}_{x}^{-1}&\color {Red}{\tilde {\theta }}_{y}^{+1}\;\;\;\color {Magenta}{\tilde {\chi }}_{z}^{+1}\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Green}{\cdot }&0&\color {Blue}{\tilde {\phi }}_{y}^{+1}&\color {Red}{\tilde {\theta }}_{x}^{+1}&0&\color {Red}{\tilde {\theta }}_{z}^{-1}\;\;\;\color {Magenta}{\tilde {\chi }}_{y}^{+1}\\\color {Magenta}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }&\color {Green}{\cdot }&0&\color {Blue}{\tilde {\phi }}_{x}^{+1}&\color {Red}{\tilde {\theta }}_{y}^{-1}&\color {Red}{\tilde {\theta }}_{z}^{+1}&0\;\;\;\;\;\color {Magenta}{\tilde {\chi }}_{x}^{+1}\\\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{\cdot }&0&\color {Cyan}{\tilde {\psi }}^{+1}&\color {Magenta}{\tilde {\chi }}_{z}^{-1}&\color {Magenta}{\tilde {\chi }}_{y}^{-1}&{\color {Magenta}{\tilde {\chi }}_{x}^{-1}}\;\;\;\;0\\\end{bmatrix}}}
Συμφανταστικός [ ]
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{\displaystyle {\mathcal {R}}_{co-imag}={\begin{bmatrix}\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{\cdot }&0&\color {Cyan}i{\tilde {\psi }}^{-1}&\color {Magenta}i{\tilde {\chi }}_{z}^{+1}&\color {Magenta}i{\tilde {\chi }}_{y}^{+1}&{\color {Magenta}i{\tilde {\chi }}_{x}^{+1}}\;\;\;0\\\color {Magenta}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }&\color {Blue}{\cdot }&0&\color {Green}i{\tilde {\phi }}_{x}^{-1}&\color {Brown}{i{\tilde {\theta }}}_{y}^{-1}&\color {Brown}{i{\tilde {\theta }}}_{z}^{+1}&0\;\;\;\;\color {Magenta}i{\tilde {\chi }}_{x}^{-1}\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Blue}{\cdot }&0&\color {Green}i{\tilde {\phi }}_{y}^{-1}&\color {Brown}{i{\tilde {\theta }}}_{x}^{+1}&0&\color {Brown}{i{\tilde {\theta }}}_{z}^{-1}\;\;\;\;\color {Magenta}i{\tilde {\chi }}_{y}^{-1}\\\color {Magenta}{\cdot }&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Blue}{\cdot }&0&\color {Green}i{\tilde {\phi }}_{z}^{-1}&0&\color {Brown}{i{\tilde {\theta }}}_{x}^{-1}&\color {Brown}{i{\tilde {\theta }}}_{y}^{+1}\;\;\;\color {Magenta}i{\tilde {\chi }}_{z}^{-1}\\\color {Cyan}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }&\cdot &0&0&\color {Green}i{\tilde {\phi }}_{z}^{+1}&\color {Green}i{\tilde {\phi }}_{y}^{+1}&\color {Green}i{\tilde {\phi }}_{x}^{+1}\;\;\;\color {Cyan}i{\tilde {\psi }}^{+1}\\0&0&0&0&0&0&0&0&0&0\;\;\;\;\;\;\;0\\\color {Cyan}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }&\color {Green}{\cdot }&\cdot &0&\cdot &\color {Blue}{\cdot }&\color {Blue}{\cdot }&\color {Blue}{\cdot }\;\;\;\;\;\;\;\color {Cyan}{\cdot }\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Green}{\cdot }&0&\color {Blue}{\cdot }&\cdot &\color {Red}{\cdot }&\color {Red}{\cdot }\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\color {Brown}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Green}{\cdot }&0&\color {Blue}{\cdot }&\color {Red}{\cdot }&\cdot &\color {Red}{\cdot }\;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\color {Magenta}{\cdot }&\cdot &\color {Brown}{\cdot }&\color {Brown}{\cdot }&\color {Green}{\cdot }&0&\color {Blue}{\cdot }&\color {Red}{\cdot }&\color {Red}{\cdot }&\cdot \;\;\;\;\;\;\;\color {Magenta}{\cdot }\\\cdot &\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&\color {Cyan}{\cdot }&0&\color {Cyan}{\cdot }&\color {Magenta}{\cdot }&\color {Magenta}{\cdot }&{\color {Magenta}{\cdot }}\;\;\;\;\;\;\;\cdot \\\end{bmatrix}}}
Κίνδυνοι Χρήσης
Αν και θα βρείτε εξακριβωμένες πληροφορίες
σε αυτήν την εγκυκλοπαίδεια
ωστόσο, παρακαλούμε να λάβετε σοβαρά υπ' όψη ότι
η "Sciencepedia " δεν μπορεί να εγγυηθεί, από καμιά άποψη ,
την εγκυρότητα των πληροφοριών που περιλαμβάνει.
"Οι πληροφορίες αυτές μπορεί πρόσφατα
να έχουν αλλοιωθεί, βανδαλισθεί ή μεταβληθεί από κάποιο άτομο,
η άποψη του οποίου δεν συνάδει με το "επίπεδο γνώσης"
του ιδιαίτερου γνωστικού τομέα που σας ενδιαφέρει."
Πρέπει να λάβετε υπ' όψη ότι
όλα τα άρθρα μπορεί να είναι ακριβή, γενικώς,
και για μακρά χρονική περίοδο,
αλλά να υποστούν κάποιο βανδαλισμό ή ακατάλληλη επεξεργασία ,
ελάχιστο χρονικό διάστημα, πριν τα δείτε.
Επίσης,
Οι διάφοροι "Εξωτερικοί Σύνδεσμοι (Links)"
(όχι μόνον, της Sciencepedia
αλλά και κάθε διαδικτυακού ιστότοπου (ή αλλιώς site)),
αν και άκρως απαραίτητοι,
είναι αδύνατον να ελεγχθούν
(λόγω της ρευστής φύσης του Web ),
και επομένως είναι ενδεχόμενο να οδηγήσουν
σε παραπλανητικό, κακόβουλο ή άσεμνο περιεχόμενο .
Ο αναγνώστης πρέπει να είναι
εξαιρετικά προσεκτικός όταν τους χρησιμοποιεί.
- Μην κάνετε χρήση του περιεχομένου της παρούσας εγκυκλοπαίδειας
αν διαφωνείτε με όσα αναγράφονται σε αυτήν
>>Διαμαρτυρία προς την wikia <<
- Όχι, στις διαφημίσεις που περιέχουν απαράδεκτο περιεχόμενο (άσεμνες εικόνες, ροζ αγγελίες κλπ.)