User:Rjowsey: Difference between revisions
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http://www.jowsey.org/physics/SpaceTime.pdf |
http://www.jowsey.org/physics/SpaceTime.pdf |
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=== [[Special Relativity]] in 6D |
=== [[Special Relativity]] in 6D: === |
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http://www.jowsey.org/physics/Relativity6D.pdf |
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[[james_clerk_maxwell|Maxwell]]'s frame: ''(x, y, z, iλ<sub>1</sub>, jλ<sub>2</sub>, kλ<sub>3</sub>)'' where ''ijk = i<sup>2</sup> = j<sup>2</sup> = k<sup>2</sup>'' ≡ −1 |
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Animation showing a test particle of [[Planck mass]] being accelerated to the [[speed of light]], where it has [[Planck momentum]] and [[Planck_energy|Planck kinetic energy]]. The [[Minkowski diagram]] at top-left shows the "4D [[Lorentz_factor|Lorentz rotation]]" of the moving frame of reference inhabited by the particle. The top-right '''time/energy''' projection shows [[time dilation]] approaching infinity at light speed, and the bottom-left '''position/momentum''' projection shows [[length contraction]] in the moving [[frame of reference]].<br \> |
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<p align=center>[[File:6D Special Relativity.gif|Special Relativity in 6 dimensions]]</p> |
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The [[Lorentz factor]] is the inverse-cosine of the [[Phasor|phase angle]] (0 < φ < <sup>π</sup>/<sub>2</sub>), i.e. γ = 1/cos(φ), and the ratio of the particle's velocity to light speed is β = <sup>v</sup>/<sub>c</sub> = sin(φ). Thus, time dilation and length contraction simplify to τᵩ = t∙cos(φ) and ʀᵩ = r∙cos(φ). The y-axis in the bottom-right projection represents the imaginary component of the particle's kinetic energy, while the x-axis represents the imaginary component of its potential energy mc<sup>2</sup>, in units of Planck energy (E<sub>P</sub>). |
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Thus, the particle's total energy Eᵩ is a function of √((t∙sin(φ))<sup>2</sup> + (r∙sin(φ))<sup>2</sup>). At light speed, the particle's rest-mass energy and its momentum can be seen as inhabiting two imaginary spatial dimensions. A Planck mass at velocity v = c has total energy of √2∙E<sub>P</sub>, assuming no losses due to gravitational radiation. The particle's [[Matter_wave|matter-wave]] now has a [[Louis_de_Broglie|de Broglie]] and [[Compton wavelength]] λᵩ = [[Planck length]], oscillating at [[Planck frequency]]. |
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=== [[General Relativity]] in 6D [[Quaternion-Kähler manifold|complex spacetime]]: === |
=== [[General Relativity]] in 6D [[Quaternion-Kähler manifold|complex spacetime]]: === |
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Revision as of 22:42, 24 November 2015
The Geometry of SpaceTime
http://www.jowsey.org/physics/SpaceTime.pdf
Special Relativity in 6D:
http://www.jowsey.org/physics/Relativity6D.pdf
"Think different"