Quintessence (Planck unit)

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Quintessence = sqrt(velocity/mass) as a 5th and principal Planck unit

The MKSA system of units is a physical system of measurement that uses the meter, kilogram, second and ampere (MKSA) as base units and forms the base of the SI International System of Units. As Planck units these would constitute Planck mass, Planck length, Planck time, Planck ampere. Quintessence as a Planck unit would be characterized by encompassing the 4 MKSA Planck units (i.e.: being that unit from which the 4 MKSA units may be derived), thus qualifying as a 5th Planck unit in the classical elements sense.


Quintessence historical[edit | edit source]

Quintessence[edit | edit source]

According to ancient and medieval science, quintessence (quinta essentia or fifth element), also called aether, æther, aither, or ether, is the material that fills the region above the terrestrial sphere. Believing that the movements of the heavenly bodies are continuous, natural and circular, and that the natural movements of the four terrestrial elements (water, earth, fire, air) are rectilinear and discontinuous, Aristotle concluded that the heavenly bodies must be composed of a fifth element, aither [sic] [1]


Classical elements[edit | edit source]

Classical elements typically refer to water, earth, fire, air, and (later) aether, which were proposed to explain the nature and complexity of all matter in terms of simpler substances. [2][3] Ancient cultures in Greece, w:Ancient Egypt, Persia, w:Babylonia, Japan, Tibet, and India had all similar lists, sometimes referring in local languages to "air" as "wind" and the fifth element as "void". The Chinese Wu Xing system lists Wood ( ), Fire ( huǒ), Earth ( ), Metal ( jīn), and Water ( shuǐ), though these are described more as energies or transitions rather than as types of material. These five elements have been associated since Plato's Timaeus with the five w:platonic solids.


Platonic solids[edit | edit source]

In Timaeus, Plato talks about the five, and only five, possible regular solids – those with equivalent faces and with all lines and angles, formed by those faces, equal. They are the four-sided tetrahedron (fire), the six-sided hexahedron or cube (earth), the eight-sided octahedron (air), the twelve-sided dodecahedron (quintessence), and the twenty-sided icosahedron (water).

w:Tetrahedron w:Cube w:Octahedron Dodecahedron Icosahedron
Four faces Six faces Eight faces Twelve faces Twenty faces
Tetrahedron.svg

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(3D model)

Hexahedron.svg

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(3D model)

Octahedron.svg

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(3D model)

Dodecahedron.svg

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(3D model)

Icosahedron.svg

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(3D model)


Godai (Japanese philosophy)[edit | edit source]

Godai, (五大?, lit. "five – great, large, physical, form") five elements philosophy in Japan is derived from Buddhist w:dharma and traditional Chinese medical doctrine that traveled from China throughout east Asia to Japan.[4][5]

The Japanese Buddhist Godai is attributed to esoteric Japanese Buddhism during the tenth century CE under the name of gorin (the "five wheels" or the "five rings"). Godai and gorin is also seen within the practice of w:ninjutsu, where these principles became an essential aspect of the esoteric ninja teachings (the ninpo-mikkyo) whereas the theory of gogyo moved into the functional theory of traditional Japanese medicine and exoteric Buddhism.[6]

The godai is a static or inert philosophical understanding of the traditional Japanese elements and study, similar to the Greek w:classical elements. The four main elements or building blocks are Earth, Water, Fire, Wind, and Void is non substantial.[7]


Fifth element[edit | edit source]

In Plato's Timaeus (58d) speaking about air, Plato mentions that "there is the most translucent kind which is called by the name of aether (αἰθήρ)"[9] but otherwise he adopted the classical system of four elements. w:Aristotle, who had been Plato's student at the Academy, agreed on this point with his former mentor, emphasizing additionally that fire has sometimes been mistaken for aether. However, in his Book w:On the Heavens he introduced a new "first" element to the system of the w:classical elements of Ionian philosophy. He noted that the four terrestrial classical elements were subject to change and naturally moved linearly. The first element however, located in the celestial regions and heavenly bodies, moved circularly and had none of the qualities the terrestrial classical elements had. It was neither hot nor cold, neither wet nor dry. With this addition the system of elements was extended to five and later commentators started referring to the new first one as the fifth and also called it aether, a word that Aristotle had not used.[10]

Aether differed from the four terrestrial elements; it was incapable of motion of quality or motion of quantity. Aether was only capable of local motion. Aether naturally moved in circles, and had no contrary, or unnatural, motion. Aristotle also noted that w:celestial spheres made of aether held the stars and planets. The idea of aethereal spheres moving with natural circular motion led to Aristotle's explanation of the observed orbits of stars and planets in perfectly circular motion.


Quintessence (Physics)[edit | edit source]

In w:physics, quintessence is a hypothetical form of w:dark energy, more precisely a w:scalar field, postulated as an explanation of the observation of an accelerating rate of expansion of the universe. It has been proposed by some physicists to be a fifth fundamental force.[11][12][13][14]



Quintessence as a Planck unit[edit | edit source]

Assigning geometrical objects to the Planck units via 2 dimensionless physical constants, the fine structure constant α and Omega Ω and by setting a mathematical relationship un between them, we can construct this table.

Geometrical units
Attribute Geometrical object Relationship
Quintessence
mass
time
length
speed of light
ampere


From these relationships, we note that certain ratios of units cancel and become unit-less


SI units (derivations)[edit | edit source]

Setting 2 unit-less ratios (x, y) in terms of MLT:


Gives the units for the dimensioned constants;

(Ampere)
Gravitation constant
Planck length
Planck mass
speed of light
Planck constant
elementary charge
Boltzmann's constant
Planck time


SI constants (derivations)[edit | edit source]

To convert to the SI unit values we need 2 scalars, here are used r and v, numerically


Assigning (with i as the numerical x and j as the numerical y from above)


Gives


Solutions[edit | edit source]

Solving for these constants using α, Ω, r, v


Physical constants; geometrical vs experimental (CODATA)
Constant In Planck units Geometrical object Calculated (r, v, Ω, α*) SI CODATA 2014 [15]
Speed of light V c* = 299 792 458, unit = u17 c = 299 792 458 (exact)
Fine structure constant α* = 137.035 999 139 (mean) α = 137.035 999 139(31)
Rydberg constant R* = 10 973 731.568 508, unit = u13 R = 10 973 731.568 508(65)
Vacuum permeability μ0* = 4π/10^7, unit = u56 μ0 = 4π/10^7 (exact)
Planck constant h* = 6.626 069 134 e-34, unit = u19 h = 6.626 070 040(81) e-34
Gravitational constant G* = 6.672 497 192 29 e11, unit = u6 G = 6.674 08(31) e-11
Elementary charge e* = 1.602 176 511 30 e-19, unit = u-19 e = 1.602 176 620 8(98) e-19
Boltzmann constant kB* = 1.379 510 147 52 e-23, unit = u29 kB = 1.380 648 52(79) e-23
Electron mass me* = 9.109 382 312 56 e-31, unit = u15 me = 9.109 383 56(11) e-31
Classical electron radius λe* = 2.426 310 2366 e-12, unit = u-13 λe = 2.426 310 236 7(11) e-12
Planck mass M mP* = .217 672 817 580 e-7, unit = u15 mP = .217 647 0(51) e-7
Planck length L lp* = .161 603 660 096 e-34, unit = u-13 lp = .161 622 9(38) e-34
Planck time T tp* = 5.390 517 866 e-44, unit = u-30 tp = 5.391 247(60) e-44
Ampere A A^* = 0.148 610 6299 e25, unit = u3


Conclusion[edit | edit source]

In the Trialogue on the number of fundamental constants [16] was debated the number of fundamental constants required by the universe. In terms of dimensioned constants (alpha and Omega are dimensionless) it appears that 1 (Quintessence) is required as from this unit the 4 mksa units can be derived.



External links[edit | edit source]


References[edit | edit source]

  1. Lloyd, G. E. R. (1968), Aristotle: The Growth and Structure of his Thought, Cambridge: Cambridge Univ. Pr., pp. 133–139, ISBN 0-521-09456-9,.
  2. Boyd, T.J.M.; Sanderson, J.J. (2003). The Physics of Plasmas. Cambridge University Press. p. 1. ISBN 9780521459129. https://archive.org/details/physicsofplasmas0000boyd. 
  3. Ball, P. (2004). The Elements: A Very Short Introduction. Very Short Introductions. OUP Oxford. p. 33. ISBN 9780191578250. https://books.google.com/books?id=uaBczzC4wvIC&pg=PT33. 
  4. "Kampo Medicine: The Practice of Chinese Herbal Medicine in Japan". www.itmonline.org. Retrieved 2020-11-24.
  5. "East Asian Buddhist Studies: A Reference Guide". www.international.ucla.edu. Retrieved 2020-11-24.
  6. Baracco, Luciano (2011). National Integration and Contested Autonomy: The Caribbean Coast of Nicaragua (in en). Algora Publishing. ISBN 978-0-87586-823-3. https://books.google.com/books?id=3x5T23r6nUUC&pg=PA154. 
  7. "East Asian Buddhist Studies: A Reference Guide". www.international.ucla.edu. Retrieved 2020-11-27.
  8. Hayes, Stephen K. (1981/2003). Warrior Ways of Enlightenment, Vol. 2, p.26. Ohara Publications, Santa Clarita, California. 22nd edition. ISBN 0-89750-077-6
  9. Plato, Timaeus 58d.
  10. Hahm, David E. (1982). "The fifth element in Aristotle's De Philosophia: A Critical Re-Examination". The Journal of Hellenic Studies 102: 60–74. doi:10.2307/631126. 
  11. Carroll, S.M. (1998). "Quintessence and the Rest of the World: Suppressing Long-Range Interactions". Phys. Rev. Lett. 81 (15): 3067–3070. doi:10.1103/PhysRevLett.81.3067. 
  12. Wetterich, C. "Quintessence --a fifth force from variation of the fundamental scale" (PDF). Heidelberg University.
  13. Dvali, Gia; Zaldarriaga, Matias (2002). "Changing α With Time: Implications For Fifth-Force-Type Experiments And Quintessence". Physical Review Letters 88 (9): 091303. doi:10.1103/PhysRevLett.88.091303. PMID 11863992. http://cds.cern.ch/record/515241/files/0108217.pdf. 
  14. Cicoli, Michele; Pedro, Francisco G.; Tasinato, Gianmassimo (23 July 2012). "Natural Quintessence in String Theory" – via arXiv.org.
  15. [1] | CODATA, The Committee on Data for Science and Technology | (2014)
  16. Michael J. Duff, Lev B. Okun and Gabriele Veneziano, Journal of High Energy Physics, Volume 2002, JHEP03(2002)