Quintessence (Planck unit)

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
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]

Classical elements
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. Ancient cultures in Greece, Ancient Egypt, Persia, 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 (木 mù), Fire (火 huǒ), Earth (土 tǔ), Metal (金 jīn), and Water (水 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 platonic solids.

Platonic solids
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).

Godai (Japanese philosophy)
Godai, (五大) five elements philosophy in Japan is derived from Buddhist dharma and traditional Chinese medical doctrine that traveled from China throughout east Asia to Japan.

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 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.

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

"[In mikkyo it is taught that] All physical aspects of existence originate from a common source and can be classified in of the godai five elemental manifestations of physical. Chi, or the earth, symbolizes solid matter. Sui, the water, symbolizes liquids. Ka, the fire, is the symbol of combustion, or the elements in an energy-releasing state. Fu, the wind, symbolizes gases. Ku, the void, is representative of the formless subatomic energy that is the basis for the structure of all things."

- Stephen K. Hayes

Fifth element
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)" but otherwise he adopted the classical system of four elements. 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 On the Heavens he introduced a new "first" element to the system of the 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.

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 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)
In physics, quintessence is a hypothetical form of dark energy, more precisely a 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.

Quintessence as a Planck unit
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.

From these relationships, we note that certain ratios of units cancel and become unit-less
 * $$\frac{u^{3*3} u^{-13*3}}{u^{-30}} = \frac{u^{-13*15}}{u^{15*9} u^{-30*11}} \;...\; = 1$$

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


 * $$u,\; units = \sqrt{\frac{L}{M T}}$$


 * $$x,\;units = \sqrt{\frac{M^9 T^{11}}{L^{15}}} = u^0 = 1 $$


 * $$y,\;units = M^2T = u^0 = 1$$

Gives the units for the dimensioned constants;


 * $$u^3 = \frac{L^{3/2}}{M^{3/2} T^{3/2}} = A$$ (Ampere)


 * $$u^6 (y) = L^3/T^2 M,\; (G)$$ Gravitation constant


 * $$u^{13} (xy) = 1/L,\; (1/l_p)$$ Planck length


 * $$u^{15} (xy^2) = M,\; (m_P)$$ Planck mass


 * $$u^{17} (xy^2) = V,\; (c)$$ speed of light


 * $$u^{19} (xy^3) = ML^2/T,\; (h)$$ Planck constant


 * $$u^{27} (x^2y^3) = \frac{M^{3/2}\sqrt{T}}{L^{3/2}} = 1/AT,\;(e)$$ elementary charge


 * $$u^{29} (x^2y^4) = \frac{M^{5/2}\sqrt{T}}{\sqrt{L}} = ML/AT,\; (k_B)$$ Boltzmann's constant


 * $$u^{30} (x^2 y^3) = 1/T,\; (1/t_p)$$ Planck time

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


 * $$v = 11843707.9...$$


 * $$r = .712562514... $$

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


 * $$Q = 2\pi\Omega \frac{v}{r^2},\; unit = u$$


 * $$i = \frac{1}{2\pi {(2\pi \Omega)}^{15}},\; unit = 1$$


 * $$j = \frac{r^{17}}{v^8},\; unit = 1$$

Gives


 * $$A = Q^3 (\frac{2^3}{\alpha}) = \frac{2^6 \pi^3 \Omega^3}{\alpha}\frac{v^3}{r^6},\; u^3$$


 * $$G = \frac{Q^6}{2^3 \pi^2} (j) = 2^3 \pi^4 \Omega^6 \frac{r^5}{v^2},\; u^6$$


 * $$L^{-1} = 4\pi Q^{13} (ij) = \frac{1}{2\pi^2 \Omega^2} \frac{v^5}{r^9},\; u^{13}$$


 * $$M = 2\pi Q^{15} (ij^2) = \frac{r^4}{v},\; u^{15}$$


 * $$P = Q^{16} (ij^2) = \Omega r^2,\; u^{16}$$


 * $$V = Q^{17} (ij^2) = 2\pi \Omega^2 v,\; u^{17}$$


 * $$h = \pi Q^{19} (ij^3) = 8\pi^4 \Omega^4 \frac{r^{13}}{v^5},\; u^{19}$$


 * $$e^{-1} = \frac{\alpha \pi Q^{27} (i^2j^3)}{4} = \frac{\alpha}{128\pi^4 \Omega^3} \frac{v^3}{r^{3}},\; u^{27}

$$


 * $$k_B = \frac{\alpha \pi^2 Q^{29}(i^2j^4)}{4} = \frac{\alpha}{32 \pi \Omega} \frac{r^{10}}{v^3},\; u^{29}$$


 * $$T^{-1} = 2\pi Q^{30} (i^2 j^3) = \frac{1}{2\pi}\frac{v^6}{r^9},\; u^{30}$$

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

Conclusion
In the Trialogue on the number of fundamental constants 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.