Quintessence (momentum)

Quintessence momentum is a hypothetical (mathematical) square root solution to Planck momentum, a derived Planck unit.

$Q = 1.019\;113\;431\;5836\; \sqrt{\frac{kg m}{s}} \;$

where:

Planck momentum = 2πQ2 

Planck mass $m_p = \frac{2 \pi Q^2}{c} \;$

Deriving the fundamental constants G, h, e, me, (α, c) in terms of Q, lp, (α, c)

Gravitation constant $G = \frac{l_p c^3}{2 \pi Q^2} \;$

Planck's constant h = 2πQ22πlp 

Elementary charge $e = \frac{16 l_p c^2}{\alpha Q^3} \;$

where:

  • lp is Planck length
  • c is the speed of light in a vacuum
  • α is the Fine structure constant

Coulomb

The Coulomb as a mathematical (SI) unit: $\frac{m^2}{kg s \sqrt{\frac{kg m}{s}}} \;$

The ampere then becomes: $A^2 = \frac{m^3}{kg^3 s^3} \;$

this gives:

Vacuum permeability $\mu_0 = \frac{\pi^2 \alpha Q^8}{32 l_p c^5} \;$ units $\frac{kg^4 s}{m^2} \;$

Vacuum permittivity $\epsilon_0 = \frac{32 l_p c^3}{\pi^2 \alpha Q^8} \;$ units $\frac{s}{kg^4} \;$

Coulomb's constant $k_e = \frac{\pi \alpha Q^8}{128 l_p c^3} \;$ units $\frac{kg^4}{s} \;$

Common formulas

$\alpha = \frac{2 h}{\mu_0 e^2 c} = {2}\; {2 \pi Q^2 2 \pi l_p}\; \frac{32 l_p c^5}{\pi^2 \alpha Q^8}\; \frac{\alpha^2 Q^6}{256 l_p^2 c^4}\; \frac{1}{c} \; = \alpha \;$

$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \;$ where ${\mu_0 \epsilon_0} = \frac{\pi^2 \alpha Q^8}{32 l_p c^5} \; \frac{32 l_p c^3}{\pi^2 \alpha Q^8} \; = \frac{1}{c^2}\;$

$R_\infty = \frac{m_e e^4 \mu_0^2 c^3}{8 h^3} = {m_e}\; \frac{65536 l_p^4 c^8}{\alpha^4 Q^{12}}\; \frac{\pi^4 \alpha^2 Q^{16}}{1024 l_p^2 c^{10}}\; {c^3}\; \frac{1}{8}\; \frac{1}{8 \pi^3 Q^6 8 \pi^3 l_p^3}\; = \frac{m_e}{4 \pi l_p \alpha^2 m_P} \;$

$E_n = {-}\frac{2 \pi^2 k_e^2 m_e e^4}{h^2 n^2} = {2 \pi^2}\; \frac{\pi^2 \alpha^2 Q^{16}}{16384 l_p^2 c^6}\; {m_e}\; \frac{65536 l_p^4 c^8}{\alpha^4 Q^{12}}\; \frac{1}{4 \pi^2 Q^4 4 \pi^2 l_p^2}\; = {-}\frac{m_e c^2}{2 \alpha^2 n^2} \;$

$q_p = \sqrt{4 \pi \epsilon_0 \hbar c} = \sqrt{4 \pi\; \frac{32 l_p c^3}{\pi^2 \alpha Q^8}\; {2 \pi Q^2 l_p}\; c} \; = \sqrt{\alpha}{e} \;$

$r_e = \frac{e^2}{4 \pi \epsilon_0 m_e c^2} = \frac{256 l_p^2 c^4}{\alpha^2 Q^6}\; \frac{1}{4 \pi}\; \frac{\pi^2 \alpha Q^8}{32 l_p c^3}\; \frac{1}{m_e c^2}\; = \frac{l_p m_P}{\alpha m_e} \;$

the ratio of the electrical to the gravitational forces between a proton and an electron:

$\frac{4 \pi \epsilon_0 G m_e m_p}{e^2} \; = {4 \pi} \; \frac{32 l_p c^3}{\pi^2 \alpha Q^8} \; \frac{l_p c^3}{2 \pi Q^2} \; {m_e m_p} \; \frac{\alpha^2 Q^6}{256 l_p^2 c^4}\; = \frac{\alpha m_e m_p}{m_P^2}\;$

where:

  • R is the Rydberg constant,
  • En refers to the Bohr model energy levels,
  • qp is Planck charge,
  • re is the Classical electron radius.

Electron

An electron depicted as a hypothetical (dimensionless) spherical Magnetic monopole (ampere-meter = elementary charge e x velocity c).

me = 2mP txge3  where $g_e = \frac{2 \pi^2}{3 \alpha e_x c_x} \;$ and $t_x = \frac{l_{px}}{c_x} \;$

where:

  • me is the rest mass of the electron.
  • tp is Planck time. $\frac{t_p}{t_x} = 1s \;$
  • $\frac{l_p}{l_{px}} = 1m \;$
  • $\frac{e}{e_x} = 1C \;$
  • $\frac{c}{c_x} = 1m/s \;$

Cross reference

The Rydberg constant incorporates the fundamental constants and is known precisely to 12 digits. The 2006 CODATA results:

R∞ = 10 973 731.568 527 (73)m−1

The Rydberg constant in terms of the derived fundamental constants

  • lp assigned the value 1.616 036 696 6729 e-35 m
  • α assigned the value 137.035 999 2539

$R_\infty = \frac{m_e e^4 \mu_0^2 c^3}{8 h^3} = 10\;973\;731.568\;509 \mathrm{m}^{-1}$

Background

Quintessence (charged) momentum occurs in mathematical (geometrical) entities (mathematical realism) in the mass domain as 2πQ2  (Planck momentum) or in the charge domain as αQ3 .

It was first proposed in the 2003 semi-technical publication; "Chess board universe (geometry of momentum)".

See also

  • Planck units
  • Natural units
  • Coulombs Law