# User:MarianGheorgheWiki

### Planck units and Schwarzschild units

Planck units and Schwarzschild units from Schwarzschild radius and $\kappa$ - Einstein's costant.

Gravitational Constant from Stefan-Boltzmann Law and Planck Units with the Introduce of Schwarzschild Units.

Here the most importants physicals constants used for Plack units tables:

Base Planck units in MKSI:

Table 1: Dimensional universal physical constants normalized with Planck units
Constant Symbol Dimension Value 2019 (SI units)
Speed of light in vacuum

Velocità della Luce nel vuoto

c L T−1 299 792 458 m/s  (exact by definition of metre)
Gravitational constant G L3 M−1 T−2 6.674 30 (15) × 10−11 m3kg−1s−2 
Reduced Planck constant

Costante di Planckridotta

$\hbar ={\frac {h}{2\pi }}$ where h is the Planck constant L2 M T−1 1.054 571 817... × 10−34 Js  (exact by definition of the kilogram since 20 May 2019)
Vacuum Permeability $\mu _{0}={\frac {1}{\varepsilon _{0}c^{2}}}\approx 4\pi \times {10}^{-7}$ L M Q−2 1.256 637 062 12... × 10−6 N/A2  or Tm/A or H/m
Coulomb Magnetic constant

Costante Magnetica di Coulomb

$k_{m}={\frac {4\pi }{\mu _{0}}}={\frac {c^{2}}{{k}_{e}}}={4\pi {\varepsilon }_{0}c^{2}}$ L−1 M−1 Q2 9.999 999 994 5 (85) × 106 m/H  or A2/N or A/(Tm) or Am/Wb

= 1/1.000 000 000 55 (15) × 107 H/m  or N/A2 or Tm/A

Vacuum Permittivity $\varepsilon _{0}={\frac {1}{{\mu }_{0}c^{2}}}$ L−3 M−1 T2 Q2 8.854 187 812 8 (13) × 10−12 F/m  or N/V2

(exact by definitions of ampere and metre until 20 May 2019)

Coulomb constant $k_{e}={\frac {1}{4\pi {{\varepsilon }_{0}}}}$ where ε0 is the permittivity of free space

also as know as Elastivity

L3 M T−2 Q−2 8.987 551 787 368 176 4 × 109 kgm3s−4A−2  or V2/N or m/F or H⋅m/s2

(exact by definitions of ampere and metre until 20 May 2019)

Elementary Charge e Q 1.602 176 634 × 10−19 C  or A⋅s or J/V
Magnetic Charge $g_{m}={\frac {h}{{\mu }_{0}e}}={\frac {2\pi \,\hbar }{{\mu }_{0}e}}={\frac {e\,c}{2{\,\alpha }}}$ L T−1 Q 3.291 059 782 962 960... × 10−9 A⋅m 
Fine Structure Constant α or

1/α, which is approximately 1/137

Dimensionless 0.007 297 352 569 3 (11) 

1/137.035 999 084 (21)

Boltzmann constant kB L2 M T −2 Θ−1 1.380 649 × 10−34 J/K 

(exact by definition of the kelvin since 20 May 2019)

Stefan–Boltzmann law $\sigma ={\frac {{\pi }^{2}{k}_{B}^{4}}{60\,{\hbar }^{3}{c}^{2}}}={\frac {{2\pi }^{5}{k}_{B}^{4}}{15\,{h}^{3}{c}^{2}}}$ M T−3 Θ−4 5.670 374 419... × 10−8 W/m2K−4 

Key: L = length, M = mass, T = time, Q = electric charge, Θ = Temperature.

And so on in Planck Units:

Table 2: Base Planck units
Name Dimension Expression Value 2019 (SI units)
Planck Length Length (L) $l_{\text{P}}={\sqrt {\frac {\hbar \,G}{c^{3}}}}$ 1.616 255 (18) × 10−35 m
Planck Mass Mass (M) $m_{\text{P}}={\sqrt {\frac {\hbar \,c}{G}}}$ 2.176 434 (24) × 10−8 kg
Planck Time Time (T) $t_{\text{P}}={\frac {l_{\text{P}}}{c}}={\frac {\hbar }{m_{\text{P}}c^{2}}}={\sqrt {\frac {\hbar \,G}{c^{5}}}}$ 5.391 245 (60) × 10−44 s
Planck Charge Electric charge (Q) $q_{\text{P}}={\sqrt {4\pi \varepsilon _{0}\hbar \,c}}={\frac {e}{\sqrt {\alpha }}}$ 1.875 545 956 × 10−18(41) C
Planck Temperature Temperature (Θ) $T_{\text{P}}={\frac {m_{\text{P}}c^{2}}{k_{\text{B}}}}={\sqrt {\frac {\hbar \,c^{5}}{G\,k_{\text{B}}^{2}}}}$ 1.416 784 (16) × 1032 K

Now we see the Schwarzschild Units or Einstein's Constant or simple Planck Units by reference to mass, M.

Table 3: Base Schwarzschild units
Name Dimension Expression Value 2019 approx
Schwarzschild Gravitational Coupling Constant (M−2) $\alpha _{\mathrm {r_{s}} }={\frac {G\,m_{\mathrm {r_{s}} }^{2}}{\hbar \,c}}=\left({\frac {m_{\mathrm {r_{s}} }}{m_{\mathrm {P} }}}\right)^{2}={\frac {1}{m_{\mathrm {P} }^{2}}}={\frac {G}{\hbar \,c}}$ 2.111 100 × 10–15 kg−2
Schwarzschild Length Gravitational Length (LM−1) ${{l}_{{\text{r}}_{\text{s}}}}={\frac {{l}_{P}}{{m}_{P}}}={\sqrt {{\frac {\hbar \,G}{{c}^{3}}}{\frac {G}{\hbar \,c}}}}={\sqrt {\frac {{{\alpha }_{{\text{r}}_{\text{s}}}}\hbar \,G}{{c}^{3}}}}={\frac {{r}_{s}}{2}}={\frac {G}{{c}^{2}}}$ 7.426 160 × 10–28 m·kg−1 

rs = 1.485 232 × 10–27  m·kg−1

Schwarzschild Time Gravitational Time (M−1T) ${{t}_{{\text{r}}_{\text{s}}}}={\frac {{l}_{{\text{r}}_{\text{s}}}}{c}}={\frac {{t}_{P}}{{m}_{P}}}={\sqrt {{\frac {\hbar \,G}{{c}^{5}}}{\frac {G}{\hbar \,c}}}}={\sqrt {\frac {{{\alpha }_{{\text{r}}_{\text{s}}}}\hbar \,G}{{c}^{5}}}}={\frac {{r}_{s}}{2\,c}}={\frac {G}{{c}^{3}}}$ 2.477 100 × 10–36 s·kg−1
Schwarzschild Mass Gravitational Mass (unknown units nats?) ${{m}_{{\text{r}}_{\text{s}}}}={\frac {{m}_{\text{P}}}{{m}_{\text{P}}}}={\frac {{l}_{{\text{r}}_{\text{s}}}}{{l}_{{\text{r}}_{\text{s}}}}}={\frac {G}{{c}^{2}}}{\frac {{c}^{2}}{G}}={\sqrt {{\alpha }_{{\text{r}}_{\text{s}}}}}\,{{m}_{P}}={\sqrt {\frac {{{\alpha }_{{\text{r}}_{\text{s}}}}\hbar \,c}{G}}}$ 1
Schwarzschild Energy Gravitational Potential (L2T−2) ${{E}_{{\text{r}}_{\text{s}}}}={{m}_{{\text{r}}_{\text{s}}}}{{c}^{2}}={\sqrt {{\alpha }_{{\text{r}}_{\text{s}}}}}\,{{E}_{P}}={\sqrt {\frac {{{\alpha }_{{\text{r}}_{\text{s}}}}\hbar \,{{c}^{5}}}{G}}}={{\Phi }_{G}}={{c}^{2}}$ 8.987 551 787 368 176 4 × 1016 J·kg−1
Schwarzschild Charge Gravitational Electric Charge (M−1Q) ${{q}_{{\text{r}}_{\text{s}}}}={{q}_{\text{P}}}{\sqrt {{\alpha }_{{\text{r}}_{\text{s}}}}}={\frac {{q}_{P}}{{m}_{\text{P}}}}={\sqrt {{\frac {4\pi {}}{{\mu }_{0}}}{l}_{{\text{r}}_{\text{s}}}}}={\sqrt {4\pi {{\varepsilon }_{0}}G}}$ 8.617 517 × 10–11 C·kg−1 (Hz/T) or K/N
Schwarzschild Monopole Gravitational Magnetic Charge (LT−1M−1Q) $q_{{\text{r}}_{\text{s}}}^{m}={{q}_{{\text{r}}_{\text{s}}}}c={\frac {{{q}_{P}}c}{{m}_{P}}}={\sqrt {4\pi {{\varepsilon }_{0}}{G\,{c}^{2}}}}={\sqrt {{\frac {4\pi }{{\mu }_{0}}}G}}$ 0.025 834 A·m·kg−1 (a/T)
Schwarzschild Temperature Gravitational Temperature (MΘ) ${{T}_{{\text{r}}_{\text{s}}}}={\frac {{C}_{2}}{{l}_{{\text{r}}_{\text{s}}}}}={\frac {h\,c}{{{k}_{B}}{{l}_{{\text{r}}_{\text{s}}}}}}={\frac {2\pi \,{T}_{P}}{\sqrt {{\alpha }_{{\text{r}}_{\text{s}}}}}}={\sqrt {\frac {4{{\pi }^{2}}\hbar \,{{c}^{5}}}{{{\alpha }_{{\text{r}}_{\text{s}}}}Gk_{B}^{2}}}}={\frac {h\,{{c}^{3}}}{G{{k}_{B}}}}$ 1.937 443 × 1025 K·kg
Schwarzschild Entropy Gravitational Entropy ( L2M−1 T−2 Θ−1) ${{S}_{{\text{r}}_{\text{s}}}}={\frac {{{k}_{B}}r_{\text{s}}^{2}}{4l_{P}^{2}}}={\frac {{{k}_{B}}l_{{\text{r}}_{\text{s}}}^{2}}{l_{P}^{2}}}={\frac {{k}_{B}}{m_{P}^{2}}}={\frac {{{k}_{B}}{{l}_{{\text{r}}_{\text{s}}}}{{E}_{{\text{r}}_{\text{s}}}}}{\hbar \,c}}={\frac {{{k}_{B}}{{l}_{{\text{r}}_{\text{s}}}}{{c}^{2}}}{\hbar \,c}}={\frac {G\,{{k}_{B}}}{\hbar \,c}}={{\alpha }_{{\text{r}}_{\text{s}}}}{{k}_{B}}$ 2.914 688 × 10−8 J/K kg−2

11Nov2018_04:42AM Italy. 28June2019_16:31PM Italy. The relation between properties of mass and their associated physical constants. Every massive object is believed to exhibit all five properties. However, due to extremely large or extremely small constants, it is generally impossible to verify more than two or three properties for any object. The Schwarzschild radius (rs) represents the ability of mass to cause curvature in space and time. The standard gravitational parameter (μ) represents the ability of a massive body to exert Newtonian gravitational forces on other bodies. Inertial mass (m) represents the Newtonian response of mass to forces. Rest energy (E0) represents the ability of mass to be converted into other forms of energy. The Compton wavelength (λ) represents the quantum response of mass to local geometry.

Now we can use the Schwarzschild Units has use it on Schwarzschild Radius with any give Mass (M),

to calculate the proper Units of any Black Holes proprieties:

The Schwarzschild radius is given as:

$r_{s}={\frac {2GM}{c^{2}}}$ So The Schwarzschild Length is given as:
${{l}_{{\text{r}}_{\text{s}}}}\equiv {\frac {{r}_{s}}{2}}={\frac {G}{{c}^{2}}}M$ Such as the others metric units of Schwarzschild Units:

${{t}_{{\text{r}}_{\text{s}}}}\equiv {\frac {{r}_{s}}{2c}}={\frac {G}{{c}^{3}}}M$ We can obtain the Time of the any given Mass object as a Black Holes, only for Black Holes because depends of Speed of Lights (c) as velocity change it in others normals objects has Mass.

The Schwarzschild Energy is the famous Einstein's formula E=mc2 of Energy conversion by Mass.

${{E}_{{\text{r}}_{\text{s}}}}\equiv {{\Phi }_{G}}=M{{c}^{2}}$ This came from Units conversions of Schwarzschid Units in MKSI, we need to took any unit and normal and adding on it or divide it per the kg (Mass) units as showing in Schwarzschild radius. So the key is to use it for all others unknown units. The kg is like a phantom units, invisible in normals units but visible in Gravitational units. Is like a switch unit. the Schwarzschild Units is more like it to be Planck Units with Planck Mass aside it. As told in Schwarzschild radius page.

#### Schwarzschild radius for Planck mass

For the Planck mass $m_{\rm {P}}={\sqrt {\hbar c/G}}$ , the Schwarzschild radius $r_{\rm {S}}=2l_{\rm {P}}$ and the Compton wavelength $\lambda _{\rm {C}}=2\pi l_{\rm {P}}$ are of the same order as the Planck length $l_{\rm {P}}={\sqrt {\hbar G/c^{3}}}$ ."

Planck Units Removed from Wiki 2018Nov8_5AM

Image on: Sun 3 February 2019, 17:10:53. Derived Planck units approximates in $\pi$ number

## Derived Planck units

Table 3: Derived Planck Units from 2019 CODATA
Name Dimension Expression Approximate SI equivalent
Planck Area Area (L2) $l_{\text{P}}^{2}={\frac {\hbar \,G}{c^{3}}}$ 2.612 280 × 10−70 m2
Planck Volume Volume (L3) $l_{\text{P}}^{3}={{\left({\frac {\hbar \,G}{{c}^{3}}}\right)}^{\frac {3}{2}}}={\sqrt {\frac {{{\hbar }^{3}}{{G}^{3}}}{{c}^{9}}}}$ 4.222 111 × 10−105 m3
Planck Momentum Momentum (LMT−1) $m_{\text{P}}c={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar \,c^{3}}{G}}}$ 6.524 786 kgm/s
Planck Energy Energy (L2MT−2) $E_{\text{P}}=m_{\text{P}}c^{2}={\frac {\hbar }{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{G}}}$ 1.956 082 × 109 J
Planck Force Force (LMT−2) $F_{\text{P}}={\frac {E_{\text{P}}}{l_{\text{P}}}}={\frac {\hbar }{l_{\text{P}}t_{\text{P}}}}={\frac {c^{4}}{G}}$ 1.210 256 × 1044 N
Planck Power Power (L2MT−3) $P_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {\hbar }{t_{\text{P}}^{2}}}={\frac {c^{5}}{G}}$ 3.628 255 × 1052 W
Planck Intensity Intensity (MT−3) $I_{\text{P}}^{w}=\rho _{\text{P}}^{E}c={\frac {P_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {c^{8}}{\hbar G^{2}}}$ 1.388 923 × 10122 W/m2
Planck Density Density (L−3M) $\rho _{\text{P}}={\frac {m_{\text{P}}}{l_{\text{P}}^{3}}}={\frac {\hbar t_{\text{P}}}{l_{\text{P}}^{5}}}={\frac {c^{5}}{\hbar G^{2}}}$ 5.154 849 × 1096 kg/m3
Planck Energy Density Energy Density (L−1MT−2) $\rho _{\text{P}}^{E}={\frac {E_{\text{P}}}{l_{\text{P}}^{3}}}={\frac {c^{7}}{\hbar G^{2}}}$ 4.632 947 × 10113 J/m3
Planck Pressure Pressure (L−1MT−2) $p_{\text{P}}={\frac {F_{\text{P}}}{l_{\text{P}}^{2}}}={\frac {\hbar }{l_{\text{P}}^{3}t_{\text{P}}}}={\frac {c^{7}}{\hbar G^{2}}}$ 4.632 947 × 10113 Pa
Planck Angular Frequency Angular Frequency (T−1) $\omega _{\text{P}}={\frac {1}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{\hbar G}}}$ 1.854 859 × 1043 rad/s
Planck Current Electric Current (T−1Q) $I_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {4\pi \varepsilon _{0}c^{6}}{G}}}$ 3.478 873 × 1025 A
Planck voltage Voltage (L2MT−2Q−1) $V_{\text{P}}={\frac {E_{\text{P}}}{q_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}t_{\text{P}}}}={\sqrt {\frac {c^{4}}{4\pi \varepsilon _{0}G}}}$ 1.042 940 × 1027 V
Planck Impedance Resistance (L2MT−1Q−2) $Z_{\text{P}}={\frac {V_{\text{P}}}{I_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}^{2}}}={\frac {1}{4\pi \varepsilon _{0}c}}={\frac {Z_{0}}{4\pi }}$ 29.979 245 8 Ω
Planck Resistivity Resistivity (L3MT−1Q−2) $Z_{P}^{\rho }={\frac {{{V}_{\text{P}}}{{l}_{\text{P}}}}{{I}_{P}}}={\frac {\hbar {{l}_{\text{P}}}}{q_{P}^{2}}}={\frac {\sqrt {t_{P}}}{4\pi {\varepsilon _{0}}}}={\sqrt {\frac {\hbar G}{16{{\pi }^{2}}\varepsilon _{0}^{2}{{c}^{5}}}}}$ 4.845 411 × 10−34 Ω·m
Planck Electric Flux Electric Flux (L3MT−2Q) $\phi _{P}^{E}={{V}_{\text{P}}}{{l}_{\text{P}}}={\frac {\hbar {{l}_{\text{P}}}}{{{t}_{P}}{{q}_{\text{P}}}}}={\sqrt {\frac {\hbar c}{4\pi {{\varepsilon }_{0}}}}}$ 1.685 657 × 10−8 V·m
Planck Electric Field Strength Electric Field Strength (LMT−2Q) ${\bf {E}}_{P}={\frac {{V}_{\text{P}}}{{l}_{\text{P}}}}={\frac {{F}_{P}}{{q}_{\text{P}}}}={\sqrt {\frac {p_{P}}{4\pi \varepsilon _{0}}}}={\frac {\hbar }{{{t}_{P}}{{q}_{\text{P}}}{{l}_{\text{P}}}}}={\sqrt {\frac {{c}^{7}}{4\pi {{\varepsilon }_{0}}\hbar {{G}^{2}}}}}$ 6.452 817 × 1061 V/m
Planck Magnetic Inductance Magnetic Induction (MT−1Q−1) ${\bf {B}}_{\text{P}}={\frac {{\bf {E}}_{P}}{c}}={\frac {F_{\text{P}}}{l_{\text{P}}I_{\text{P}}}}={\sqrt {\frac {\rho _{P}}{4\pi \varepsilon _{0}}}}={\frac {\hbar }{q_{\text{P}}l_{\text{P}}^{2}}}={\sqrt {\frac {c^{5}}{4\pi \varepsilon _{0}\hbar G^{2}}}}$ 2.152 428 × 1053 T
Planck Magnetic Flux Magnetic Flux (L2MT−1Q−1) $\Phi _{\text{P}}={\frac {E_{\text{P}}}{I_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}}}={\sqrt {\frac {\hbar }{4\pi \varepsilon _{0}c}}}$ 5.622 746 × 10−17 Wb
Planck Magnetic Charge Magnetic Charge (LT−1Q) $q_{P}^{m}=q_{\text{P}}c={\frac {F_{\text{P}}}{\bf {B_{\text{P}}}}}={\frac {4\pi }{\mu _{0}}}\Phi _{\text{P}}={\sqrt {4\pi {{\varepsilon }_{0}}\hbar {{c}^{3}}}}$ 5.622 746 × 10−10 A·m
Planck Magnetic Potential Magnetic Potential (LMT−1Q−1) ${{\bf {A}}_{P}^{\phi }}={\frac {{E}_{P}}{q_{P}^{m}}}={{\bf {B}}_{\text{P}}}{{l}_{P}}={\frac {\hbar }{{{q}_{\text{P}}}{{l}_{P}}}}={\sqrt {\frac {{c}^{2}}{4\pi {{\varepsilon }_{0}}G}}}$ 3.478 873 × 1018 T·m or Wb/m
Planck's Verdet Costant Optical (L−1M−1TQ) ${{V}_{P}^{\theta }}={\frac {rad}{{\bf {A}}_{P}^{\phi }}}={\frac {{q}_{P}^{m}}{2\pi E_{P}}}={\frac {1}{2\pi {\bf {B}}_{P}{l}_{P}}}={\frac {{{q}_{\text{P}}}{{l}_{P}}}{2\pi \hbar }}={\sqrt {\frac {{{\varepsilon }_{0}}G}{\pi {c}^{2}}}}$ 4.574 900 × 1020 rad/T·m
Planck Magnetic Dipole Magnetic Dipole Moment

(L2T−1Q)

$\mu _{P}^{d}=q_{P}^{m}{{l}_{P}}={{I}_{P}}{{l}_{P}}^{2}={\sqrt {4\pi {{\varepsilon }_{0}}{{\hbar }^{2}}G}}$ 9.087 791 × 10−45 A·m2
Planck Magnetic Displacement Magnetic Field Strength

(L−1T−1Q)

${{\bf {H}}_{\text{P}}}={\frac {{I}_{P}}{{l}_{\text{P}}}}={\frac {{q}_{\text{P}}}{{{t}_{P}}{{l}_{P}}}}={\sqrt {\frac {4\pi {{\varepsilon }_{0}}{{c}^{9}}}{\hbar {{G}^{2}}}}}$ 2.152 428 × 1060 A/m
Planck Current Density Current Density (L−2T−1Q) ${{\bf {J}}_{P}}={\frac {{I}_{P}}{{{l}_{\text{P}}}^{2}}}={\frac {{q}_{\text{P}}}{{{t}_{P}}{{l}_{P}}^{2}}}={\sqrt {\frac {4\pi {{\varepsilon }_{0}}{{c}^{12}}}{{{\hbar }^{2}}{{G}^{3}}}}}$ 1.331 738 × 1095 A/m2
Planck Electrical Inductance Inductance (L2MQ−2) $L_{\text{P}}={\frac {E_{\text{P}}}{I_{\text{P}}^{2}}}={\frac {m_{\text{P}}l_{\text{P}}^{2}}{q_{\text{P}}}}={\frac {\hbar }{{{q}_{\text{P}}}{{I}_{P}}}}={\sqrt {\frac {G\hbar }{16\pi ^{2}\varepsilon _{0}^{2}c^{7}}}}$ 1.616 255 (18) × 10−42 H
Planck Permeability Permeability (LMQ−2) ${{\mu }_{\text{P}}}={\frac {{{V}_{\text{P}}}{{t}_{\text{P}}}}{{{I}_{P}}{{l}_{P}}}}={\frac {\hbar }{{{q}_{\text{P}}}{{I}_{P}}{{l}_{P}}}}={\frac {{k}_{e}}{{c}^{2}}}={\frac {1}{4\pi {{\varepsilon }_{0}}{{c}^{2}}}}$ 1.000 000 000 55 × 10−7  H/m
Planck Electric Dipole Electric Dipole Moment (LQ) ${{d}_{P}}={{q}_{P}}{{l}_{P}}={\sqrt {\frac {4\pi {{\varepsilon }_{0}}{{\hbar }^{2}}G}{{c}^{2}}}}$ 3.031 361 × 10−53 C·m
Planck Electric Induction Electric Displacement Field (L−2Q) ${{\bf {D}}_{P}}={\frac {{q}_{\text{P}}}{l_{P}^{2}}}={\sqrt {{4\pi \varepsilon _{0}}\,{p_{P}}}}={\sqrt {\frac {4\pi {{\varepsilon }_{0}}{{c}^{7}}}{\hbar {{G}^{2}}}}}$ 7.179 727 × 1051 C/m2
Planck Capacitance Capacitance (L−2M−1T2Q2) ${{C}_{\text{P}}}={\frac {{q}_{\text{P}}}{{V}_{\text{P}}}}={\frac {{{t}_{P}}{{q}_{\text{P}}}^{2}}{\hbar }}={\frac {{l}_{P}}{{k}_{e}}}={\sqrt {\frac {16{{\pi }^{2}}\varepsilon _{0}^{2}\hbar G}{{c}^{3}}}}$ 1.798 326 × 10−45 F
Planck Permittivity Permittivity (L−3M−1T2Q2) ${{\varepsilon }_{\text{P}}}={\frac {{q}_{\text{P}}}{{{V}_{\text{P}}}{{l}_{P}}}}={\frac {{{t}_{P}}{{q}_{\text{P}}}^{2}}{\hbar {{l}_{\text{P}}}}}={\frac {1}{{k}_{e}}}=4\pi {{\varepsilon }_{0}}$ 1.112 650 055 × 10−10 F/m
Planck Conductance Conductance (L−2M−1TQ2) ${{G}_{P}}={\frac {{I}_{P}}{{V}_{\text{P}}}}={\frac {q_{P}^{2}}{\hbar }}=4\pi {{\varepsilon }_{0}}c={\frac {4\pi }{{Z}_{0}}}$ 0.033 356 S or Ω−1
Planck Electric Conductivity Conductivity (L−3M−1TQ2) ${{\sigma }_{P}}={\frac {{G}_{P}}{{l}_{P}}}={\frac {{I}_{P}}{{{V}_{\text{P}}}{{l}_{\text{P}}}}}={\frac {{\omega }_{P}}{{k}_{e}}}={\frac {q_{P}^{2}}{\hbar {{l}_{\text{P}}}}}={\sqrt {\frac {16{{\pi }^{2}}\varepsilon _{0}^{2}{{c}^{5}}}{\hbar G}}}$ 2.063 809 × 1033 S/m
Planck Volumetric Flow Rate Volumetric Flow Rate (L3T−1) $Q_{\text{P}}=l_{\text{P}}^{2}c={\frac {l_{\text{P}}^{3}}{t_{\text{P}}}}={\frac {\hbar G}{c^{2}}}$ 7.831 419 × 10−62 m3/s
Planck Viscosity Dynamic Viscosity (L−1MT−1) $\eta _{\text{P}}=p_{\text{P}}t_{\text{P}}={\sqrt {\frac {c^{9}}{\hbar G^{3}}}}$ 2.497 736 × 1070 Pas
Planck Acceleration Acceleration (LT−2) $a_{\text{P}}={\frac {c}{t_{\text{P}}}}={\frac {4\pi }{\mu _{0}\,C_{P}}}={\sqrt {\frac {c^{7}}{\hbar G}}}$ 5.560 726 × 1051 m/s2
Planck Monopole Current Magnetic Current (LT−2Q) $I_{P}^{m}={{I}_{P}}c={{a}_{P}}{{q}_{P}}={\frac {q_{P}^{m}}{{t}_{P}}}={\sqrt {\frac {4\pi {{\varepsilon }_{0}}{{c}^{8}}}{G}}}$ 1.042 940 × 1034 Ams1 or W/T·m
Planck Temperature over 2 π Temperature (Θ) $T_{P}^{2\pi }={\frac {{C}_{2}}{{l}_{P}}}={\frac {hc}{{k}_{B}{l}_{P}}}={\frac {2\pi {E}_{P}}{{k}_{B}}}\equiv {\sqrt {\alpha }}{I}_{P}^{m}$ 8.901 917 × 1032 K
Planck Entropy Entropy ( L2M T−2Θ−1) ${{S}_{P}}={\frac {E_{P}}{T_{P}}}={\sqrt {k_{B}^{2}}}={{k}_{B}}$ 1.380 649 × 10−23 J/K
Planck Entropy over Fine Structure Constant Entropy ( L2M T−2Θ−1) ${{S}_{P}^{\alpha }}={\frac {{\sqrt {\alpha }}\,E_{P}}{T_{P}^{2\pi }}}={\frac {{\sqrt {\alpha }}\,{k}_{B}}{2\pi }}\cong {\frac {E_{P}}{I_{P}c}}={\frac {\mu _{0}q_{P}}{4\pi }}={\frac {\hbar }{q_{P}c}}={\sqrt {\frac {\hbar }{4\pi \varepsilon _{0}c^{3}}}}$ 1.877 094 × 10−25 J/K

≈ 1.875 546 × 10−25

kgm/C or T·m/Hz

Planck's Bekenstein Bound Information Theory $I_{P}^{\text{bit}}={\frac {2\pi ~{{l}_{P}}{{E}_{P}}}{\hbar ~c~{\text{Log}}\left[2\right]}}={\frac {2\pi }{~{\text{Log}}\left[2\right]}}$ 9.064 720 ... bit

≈ 23.18 ≈ 1.133 Bytes

Planck's Stefan Law Constant of Proportionality (M T−3Θ−4) $\sigma _{P}={\frac {{P}_{P}}{{l}_{P}^{2}{T}_{P}^{4}}}={\frac {{k}_{B}^{4}}{{\hbar }^{3}{c}^{2}}}={\frac {{16}\pi ^{4}\hbar {c}^{2}}{C_{2}^{4}}}$ 3.447 174 × 10−8 W/m−2 K-4
Planck Locus Second Radation Constant (L Θ) $C_{2_{P}}={\frac {C_{2}}{\sqrt {\alpha }}}={\frac {hc}{{k}_{B}{\sqrt {\alpha }}}}={\frac {2\pi {E}_{P}{l}_{P}}{{k}_{B}{\sqrt {\alpha }}}}$ 0.168 427 K m
Planck Thermodynamic Beta  Negative Temperature (L2M−1T2) $\beta _{P}={\frac {1}{k_{B}T_{P}}}={\frac {1}{E_{P}}}={\frac {t_{\text{P}}}{\hbar }}={\sqrt {\frac {G}{\hbar c^{5}}}}$ 5.112 261 × 10−10 J1
Planck Heat Capacity Specific Heat Capacity $C_{{\text{mp}}_{P}}={\frac {S_{P}}{m_{P}}}={\frac {k_{B}}{m_{P}}}={\sqrt {\frac {G{k_{B}^{2}}}{\hbar \,c}}}$ 6.343 628 × 10−16 kg−1·K−1
Planck molar Heat Capacity Molar Heat Capacity $C_{{\text{np}}_{P}}={\frac {5\,S_{P}}{2\,{\text{mol}}}}={\frac {5\,k_{B}}{2\,R\,m_{P}}}={\frac {5\,k_{B}\,M_{u}}{2\,m_{P}}}$ 1.585 907 × 10−18 J·K−1·mol−1
Planck Heat Capacity volume costant Volume Molar Heat Capacity $C_{{\text{Vm}}_{P}}={\frac {3\,S_{P}}{2\,{\text{mol}}}}={\frac {3\,k_{B}}{2\,R\,m_{P}}}={\frac {3\,k_{B}\,M_{u}}{2\,m_{P}}}$ 9.515442 × 10−18 J·K−1·mol−1
Planck Heat Capacity Ratio Dimensionless $\gamma ={\frac {C_{{\text{mp}}P}}{C_{{\text{mV}}P}}}={\frac {{k_{B}}{l_{P}^{3}}}{{m_{P}}{k_{B}}}}\approx {\frac {1}{\rho _{P}}}$ 1.939 921 × 10−97
Planck Volumetric Heat Capacity Volumetric Heat Capacity $S_{{\text{V}}_{P}}={\frac {S_{P}}{l_{P}^{3}}}={\frac {k_{B}}{l_{P}}}={\sqrt {\frac {c^{3}}{\hbar \,G}}}^{3}{k_{B}}$ 3.270 044 × 1081 J·K−1·m−3
Planck Gravitational Gravitation (L3M−1T−2) $G={\frac {{{l}_{P}}^{3}}{{{m}_{P}}{{t}_{P}}^{2}}}={\frac {{{E}_{P}}{{l}_{P}}}{m_{P}^{2}}}={\frac {{{F}_{P}}{{l}_{P}^{2}}}{m_{P}^{2}}}={\frac {c^{4}}{F_{P}}}$ 6.674 30 (15) × 10−11 J·m kg−2

(L16T−16Q8)

$G_{\Theta }\cong {\frac {{{q}_{P}^{m8}}{{c}^{8}}}{32\pi ^{5}}}={\frac {{{q}_{P}^{8}}{{c}^{16}}}{32\pi ^{5}}}\cong {\frac {{{8}\pi ^{3}\hbar ^{8}}{{c}^{8}}}{{k}_{B}^{8}\alpha ^{4}}}$ 6.612 823 5 × 10−11 K8·m8≈ 6.656 619 5 × 10−11 W8·T8
Planck Coupling Constant Gravitational Coupling Constant $\alpha _{G_{P}}={\frac {{{m}_{P}}^{2}}{{{m}_{P}}^{2}}}={\frac {{{l}_{P}}^{2}}{{{l}_{P}}^{2}}}={\frac {{{t}_{P}}^{2}}{{{t}_{P}}^{2}}}={\frac {{{q}_{P}}^{2}}{{{q}_{P}}^{2}}}=...$ 1
Planck Action Action (L2MT−1) $\hbar ={{E}_{P}}{{t}_{P}}={{\alpha }_{{G}_{P}}}\hbar ={\sqrt {{\frac {\hbar c^{5}}{G}}{\frac {\hbar G}{c^{5}}}}}$ 1.054 571 817 ... × 10−34 J·s
Planck Units Dimensionless ${\sqrt {{\alpha }_{{G}_{P}}}}={\frac {{m}_{P}}{{m}_{P}}}={\frac {{l}_{P}}{{l}_{P}}}={\frac {{t}_{P}}{{t}_{P}}}={\frac {{q}_{P}}{{q}_{P}}}=...$ 1

Update 11 June 2019 Tuesday, 13:38. +1UTC _ Milan. Marian Gheorghe.

25 June 2019, 17:34. Rome +1UTC _ Milan.

28 June 2019, 19:06. Rome +1UTC _ Milan.

## Maxwell 's equation in Entropy

Electromagnetism as entropy view from Newton second law.

General Relativity as thermodynamics propriety from Boltzmann costant and so by Maxwell's equations in entropy relationship as permeability by charge.

from Newton's law interpretation:

• F is force.
• m is mass.
• a is acceleration.
• T is temperature.
• q is charge.
• V is voltage/.
• S is entropy.
• A is vector potential.
• B is magnetic induction.
• t is time.

General Relativity in entropic view:

• ${\bf {G_{\mu \upsilon }}}$ is Einstein's costant.
• ${\bf {T_{\mu \upsilon }}}$ is tensor energy-impulse.

To descrive Gravitational constant, G is:

• ħ is Planck constant.
• c is speed of light.
• $k_{B}$ is Boltzmann constat
• $\alpha$ is fine structure constant.

Permeability constant by speed of light sqrt  to get inverse Gyromagnetic ratio per Force. Units is Tesla sqrt second sqrt by Newton. or in entropic view is Newton by Kelvin^2. Or Entropy, S, per Second radiation constant or Kelvin metre.

Maxwell's equations in Thermodynamic as Entropy views. Nothing change the old Maxwell's equations just seen it from others prospettives angles.

## Prove of Gravitational Constant by Stefan-Boltzmann law and Planck units and Schwarzschild units

Gravitational constant by Stefan Boltzmann Law from Planck-Schwarzschild units. G from Planck Units and Schwarzschild units and relationship of Stefan law. is not easy to views this missing units of G. but if u can see the stean law of Planck units and Schwarzschild units, or simle yet again Planck units by Planck mass. we see the real deep missing Gravitational constant ratio and is missing MKS units.

Date: 12 Nov 2018, 08:26. Move from Wikipedia users to here, Is a Draft! Need to work out to clean it and set study on it.

Date: 12 Nov 2018, 09:05.

Date:13 June 2019. update back on work

Date: 14 June 2019, 01:01.

Date: 14 June 2019, 02:38.

Date: 28 June 2019, 16:50. Milan

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