Planck energy

Plankovsky energy is a physical constant numerically equal to the Planck mass times the square of the speed of light . In a Planck system of units, Planck energy is a unit of energy . Designated $E_{P}$ ${\ displaystyle E_ {P}}$ $E_ {P}$ .

E_{p}=m_{p}c^{2}={\sqrt {\frac {\hbar c^{5}}{G}}}\approx

{\ displaystyle E_ {p} = m_ {p} c ^ {2} = {\ sqrt {\ frac {\ hbar c ^ {5}} {G}}} \ approx}

E_ {p} = m_ {p} c ^ {2} = {\ sqrt {{\ frac {\ hbar c ^ {5}} {G}}}} \ approx

1,956⋅10 ⁹ J

\approx

{\ displaystyle \ approx}

\ approx

1.22⋅10 ²⁸ eV

\approx

{\ displaystyle \ approx}

\ approx

543.3 kWh

\approx

{\ displaystyle \ approx}

\ approx

4.6718⋅10 ⁸ cal .

For comparison, it exceeds by about eight orders of magnitude the maximum measured energy of cosmic rays and by about 6% the muzzle energy of the most powerful artillery gun in history - the 800 mm Dora railway cannon :

E_{Dora}={\frac {mv^{2}}{2}}\approx {\frac {7100*720^{2}}{2}}\approx

{\ displaystyle E_ {Dora} = {\ frac {mv ^ {2}} {2}} \ approx {\ frac {7100 * 720 ^ {2}} {2}} \ approx}

E _ {{Dora}} = {\ frac {mv ^ {2}} {2}} \ approx {\ frac {7100 * 720 ^ {2}} {2}} \ approx

1,840⋅10 ⁹ ( J )

In the Planck era , about 13.8 billion years ago, the substance of the Universe had Planck energy, Planck radius ( ^10–35 m), Planck temperature (10 ³² K) ^[1] and Planck density (~ 10 ⁹⁷ kg / m³).

Content

1 Connection of photon energy and gravitational signal delay
2 See also
3 notes
4 Literature
5 Links

The relationship of photon energy and gravitational signal delay

For a signal traveling around a point gravitational mass , the gravitational delay can be calculated using the following formula:

\Delta t=-{\frac {2GM}{c^{3}}}\ln(1-\mathbf {R} \cdot \mathbf {x} ).

{\ displaystyle \ Delta t = - {\ frac {2GM} {c ^ {3}}} \ ln (1- \ mathbf {R} \ cdot \ mathbf {x}).}

(one)

Here $\mathbf {R}$ ${\ displaystyle \ mathbf {R}}$ Is a unit vector directed from the observer to the source, and $\mathbf {x}$ ${\ displaystyle \ mathbf {x}}$ Is the unit vector directed from the observer to the gravitating point of mass M.

It follows that in order to cause a signal delay equal to a fixed and a priori specified time interval $\tau$ ${\ displaystyle \ tau}$ mass required

M=-{\frac {\tau c^{3}}{2ln(1-\mathbf {R} \cdot \mathbf {x} )G}}.

{\ displaystyle M = - {\ frac {\ tau c ^ {3}} {2ln (1- \ mathbf {R} \ cdot \ mathbf {x}) G}}.}

(2)

The energy equivalent to this mass is:

E_{1}(\tau )=-{\frac {\tau c^{5}}{2ln(1-\mathbf {R} \cdot \mathbf {x} )G}}.

{\ displaystyle E_ {1} (\ tau) = - {\ frac {\ tau c ^ {5}} {2ln (1- \ mathbf {R} \ cdot \ mathbf {x}) G}}.}

(3)

On the other hand, the quantum energy of EM radiation with a period $\tau$ ${\ displaystyle \ tau}$ is equal to

E_{2}(\tau )={\frac {h}{\tau }}={\frac {2\pi \hbar }{\tau }}.

{\ displaystyle E_ {2} (\ tau) = {\ frac {h} {\ tau}} = {\ frac {2 \ pi \ hbar} {\ tau}}.}

(four)

The product of these 2 energies defined by formulas (3) and (4) is equal to:

E_{1}(\tau )E_{2}(\tau )=-{\frac {\tau c^{5}}{2ln(1-\mathbf {R} \cdot \mathbf {x} )G}}{\frac {2\pi \hbar }{\tau }}=-{\frac {2\pi \hbar c^{5}}{2ln(1-\mathbf {R} \cdot \mathbf {x} )G}}=-{\frac {\pi \hbar c^{5}}{ln(1-\mathbf {R} \cdot \mathbf {x} )G}}=-{\frac {\pi E_{P}^{2}}{ln(1-\mathbf {R} \cdot \mathbf {x} )}}.

{\ displaystyle E_ {1} (\ tau) E_ {2} (\ tau) = - {\ frac {\ tau c ^ {5}} {2ln (1- \ mathbf {R} \ cdot \ mathbf {x} ) G}} {\ frac {2 \ pi \ hbar} {\ tau}} = - {\ frac {2 \ pi \ hbar c ^ {5}} {2ln (1- \ mathbf {R} \ cdot \ mathbf {x}) G}} = - {\ frac {\ pi \ hbar c ^ {5}} {ln (1- \ mathbf {R} \ cdot \ mathbf {x}) G}} = - {\ frac { \ pi E_ {P} ^ {2}} {ln (1- \ mathbf {R} \ cdot \ mathbf {x})}}.}

(5)

Thus, the product of the energy equivalent to the mass causing the delay is equal to $\tau$ ${\ displaystyle \ tau}$ , and photon energies with a period $\tau$ ${\ displaystyle \ tau}$ independent of $\tau$ ${\ displaystyle \ tau}$ and equal to the square of Planck energy up to a dimensionless coefficient: $-{\frac {\pi }{ln(1-\mathbf {R} \cdot \mathbf {x} )}}$ ${\ displaystyle - {\ frac {\ pi} {ln (1- \ mathbf {R} \ cdot \ mathbf {x})}}}$ .

Accordingly, the ratio of these 2 energies is equal to

{\frac {E_{1}(\tau )}{E_{2}(\tau )}}=-{\frac {\tau ^{2}c^{5}}{4G\pi ln(1-\mathbf {R} \cdot \mathbf {x} )\hbar }}=={\frac {\tau ^{2}}{4\pi ln(1-\mathbf {R} \cdot \mathbf {x} )t_{P}^{2}}}=-{\frac {1}{4\pi ln(1-\mathbf {R} \cdot \mathbf {x} )}}({\frac {\tau }{t_{P}}})^{2}.

{\ displaystyle {\ frac {E_ {1} (\ tau)} {E_ {2} (\ tau)}} = - {\ frac {\ tau ^ {2} c ^ {5}} {4G \ pi ln (1- \ mathbf {R} \ cdot \ mathbf {x}) \ hbar}} == {\ frac {\ tau ^ {2}} {4 \ pi ln (1- \ mathbf {R} \ cdot \ mathbf {x}) t_ {P} ^ {2}}} = - {\ frac {1} {4 \ pi ln (1- \ mathbf {R} \ cdot \ mathbf {x})}} ({\ frac { \ tau} {t_ {P}}}) ^ {2}.}

(6)

Where $t_{P}$ ${\ displaystyle t_ {P}}$ - Planck time .

Notes

↑ "God and the Multiverse." Chapter from Victor Stenger's Chaotic Inflation Book

Literature

Peter J. Mohr and Barry N. Taylor. CODATA recommended values of the fundamental physical constants: 2002 (eng) // Reviews of Modern Physics : journal. - January 2005. - Vol. 77 . - P. 1-107 .

Links

Lectures on General Astrophysics for. 1.5 Planck units

[1] "God and the Multiverse." Chapter from Victor Stenger's Chaotic Inflation Book