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'''Planck force''' is the derived unit of [[force]] resulting from the definition of the base [[Planck units]] for time, length, and mass.  It is equal to the natural unit of [[momentum]] divided by the natural unit of time.
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


:<math>F_\text{P} = \frac{m_\text{P} c}{t_\text{P}} = \frac{c^4}{G} = 1.21027 \times 10^{44} \mbox{ N.}</math>
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


==Other derivations==
Registered users will be able to choose between the following three rendering modes:


The Planck force is also associated with the equivalence of gravitational potential energy and electromagnetic energy [http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/blahol.html#c2] and in this context it can be understood as the force that confines a self-gravitating mass to half its [[Schwarzschild radius]]:
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


:<math>F_\text{P} = \frac{G m^2}{r_\text{G}^2} </math>,
<!--'''PNG'''  (currently default in production)
:<math>r_\text{G} = \frac{r_\text{s}}{2} = \frac{G m}{c^2}.</math>,
:<math forcemathmode="png">E=mc^2</math>


where ''G'' is the [[gravitational constant]], ''c'' is the [[speed of light]], ''m'' is any mass and ''r''<sub>G</sub> is half the Schwarzschild radius, ''r''<sub>s</sub>, of the given mass.
'''source'''
Since the dimension of force is also a ratio of energy per length, the Planck force can be calculated as energy divided by half the Schwarzschild radius:
:<math forcemathmode="source">E=mc^2</math> -->


:<math>F_\text{P} = \frac{m c^2}{\frac{Gm}{c^2}}=\frac{c^4}{G}.</math>
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


As mentioned above, Planck force has a unique association with the [[Planck mass]]. This unique association also manifests itself when force is calculated as any energy divided by the reduced [[Compton wavelength]] (reduced by 2π) of that same energy:
==Demos==
:<math>F = \frac{m c^2}{\frac{\hbar}{m c}} = \frac{m^2 c^3}{\hbar}.</math>


Here the force is different for every mass (for the electron, for example, the force is responsible for the [[Schwinger effect]] (see page 3 here [http://prst-ab.aps.org/pdf/PRSTAB/v5/i3/e031301]). It is Planck force only for the Planck mass (approximately 2.18 &times; 10<sup>-8</sup>&nbsp;kg). This follows from the fact that the [[Planck length]] is a reduced Compton wavelength equal to half the Schwarzschild radius of the Planck mass:
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


:<math>\frac{\hbar}{m_\text{P} c} = \frac{G m_\text{P}}{c^2}</math>


which in turn follows from another relation of fundamental significance:
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


:<math>c \hbar = G m_\text{P}^2.</math>
==Test pages ==


==General relativity==
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


Planck force is often useful in scientific calculations as a ratio of electromagnetic energy per gravitational length. Thus for example it appears in the [[Einstein field equations]], describing the properties of a gravitational field surrounding any given mass:
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
:<math>G_{\mu\nu}=8\pi\frac{G}{c^4} T_{\mu\nu}</math>
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
where <math>G_{\mu\nu}</math> is the [[Einstein tensor]] and <math>T_{\mu\nu}</math> is the [[energy-momentum tensor]].
 
{{Planckunits}}
 
[[Category:Units of force]]
[[Category:Natural units|Force]]
 
[[ar:قوة بلانك]]
[[bs:Planckova sila]]
[[es:Fuerza de Planck]]
[[eo:Forto de Planck]]
[[fr:Force de Planck]]
[[ko:플랑크 힘]]
[[it:Forza di Planck]]
[[hu:Planck-erő]]
[[ja:プランク力]]
[[pl:Siła Plancka]]
[[pt:Força de Planck]]
[[ru:Планковская сила]]
[[sl:Planckova sila]]
[[fi:Planckin voima]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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