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A '''Planck particle''', named after physicist [[Max Planck]], is a hypothetical particle defined as a tiny [[black hole]] whose [[Compton wavelength]] is equal to its [[Schwarzschild radius]].<ref>Michel M. Deza; Elena Deza. ''[http://books.google.com/books?id=LXEezzccwcoC Encyclopedia of Distances]''. Springer; 1 June 2009. ISBN 978-3-642-00233-5. p. [http://books.google.com/books?id=LXEezzccwcoC&pg=PA433 433].</ref> Its mass is thus approximately the Planck mass, and its Compton wavelength and Schwarzschild radius are about the Planck length.<ref>[http://www.springerlink.com/content/q525116713762240/ "Light element synthesis in Planck fireballs" - SpringerLink]</ref>  Planck particles are sometimes used as an exercise to define the Planck mass and Planck length.<ref>B. Roy Frieden; Robert A. Gatenby. ''[http://books.google.com/books?id=qw5ka5HezacC Exploratory data analysis using Fisher information]''. Springer; 2007. ISBN 978-1-84628-506-6. p. [http://books.google.com/books?id=qw5ka5HezacC&pg=PA163 163].</ref>  They play a role in some models of the evolution of the universe during the [[Planck epoch]].<ref>{{citation|first=Edward Robert |last=Harrison |
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url=http://books.google.com/books?id=-8PJbcA2lLoC |title=Cosmology: the science of the universe | publisher=Cambridge University Press | year=2000 | isbn=978-0-521-66148-5}} p. [http://books.google.com/books?id=–8PJbcA2lLoC&pg=PA424 424]</ref>
 
Compared for example to a [[proton]], the Planck particle would be extremely small (its radius being  equal to the [[Planck length]], which is about 10<sup>−20</sup> times the proton's radius) and heavy (the [[Planck mass]] being 10<sup>19</sup> times the proton's mass).{{sfn|Harrison|2000|p=[http://books.google.com/books?id=–8PJbcA2lLoC&pg=PA478 478]}}
 
It is thought that such a particle would vanish in [[Hawking radiation]].{{cn|date=March 2013}}
 
== Derivation ==
 
While opinions vary as to its proper definition, the most common definition of a Planck particle is a particle whose [[Compton wavelength]] is equal to its [[Schwarzschild radius]]. This sets the relationship:
 
: <math> \lambda = \frac{h}{m c} = \frac{2 G m}{c^2} </math>
 
Thus making the mass of such a particle:
 
: <math> m = \sqrt{\frac{h c}{2 G}} </math>
 
This mass will be <math> \sqrt{\pi } </math> times larger than the [[Planck mass]], making a Planck particle 1.772 times more massive than the Planck unit mass.
 
Its radius will be the Compton wavelength:
 
: <math> r = \frac{h}{m c} = \sqrt{\frac{2G h}{c^3}} </math>
 
== Dimensions ==
 
Using the above derivations we can substitute the universal constants ''h'', ''G'', and ''c'', and determine physical values for the particle's mass and radius. Assuming this radius represents a sphere of uniform density we can further determine the particle's volume and density.
 
{| class="wikitable"
|+Table 1: Physical dimensions of a Planck particle
! Parameter
! Dimension
! Value in [[International System of Units|SI]] units
|-
| Mass
| M
| {{val|3.85763|e=-8|u=kg}}
|-
| Radius
| L
| {{val|5.72947|e=-35|u=m}}
|-
| Volume
| L<sup>3</sup>
| {{val|7.87827|e=-103|u=m<sup>3</sup>}}
|-
| Density
| M L<sup>−3</sup>
| {{val|4.89655|e=94|u=kg m<sup>-3</sup>}}
|}
 
It should be noted that the above dimensions do not correspond to any known physical entity or material.
 
==See also==
* [[Micro black hole]]
* [[Planck units]]
* [[Max Planck]]
* [[Black hole electron]]
 
==References==
{{reflist}}
 
==External links==
* [http://adsabs.harvard.edu/full/1996A&A...313..703S "The quasi-steady state cosmology: analytical solutions of field equations and their relationship to observations" - Astrophysics Data Systems]
* [http://books.google.com/books?id=fKgQ9YpAcwMC&pg=PA266&lpg=PA266&dq=%22Planck+Particle%22&source=bl&ots=1dkoz0CNXK&sig=ulu3rt9u5GZ1lBl8HR-8rR0-Grk&hl=en&ei=NRCnS5T_B4ekswPdg4C9BA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CA4Q6AEwAzg8#v=onepage&q=%22Planck%20Particle%22&f=false "Mach's principle: from Newton's bucket to quantum gravity" - Google Books]
* [http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-12528.pdf "Mysteries of Mass: Some Contrarian Views From an Experimenter"]
* [http://cdsweb.cern.ch/record/876637 "The Gauge Hierarchy Problem and Planck Oscillators" - CERN Document Server]
* [http://maeresearch.ucsd.edu/~cgibson/Documents2007/PapersAList%20copy/A97_Gibson_FirstFossilTurb.pdf "The First Turbulence and First Fossil Turbulence"]
* [http://www.komac.re.kr/npet/new_proton/down/study-data/jhchang_lect4%28090324%29.pdf "Lecture on Nuclear Physics for Plasma Engineers"]
* [http://math.ucr.edu/home/baez/planck/node2.html The Planck Length]
 
{{DEFAULTSORT:Planck Particle}}
[[Category:Black holes]]
[[Category:Hypothetical elementary particles]]

Latest revision as of 03:48, 29 September 2014

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