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# Planck particle

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.^{[1]} Its mass is thus approximately the Planck mass, and its Compton wavelength and Schwarzschild radius are about the Planck length.^{[2]} Planck particles are sometimes used as an exercise to define the Planck mass and Planck length.^{[3]} They play a role in some models of the evolution of the universe during the Planck epoch.^{[4]}

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^{−20} times the proton's radius) and heavy (the Planck mass being 10^{19} times the proton's mass).^{[5]}

It is thought that such a particle would vanish in Hawking radiation.

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:

\( \lambda = \frac{h}{m c} = \frac{2 G m}{c^2} \)

Thus making the mass of such a particle:

\( m = \sqrt{\frac{h c}{2 G}} \)

This mass will be \( \sqrt{\pi } \) 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:

\( r = \frac{h}{m c} = \sqrt{\frac{2G h}{c^3}} \)

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.

Parameter | Dimension | Value in SI units |
---|---|---|

Mass | M | 3.85763×10^{−8} kg |

Radius | L | 5.72947×10^{−35} m |

Volume | L^{3} |
7.87827×10^{−103} m^{3} |

Density | M L^{−3} |
4.89655×10^{94} kg m^{-3} |

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

^ Michel M. Deza; Elena Deza. Encyclopedia of Distances. Springer; 1 June 2009. ISBN 978-3-642-00233-5. p. 433.

^ "Light element synthesis in Planck fireballs" - SpringerLink

^ B. Roy Frieden; Robert A. Gatenby. Exploratory data analysis using Fisher information. Springer; 2007. ISBN 978-1-84628-506-6. p. 163.

^ Harrison, Edward Robert (2000), Cosmology: the science of the universe, Cambridge University Press, ISBN 978-0-521-66148-5 p. 424

^ Harrison 2000, p. 478.

External links

"The quasi-steady state cosmology: analytical solutions of field equations and their relationship to observations" - Astrophysics Data Systems

"Mach's principle: from Newton's bucket to quantum gravity" - Google Books

"Mysteries of Mass: Some Contrarian Views From an Experimenter"

"The Gauge Hierarchy Problem and Planck Oscillators" - CERN Document Server

"The First Turbulence and First Fossil Turbulence"

"Lecture on Nuclear Physics for Plasma Engineers"

The Planck Length

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