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 to a proton, for example, 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 massive (the Planck mass being 10¹⁹ times the proton's mass).^[5]

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:

$\lambda ={\frac {h}{mc}}={\frac {2Gm}{c^{2}}}$

Thus making the mass of such a particle:

$m={\sqrt {\frac {hc}{2G}}}$

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:

$r={\frac {h}{mc}}={\sqrt {\frac {2Gh}{c^{3}}}}$

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.

Table 1: Physical dimensions of a Planck particle

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

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

1. Michel M. Deza; Elena Deza. Encyclopedia of Distances. Springer; 1 June 2009. ISBN 978-3-642-00233-5. p. 433.
2. "Light element synthesis in Planck fireballs" - SpringerLink
3. B. Roy Frieden; Robert A. Gatenby. Exploratory data analysis using Fisher information. Springer; 2007. ISBN 978-1-84628-506-6. p. 163.
4. Harrison, Edward Robert (2000), Cosmology: the science of the universe, Cambridge University Press, ISBN 978-0-521-66148-5 p. 424
5. 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