Planck particle

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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.^[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 10¹⁹ times the proton's mass).^[5]

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

Contents

1 Derivation
2 Dimensions
3 See also
4 References
5 External links

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.

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	L³	7.87827×10⁻¹⁰³ m³
Density	M L⁻³	4.89655×10⁹⁴ kg m^-3

It should be noted that the above dimensions do not correspond to any known physical entity or material.

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, http://books.google.com/books?id=-8PJbcA2lLoC p. 424
^ Harrison 2000, p. 478.

External links

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