Planck particle

A Planck particle, or planckion,[1] named after physicist Max Planck, is a hypothetical particle defined as a tiny black hole whose Compton wavelength is equal to its Schwarzschild radius.[2] Its mass is thus approximately the Planck mass, and its Compton wavelength and Schwarzschild radius are about the Planck length.[3] Planck particles are sometimes used as an exercise to define the Planck mass and Planck length.[4] They play a role in some models of the evolution of the universe during the Planck epoch.[5]

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).[6] The Planck particle would also have a very fleeting existence, evaporating due to Hawking radiation after approximately 5×10−39 seconds.

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:

Thus making the mass of such a particle:

This mass will be 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:

The Planck length ℓP is defined as

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 Expression Value in SI units Value in Planck units
Mass M 3.85763×10−8 kg 1.7724
Radius L 5.72947×10−35 m 3.5449
Maximum charge Q 2.86474×10−18 C 1.7724
Volume L3 7.87827×10−103 m3 186.6137
Density M L−3 4.89655×1094 kg m−3 0.0095
Lifetime T 4.826512×10−39 s 89524.9652 [7]

See also

References
  1. H. J., Treder (1985). "The planckions as largest elementary particles and as smallest test bodies" (PDF). Foundations of Physics. Springer. 15: 161–166. doi:10.1007/BF00735287.
  2. Michel M. Deza; Elena Deza. Encyclopedia of Distances. Springer; 1 June 2009. ISBN 978-3-642-00233-5. p. 433.
  3. Hoyle, F. (1993). "Light element synthesis in Planck fireballs". Astrophysics and Space Science. 198 (2): 177–193. doi:10.1007/BF00644753.
  4. B. Roy Frieden; Robert A. Gatenby. Exploratory data analysis using Fisher information. Springer; 2007. ISBN 978-1-84628-506-6. p. 163.
  5. Harrison, Edward Robert (2000), Cosmology: the science of the universe, Cambridge University Press, ISBN 978-0-521-66148-5 p. 424
  6. Harrison 2000, p. 478.
  7. i.e. 5.5683 times longer than a hypothetical black hole of 1 of mass
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