Planck particle

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

Derivation[edit]

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 as large as the Planck mass, making a Planck particle 1.772 times as massive as the Planck unit mass.

Its radius will be the Compton wavelength:

The Planck length P is defined as

Dimensions[edit]

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
Lifetime T 4.826512×10−39 s 89524.9652 [6]

See also[edit]

References[edit]

  1. ^ H. J., Treder (1985). "The planckions as largest elementary particles and as smallest test bodies" (PDF). Foundations of Physics. Springer. 15 (2): 161–166. Bibcode:1985FoPh...15..161T. doi:10.1007/BF00735287. S2CID 121960540.
  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. S2CID 121245869.
  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.
  6. ^ i.e. 5.5683 times longer than a hypothetical black hole of 1 of mass

External links[edit]