Planck particle

A Planck particle, named after physicist Max Planck

Max Planck

Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

, is a hypothetical particle defined as a tiny black hole

Black hole

A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

 whose Compton wavelength

Compton wavelength

The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons...

 is comparable to its Schwarzschild radius

Schwarzschild radius

The Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...

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

Planck epoch

In physical cosmology, the Planck epoch , named after Max Planck, is the earliest period of time in the history of the universe, from zero to approximately 10−43 seconds , during which, it is believed, quantum effects of gravity were significant...

.

Compared for example to a proton

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

, 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).

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

Hawking radiation

Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...

.

Derivation

While opinions vary as to its proper definition, the most common definition of a Planck particle is a particle whose Compton wavelength

Compton wavelength

The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons...

 is equal to its Schwarzschild radius

Schwarzschild radius

The Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...

. 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:

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 International System of Units The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units... units
Mass	M
Radius	L
Volume	L3
Density	M L-3

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

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