Planck Units

In physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify particular algebraic expressions appearing in physical law. Originally proposed in 1899 by German physicist Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one system of natural units among other systems, but are considered unique in that these units are not based on properties of any prototype object, or particle (that would be arbitrarily chosen) but are based only on properties of free space. The universal constants that Planck units, by definition, normalize to 1 are the:

  • Gravitational constant, G;
  • Reduced Planck constant, ħ;
  • Speed of light in a vacuum, c;
  • Coulomb constant, (4πε0)−1 (sometimes ke or k);
  • Boltzmann constant, kB (sometimes k).

Each of these constants can be associated with at least one fundamental physical theory: c with electromagnetism and special relativity, G with general relativity and Newtonian gravity, ħ with quantum mechanics, ε0 with electrostatics, and kB with statistical mechanics and thermodynamics. Planck units have profound significance for theoretical physics since they simplify several recurring algebraic expressions of physical law by nondimensionalization. They are particularly relevant in research on unified theories such as quantum gravity.

Physicists sometimes semi-humorously refer to Planck units as "God's units". Planck units are free of anthropocentric arbitrariness. Some physicists argue that communication with extraterrestrial intelligence would have to employ such a system of units in order to be understood. Unlike the meter and second, which exist as fundamental units in the SI system for (human) historical reasons, the Planck length and Planck time are conceptually linked at a fundamental physical level.

Natural units help physicists to reframe questions. Frank Wilczek puts it succinctly:

...We see that the question is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in Natural (Planck) Units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number ...

June 2001 Physics Today

The strength of gravity is simply what it is and the strength of the electromagnetic force simply is what it is. The electromagnetic force operates on a different physical quantity (electric charge) than gravity (mass) so it cannot be compared directly to gravity. To note that gravity is an extremely weak force is, from the point-of-view of Planck units, like comparing apples to oranges. It is true that the electrostatic repulsive force between two protons (alone in free space) greatly exceeds the gravitational attractive force between the same two protons, and that is because the charge on the protons is approximately the Planck unit of charge but the mass of the protons is far, far less than the Planck mass.

Read more about Planck Units:  Base Planck Units, Derived Planck Units, Planck Units Simplify Key Equations, Other Possible Normalizations, Uncertainties in Values, Discussion

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