- = 4.341 × 10-9 kg = 2.435 × 1018 GeV/c2.
The added factor of simplifies a number of equations in general relativity.
The formula for the Planck mass can be derived by dimensional analysis. In this approach, one starts with the three physical constants ħ, c, and G, and attempt to combine them to get a quantity with units of mass. The expected formula is of the form
where are constants to be determined by matching the dimensions of both sides. Using the symbol L for length, T for time, M for mass, and writing "[x]" for the dimensions of some physical quantity x, we have the following:
If one wants dimensions of mass, the following equations must hold:
The solution of this system is:
Thus, the Planck mass is:
Unlike all other Planck units and most Planck derived units, the Planck mass is a macroscopic amount, having a scale more or less conceivable to humans. For example, the body mass of a flea is roughly 4000 to 5000 mP.
The Planck mass has the Schwarzschild radius equals to its Compton wavelength divided by . The Planck mass is also the mass of the Planck particle, a hypothetical tiny black hole whose Schwarzschild radius equals the Planck length.
The Planck mass is an idealized mass thought to have special significance for quantum gravity when general relativity and the fundamentals of quantum physics become mutually important to describe mechanics.
- Sivaram C. WHAT IS SPECIAL ABOUT THE PLANCK MASS? PDF
- Johnstone Stoney, Phil. Trans. Roy. Soc. 11, (1881)
- Stephen J. Crothers and Jeremy Dunning-Davies†. Planck Particles and Quantum Gravity. PROGRESS IN PHYSICS, Vol.3, July, 2006