In physics, the Planck charge, denoted by , is one of the base units in the system of natural units called Planck units. It is a quantity of electric charge defined in terms of fundamental physical constants.
- is the speed of light in the vacuum,
- is the reduced Planck constant,
- is the permittivity of free space
- is the elementary charge
- is the fine structure constant.
The Planck charge is times larger than the elementary charge e carried by an electron. A Planck charge concentrated within a Planck length possesses an electric potential energy that equals (converted to mass) one Planck mass.
As an example, packing together twelve electrons (11.706 is a fractional number and cannot be used) will make them weigh ×10−8 kg, slightly more than the Planck mass ( 2.287×10−8 kg), and roughly the mass of a 2.176flea egg, solely by virtue of their electric potential energy. Note that the rest mass of the electron alone is ×10−31 kg, or 23 9.109orders of magnitude smaller.
The Gaussian cgs units are defined so that , in which case has the following simple form,
It is customary in theoretical physics to adopt the Lorentz–Heaviside units (also known as rationalized cgs). When made natural (ħ=1, c=1), they are like the SI system with . Therefore, it is more appropriate to instead define the Planck charge as
When charges are measured in units of , i.e., when is set equal to 1, we obtain
which is commonly used in quantum field theory, so that e≅0.30282212088.
By contrast, in (non-rationalized) natural cgs units where we have .
Notes and references
- Stock, Michael; Witt, Thomas J (2006). "CPEM 2006 round table discussion 'Proposed changes to the SI'". Metrologia. 43 (6): 583. Bibcode:2006Metro..43..583S. doi:10.1088/0026-1394/43/6/014.
- Pavšič, Matej (2001). The Landscape of Theoretical Physics: A Global View. Dordrecht: Kluwer Academic. pp. 347–352. ISBN 0-7923-7006-6.