Planck Length

Explanation

Another fundamental physical constant named after Max Planck, it is thought to be the smallest possible length, at an incredibly small 1.616 x 10-35 meters. Its true meaning remains unknown, but there is an obvious relationship between gravity and the Planck length as found in gravity equations, and also a relationship with the electron’s classical radius.  

Planck Length Explained 

See also: Planck time

 


 

Derivation – Planck Length

It is found in classical terms as a ratio of the electron’s classical radius and the square of two coupling constants for the electron: 1) the gravitational coupling constant and 2) the strong force coupling constant (the fine structure).  As expressed mathematically in the classical equation, if the relative strength of gravity was equal to the relative strength of the strong force (when compared to the electric force), the ratio would be one and Planck length would be equal to the electron’s radius.  The weaker gravity is compared to the electric force, the shorter the distance for Planck length. The wave constant form is derived from the classical form.

 

Classical Constant Form

Planck Length Derived

Wave Constant Form

Planck Length Derived Wave Constants

Using classical constants Using energy wave constants

 

Calculated Value: 1.6162E-35
Difference from CODATA: 0.000%
Calculated Units: m
G-Factor: gλ3

 

Its value was calculated and shown to match the known value in the Summary of Calculations table. The derivation of this constant is available in the Fundamental Physical Constants paper.