In theoretical physics we have the Planck constant h representing a minimum quantity in the fabric of space and time.
The Planck constant is very often divided by 2π
This happens so often in quantum mechanics that they came up with a new mathematical symbol called the reduced Planck constant ħ or h-bar to get rid of the 2π.
This reduced the size of equations, but I believe it also removes something fundamental about the process that the mathematics is representing.
In this theory the 2π represents circular geometry that is formed by spherical symmetry.
The spherical geometry can be based on Huygens’ Principle of 1670, that says:
“Every point on a wave front has the potential for a new spherical 4πr² wave”
Each point on the curvature of the wave front forms the potential for a new light photon ∆E=hf of energy, a new oscillation or vibration as the future unfolds.
We have to square the radius r² of the sphere 4πr² because the process in unfolding on the spherical surface. Therefore we have the speed of light squared c² we have the charge of the electron squared e² and the probability wave function is squared Ψ².
The interior of the sphere 4πr² is naturally three-dimensional forming our three dimensional space of everyday life.
The two dimensional spherical surface forms a manifold for the movement of positive and negative charge.
Our ever changing world is based on this manifold and it could be called the fourth dimension of time.
Within this process the Planck constant h/2π represents a minimum quantity in space and time. This is formed by the centre of the sphere being a constant, with the radius r² squared being a constant relative to the spherical surface. The 2π represents circular geometry that is formed by the spherical symmetry with a constant πr² relationship between the radius of the circle and its area.
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