the Planck constants

The Planck constants are the coherent building blocks that structure all physical constants of Nature. Here we showcase their phase plots, 3D and 2D surface plots, and their quantized plane-wave definitions.

Phase plots of the 5 Planck constants.

Planck time
Planck time
Planck length
Planck length
Planck charge
Planck charge
Planck temperature
Planck temperature
Planck mass
Planck mass

3D and 2D surface plots of the 5 Planck constants.

Planck time
Planck time
Planck length
Planck length
Planck charge
Planck charge
Planck temperature
Planck temperature
Planck mass
Planck mass

Quantized plane-wave definitions of the 5 Planck constants.

Planck time equation
Planck length equation
Planck charge equation
Planck temperature equation
Planck mass equation

Where pi = Archimedes' constant, i = the imaginary unit, e = Euler's number, W_We = the Weierstrass constant, sinh(x) = the hyperbolic sine function, and cos(x) = the cosine function.

These constructions define 5 scalars ( phi_0, phi_1, phi_2, phi_3, and phi_4 ). Combining those scalars with their quantized powers we arrive at exact geometric definitions for the Planck constants.

phi_0 equation
phi_1 equation
phi_2 equation
phi_3 equation
phi_4 equation

Where integers .

Planck final results