Dimensional analysis derives frequency with other Planck Units.
Planck units do not curve space because potential energies and kinetic energies are equal.
ZPE is derived from kinetic energies (1/2)hf and would curve space backward if not balanced by an equal potential energy. Something is missing from ZPE explanation.
One possible explanation is that Planck energy kinetic half accounts for ZPE while providing the potential energy balance. Casimir forces are suggesting excess of kinetic energy.
In ZPE Are The Frequencies Defined By Planck Units?
ZPE is thought to have all possible frequencies and wave lengths. There is no way to predict how many of each frequency there are, or to put a limit on the energy total, except by reference to Planck units.
ZPE must exist from quantum effects if there is any type of frequency acting in vacuum. Frequencies require a source and Planck units provide a source.
Vacuum space is defined by measurables c, h, G, and either ϵ or μ. From these the method of dimensional analysis provides all the Planck units. Why this is found in nature is not known. It might be inherited from a previous universe.
A minimum inheritance seems to be conserved quantities photon energy E, photon momentum p, and angular momentum h. Impedance X should be inherited as the only property of vacuum space that does not become variable in Hierarchy of Plancks. General relativity is the 4D representation of Hierarchy. The reason for constant impedance is possibly explained by the same geometry describing capacitance C and inductance L which relate to ϵ and μ.
E = pc
c = E/p
ν = E/h
λ = c/ν
ϵ = 1/ cX
μ = X/c
X2 = μ/ϵ = L/C
C = λϵ = λ/cX
L = λμ = λX/c
ν2 = 1/LC
c2 = (λν)2 = 1/ϵμ
Defining G from inheritance when no rest mass is inherited requires half of the energy to be expressed as equivalent mass.
m = E/c2
Gm2/2λ = GE2/4λc4 = E/2
G = 2c4λ/E
The proposed inheritance is sufficient to derive the Planck units.
When G is involved gravity is working. Presence of h shows that some aspect of quantum mechanics is applied. Presence of ϵ and μ shows electric and magnetic forces. Light speed c is a link between mechanics and electromagnetism. Through uncertainty principle Planck h is a link to the the weak force gage. How the strong force applies to Planck units is not clear, except the small Planck length requires it to be effective when protons and neutrons are present.
Both average frequency and Planck units seem to arise as inheritance from a previous universe. Planck units calculation can predict the average ZPE frequency. Collisions create the frequency distribution as a black body equilibrium. A limit is placed on energy total in ZPE.
Uncertainty may increase E and p from one an old universe to a new universe.
ΔEΔt =
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