Atomic clock gravity correction

[Bengt Nyman]

Dipole elongation and the atomic clock.

An atomic clock runs 30 microseconds per day slower at earths surface than it does in GPS satellite orbit. This corresponds to a relative error of 3.472*10^-10.
A Hydrogen atomic clock uses hydrogen atoms as a frequency medium. In gravity free space a hydrogen atom is externally neutral while the electron orbit is centered around the proton. In earth gravity a hydrogen atom is slightly elongated into a dipole where the center of the electron orbit is offset from the center of charge of the proton. This slows the frequency of the electron orbit. Knowing the Coulomb attraction force between proton and electron in a hydrogen atom, as well as the Coulomb dipole gravity between the hydrogen atom and earth we can calculate the expected orbital disturbance and associated orbital frequency reduction of the electron in the hydrogen atom while in earth gravity.

Hydrogen atom centering force:
F1 = K(e*e)/r^2 = 4.357*10^20
Dipole gravity distraction force:
F2 = K(e*N)/L^2 = 1.468*10^11

Assuming a linear relationship between dipole elongation and hydrogen clock frequency reduction at this very low level of disturbance, the reduction in clock frequency at earths surface should be:

(1.468*10^11)/(4.357*10^20) = 3.369*10^-10
The measured relative error is = 3.472*10^-10

Using nothing but the Dipole theory based on electric charge and Coulombs law produces remarkable alignment with measured values.

[Bengt Nyman]

Dipole elongation and the atomic clock.
Calculation details:

1. Hydrogen atom centering force:
This is the electrostatic attraction between the electron and the proton in the hydrogen atom according to Coulombs law.
F1 = K(e*e)/r^2
K = 8.99×109 N m2 C−2
e = 1.60217662 × 10-19 coulombs
r = Bohr's radius = 5.29×10−11 m
F1 = 4.357*10^20

2. Dipole gravity distraction force:
This is is the electrostatic attraction between the negative charge of the electron in the hydrogen atom and the sum of the positive dipole charges in earth, resulting in dipole elongation of the hydrogen atom and corresponding slowing of the hydrogen clock frequency.
F2 = K(n*e*e)/L^2
K = 8.99×109 N m2 C−2
e = 1.60217662 × 10-19 coulombs
n*e = N = The sum of positive charges in earth calculated by the mass of earth divided by the mass of one proton:
N = (5.972*10^24)kg / (1.673*10^-27)kg
L = The distance between the hydrogen atom and the integrated center of effort of the dipole charges in earth, which is is at the center of the earth = the radius of the earth = 6378*10^3 m
F2 = 1.468*10^11

Assuming a linear relationship between dipole elongation and hydrogen clock frequency reduction, the error in clock frequency at earths surface caused by (dipole) gravity should be:
F2 / F1 = (1.468*10^11)/(4.357*10^20) = 3.369*10^-10

The expected atomic clock error at earth level of 3.369*10^-10, calculated above using dipole gravity, corresponds within 3% to the observed and measured value of 3.472*10^-10