If you look at precisely how they solved the second order differential Schrödinger equation for the hydrogen atom (the only one with an analytical solution), and see how they derived the equation that precisely links the QUANTUM energy steps to frequency/energy (the photon frequency/energy for when the electron jumps shells; Rydberg equation - THE FULL ONE), AND solve it precisely without making their reduced mass approximation, you get the solution to the proton radius puzzle and much more. Requires iteration on a computer to solve AND it is precise.
Abstract: The status of the proton radius puzzle (as of the date of the Confer- ence) is reviewed. The most likely potential theoretical and experimental explanations are discussed. Either the electronic hydrogen experiments were not sufficiently accurate to measure the proton radius, the two- photon exchange effect was not properly accounted for, or there is some kind of new physics.
Abstract: We extract the proton charge radius from the elastic form factor data using a theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike form factor in different $Q^2$ regions and permits the use of data up to $Q^2 \sim$ 0.5 GeV$^2$ in constraining the radius.
The work done by the 4th Order Polynomial paper solves all of this and it is a refinement of Haramein’s work:
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Abstract: We present a new measurement of the $1S-3S$ two-photon transition frequency of hydrogen, realized with a continuous-wave excitation laser at 205 nm on a room-temperature atomic beam, with a relative uncertainty of $9\times10^{-13}$. The proton charge radius deduced from this measurement, $r_\text{p}=0.877(13)$ fm, is in very good agreement with the current CODATA-recommended value.
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phxmarker.blogspot.com. 1,408 likes · 1 talking about this. Unified Physics of Nassim Haramein, an extension of Einstein's work that merges with Planck's work, for a unified cosmological and quantum...
March 11 - Mark Rohrbaugh: phxmarker.blogspot.fr -When Mark co-authored www.fractalfield.com/conjugategravity he showed that implosive charge collapse not only
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From the Entropy (S or E) equation, we can intuit the force of gravity equation:
$$S\stackrel{?}{=}mGc\oint_{A_c}^{A_s}\mathrm{d}s$$
$$F_{12}\stackrel{?}{=}{1\over{4\pi\epsilon_0}}{Q_1Q_2\over R^2}\oint_{A_c}^{A_s}\mathrm{d}s$$
$$F_{1T}\stackrel{?}{=}{1\over{4\pi\epsilon_0}}{Q_1Q_T\over R^2}\oint_{A_c}^{A_s}\mathrm{d}s$$
Using the "Test Charge" concept to determine E-field (thus G-field):
$$E_{1T}\stackrel{?}{=}G{M_r\over R^2}\oint_{A_c}^{A_s}\mathrm{d}s$$
$$E_{1T}\stackrel{?}{=}{1\over{4\pi\epsilon_0}}{Q_r\over R^2}\oint_{A_c}^{A_s}\mathrm{d}s$$
Then, the force of gravity is then equal to the residual electric field time the test charge, $q_T$:
$$F_{12}=E_{1T}\times q_2$$
$A_c$ and $A_s$ are the equatorial cross-sectional area and the surface area - identical to our information theory, geometric approach to calculating masses (the Haramein technique). These are EVENT HORIZON areas!!!
This is THE FAST WAY to answers...
The classical mainstream method requires a detailed vector analysis and force projection calculation, etc.
More later.
(detail, notation, etc plus a precise definition for all terms, corrections, typo fixes - this is live blogged/channeled)
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The gravitational field is a vector field that describes the gravitational force which would be applied on an object in any given point in space, per unit mass. It is actually equal to the gravitational acceleration at that point.
It is a generalisation of the vector form, which becomes particularly useful if more than 2 objects are involved (such as a rocket between the Earth and the Moon). For 2 objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r12 and m instead of m2 and define the gravitational field g(r) as:
so that we can write:
This formulation is dependent on the objects causing the field. The field has units of acceleration; in SI, this is m/s2.
Gravitational fields are also conservative; that is, the work done by gravity from one position to another is path-independent. This has the consequence that there exists a gravitational potential field V(r) such that
If m1 is a point mass or the mass of a sphere with homogeneous mass distribution, the force field g(r) outside the sphere is isotropic, i.e., depends only on the distance r from the center of the sphere. In that case
the gravitational field is on, inside and outside of symmetric masses.
As per Gauss Law, field in a symmetric body can be found by the mathematical equation:
where is a closed surface and is the mass enclosed by the surface.
Hence, for a hollow sphere of radius and total mass ,
For a uniform solid sphere of radius and total mass ,
