The short answer is, No. What Kaluza and Klein realized was that, in a 5-dimensional spacetime, in which one, space-like, dimension was compactified, it was possible to describe the components of the metric and the components of a U(1) gauge field-which could be identified with the gauge potential of electromagnetism-with components of the 5-dimensional metric. There is thus a 5-dimensional Newton's constant, that is, then, related to the 4-dimensional Newton's constant and the radius of the compactification of the additional dimension. So it's a parametrization rather than an explanation of the hierarchy of couplings.

However there are additional fields, beyond the 4-dimensional metric tensor and one vector field, (gμ4=g4μ), namely, a scalar (g44). So even if the vector field could be identified with the gauge potential of electromagnetism, there is another field that would lead to violations of the equivalence principle, namely the scalar, aka the dilaton, if it remained part of the gravitational part in 4d and couldn't be given any interpretation as matter fields in 4d, since, in fact, it would retain a dependence on the fifth coordinate, whose compactification must be put in by hand, in order to eliminate it (and the same remark holds for the gauge field as well). Otherwise there would be a ``tower'' of such states. Now the masses of these states-apart from the lowest one-can be set to be beyond experimental reach, which is what is done in the applications this formalism has been used.

Robert Doti

Quote: "Was there a thought that somehow linkage of these forces would somehow explain why one force (gravity) is so weak versus electromagnetic."

Actually, despite this difference still being taught as a fact in standard textbooks, it is easily explained why this is still taught as a fact, and mathematically explained why it is due only to a century long neglect in numerically verifying all parameters in these equations.

If interested, this is demonstrated in this paper published in 2013:

Article Unifying All Classical Force Equations

If you own a simple pocket scientific calculator, you will be able to numerically verify this for yourself.

You will also see how G can be related to the Coulomb equation with a numerical example given with the case of the hydrogen atom and numerically verify the relation yourself.

Andre Michaud: I am a chemist, and I admonish students to remember the force of gravitation is much weaker than the electrostatic force .Your paper turns this up on its end by claiming G changes from a cosmic to an atomic frame. You are able to use Bohr's quantized equation and calculate and orbital velocity and orbital period. From equating centripetal force to Newton's force equation of two bodies you equate the proton of the nucleus with attraction via gravitational of the electron me mp/r 2 you calculate (my term) modified G. Now you take this G (much larger than Newton's cosmic) and calculate a force that is not only the same magnitude of the Coulomb force but is equal to it! That is a bizarre coincidence. If not then some hidden connection of both forces. For the chemist nuclear shielding and atomic number determines atomic property as radius, electron affinity, ionization and electronegativity. However, their exceptions to this order. Do suspect a gravitational aspect would explain this?

The objections are beyond my pay grade. I will not change how I teach however this poses interesting other questions. One would be what is the significance F of columbic equals with this modified G that the forces are the same? You used this for a 1 s orbital, but this would not work for 2s orbital or more complicated (p, d or f) in the hydrogen atom. Does this work for any other atom? For G to be larger on the atomic scale-would you postulate 11-dimensional M string theory actually gets simpler to that less dimensions means gravitational force is not leaking so it gets stronger?

If string theory can indecently confirm modified G on atomic scale by high school equations one can calculate mass of proton and electron directly!

My last questions of Bohr realized this in 'early' quantum mechanics which you draw from would that affect Schoedinger and Dirac in 'later' quantum mechanics. Would gravitational force be more incorporated? I can imagine a collaboration with Einstein and Bohr might have happened sooner. Any thoughts of what may come later.

Thanks for sharing your provocative paper.

Robert Doti

Dear Robert,

Note to start with, that I seldom get any feedback from people interested in my analyses.

Actually, your surprise couldn't be bigger than mine as I first did this numerical verification, then repeatedly redone from the start before deciding to try and have it published.

This paper whose analysis so surprises you is part of a set on electromagnetic mechanics, a discipline that was not taught in any institution since the Special Relativity theory was adopted by the physics theoreticians community in 1907.

Fortunately, the engineering community consistently kept using the Lorentz force equation (the first and until lately the only established electromagnetic mechanics equation) ever since its validity was confirmed by Walter Kaufmann, who was the first to use it to collect experimental data about free moving accelerating electrons, then analyzed and confirmed valid in the first few years of the 1900's. Which is what eventually drew my attention to electromagnetic mechanics in the mid-1990's.

If further interested in this series of papers published since 2007, links to the whole series are available from this index:

Article INDEX -Electromagnetic Mechanics (The 3-Spaces Model)

The final paper of the project was published in July of 2024.

I will try to give meaningful answers to your specific questions.

You wrote: " The objections are beyond my pay grade. I will not change how I teach "

Interesting that you would say this. I manufacture a lab apparatus meant to help teachers make Newtons's mechanics more hands on obvious for their students, and the Lab manual that I provide remains strict classical mechanics, devoid of any potentially new developments that my research on electromagnetic mechanics seems to reveal. Like you, my pay grade in no way authorises me to teach or to even hint at these potentially major developments in my lab manual.

You wrote: " however this poses interesting other questions. One would be what is the significance F of columbic equals with this modified G that the forces are the same?"

Potentially, that only one force is involved underlying all these equations that all can be derived from F=ma and the reverse.

You wrote: "You used this for a 1 s orbital, but this would not work for 2s orbital or more complicated (p, d or f) in the hydrogen atom. "

Well, considering that the hydrogen atom accommodates only one electron and that its rest state is at the 1 s orbital, all other possible orbitals can only be an actual integer sequence related series of resonance states of the ground orbital energy that the electron will only fleetingly occupy after having been energized away from its 1 s rest state, as it returns to the 1 s orbital, releasing the related photon of the basic Lyman series, as discovered by de Broglie and explained in his 1924 thesis. So yes, due to this easy to calculate resonance series, it does seem to work for all orbitals of the hydrogen atom. I did not go all the way to the hyperfine series. I spent 30 years just exploring and analyzing the main features of electromagnetic mechanics proper. Others who take interest will certainly explore and analyze the remaining nooks and crannies.

You ask: " Does this work for any other atom?"

If electromagnetic mechanics is well grounded, I have no doubt that it does. As I said, others who take interest will certainly explore and establish the relations.

You ask: " For G to be larger on the atomic scale-would you postulate 11-dimensional M string theory actually gets simpler to that less dimensions means gravitational force is not leaking so it gets stronger?"

I couldn't tell in the case of 11-dimension M string theory, but it certainly fits like hand in glove with 10-dimension trispatial geometry that emerged from Hamilton's quaternion geometry, and on which all of electromagnetic mechanics is built:

Article Evolution From the Complex Plane to the Quaternion Coordinat...

You wrote: " If string theory can indecently confirm modified G on atomic scale by high school equations one can calculate mass of proton and electron directly!"

Actually, they can be calculated directly from the manner in which electron-positron pairs decouple from destabilized 1.022+ MeV electromagnetic photons:

Article The Mechanics of Electron-Positron Pair Creation in the 3-Spaces Model

The same for protons and neurons:

Article The Mechanics of Neutron and Proton Creation in the 3- Spaces Model

You write: " My last questions of Bohr realized this in 'early' quantum mechanics which you draw from would that affect Schoedinger and Dirac in 'later' quantum mechanics "

Actually, early quantum mechanics was demonstrably grounded on a calculation error just as surprising as that allowing this different G for the atomic level of magnitude. Paper published just last year:

Article Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

You ask: "Any thoughts of what may come later."

I certainly do. Since the whole sequence of papers directly links the historical papers on which all of electromagnetic mechanics is grounded, complemented by references to all confirming experimental evidence collected since, my view is that the upcoming generation of researchers will progressively integrate this understanding in their worldviews and should eventually complete the research and integrate it in the general pool of knowledge, just like the other main mechanics were, classical kinematic mechanics and wave mechanics.

You conclude: "Thanks for sharing your provocative paper."

Thank you for your appreciation. But if you remain interested in this series of papers, you are likely to find some of the others just as provocative, if not more.

Best Regards, André