Adventures in h-bar

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Adventures in h-bar

Postby hyksos on July 4th, 2020, 2:01 am 

Any theory of Quantum Gravity will say a lot about the Hierarchy Problem. This is the strange fact that the force of gravity is on the order of 10-39 times weaker than the strength of the electromagnetic force. This is even true inside a regular hydrogen atom where particles are nearly "on top" of each other.

These extremely large factors, inexplicable in any naturalistic terms, caught the attention of Paul Dirac, who began to find strange coincidences among them. Start here https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis

I did some doodling around with Dirac's strange constants. In less than a few hours, I unexpectedly derived this spooky relationship.


Image

Here, mp is the proton mass
rp is the proton charge radius.
c is the speed of light.
hbar is the reduced Planck's constant.

The fact that pi cancelled out on the rhs was miraculous, and added to the spookiness of this derivation.

Proton radius shenanigans
The radius of the proton is hotly debated, and this has been going on for about 10 years now. I invite the reader to google up on the proton radius puzzle to get a sense of the drama surrounding the measurement of the proton's radius.

Things got significantly more interesting , when at some point I realized the spooky equation above could be solved for rp , giving a closed formula for the radius of a proton.

Image

At this point, I had to try it out. I plugged in the most accurate experimental values on the rhs, predicting a proton radius of 0.8412356 femtometers.

That number differs from the experimentally measured value by 6 parts in 10,000. (Pohl et al, 2010)

That number fits inside the standard dev of experimental proton radii measured by (Gasparian et al, 2014) and also by (Hessels et al, 2019)

For the curious, Pohl's experiment observed 0.84184(67) femtometers.

Publish
Under penalty of perjury, I attest that the above equations do not exist in any existing physics textbook or publication. The primary finding is the cancellation of the factor of pi on the rhs, along with some additional constant factors.

I hereby release the above material to the public domain. Any motivated person with free time should attempt to publish these results on vixrA. ( *cough* you-know-who *cough*) The stuff so far shows the tail end of the derivation. A good titles for the article would be

() "A new relation between proton mass and proton radius."
() "Is this the exact form of the proton radius?"

The danger is that someone has already published this result. Possibly Wolfgang Finkelnburg in 1947. However, I was unable to find any such publication.

Pohl experiment result. The citation is :
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Pohl, R., Antognini, A., Nez, F. et al. The size of the proton. Nature 466, 213–216 (2010). https://doi.org/10.1038/nature09250


This video will help in the full derivation. Note this video does not contain the equations here, as the ones above differ by factors. You might include Unzicker as co-author.
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https://www.youtube.com/watch?v=cwUFUr24R-k
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Re: Adventures in h-bar

Postby hyksos on July 4th, 2020, 2:14 am 

(also. I can show you my full derivation. if anyone wants.)
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Re: Adventures in h-bar

Postby hyksos on November 14th, 2020, 1:58 am 

Nobody?
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