User:Umair khalid1991/Mathematical Constants and Gyromagnetic ratio (relationship)



In reference to the mathematical relation ship between mass of a neuron, mass of an electron, Apery's Constant, and the golden ratio; mentioned in the Wikipedia article I began investigating relationships of similar kind. So far the results have been encouraging. I discovered two more relation ships between mathematical constants and the Gyromagnetic ratios of sub atomic particles, namely; electron, proton and neutron.

One of the relationship i shall present here. This contribution is merely to promote the discussion on these intriguing relationships between the mathematical constants and properties of sub-atomic particles.The relationship presented as follows provides a reasonable approximation ("reasonable" being a relative term, I prefer to call it reasonably accurate within my own intellectual context) to  the relationship of subatomic properties namely, The Gyromagnetic Ratio of electron, proton, neutron and there respective masses; with the mathematical constants (The golden ratio,The Reimann Zeta function evaluated at the value of golden ratio and The Feigenbaum constants)

This relationship can easily be verified by substituting the values of the mathematical and physical constants. The relationship is stated as follows:

1/√φ ≃ [-ζ(φ)] + (√10^19)(√[(|γn|×Mn)+(|γp|×Mp)+(|γe|×Me)]) or (1/sqrt(φ)) ≃ [-ζ(φ)] + (sqrt(10^19))×(sqrt([(|γn|*Mn)+(|γp|*Mp)+(|γe|*Me)]))

here, φ = The Golden ratio ( (1+sqrt(5))/2) ζ(φ)= The Reimann Zeta function evaluated at The Golden Ratio(≃2.238334343912425) |γn|= The gyromagnetic ratio of a neutron ( 1.832 471 85 x 10^8 )(magnitude) |γp|= The gyromagnetic ratio of a proton (  2.675 222 099 x 10^8 ) (magnitude) |γe|= The gyromagnetic ratio of an electron ( 1.760 859 770 x 10^11)(magnitude) Mn= The mass of a neutron Mp= The mass of a proton Me= The mass of an electron

This relationship in words would go like: "The square root of The Golden Ratio when reciprocated equals in value to the relation ship "Reimann zeta function (evaluated at golden ratio) added to the negative of product of "square root of (10 to the power 19)" and "square root of the quantity [ |γn|*Mn)+(|γp|*Mp)+(|γe|*Me)]". Here, "the quantity" refers to the sum of three terms, each being the product of The Gyromagnetic Ratio (absolute value) and the mass of the respective subatomic particle. Sub Atomic Particles being 'neutron', 'proton' and 'electron' respectively.

http://physics.nist.gov/cgi-bin/cuu/Value?gammap http://physics.nist.gov/cgi-bin/cuu/Value?gamman http://en.wikipedia.org/wiki/Gyromagnetic_ratio