Archive for February, 2008

Feb 24 2008

G = 4hf/3

Published by under Quantum Mechanics

With activity increasing on the use of my calculations, it may be a good time to make a statement on the copyright of my main calculation.
The formula G = 4hf/3 was derived in November 2005.  The formula appears in an autumn 2006 family coat of arms done in a Fairmont public school art class by my daughter, and which hangs at the end of our hallway at home.  The formula also appeared in a January 8, 2007 article in the Fairmont Sentinel, and on a sheet of paper I held up in a KEYC – Mankato television interview aired on January 18, 2007.
The formula G = 4hf/3 can be used one of two ways.  One can use a conventional, measured value of the gravitational constant for G, and calculate the frequency of a graviton.  Alternatively, one can convert exactly one third the proton mass to equivalent energy as a massless photon through Einstein’s equation E = mc2, solve for f, the frequency of the photon, through the formula E = hf, and come up with a value of the gravitational constant through my formula G = 4hf/3.  This value of G will then be as accurate as the measured value of the mass of the proton.
For those just starting to learn physics, “h” is Planck’s constant and is equal to 6.626 x 10-34 J-s.  It is easiest if you keep all units in the ‘kg-m-s’ system for these calculations.

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Feb 14 2008

Half-integer spin contribution

Published by under Quantum Mechanics

With the emission of a graviton, an electron in an atomic quantum orbit must either undergo a nutation, or reverse its spin orientation as it contributes to the particle angular momentum.
The shape of an orbital that you see at the top of this blog is similar to what many of us picture, however reality may be something different.  Let us say, for discussion purposes, that an electron reverses its spin orientation when it gives off a graviton.  The electron as a particle with half-integer spin changes sign “when the system of coordinates is completely rotated about an axis” ([1], §54).   Should each orbital then include graviton emitting turns of quantity 2n+1, n=1,2,3, the spin orientation of the electron would reverse for every course that brings it back to its orientation and position relative to starting coordinates within d(q-q’).  The total particle angular momentum will then alternate along any prescribed axis between j = l + ½ and j = l – ½.
Another way of stating it is that for half-integer j, Χ(Ф+2π) = – Χ (Ф).  The base function changes sign under a rotation of 2π ([1], §95).
It is the statistical nature of quantum mechanics that has allowed its angular momentum and energy eigenvalue determinations to be very useful in physics.  The average intrinsic spin angular momentum of the electron has thus been able to be used without respect to the emission and absorption of gravitons.

[1] Landau, L. D. and Lifshitz, E. M., Quantum Mechanics, Non-relativistic Theory, Translated from the Russian by J. B. Sykes and J. S. Bell, Addison-Wesley Publishing, 1958

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