Archive for September, 2008

Sep 03 2008

The Graviton as a Momentum Operator

Published by under Quantum Mechanics

The fundamental commutator relation [x, p] = iћ, between the operators of coordinate and momentum, provides a way to show how a graviton can add linear momentum to an electron.
An energy relation for a synchronous encounter by a graviton with an oncoming electron in an atomic orbital can start with:
[x, pg]2 = i2ћ2 = -ћ2,
the added kinetic energy being ћ2ki2/2mi, and the added momentum -√(ћ2ki2).
The added momentum, as shown by the minus sign, is in the opposite direction of that in which the graviton was traveling at the speed of light in a vacuum before it was absorbed by the electron.
Internal to the electron we can use the {N} representation to form the basis of a set of wavefunctions forming orthonormal vectors: │0 >, │1 >, …, │n >, …, with eigenvalues of N: 0, 1, …, n, … [Messiah, XII.16, pg 436].  The graviton in the process of being absorbed by an electron in a quantum atomic orbital can then be seen as a raising operator, where
aφn = φn+1 and aφn+1 = φn+2 ,
and the release of a graviton a lowering operator, with
aφn = φn-1 and aφn-1 = φn-2 .
The Hamiltonian for such a system is represented as:
H φn = ћω0(aa + ½) φn        [Liboff, Section 7.2],
with energy eigenvalues
En = ћω0(n + ½)        n = (0, 1, 2, …, 68, …nmax).
Here 68 represents the average n value at the face of the earth, and nmax depends on the orbital.
If the mass of the electron diminishes as the gravitational field diminishes, the characteristic wavenumber β of the electron also diminishes.  For each graviton internal to the electron βi2 = miω0/ћ, and for the mass of the electron at the face of the earth we have Σmi = me = 9.1095 x 10-31 kg.

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Sep 01 2008


Published by under General

In October 1976 the musical group Kansas came out with its fourth album, called Leftoverture.  At social gatherings and on the radio that autumn of my freshman year at the University of Wisconsin it was not uncommon to hear the song “Carry On Wayward Son”.  Around the time I was finishing up three semesters of calculus and two of physics as a sophomore, still living in the lakeshore dorms, the group had given us “Point Of Know Return” and “Dust In The Wind” from a fifth album.
Two years ago near the end of this month, I took a circuit drive with copies of my physics paper.  Kansas State University was one of the places I stopped.  It was a fruitful visit because on Ocotober 3, 2006 I received an analysis of the paper from KSU Physics, – only the second one offered independent of the journals.  Something in the KSU analysis prompted me to look for a way to clean up the Rotational Energy section of my paper, which I then did.  That section however, does not have anything to do with the calculation of the frequency of a graviton, but rather is there only to show that there is enough energy in the electron to do the job.
If you see Kerry Livgren, Steve Walsh, Robby Steinhardt or the others of Kansas the band please tell them the ‘point of know return’ in physics has come.  “How long?” does not have to be asked anymore, – it took 28 years.

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