Name: Anonymous 2008-09-01 16:04
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
a†φn = φn+1 and a†φn+1 = φn+2 ,
and the release of a graviton a lowering operator. The Hamiltonian for such a system is represented as:
H φn = ћω0(a†a + ½) φn [Liboff, Section 7.2],
with energy eigenvalues
En = ћω0(n + ½) n = (0, 1, 2, …, 68).
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.
http://www.fruechtetheory.com/blog/
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
a†φn = φn+1 and a†φn+1 = φn+2 ,
and the release of a graviton a lowering operator. The Hamiltonian for such a system is represented as:
H φn = ћω0(a†a + ½) φn [Liboff, Section 7.2],
with energy eigenvalues
En = ћω0(n + ½) n = (0, 1, 2, …, 68).
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.
http://www.fruechtetheory.com/blog/