Alpha Institute for Advanced Studies

m = (h bar / c) root R

I have been referring to R as curvature but more accurately it depends on torsion and curvature. R is the last vestige of the old Einstein general relativity, in which R = – kT. As soon as momentum conservation is considered the old physics fails very badly, indeed fails completely. It can describe only the energy conservation. In quantum field theory Ryder describes the methods of dealing with more than one particle in quantum field theory. we are right at the start of a new era in natural philosophy, so anyone’s ideas are equally valid provided they can be put into mathematics and are not too vague.

R = mm*

and an apparently complex mass:

m = m’ + i m”

will give a curvature proportional to mm* again, where m* is the complex conjugate of m. The elementary particle mass m0 is always positive, real valued and constant.

m2 squared = (R / R0) m squared

where m is the mass of the electron appearing in the standards laboratories, and where m2 is the apparent mass given by the general theory of Compton scattering.

a161stpapernotes6.pdf

x = R / R0 = (h bar omega’ / (m c squared)) all squared

It is seen that the curvature R of general relativity varies in proportion to omega’ squared while the mass m is constant. This is in the special case of 90 degree Compton scattering of an electron off another electron.

R = xR0

The Cartan geometry is worked out for Compton scattering at 90 degrees, giving the result (28). These are powerful new methods of physics and generalise the de Broglie Einstein equations, solving the self inconsistency problem found in UFT 158 to UFT 160 using ECE theory. The latter is preferred to the standard model from comparison with experimental data and Compton scattering is shown to be a phenomenon of general relativity and unified field theory, not of special relativity.

a161stpapernotes5.pdf

E = <h bar omega> = gamma m c squared

and for momentum:

p = <h bar kappa> = gamma m v

where < > denotes the thermal average calculated from the Planck distribution. This postulate will introduce temperature into the analysis as in UFT 155. The ECE theory, as for any other valid theory of physics, produces good results in quantum mechanics and special relativity when the two aspects are independent, but will run into the same problem as in UFT 158 – UFT 160. This is a profound problem needing the simplest plausible solution. Anyone’s ideas are as good as mine. These seem to be solid postulates, because at any finite temperature T, the average energy of one photon must be used. This is:

<h bar omega> = h bar omega exp (-x) (1 – exp (-x))

x = h bar omega / (kT)

Each frequency has a different temperature. This modified postulate may fail as badly as the original, I must work this next.

x2 = (omega omega’ – x1 squared) / (omega – omega’)

which is negative because

x1 = 7.76343 ten power 20 radians per second
x2 = 1.6959 ten power 25 radians per second

My hand calculator checks can be repeated by Dr Horst Eckardt with a desktop, and the results graphed. This is not just a minor failure, but a total failure of basic theory on the classical relativistic level. I will now proceed to write up UFT 160 with the new and much more transparent formulae. Recall that only the basic equations of the theory have been used, but used in a new way that reveals the theory to be drastically self inconsistent. Anyone with a hand calculator or desktop can check note 160(5). There must be books full of electron scattering data that can be used to make this check.

1 / omega’ – 1 / omega = (h bar / (m2 c squared) (1 – cos theta)

whish is the textbook equation for Compton scattering for zero photon mass. Here:

omega / c = 2 pi / lambda

so

lambda’ – lambda = (h / m2 c) (1 – cos theta)

which is the usual textbook equation. So the textbook result is a mirage, it works only for zero photon mass. This is self contradictory because de Broglie postulated non zero photon mass. The theory does not work at all for the general scattering of m1 off m2 and does not work for finite photon mass m1.