Alpha Institute for Advanced Studies

omega” = omega

the angular frequency omega” of the initially stationary target electron must be the same as the angular frequency of the incoming electron if M is considered to be a constant of the theory. I have not been able to find any experimental data yet for electron electron Compton scattering at right angles, but this is another stringent test of the de Broglie Einstein theory used for the electron of known constant mass M. I think that the ECE solution to this disaster for standard physics should be adopted quickly and easily by all scientists, simply use the ECE wave equation with

R = (mc / h bar) squared

for all particles including the photon.

T = h bar omega = (gamma – 1) m c squared = E – E0
p = gamma m v
E = gamma m c squared
E0 = m c squared

M = h bar omega’ / c squared

This was also found by computer algebra. Our algebra is right but in physics this is an absurd result becasue the electron mass M is not constant, so the de Broglie Einstein theory fails completely. This is a major discovery immediately obvious to all. Dr Eckardt and I can now proceed to writing up UFT 159 based on these last two notes 14 and 15.

a159thpapernotes15.pdf

E = h bar omega = gamma m c squared

It would be a good idea to apply momentum conservation to interference of electron beams in a Young interferometer or in an electron microscope. Usually, only energy is considered, in the form:

E squared= p squared c squared + m squared c fourth

i.e.

p sup mu p sub mu = m squared c squared

This is of course the Einstein energy equation of special relativity, which quantizes to the Dirac equation. This equation is simply a re-expression of the relativistic momentum gamma m v, so contains information on momentum (Marion and Thornton, “Classical Dynamics”).

E = h bar omega = gamma m c squared

and gives a simple expression for the electron mass (eq. (28)). The theory can be tested further with the momentum transfer equations. Data are needed on electron electron Compton scattering, but this type of test is also valid for any equal mass particle particle interaction. From the Rydberg constant, Penning trap and other standards laboratory methods, the electron mass M is known accurately to a relative uncertainty of ten power minus eight. The three frequencies in eq. (28) can be measured experimentally. The momentum conservation equations in the next note will give a further test and eliminate one of the frequencies. The other two are found in an electron electron Compton scattering experiment. The de Broglie momentum hypothesis is for the relativistic momentum of any particle:

p = h bar kappa = gamma m v

a159thpapernotes14.pdf

R = (mc / bar) squared

which in the free field limit is also the Dirac and Proca expression for mass. In general there is no reason why R should be a constant, while m must be a constant in the old theory. The latter is now completely refuted and obsolete.

R = (mc / bar) squared

which in the free field limit is also the Dirac and Proca expression for mass. In general there is no reason why R should be a constant, while m must be a constant in the old theory. The latter is now completely refuted and obsolete.

M = 9.10938215(45) ten power minus 31 kilograms

The relative uncertainty of 5 power minus eight is due to that in the Planck constant. This is a non relativistic definition and does not use the de Broglie Einstein theory. The latter theory when used with electron Compton scattering off the carbon atom in methane will produce a greatly varying electron M, which means that the de Broglie Einstein theory is wildly wrong. I suggest that this be shown in UFT 159 by using a fixed carbon mass, as given yesterday, and investigating M. In standards laboratories the electron mass is also determined with a Penning trap and using antiprotonic helium atoms. These methods all define M in a specific way, in a non relativistic context. More generally, M is proportional to the square root of scalar curvature.

Mass in the ECE wave equation is, as you know, a limit:

R = (mc/ h bar) squared

but its general expression is in terms of the gamma and spin connections and tetrads of Cartan geometry. For example in UFT 62, eqs. (8.25) onwards the ECE Lemma is reduced to the Einstein energy equation as a limit. Mass in general has the units of

m = (root R) h bar / c

and is proportional to root R. So to fit the numerical results from Section 3 of UFT 158, I propose that root R be used as a fitting parameter to try to mend the failure of the de Broglie Einstein theory. I agree that this will give a profound insight to the nature of mass and a new energy transfer in nature. In the EP series B(3) theory and O(3) electrodynamics were developed extensively in many directions, and that developed into ECE as you know. By now there are hundreds of ideas (literally) that are available. UFT 158 is such a high point that concentration on its development should be one central theme, energy from spacetime another.