Alpha Institute for Advanced Studies

E2 – E1 = h bar omega

but with considerations of conservation of linear momentum included for the first time. The concepts are simple and clear. Compared with this flood of new results from ECE theory, something like CERN is a complete waste of time and about as exciting as growing grass. It may have produced technological spin offs, but there are cheaper ways of doing that. It is important to criticise all these white elephants because they seriously inhibit real science. The US Government has pointed towards this conclusion.

a165thpapernotes7.pdf

1) In eq. (43) of UFT 160 and (36) of UFT 161 A should be defined as

A = omega omega’ – x sub 2 (omega – omega’)

2) In Eq. (41) of UFT 161:

omega omega’ – x sub 2 (omega – omega’) = omega omega’ cos theta

a165thpapernotes4.pdf

E1 = -2.2; E2 = -0.55; E3 = -0.244; E4 = -0.1375; E5= -0.088; E6 = -0.061; E sub n = E1 / n squared.

They are total relativistic energy in the limit when the Dirac equation becomes the Schroedinger equation. They are experimentally determined and there is no need to change them in any way. So the various R spectra can be calculated. The way in which Dirac reduces to Schroedinger is non-trivial and described by Ryder for example. The E of the Dirac equation is always the TOTAL relativistic energy, p is always the relativistic momentum. The Dirac equation of H gives features that the Schroedinger equation of H does not. For example, choose E1 and E2 and plot R against theta incremented from near zero to pi radians. Another is to choose E2 and E3 and repeat; another is to choose E3 and E4 and repeat. In all cases there is R sub + and R sub – . All the R spectra are different and completely new in concept. They turn the old physics into the new: a phoenix from the ashes type of happening.

(R / R0) = gamma squared

a163rdpapernotes7.pdf

E = T + E0 = T + m c squared

so the Newtonian kinetic energy is defined as the limit of E – E0 when v << c. The E0 was of course unknown to Newton. The energy associated with relativistic momentum is always E, the total energy. The famous equation:

E0 = m c squared

means that mass at rest or in motion has an energy m c squared. The relativistic momentum gamma m v is necessary for conservation of momentum in special relativity (see Marion and Thornton). The four momentum is
p sup mu = (E / c, p)

where E is the total relativistic energy and where p is the relativistic momentum. If the velocity of the particle is zero, then:

p sup mu = (E0, 0)

The rest energy E0 is so called because it exists when v is zero. In Newtonian physics a particle at rest has no kinetic energy. So E0 is more precisely “the kinetic rest energy”.

E = h bar omega = h bar (omega sub f – omega sub i)

p = h bar Q = h bar (kappa sub f – kappa sub i)

and only these equations are used (www.isis.stfc.ac.uk, google “inelastic scattering theory”). The trouble starts when one uses

E = h bar omega = gamma m c squared
p = h bar kappa = gamma m v

and we already know from equal mass scattering in UFT 158 to 162 that the theory will collapse entirely. The masses must be replaced by covariant masses.

T = E – E0 = (gamma – 1) m c squared

The electron at rest in this case would have no rest energy (E0), which contradicts nuclear physics.

p = h bar kappa

but if we dig a little deeper it is found that the theory does not work if we try:

p = h bar kappa = gamma m v

combined with

E = h bar omega = gamma m c squared.

and energy and momentum conservation. To find the point of collapse of the theory was by no means trivial. The computer algebra could not do it, and human experience was needed.