Archive for November, 2010
Tuesday, November 30th, 2010
Feed: Dr. Myron Evans
Posted on: Saturday, November 27, 2010 11:54 PM
Author: metric345
Subject: Curvatures for atomic H transition
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Friday, November 26th, 2010
Feed: Dr. Myron Evans
Posted on: Friday, November 26, 2010 7:51 AM
Author: metric345
Subject: 165(7) : R Theory of Group Velocity, Superluminal Signalling
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Tuesday, November 23rd, 2010
Feed: Dr. Myron Evans
Posted on: Tuesday, November 23, 2010 5:55 AM
Author: metric345
Subject: 165(4): Unification of the Theory of Optical Refraction and Compton Scattering
These theories are unified in eq. (6), in terms of R1 and R2, both of which can be found experimentally. During the course of my routine multiple checking work I found the following minor errata, which should be fixed in UFT 160 and 161. These do not affect any conclusions, they are just misplaced brackets.
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

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Tuesday, November 23rd, 2010
Feed: Dr. Myron Evans
Posted on: Monday, November 22, 2010 11:08 PM
Author: metric345
Subject: Reduction of the Dirac to Schroedinger Equations
The clearest method is based on the reduction of the relativistic momentum gamma m v to the non relativistic limit, p = mv. The Dirac equation is essentially the quantization of the relativistic momentum in the format of the Einstein energy equation E = T + E0, where T is the relativistic kinetic energy and where E0 is the rest energy. The Einstein energy equation is another algebriac format of the relativistic momentum. Here E is known as the total relativistic energy. The Schroedinger equation H psi = E psi is obtained from the expression for non relativistic kinetic energy, T = p squared / (2m). The operators to be used for quantization are found from p sup mu = i h bar partial sup mu. Here p sup mu is (E / c, p), i.e. is defined by the total relativistic energy E and relativistic momentum p. To find the Dirac equation the d’Alembertian is expressed in terms of the metric and Dirac matrices. However, in UFT 129 and UFT 130 I developed the Dirac equation using only 2 x 2 matrices, another basic discovery of the development of ECE theory. The relativistic momentum emerged from the conservation of momentum in special relativity (J. B. Marion and S. T. Thornton, “Classical Dynamics”, third edition, pp. 525 ff.) If re expressed, the relativistic momentum becomes the Einstein energy equation. If the relativistic force is derived from the relativistic momentum, the relativistic kinetic energy is the work integral eq. (14.55) , page 527 of Marion and Thornton. The total energy is E = gamma m c squared, the relativistic kinetic energy is T = (gamma – 1) m c squared. In the limit v << c, T reduces to p squared / (2 m), and the Schroedinger equation is the quantization of this. It is very important to bear these basic definitions in mind. Both Dirac and Schroedinger come from gamma m v, but in different ways.

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Tuesday, November 23rd, 2010
Feed: Dr. Myron Evans
Posted on: Monday, November 22, 2010 11:20 AM
Author: metric345
Subject: R Spectra of the Hydrogen Atom
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Tuesday, November 16th, 2010
Feed: Dr. Myron Evans
Posted on: Monday, November 15, 2010 2:01 AM
Author: metric345
Subject: 163(7): The Covariant Mass Ratio in Elastic Scattering
On reflection, I think that the idea of note 163(6) is over complicated, so using Ockham’s Razor I replaced it by this idea, in which the covariant mass ratio for elastic scattering is gamma, the Lorentz factor. The mass m2 of the static particle is its rest mass, which in elastic scattering does not move, so the covariant mass ratio for m2 is unity throughout. In this idea of note 163(7), the dynamic mass is different from the rest mass. We can only detect dynamic mass in a collision or interaction, so this idea seems to be self consistent and make sense. I will now extend it to other simple situations such as ninety degree scattering. So the covariant mass ratio is the ratio of the dynamic mass (a new concept entirely) to the rest mass, the mass of a particle at rest. Completely new thinking is needed now, and this seems to be the simplest solution. A moving particle can only be detected to be moving by reference to something, and the new idea is that the mass of a moving particle is different from its mass when it is at rest. “At rest” is an anthropomorphic concept, at rest with respect to what? We are at rest with respect to the earth, but the earth is moving and so on. Thus:
(R / R0) = gamma squared
a163rdpapernotes7.pdf

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Thursday, November 11th, 2010
Feed: Dr. Myron Evans
Posted on: Wednesday, November 10, 2010 9:36 AM
Author: metric345
Subject: Note on the Newtonian Kinetic Energy
As in 163(3) this is the nonrelativistic limit of T = (gamma – 1) mc squared. The total energy is
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”.

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Thursday, November 11th, 2010
Feed: Dr. Myron Evans
Posted on: Wednesday, November 10, 2010 9:15 AM
Author: metric345
Subject: Elastic and Inelastic Scattering Theory
This is essentially the same as the equations for note 163. There is non zero energy transfer. So the theory of inelastic electron and neutron scattering for example will suffer from the same catastrophic defects as the theory of Compton scattering. Elastic scattering is defined as zero energy transfer and magnitudes of wave vectors the same. Scattering theory is self inconsistent on the most fundamental level so will remain so on any level. So I will develop this point next. The vast amount of experimental work done on crystallography is of course unaffected, but its natural philosophy has been overturned by UFT 158 to 162, and notes so far for 163. Scattering theory in general rests on:
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.

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Thursday, November 11th, 2010
Feed: Dr. Myron Evans
Posted on: Tuesday, November 09, 2010 6:40 AM
Author: metric345
Subject: Atomic Beam Diffraction and Neutron Diffraction
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Thursday, November 11th, 2010
Feed: Dr. Myron Evans
Posted on: Tuesday, November 09, 2010 5:48 AM
Author: metric345
Subject: Atomic Beam Diffraction and Neutron Diffraction
These are two more experiments that show the wave nature of matter. Another is the Sagnac effect with electron beams. If a Young interferometer is set up for atomic beam or neutron diffraction, and the diffracting beams are disturbed by for example an electron beam at different angles, that would be an experimental test of the type described in notes 163(1) and 162(2). There must be extensive data on electron Compton scattering, already existing data that can be used as in UFT 159 and 160. The idea of wave particle duality is correct insofar as
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.

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