Archive for November, 2010

Curvatures for atomic H transition

Feed: Dr. Myron Evans
Posted on: Saturday, November 27, 2010 11:54 PM
Author: metric345
Subject: Curvatures for atomic H transition

These are very interesting results again from Dr Horst Eckardt. They show that every transition in atomic H will have its own R pattern which can be used for spectral analysis. The same is true for all atomic and molecular spectra. So this is the first description of atoms and molecules in terms of general relativity as corrected by ECE theory. The basic equation is very simple and is the absorption equation itself:

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.

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165(7) : R Theory of Group Velocity, Superluminal Signalling

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

This theory accounts for why the group velocity has recently been observed to be zero, negative or greater than c, and the de Broglie equation v sup p v sub g = c squared is developed for use in ECE theory and general relativity. If the numerator in eq. (5) is greater than omega, then v sub g is greater than c. Unlike the standard model this may allow for superluminal signalling, the signal velocity v sub g is greater than c. There are many reports by now of superluminal signalling. Superluminal effects may occur in matter waves.

a165thpapernotes7.pdf

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165(4): Unification of the Theory of Optical Refraction and Compton Scattering

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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Reduction of the Dirac to Schroedinger Equations

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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R Spectra of the Hydrogen Atom

Feed: Dr. Myron Evans
Posted on: Monday, November 22, 2010 11:20 AM
Author: metric345
Subject: R Spectra of the Hydrogen Atom

The atomic spectrum of H is described excellently by sometime Oxford colleague Peter Atkins in the second edition of “Molecular Quantum Mechanics”. The energy levels that should be used in eq. (6) of note 165(1) are as follows (in units of ten power minus eighteen joules, see UFT 162, eq. (31)). They are all negative, because they are bound states of the atom. They are as follows;

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.

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163(7): The Covariant Mass Ratio in Elastic Scattering

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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Note on the Newtonian Kinetic Energy

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 non-relativistic 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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