Alpha Institute for Advanced Studies

Calculation of Lamb shift

The frequency of the 2S state increases to about a gigahertz above the 2P state (Wiki, Lamb shift entry). So the energy of the 2S state increases with respect to that of the 2P state. The energy is h bar omega multiplied by a correction value integral psi* (1 / m(r) half psi dtau, so the correction value must increase, i..e become greater than 1.

Calculation of Lamb shift: sign problem

To make it clear: If the energy level of 2S becomes less negative valued, the absolute value decreases. Therefore the correction factor of the 2S state becomes smaller than one. Do you agree to this argument?

Horst

Am 25.03.2019 um 15:11 schrieb Myron Evans:

Calculation of Lamb shift: sign problem

OK thanks, I would suggest experimenting to find the m(r) function that gives the experimental result. As long as m(r) becomes one in the Minkowski space, there is freedom of choice, so it can become greater than one. It is encouraging that an exponential m(r) gives the correct result of S being shifted and P not being shifted. There is a rise of about 1000 MHz of the 2S level. This means that the energy level of 2S becomes less negative valued, and the frequency increases. The absolute value of energy increases, so the absolute value of the theoretical result would match the experimental result.

Calculation of Lamb shift: sign problem

Accoring to the diagram of Fig. 1 in UFT429, the Lamb shift affects the
2S1/2 state, not the 2P1/2 state. This is verified by our exponential
m(r) functions. However the absolute value of the energy level shrinks
(because the levels in the diagram are negative). This is in conflict
with the expectation value

integral psi* 1/m(r)^(1/2) psi dtau

which gives values >1 because m(r)<1 near to the centre. The situation
could be remedied by using a m(r)>1, but this would change all our
assumptions we made before.
I appended the diagram with relative energy change of the 2S1/2 state.
The experimental shift has been added. The parameter R is about 0.015
Bohr radii which is about twice the value obtained form s-o coupling in
UFT 429.

Horst

PS Experimenting with m functions

I agree with Horst in Section 3 of UFT434 that a rich spectral structure emerges by experimenting with m functions. The same structure must appear from both sides of the time dependent Schroedinger equation, so this fact produces useful constraint equations. When m(r) = 1 we get E = h bar omega = <H>. The left hand side of the time dependent Schroedinger equation gives h bar omega, the right hand side gives E = <H>. For any finite m(r) we have more than one h bar omega, and more spectral structure.

Continuing with UFT435

The expectation values (energy levels) on both sides of Eq. (1) must be the same, so for a given wavefunction such as 2P or 2S that will give equations for m(r). An experimental Lamb shift is given by Eq. (6). So I will develop the theory in this direction in the next note.

435(1): Experimental Deter you can find splittings where normination of m(r)

The Lamb shifts must emerge from Eq. (1), so must be described by both sides of Eq. (1) self consistently and must of course agree with experimental data. So the result from Eq. (6) of the note must also be produced by the right hand side of Eq. (1). This was the method referred to yesterday in your comment. For example 2P sub 1/2 is not Lamb shifted, so this is equivalent to m (r) = 1, but 2S sub 1/2 is Lamb shifted to a higher frequency, omega sub 1, where omega sub 1 / omega is given by Eq. (6). The expectation value E sub 1 from Eq. (4) must be the same as the expectation value <H sub 1>, worked out in a previous UFT paper. Another method is to solve Eqs. (3) and (4) simultaneously for m(r). I agree that the effect of the vacuum is always present, i.e. the mechanism for the Lamb shift is always present, but whether or not it manifests itself depends on the wavefunction.

435(1): Experimental Deter you can find splittings where normination of m(r)

For comments see my emil from yesterday. There was a table with equivalencing relativistic and non-relatovistic quantum numbers in one of the older papers dealing with spin orbit coupling, as far as I remember.
In experiment there are only the values including all effects available, you cannot switch off Lamb shift or s.o. coupling. However you can find splittings wher none are predicted by theory.
Horst

Von meinem Samsung Gerät gesendet.

To Russ Davis

Interesting question. Both approaches are based on geometry, and are linked through the wave equation and tetrad postulate. The m theory is based on the infinitesimal line element, while UFT357 is based on Cartan geometry. The m theory is simpler and can be applied to give startlingly new results as in UFT415 ff. The m theory is very fundamental and radically new, because it uses the most general spherically symmetric space, which transforms the infinitesimal line element of special relativity to that of general relativity. The latest idea in Note 435(1) is to allocate an m function to each spectral line. The Schroedinger quantization takes place in the most general spherically symmetric space, and the method of Note 435(1) is simple, it gives the Lamb shift without having to work out the expectation value of the hamiltonian. The Einsteinian general relativity (EGR) was the first to use an m function, m(r) = 1 – r0 / r where r0 is the Schwarzschild radius. However that was a function derived in the absence of any consideration of torsion, and EGR is known to fall apart in almost a hundred independent ways in the UFT papers and books. The m theory is more powerful because it is simpler, and also uses an m(r) that can be determined from experimental data. The m theory describes the interaction of H, or any atom or molecule, with the "vacuum". "The vacuum" is now known to be m space.

Re: 435(1): Experimental Determination of m(r)

Hi Myron,

Would you comment on a comparison of the fluid spacetime description of the Lamb shift (UFT357) with the most recent m-theory formulation; can one conclude, perhaps, that the m-theory description is more powerful, and affords additional clarity of detail?

cheers,

Russ Davis

435(1): Experimental Determination of m(r)

In this note the Lamb shift is understood in terms of Eq. (6), from which m(r) may be determined numerically, because the quantities on the left hand side are known experimentally to high precision. For H lines that are not Lamb shifted, m(r) = 1. So m(r) becomes a fundamental spectral function of the generally covariant H atom. It is shown that there is no Lamb shifting the Dirac atom (cf. UFT430). This method has the great advantage of not having to model the m(r) function.

a435thpapenotes1.pdf

The Time Dependent Schroedinger Equation in m Theory and General Relativity

Many thanks! I would say that the theory is already proven experimentally in many ways, for example B(3) was based from the outset on the inverse Faraday effect, which is why it has already been nominated for a Nobel Prize about half a dozen times. It was recognized by a Civil List Pension, much less well known than the Nobel Prize but a higher honour, being a State honour. Vigier was particularly pleased with the fact that B(3) was inferred from the inverse Faraday effect, which therefore proves photon mass, his life’s work. In the latest paper UFT434 the Lamb shifts are predicted from general relativity for the first time, and these Lamb shifts have already been observed of course. It is a matter of adjusting m(r). There are consultations from literally hundreds of universities, but none has been asked to cooperate as yet, and we have not applied for funding. So the spectroscopic measurements on the Lamb shift are very precise and have already been carried out of course. In my opinion, recognition does not depend on a Nobel Prize. I have shown that the h and g indices and output of Nobel Laureates are abysmally low compared with the group and myself. There is already a vast amount of recognition around the world. I would suggest a phone call to the University of Muenich for example. I would say that it is a good thing to predict a completely new phenomenon as you mention, but new explanations for well known phenomena also qualify for a Nobel Prize. For example the photoelectric effect. Your summary is the best one, the true understanding of the new theories must be soaked up like blotting paper.
The Time Dependent Schroedinger Equation in m Theory and General Relativity

The results of unification of quantum mechanics with general relativity in form of m theory are outstanding and – in particular – workable. However in my opinion this is not sufficient to be recognized by the complete scientific community. I was told that practical experiments have to show that the theory works. Best is to predict and then find experimentally any results not predicted by any theory hitherto known. So to earn Nobel prizes for AIAS, somebody has to execute e.g. spectroscopic measurements to find the predicted splittings. A combined theoretical/experimental effort would be needed. This is difficult to achieve because AIAS has no budget and universities are not willing to cooperate. This is a "hen egg problem".
Concerning the planned meeting, when will Steve come over for a visit?

Horst

Am 22.03.2019 um 08:01 schrieb Myron Evans:

The Time Dependent Schroedinger Equation in m Theory and General Relativity

Many thanks to Kerry Pendergast. I am about to write up UFT434 and after that the systematic development of quantum mechanics in m theory, in other words generally covariant quantum mechanics. The m space causes more energy levels of the H atom to appear, and this is essentially the Lamb shift. Of course anyone is welcome in a planning conference, or at any time. The use of m theory automatically means general relativity. The Schroedinger H atom is a limit of the relativistic Dirac H atom, and m theory produces the generally covariant H atom. It is well known that the Dirac H atom cannot produce the Lamb shift, but the generally covariant H atom produces it. The m(r) functions are chosen to produce the experimentally observed Lamb shifts. So UFT434 will deal with generally covariant Schroedinger quantization illustrated with the H atom.

The Time Dependent Schroedinger Equation in m Theory and General Relativity

This is amazing!

Can we now concentrate on general relativity for the next few weeks?

It is time for a preconference in anticipation of Steve’s annual visit!

Perhaps Horst would like to join us this year!

Best wishes

Kerry

Keep up this incredible work!

On Thursday, 21 March 2019, Myron Evans <myronevans123> wrote:

The Time Dependent Schroedinger Equation in m Theory and General Relativity

This is equation (3) and produces new energy levels, for example of the H atom. These can be observed as the Lamb shifts. As shown in previous UFT papers, the Lamb shift is due to the m function m(r), and can be interpreted as the interaction of the H atom with the vacuum in the language of the old physics, now thoroughly obsolete. The usual time dependent Schroedinger equation for the H atom produces the wave particle dualism of the atom, which is a particle and also a wave. So beams of H atoms produce interferograms, as is well known. The m theory can therefore transform classical physics into general relativity, and merge it with quantum mechanics in a simple way. This is far in advance of the old physics.

Many thanks!

434(4): Unification of General Relativity and Quantum Mechanics with m Theory

To Horst: Yes, note 434(5) should have been 434(4). To Gareth: The unification of general relativity and quantum mechanics in Eqs. (25) and (26) of Note 434(4) means that any particle in m space is also a wave in m space. The use of t1 and r1 in the Schroedinger quantization means that new wave / particles are produced by m space itself, because more energy levels and momentum levels are created. In the limit m(r) = 1 the well known de Broglie Einstein equations of special relativity are recovered. These are E = h bar omega = gamma m c squared and p =h bar kappa = gamma m v. In m theory the single energy level and momentum level are accompanied by n more levels, depending on the choice of m (r). The unification of general relativity and quantum mechanics opens the way to a vast number of possibilities which overturn the standard model in many ways. In the old physics m(r) is restricted to 1 – r0 / r but in the new physics m(r) can be any function.

434(4): Unification of General Relativity and Quantum Mechanics with m Theory

This note is numbered 434(5). Is there a 434(4) missing?

Horst

Am 19.03.2019 um 10:01 schrieb Myron Evans:

434(4): Unification of General Relativity and Quantum Mechanics with m Theory

The unification is achieved with the de Broglie / Einstein equations in m space, Eqs. (25) and (26). One of many consequencies is that the synthesis of photons with mass and particles results as a consequence of the m space and m(r) function, defined by the infinitesimal line element (1). So this is an explanation of why so many elementary particles can be observed. In early UFT papers this type of unification was achieved using the ECE wave equation and the tetrad postulate. The standard model has failed to provide any satisfactory unification of this type. The existence of the photon with mass was proven from the inverse Faraday effect in 1991, through the B(3) field, nominated several times for a Nobel Prize, and recognized with a Civil List Pension.

FOR POSTING

Section 3 of UFT 433
To: <heva709puri>

This Section 3 is full of interest as usual and initiates the numerical solution of the wave equation in m space, using wavefunctions of modified Bessel type. It is shown that there are similarities to the radial part of the Schroedinger wavefunction. In the H atom these are related to the modified Laguerre polynomials. The overall aim is to show that the energy levels of the elementary particles in nature emerge from a choice of m(r) for any given nucleon interaction. For example a neutron proton interaction taking place through the nuclear strong field gives pions, rho mesons and omega mesons. The charged pions are degenerate and have different energies from the neutral pion. The charged and neutral rho mesons are almost degenerate, and the neutral omega mesons are also degenerate. This is an excellent start.

Section 3 of UFT 433

I finished section 3. Besides some examples for usage of Bessel
functions as wave functions, I explained how the radial wave equation
for particles can be solved. A detailed numerical study is still
outstanding.

Horst

paper433-3.pdf