It has to be considered that we computed the Lamb shift as a correction to the spin orbit coupling. This was a different integral. The Lamb shift is larger by orders of magnitude than what comes out as the correction factor in this calculation. A deviation by 10 power -9 is probably not measurable by a spectroscope.

I computed the correction factor with the Einsteinian m(r) = 1 – r0 / r for curiosity. The results are nearly identical to the last curve of UFT 434 (rational function). The power of r0/r seems to be important,

m(r) = 1 – (r0/r)^n

gives results similar to the exponential m(r) for n>=2. At least the characteristic of the splitting then is similar to that of the exponential m(r).

It has to be taken in mind that H is the worst system to study such effects. in heavy elements the deviations by m(r) will be much larger. However there are no analytical wave functions known for Z>1 as you know. We would need radial wave functions from quantum chemistry. What about the effect of spin? Will m(r) be spin-dependent in spin polarized atoms?

Horst

Am 23.03.2019 um 07:34 schrieb Myron Evans:

]]>Exponential m Functions

These show precisely the behaviour seen in the Lamb shift, the 2S sub 1/2 orbital is affected by the 2P sub 1/2 orbital is not affected. In my opinion the next step would be to repeat these computations using the wavefunctions of the Dirac atom, which can be expressed in terms of the hydrogenic wavefunctions of the Schroedinger atom. That would introduce the spin angular momentum, missing from the Schroedinger atom. As a matter of curiosity it would be interesting to compute the effect of the Einsteinian m(r) = 1 – r0 / r on the H atom. That would give the effect of gravitation on the H atom spectrum. However, it is known that the Einstein theory is thoroughly obsolete, and has been superceded by ECE theory and m theory. The use of the time dependent Schroedinger equation is very powerful.

These results are full of interest, and open up the subject of generally covariant quantum mechanics in the H atom, i.e. the unification of general relativity and quantum mechanics in the H atom. It is seen that the Lamb shift is present, and as observed experimentally, very small. Different m(r) functions produce different patterns of shifts and splittings. so numerical experiments can be used to produce the observed spectrum of H, inclusive of the observed Lamb shifts. The Dirac wavefunctions of the H atom can be used for complete self consistency. These results give the influence of the vacuum on the spectrum of the H atom in a vastly simpler and more transparent manner than the old physics. In order to describe any Lamb shift to any precision, a particular m(r) function can be chosen. These results mean that the Dirac atom with m(r) = 1 is changed by the vacuum to a generally covariant H atom of m theory. In order to describe the experimentally observed spectrum of H with complete precision, the m(r) functions can be adjusted for a given wavefunction. The Lamb shift in the old physics is described by quantum electrodynamics, which uses virtual particles generated from the Heisenberg principle of indeterminacy. The old physics has multiple problems as the UFT series shows clearly, and the teaching of the old physics is being rejected. The scientometrics show that very clearly.

Section 3 of UFT 434: energy level shifts on Hydrogen

I computed the impact of several m functions on the energy levels. The

effects are very small as expected. Interestingly, different types of m

functions evoke different characteristics of the shifts.

Horst

]]>UFT 432,3: Yukawa force and Born-Landé lattice

This is indeed excellent. Well done Horst!

Sent from my Samsung Galaxy smartphone.

]]>This section is full of interest and an accurate explanation for LENR. A great deal of careful work by Horst Eckardt has gone into it and it explains the correct way of doing calculations in m theory. An example is given of the wrong way of calculating m theory. So LENR is centre stage and should be awarded an experimental Nobel Prize in due course. As usual the graphics are well thought out and greatly clarify the intricate mathematics. This is another example of a phenomenon being explained in a radically new and imaginative way, deserving a theoretical Nobel Prize. This assumes that the Nobel Prize recognizes merit.

UFT 432,3: Yukawa force and Born-Landé lattice

After some computational work that had intricate details – although

straightforward in theory – I finished section 3. I depicted the general

scheme how to work with m theory in r1 space in Fig. 1. I think everyone

learning m theory should internalize this scheme so that logical errors

can be avoided.

The section contains a comparison of the Yukawa and Coulomb potential

and force, showing that both cancel each other quite precisely. The

historic theory of the Born-Landé lattice was used to show that LENR in

NiH is possible. In addition, this method delivered a parameter-free

determination of the m function in a certain limit.

Horst

]]>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.