Archive for April, 2019

Fluctuating m Space Theory

Thursday, April 18th, 2019

Fluctuating m Space Theory

This derivation might be given in one of the background notes of the UFT papers, otherwise might be in a textbook or or on the net.

437(4): Self Consistency of the Vacuum Force and Lamb Shift

Thursday, April 18th, 2019

437(4): Self Consistency of the Vacuum Force and Lamb Shift

This note demonstrates the self consistency of the vacuum force of UFT417 and the m theory of the Lamb shift given in Eq. (1).

a437thpapernotes4.pdf

Fluctuating m Space Theory

Tuesday, April 16th, 2019

Fluctuating m Space Theory

This is based on equation the potential of m theory with that of zitterbewegung theory in Eq.(1).The results are shown to be self consistent. The Lamb shifts for any atom or molecule can be explained with the universal fluctuating m(r) given in Eq. (29). This is a method based on Eq. (31): r1 = r / m(r) power half = r + delta r, i.e. r1 = r + delta r. This defines the (r1, phi) frame. The m(r) function is defined by m(r) power half = r / (r + delta r). If m(r) = 1, then delta r = 0. So vacuum fluctuations delta r are due to the departure of the metric from flat space. The quantization rules remain the same.

a437thpapernotes3.pdf

Some Leading Scientists who Accepted B(3) and ECE Theory

Monday, April 15th, 2019

Some Leading Scientists who Accepted B(3) and ECE Theory

These include Jean Pierre Vigier (co worker of the Nobel Laureate Louis de Broglie) and Lawrence Horwitz ( Ph. D. student of the Nobel Laureate Julian Schwinger). Special editions of "Foundations of Physics Letters" were devoted to both. Ernest Sternglass listened to a lecture of mine on B(3) at Vigier One in Toronto, and accepted the lecture without criticism. The entire conference accepted the B(3) theory. Einstein invited Sternglass for a private discussion about his work and advised him not to get trapped in the academic system, but to "take a cobbler’s job" in the daytime and work on his own ideas in the evenings. Einstein wanted Sternglass to talk in German, their native language. John Wheeler sent me a very long fax message about B(3) in which he discussed it in detail. Alwyn van der Merwe, the eminent and liberal editor, accepted B(3) and ECE theory and very generously supported it before he was purged by a group of long forgotten harassers. The mathematical physicist Diego Rapaport has given the best description of the ECE theory, describing it as economical and brilliant, or similar words. John Wheeler became Einstein’s assistant after Jean-Pierre Vigier was refused a visa. Vigier was Einstein’s first choice. By now millions have accepted ECE theory and there are seven hundred papers and books on it, roughly the same as Linus Pauling’s entire output. I found out about the academic system at UNCC, which fabricated childish lies to get rid of me because B(3) did not fit in to the academic thinking at the time. My actual research record there was outstanding, teaching was good to excellent, administration was average, and I was a tenured full professor. So they had to think of something, and came with "working too much from home" or using striped toothpaste. Einstein would obviously have condemned that outright. Mansel Davies also accepted B(3) and tipped it for a Nobel Prize. This was blocked by the machinations of the standard modellers. Now it is clear that the academic system has lost the moral and ethical high ground, after an endless series of scandals. The AIAS / UPITEC group consists of eminent people, notably Horst Eckardt, who have all greatly contributed to ECE. So they have taken the moral and ethical high ground, being untainted by greed and corruption. Einstein advised Sternglass that he would never make it to full professor if he were too radical or liberal in thought. Endless obstacles were put in my way by what is now known to be a very corrupt academic system. As a young man Einstein was himself a radical, one of his teachers at ETH, Weber, called him a lazy dog because he would study on his own. The small group of unethical harassers who had van der Merwe purged also attacked the Sci Topics Editor who had tipped my work for a Nobel Prize, and also used Wikipedia as a medium of gross defamation. Wikipedia comes out of this as a third rate propagandist rag. It even tried to suppress mention of my Civil List Pension. A Nobel Prize for B(3) or ECE would mean the end of standard physics, so they are obviously reluctant to judge fairly. I do not think that they have the technical ability to judge fairly. The standard model has become thoroughly obsolete with or without a Nobel Prize because of the educational power of the internet (for example the famous UFT88). The Nobel Prize has also become obsolete, it is no longer awarded for the best up to date work, but is often awarded for work carried out up to fifty years ago, and then only standard model work – "a club like any other" in the words of Mansel Davies, a chemistry Nobel Prize advisor. It seems that there are plans in the United States for the closure of two thousand colleges and universities. This may or may not be true, but the general public no longer has respect for a University system that loots the taxpayer, producing nothing in particular, and crudely suppressing scholarship and freedom of thought in violation of the First Amendment

Fwd: FOR POSTING: UFT436, Sections 1 and 2

Saturday, April 13th, 2019

FOR POSTING: UFT436 Section 3.
This section is full of interest and uses m theory in computational quantum chemistry for the first time. The harmonic and anharmonic oscillators are developed in m space, which has various effects on this important problem in quantum mechanics. The local density approximation in an ab initio method is used to compute the charge density of nickel, which is important for low energy nuclear reactions. The effect of m theory is evaluated and graphed. It becomes clear that the concept of an m space works its way through into the whole of quantum mechanics. Both Horst Eckardt and I come from a chemical background so this type of computation gives particularly interesting results. Chemists regard quantum electrodynamics as an abstruse mathematical maze, leading nowhere in particular – dippy physics in the words of Feynman. It is particularly interesting to note that m theory dominates in nuclear physics. Clearly, its effects are also present in chemistry (the electrons outside the nucleus) as this important section 3 shows. In reproducing the spectra of atoms and molecules it will be particularly important to see whether one m(r) function is sufficient. For example Lamb shifts occur between certain states but not others. This note is essentially the application of computational quantum chemistry to the unification of quantum mechanics and general relativity. This gives the effect of the vacuum on all kinds of spectra, from radio frequency to microwave to far infra red, infra red, visible, ultra violet and gamma ray. The vacuum is now understood as the geometry of space itself.

This is section 3 of the paper. I added some graphics and a principal description of inclusion of m theory in quantum chemistry. We will see if this can be further developped.

Horst

Am 12.04.2019 um 08:26 schrieb Myron Evans:

FOR POSTING: UFT436, Sections 1 and 2

Many thanks for going through these notes.

1) The problem of the divergence was addressed in Note 436(3), by restricting the normalization to the unit sphere. The same type of problem occurs in linear motion and has to be dealt with using a limit procedure (see Atkins, "Molecular Quantum Mechanics" for example, in this case Atkins happens to be right, his treatment of the particle in a box is wrong, as we showed in UFT226 ff.).
2) The separation of variables technique used in this paper is the same as in the previous paper UFT435, and the result (8) is more general. In other words if the assumption (2) is made, Eqs. (6) and (7) result self consistently. Eq. (6) is H psi1(r) = E psi(r) and Eq. (7) is the original Schroedinger quantization of energy. Since psi2 is defined as a function of t, then its partial derivative with respect to r vanishes. Similarly psi1 is defined as a function of r so its partial derivative with respect to t vanishes. These results were used in Eqs. (3) to (5) to give the self consistent result (6) and (7). To check this conceptually, consider the hydrogenic wavefunctions. These are made up of the product ps1(r) psi2(theta, phi), so the derivative of psi with respect to theta or phi is zero, and the derivative of psi2 with respect to r is zero. 3) The quantization rules in UFT435 and UFT436 were introduced so that the wavefunction is modified, but the structure of the Schroedinger quantization remains the same:
E psi = i h bar partial psi / partial t; p psi = – i h bar del psi.

Your use of this new method in a computational quantum chemistry package produced sensible results, so my suggestion is to develop it systematically in computational quantum chemistry, in the first instance to give the Lamb shift in H.
Notes 436(3) and (5) had not come through to me before. There is a problem in both. The integral

integral m(r)^(1/2) d tau

diverges since m(r) goes to 1 for r–>inf.
The problem obviously is that replacement of time in the time part of the wave function psi_2 destroys its independence of r and even the separability of the wavefunction psi = psi_1 * psi_2.

A second point is the question if also the integration variable r had to be transformed by

r –> r / sqrt (m(r)^(1/2)) .

This would probably lead to the result that the integrals have the same values when taken in r or r1 space. From the standpoint of general covariance this would even be desirable. As I had pointed out earlier, it seems only to make sense for me to transform the RESULTS obtained in m space back to the configuration space.

Horst

Am 10.04.2019 um 09:18 schrieb Myron Evans:

FOR POSTING: UFT436, Sections 1 and 2

This paper is on the development of generally covariant standard solutions of quantum mechanics. In section 3, the same kind of development can be implemented with computational quantum mechanics, an important new development by co author Horst Eckardt.

paper436-3.pdf

437(1): Development of the Separation of Variables Method

Friday, April 12th, 2019

437(1): Development of the Separation of Variables Method

I checked all my calculations, this note gives more details of the separation of variables method, and at the end of the usual calculation of all the textbooks transforms into m space. This is where the transformation into m space should take place. In a stationary metric dm(r) / dt = 0 (Carroll notes). The normalized wavefunction is Eq. (31), and using the so called Schwarzschild metric as an example, the result (35) is obtained, a small shift in the energy levels due to m space. This is a simple example of a Lamb type shift. In the flat space limit r to infinity the result is the usual one <E> = E. So everything seems OK.

a437thpapernotes1.pdf

Fwd: FOR POSTING: UFT436, Sections 1 and 2

Friday, April 12th, 2019

Lamb Shifts in Helium

The application of this program would be full of interest, it would mean that we are no longer restricted to analytical solutions. That is a big step forward. Calculation of the Lamb shift for other elements would be exactly what is needed, provided of course that the results are compared with the data at each step. The necessary first step is to define the wave functions and compute results in the first instance with the usual wavefunction, starting with helium. This has an exchange energy as you know. The after that use the quantization rules t goes to m power half t and r goes to r / m(r) half. I think that if the wavefunctions are correctly inputted all the output will be correct. This looks like a powerful program. The calculations for the analytical solutions play an important role in clarifying the method. I did a quick literature search and there is a Lamb shift in the ground state of helium. By now these Lamb shifts must have been measured with great accuracy.

UFT436, Sections 1 and 2

Thanks for the hints. I see that normalization has to be restricted to a volume for infinitely extended states like the oscillatory time function psi_2.
The LDA program I have can compute structures of all atoms except hydrogen, because there is no electronic exchange and correlation. Therefore the Lamb shift could only be computed for other elements. I will give some demos of effects of m theory in UFT 436, but a correct handling would require both a modified Schrödinger or Dirac equation and (possibly) a change in the LDA expressions for the total energy which depends on the charge density alone. The energy eigenvalues are the so-called one-particle energies which do not represent binding energies. I guess if the wave functions have been computed self-consistently including the m function, the charge density is that of m theory automatically and needs not to be transformed any more. What do you think?

Horst

Am 12.04.2019 um 08:26 schrieb Myron Evans:

FOR POSTING: UFT436, Sections 1 and 2

Many thanks for going through these notes.

1) The problem of the divergence was addressed in Note 436(3), by restricting the normalization to the unit sphere. The same type of problem occurs in linear motion and has to be dealt with using a limit procedure (see Atkins, "Molecular Quantum Mechanics" for example, in this case Atkins happens to be right, his treatment of the particle in a box is wrong, as we showed in UFT226 ff.).
2) The separation of variables technique used in this paper is the same as in the previous paper UFT435, and the result (8) is more general. In other words if the assumption (2) is made, Eqs. (6) and (7) result self consistently. Eq. (6) is H psi1(r) = E psi(r) and Eq. (7) is the original Schroedinger quantization of energy. Since psi2 is defined as a function of t, then its partial derivative with respect to r vanishes. Similarly psi1 is defined as a function of r so its partial derivative with respect to t vanishes. These results were used in Eqs. (3) to (5) to give the self consistent result (6) and (7). To check this conceptually, consider the hydrogenic wavefunctions. These are made up of the product ps1(r) psi2(theta, phi), so the derivative of psi with respect to theta or phi is zero, and the derivative of psi2 with respect to r is zero. 3) The quantization rules in UFT435 and UFT436 were introduced so that the wavefunction is modified, but the structure of the Schroedinger quantization remains the same:
E psi = i h bar partial psi / partial t; p psi = – i h bar del psi.

Your use of this new method in a computational quantum chemistry package produced sensible results, so my suggestion is to develop it systematically in computational quantum chemistry, in the first instance to give the Lamb shift in H.
Notes 436(3) and (5) had not come through to me before. There is a problem in both. The integral

integral m(r)^(1/2) d tau

diverges since m(r) goes to 1 for r–>inf.
The problem obviously is that replacement of time in the time part of the wave function psi_2 destroys its independence of r and even the separability of the wavefunction psi = psi_1 * psi_2.

A second point is the question if also the integration variable r had to be transformed by

r –> r / sqrt (m(r)^(1/2)) .

This would probably lead to the result that the integrals have the same values when taken in r or r1 space. From the standpoint of general covariance this would even be desirable. As I had pointed out earlier, it seems only to make sense for me to transform the RESULTS obtained in m space back to the configuration space.

Horst

Am 10.04.2019 um 09:18 schrieb Myron Evans:

FOR POSTING: UFT436, Sections 1 and 2

This paper is on the development of generally covariant standard solutions of quantum mechanics. In section 3, the same kind of development can be implemented with computational quantum mechanics, an important new development by co author Horst Eckardt.

FOR POSTING: UFT436, Sections 1 and 2

Friday, April 12th, 2019

FOR POSTING: UFT436, Sections 1 and 2

Many thanks for going through these notes.

1) The problem of the divergence was addressed in Note 436(3), by restricting the normalization to the unit sphere. The same type of problem occurs in linear motion and has to be dealt with using a limit procedure (see Atkins, "Molecular Quantum Mechanics" for example, in this case Atkins happens to be right, his treatment of the particle in a box is wrong, as we showed in UFT226 ff.).
2) The separation of variables technique used in this paper is the same as in the previous paper UFT435, and the result (8) is more general. In other words if the assumption (2) is made, Eqs. (6) and (7) result self consistently. Eq. (6) is H psi1(r) = E psi(r) and Eq. (7) is the original Schroedinger quantization of energy. Since psi2 is defined as a function of t, then its partial derivative with respect to r vanishes. Similarly psi1 is defined as a function of r so its partial derivative with respect to t vanishes. These results were used in Eqs. (3) to (5) to give the self consistent result (6) and (7). To check this conceptually, consider the hydrogenic wavefunctions. These are made up of the product ps1(r) psi2(theta, phi), so the derivative of psi with respect to theta or phi is zero, and the derivative of psi2 with respect to r is zero. 3) The quantization rules in UFT435 and UFT436 were introduced so that the wavefunction is modified, but the structure of the Schroedinger quantization remains the same:
E psi = i h bar partial psi / partial t; p psi = – i h bar del psi.

Your use of this new method in a computational quantum chemistry package produced sensible results, so my suggestion is to develop it systematically in computational quantum chemistry, in the first instance to give the Lamb shift in H.
Notes 436(3) and (5) had not come through to me before. There is a problem in both. The integral

integral m(r)^(1/2) d tau

diverges since m(r) goes to 1 for r–>inf.
The problem obviously is that replacement of time in the time part of the wave function psi_2 destroys its independence of r and even the separability of the wavefunction psi = psi_1 * psi_2.

A second point is the question if also the integration variable r had to be transformed by

r –> r / sqrt (m(r)^(1/2)) .

This would probably lead to the result that the integrals have the same values when taken in r or r1 space. From the standpoint of general covariance this would even be desirable. As I had pointed out earlier, it seems only to make sense for me to transform the RESULTS obtained in m space back to the configuration space.

Horst

Am 10.04.2019 um 09:18 schrieb Myron Evans:

FOR POSTING: UFT436, Sections 1 and 2

This paper is on the development of generally covariant standard solutions of quantum mechanics. In section 3, the same kind of development can be implemented with computational quantum mechanics, an important new development by co author Horst Eckardt.

436(5): m Space Expectation Values of the Complete Schroedinger Equation

Tuesday, April 9th, 2019

436(5): m Space Expectation Values of the Complete Schroedinger Equation

The complete Schroedinger equation is the diffusion equation (1) and using the separation of variables method (2) divides into two equations (3) and (4), where the energy levels E are the same in both equations. The expectation values <E> must be the same from both equations and in m space this leads to Eq. (15).

a436thpapernotes5.pdf

436(4) : General Solution of the Schroedinger Equation

Tuesday, April 9th, 2019

Computational Quantum Chemistry

Interesting discussion. It becomes clear that computational quantum chemistry packages can be modified with t goes to m(r) power half t and r goes to r / m(r) half in the wavefunction. In general all the ideas of UFT415 ff. can be developed with computational quantum chemistry. In the IBM Clementi environment the LCAP system was used with the IBM 3096 and IBM 3084. These systems were also used at the Cornell Theory Center. I think that these computations can now be carried out on desktops. In the first instance it would be very interesting to compute the Lamb shift for 2S sub 1 / 2 to 2P sub 1/2 in atomic H and adjust m(r) for exact agreement with the data. These are known now with great precision.

Doug,

the spin connection seems to play a similar role as the so-called exchange-correlation potential in N-electron calculations. Perhaps there is a connection. Also the N-electron calculations have to be performed iteratively until a convergence is obtained, i.e. the new electron potential from your eq. (46) leads to the original total potential entering the solution of the Schrödinger equation.

Horst

Am 08.04.2019 um 17:44 schrieb Doug Lindstrom:

Horst:
I’ve attached a pdf version which opened on my computer okay. The doc file was corrupt. As far as I remember, the potential was periodic up to the first Bohr orbit.
Doug

On Apr 8, 2019, at 7:53 AM, Horst Eckardt <mail> wrote:

Doug,

I cannot open the Word document. Besides this, did you apply a periodic potential of infinite length? Normaly the charge density as well as the atomic potential have to go to zero for r –> infinity.

Horst

Am 08.04.2019 um 16:47 schrieb Doug Lindstrom:

This is somewhat similar to the structure of the hydrogen atom computed for the Serbian talk back in 2010 (paper attached), which is reassuring. Figure 1 for the electron potential has a minimum near r=0.1 and a max around r=0.5 for kappa = 2 Pi (orange). 
On Apr 7, 2019, at 9:41 PM, Myron Evans <myronevans123 wrote: Computation of the Valence Charge Density of the Nickel Atom This is an exceedingly interesting development, this program applies computational quantum chemistry to the m theory and finds an effect on the valence structure of the nickel atom. It is a small effect as expected, but nevertheless it is a real effect, similar to the Lamb shift, also a small effect. So the generally relativistic quantum mechanics can be coded up in computational quantum chemistry, and applied to a vast number of problems. This program can be used to develop the m theory far in advance of analytical solutions of the Schroedinger equation. The latter is analytical only for the H atom, as is well known. For the helium atom onwards, computational methods have to be used. It would be interesting to apply this program to a proton interacting with the nickel atom, using m theory. That might lead to low energy nuclear reaction. I think that thi sis a big step forward and this program can be used in many ways. The effect of m space is that the wave functions psi(r) are shifted to the outer region by psi(r) --> psi( r/sqrt(m(r)) ) because r/sqrt(m(r)) >= r. I succeeded in reactivating an old electronic structure program for atoms which a colleague at the TU Clausthal sent me years ago. I calculated the charge density of a Ni atom. The valence charge density (10 electrons) is graphed in the file, in original form and with shifted radius coordinate as above. One has to make the parameter R of the m function quite large to find a visible effect. I hope that jpg files go through the wordpress upload better than png files. Horst Am 07.04.2019 um 09:31 schrieb Myron Evans: 
436(4) : General Solution of the Schroedinger Equation This is given by Eq. (8) and several examples given. In the usual vacuum free quantum mechanics the expectation value of energy from Eq. (8) is given by <E> = E, but in quantum mechanics in m space (or the vacuum), i.e. generally covariant quantum mechanics, the energy levels are shifted according to Eq. (31). This is a general law of quantum mechanics, true for any spectral line. 
<rhoval-Ni.jpg>