I am not sure that I understood the second part of your question, but the interaction causes electron to accelerate, and if the electron is slightly off centered, then that changes the direction of the motion (no longer linear). And also this could be a scattering process and will not necessarily be circular.

Dear Sydney, thank for your comment and your interest in this problem. You write “If I am right, this question has a direct relation with one of your previous questions: Can the notion of a field be immaterial? Moreover, your paper “The Wave and the Quantum State” shows at first sight to be an extensive description of the underlying subject.” You are right but the difficulty is the linear motion and your suggestion is difficult.

As you know Dirac’s equation includes the operators Px, Py and Pz. The operator Px and Py give the rotation in the plane Ox,Oy; now what contribution for Pz. My approach is that the term Pz contribute to a linear motion along Oz. At the time of Sommerfeld the attempt to find a possible spatial interaction were not successful. On the other hand Dirac finds an electrical momentum very similar to the magnetic momentum. This suggest that the notion of charge is a property of the motion itself, thus the hypothesis of variation of the mass see “Total angular momentum and atomic magnetic moments". Now whatsoever the good explanation we have to understand the electrical moment and the role of the operator Pz.

Dear Miremad Aghili, Thank for your explanation. I hope that the above discussion will shed light to you.

Kind regards Xavier

Dear Sydney, I am first a chemist with two experimental theses in chemistry. I spent a lot of time to explain the crystal structures and it is fundamental to have a clear understanding of the quantum mechanics. The notion of synchronization between the periodic motions of electrons of neighbor atoms strongly indicate that the Bohr-Sommerfeld model is the good one see “Atoms and crystal structures”. The sharing of the quantum h between the motions of rotation and translation is an easy answer to the understanding of the QM.

On the other hand the existence of inert gas compounds is easier to understand with elliptical orbital than with wave approach the sum of the orbital being spherical.

Now as further justification I can add: In the paper “The Wave and the Quantum State” I wrote in section six: As we have seen repeatedly the notion of point is a significant barrier to progress towards a better understanding of atomic physics. Behind this difficulty there are mathematics prevailing in physics as master while it is physics or in a broader way the experiments that allowed to build mathematics. The result is the difficulties of the Copenhagen school and its members is that they do not takes into account the fact that that any object has a volume and that at the atomic scale the concept of point almost lost much of its value. The language of mathematics is remarkable and I always liked it; I remember Professor Laurent Schwartz teaching us symbolic algebra where operators can be manipulated as numbers that solve differential equations, I was full of admiration and I still remain so. But despite the elegance of the method, the difficulties of continuous and infinite remain. I hope that these few lines can help researchers. There is a whole field of research that I recommend to my young colleagues.

With kind regards,

Xavier

The capture of a free electron by a proton emits light. The emitted photons carry away some momentum. Their total value remains 13.53 eV/ c.

As a french reader, you may read the handbook in french:

Microphysique quantique transactionnelle, Principes et applications.

5e édition.

http://www.lulu.com/shop/http://www.lulu.com/shop/jacques-lavau/microphysique-quantique-transactionnelle-principes-et-applications/paperback/product-23657596.html

The english version is printed by the same printer.

Hello Xavier,

From another thread, I copy below my response, which is the same.

Quantum mechanics is not difficult to understand today, we evolved our thinking.

There is not only ONE way something can happen, you can consider ANY path. The theory calculates, by conservation laws, which end-result is obtained, and experimentation confirms.

Take the two-slit experiment, with electrons. Any path can be followed by the electron, the end-result is calculated, and experiment confirms. You can do it as many times as you like, the end-result is always the same. But you cannot choose or constrain the electron path, the problem is different, the end-result is different.

Cheers, Ed Gerck

I totally agree with Dr Xavier Oudet that the notion of a point particle is the main stumbling block in our understanding of the atomic world. I would go to the extent of saying that this analogy is as absurd and therefore as dangerous as picturing the spinning electron as a rotating sphere.

Regards

Dear Sydney Ernest Grimm, the Bohr-Sommerfeld model is not limited to the conservation of the energy with the trajectories of the electrons it bring a precious tool to understand the spatial properties of the atoms.

Let me now add the following discussion of the cubic structure: section 5.1 in Atoms and crystal structures,

The crystal structures are determined from their X-ray, electrons or neutrons diffraction patterns. The interpretation of these patterns uses the symmetry of the point groups where the atomic positions are considered as points. From this point of view the atomic dissymmetry is ignored. But from a strict geometrical approach with dissymmetric atoms, it is useful to underline that the cube would not be exhibited as a crystal structure. Indeed in a cube there are four body diagonals which link two by two, two opposite apexes. Yet there is no strictly periodic lattice built with non-spherical objects able to make identical the four diagonal of a hexahedron. If we search to build an arrangement with three equivalent directions; in a first step we will put together the atoms in planes since we will stack up them, thus we can build three diagonals of the cube but the fourth has its properties determined by those of the three others. For example it will be the easy direction of magnetization in some cubic magnetic compounds, a difficult difference to detect on a nom magnetic aspect. Nevertheless if we still observe cubic structures this comes from a small disorder, which is sufficient to maintain the cubic structure, the atomic dissymmetry being too small to generate a corresponding structure. From experiments the disorder is revealed in the mosaic structure of the crystals; Guinier thus conclude a discussion on the crystal perfection "In the majority of the cases, the ideally imperfect crystal is a better approximation than the perfect crystal".

With kind regards

Xavier Oudet

Dear Irfan Lone,

Thank for positive comment. Let me add that as soon as a particle has a volume we cannot consider a continuous line and it is difficult from this remark to justify the wave approach. To discuss this in the “Wave and the quantum state” section 5, I focus the attention on the choice of de Broglie: Let us now consider the hypothesis of Louis de Broglie of a wave associated with the electron which has led to the discovery of the wave equations. It leads to extend the notion of continuous to the scale of the interactions between the constituents of the atom. Thus the continuous appears to us always intimately linked to the discontinuous. But it is necessary to keep in mind that the point is a mathematical concept that has no volume and hence no physical reality. The continuous subsequently appears a convenience but one as to keep in mind that material reality remains the discontinuous. It was in noting that light came to us from atoms, therefore emitted from a finite set of atoms, that Einstein was brought to propose the hypothesis of the photon. Come back then to the symmetry between the motion of a mobile and the propagation of a wave which led de Broglie to associate a wave to the electron; It is also possible to associate a flow of material particles in the wave, for example of light, thus joining the hypothesis of the photon of Einstein. However if the number of photons becomes small, then the support of the continuum which is the wave can no longer interpret interference; one has then to consider the stocking of the photons where the interferences are observed.

Regards Xavier

Dear Sydney Ernest Grimm,

We often forget that the first quantum state publication was the Periodic Table. It is the chemistry which first have allows to discover the Quantum state.

With kind regards Xavier

Dear Xavier Oudet

Leaving aside an atom what is your opinion regarding an electron having an extended structure in space???

With kind regards

Irfan

The electron may have a spatial extension without having some "structure".

Dear Jacques Lavau

Exactly, it does have.

With regards

Irfan

Dear All thank for your interest.

Let me focus the attention on one aspect of the possible spherical interaction. Einstein in 1905 with his study of special relativity showed that there is no absolute space and that physical laws should be independent of the place of observation, which made a giant leap in physics. As a result it did not come to anybody the idea that there could be a lack in this analysis. Yet the difficulties encountered by the corpuscular approach of quantum mechanics are well related to the notion of space. Indeed there is no absolute space and one has to question how the space is built. On the macroscopic scale it is easy to define it in relation to the objects which occupy it, without forgetting the gas that fill volumes between objects, gases that transmit the sound for example. But what about the scale of the atom? Up to now electromagnetic field has allowed us to write the motion of the electron around the nucleus. But Einstein has also taught us that the mass is equivalent to an amount of energy by establishing the relationship: E= mc2. This energy is huge so that it suggests that the motion can be described by a discontinuous flow of very small grains of matter, constituting the mass, between the proton and the electron without the notion of charge.

More precisely through two fluxes: one from the proton to the electron the other from the electron to proton, these two fluxes not following everywhere the same route in such a way that the resulting action creates the movement. One of these two fluxes will give the angular momentum the others the linear motion.

Up to now we have been able to explain the angular momentum without suspecting a possible linear motion, but there is no reason to forget it. The two fluxes allow tis linear motion. See for example the wave and the quantum state.

Regards, Xavier

Dear Irfan Lone, you write: “Leaving aside an atom what is your opinion regarding an electron having an extended structure in space???” It is a puzzling question, an answer need to be able to try to observe but is it possible to observe such an electron? That I can say a structure need an interaction. Regards Xavier

I am not sure I understand the issue. If the electron approaches from a great distance the motion at least approximates as linear. As it gets closer, its states become quantized, with a total action nh, and it radiates energy as specific em frequencies that are well known. At the same time, because there are two degrees of freedom, the n quanta of action are actually described by

n = (nr + 1/2) + (ℓ + 1/2)

So the angular motion becomes more apparent as the radial quantum number nr becomes smaller. This gives the Schrödinger answer as represented in textbooks if you add the halves. Apart from that, I don't see the problem

I apologise for multiple answers. I kept tryng when an error message appeared, but it seems there was no error.

Dear Xavier Oudet

I should better have used the word extension in space instead the word extended structure in space. Word structure in this case is somewhat sloppy. My apologies.

With due regards

Irfan

Ian Miller. You can easily suppress your excess messages. I did so when surprised by the same bug.

Dear Ian Miller: You are right if we consider the rotation and the radial distance there are the two degrees of freedom of the plane motion. In other words my question is why the perpendicular direction to the rotation is not involved in the motion?

In his work “The Quantum Theory of the Electron” Dirac express the Klein Gordon operator in a product of two operators where there are variations of the three degree of freedom in the space. In fact the solution of this equation involve negative values of the quantum number k taking the value k = l or k = -(l+1) and never l=0 if k=l, a different result from that of Schrödinger. The negative value of k lead to suppose that k represent the action.

Furthermore Dirac finds an electric moment along the normal to the plane of rotation.

The quantum numbers represent the change in action per period assuming a wave. This cannot be negative as it would represent time reversal, but you do run into a problem if you consider the wave can go both ways. This should not be represented by negative quantum numbers. The motion of one particle in a central field, and the absence of any other constraint, following the Lagrange formulation, has only two degrees of freedom. Obviously if we apply an external field, such as a magnetic field, that introduces a third degree of freedom.

Equally obviously in terms of mathematics you can introduce whatever you like, but if you want it to be physical, you must not add any more than is required by observation. As far as I am aware the two degrees of freedom as required by the Lagrangian (and hence Schrödinger) properly addresses all the observational evidence we have.

The electron wave has always four components, two of them are retrochronous.

Dirac, 1928.

I was referring to the wave associated with an electron in motion. Dirac had a different mathematical representation, and the retrochronous ones are arguably non-physical. (I do not accept that a positron is an electron travelling back in time.)

Who are you to assign the natural properties of the electron to be "non-physical"? Four components, not less.

Until someone shows some evidence, going back own time is just an arbitrary mathematical trick. It is like taking the momentum of a train. You have the kinetic energy, but the momentum does not represent momentum going both ways.

Are you aware that macrophysics is not microphysics? That crowds of individual waves are not ONE individual wave? That the macroscopic waves in a collectivity of matter (such as gravity waves) are not crowd of individual waves (such as a laser beam, or a cathodic ray beam), either.

In the real world, photons at the frequency 65.05 THz converge onto a 12C16O molecule, and excellent detectors work that way.

In the real world visible photons converge onto the opsins and cis-retinal of your retinas, whichever the defects of vergence your eye may have.

Provided the clandestine hypothesis that absorbers do not exist, Heisenberg proved that according to the Schrödinger equation, an electron should dilute in all space in a striking time. Though in the real world, absorbers do exist, and no free electron dilutes in all space beyond the given dimensions of its Fermat spindle between its emitter and its absorber.

Dear All, when I read for the first time around 1971 the possible negative values of k, I think we have to understand this point it is fundamental. The quantum mechanics cannot escape to the question concerning the negative value of k. On the other hand if you have read the paper of Dirac it is clear that the solutions of his equation tend to that of Schrödinger when c the light speed tends to infinity.

Let me consider the interaction between the proton and the electron. One possible explanation is that there relative motion is a circle with a corresponding action h divided into two equal parts of h/2, one corresponding to an angular momentum the other to a linear momentum. Now the interaction leads to the emission of a photon. This emission induce an angular momentum which can be subtracted to the first angular h/2. When k = -(l + 1) the corresponding momentum must be add to the half angular momentum h/2. This is the meaning of the negative value of the action of course it is an algebraic result and the action has to be consider positive. When there is one additional electron the lower level exhibits two quanta either on the 2s states or on the 2p states. The differences between the 2p1/2 and the 2p3/2 states is that the 2p3/2 states are obtained with a small increase of the functions of the variable r have a very small additional term. See “The Quantum State and the Notions of Spin, Wave Function and Action” also in “L’Electron magnetique” de Broglie, you will find the solution explained in detail.

Would not a state with negative action imply either negative energy or negative time? For me, neither of those is attractive.

Dear Ian Miller: We know that Dirac has transformed the Klein Gordon square operator as a product of two linear operators. It is evident that the square operator work for positive or negative charge associated to positive energy or negative energy. With Dirac it has been supposed that one of the linear operator is for the negative charge and the other for the positive. It is surprising that the same operator is use for two different particles. Well, but at this time the variation of the mass giving two flux of matter between the proton and the electron was not considered. In “The symmetry of the motion, the mass and the quantum state”, I explain that: “The hypothesis of exchanges of matter divided into two fluxes of opposite directions brings a simple answer. Indeed each flux is characterized with a direction of the speed of propagation of the grains, they determine the masses active and inert, thus the energy must be considered as positive or negative according to the flux. The classical equation corresponds to the positive flux and the other equation to the negative flux.”

Yes, but mathematics is not physics. As an example I often cite, I observe a train of mass m and am told its kinetic energy is T. What is its velocity? Mathematically we get two answers, but the train remains as one unit and we do not see two trains going in opposite directions. That the positron happens to have the mass of an electron does not arise from that equation; it is merely a coincidence, but since it has the same mass and charge it should follow the other solution.

Dear Ian Miller: I agree with you it is the physics which allows to build the mathematics, in the paper “The Wave and the Quantum State” I wrote in section six: As we have seen repeatedly the notion of point is a significant barrier to progress towards a better understanding of atomic physics. Behind this difficulty there are mathematics prevailing in physics as master while it is physics or in a broader way the experiments that allowed to build mathematics. The result is the difficulties of the Copenhagen school and its members is that they do not takes into account the fact that that any object has a volume and that at the atomic scale the concept of point almost lost much of its value. The language of mathematics is remarkable and I always liked it; I remember Professor Laurent Schwartz teaching us symbolic algebra where operators can be manipulated as numbers that solve differential equations, I was full of admiration and I still remain so. But despite the elegance of the method, the difficulties of continuous and infinite remain. I hope that these few lines can help researchers. There is a whole field of research that I recommend to my young colleagues.

Now, I am first a chemist with two experimental theses in chemistry. I spent a lot of time to explain the crystal structures and it is fundamental to have a clear understanding of the quantum mechanics. The notion of synchronization between the periodic motions of electrons of neighbor atoms strongly indicate that the Bohr-Sommerfeld model is the good one see “Atoms and crystal structures”. The sharing of the quantum h between the motions of rotation and translation is an easy answer to the understanding of the QM.

Dear Xavier Oudet,

As it happens, I also started research life primarily as a chemist, but I was always concerned that the chemical bond, as considered by the Copenhagen Interpretation, had a problem in that while everything is represented in that interpretation through differential equations, you ended up with a number of constants that had to be arbitrarily assigned. It did not help that (a) as an undergrad I accidentally came across a method by which the two main properties of the hydrogen molecule could be assigned essentially by mental arithmetic, and (b) while in my PhD the consensus of computational chemists "proved" cyclopropane "conjugated" with adjacent substitution, my results showed conclusively it did not transmit such effects, which reduced the issue to the potentials A = B, B = C, but A ≠ C.

The net result is that I developed my own interpretation of QM, such that my hydrogen molecule treatment fell out logically, and I call that "Guidance Waves" because it is like the pilot wave treatment, except that for stationary states, position is irrelevant and the wave energy is defined (unlike Bohm). My view is that the mathematical treatment of an electron as a point is usually valid (in planetary science, the Earth is a point, as is the sun!) but there will be times when that is not OK.

Dear Ian Miller,

Glad to learn that you started research as chemist. For me the notion of hybridization is difficult, in magnetism the electrons behave as if they belong to a hydrogen atom. On the other hand the notion of wave with the photon is incompatible with the interferences in case of very small flux of photons in the two holes in such a way that the photons arrive successively on the place where they interfere. I spend 40 year with colleagues of the Fondation Louis de Broglie and it was not easy to suggest an approach with a corpuscular electron, but it seems to work better.

I will be glad if a have the chance to see the beginning of the acceptance increase, but I am retired since 18 year and the chance is rather small.

Kind regards, Xavier

Aha ? And how do you practice radiocrystallography with electrons under the electron microscope, if they transmute into corpuscles, and loose their wavelength ?

Dear Jacques Lavau, Thank for your interest. The answer is in Bragg law, continuity and discreteness.

Bragg law works only with waves, with a wavelength. And so does the Compton scattering. Look at the Dirac's Nobel Lecture, 1933.

In my Guidance Wave interpretation of QM, I assume there is a wave as well as a particle, and I have published an ebook outlining the concept. This is a variation on the pilot wave concept, but it has two major differences. The first follows from Euler's complex number theory, and the antinode becomes real. The second is the requirement that the phase velocity equals the particle velocity, in order to make diffraction work. Yes, that is a clear assumption, but it has the advantage of making calculations of the covalent bond easy. The interesting point then is, if you assume further that the orbitals follow the non-hydrogen-like relationships outlined in Aust. J. Phys. 40, 329-346 (1987) then you can get a realistic account of the chemical bond using only quantum numbers, and even more interesting, you require a new quantum effect because what everyone calls the screening constant changes on forming a covalent bond. Which raises the interesting question, if this is correct, how come the current computations get anywhere near a correct answer? The answer, of course, is the validation procedure, where the constants if integration are fixed by comparison with observation, and in density functional theory, apparently there are up to fifty such constants. If you cannot get agreement with observation with fifty assignable constants, then something is wrong.

Dear Jacques Lavau,

In “Bragg law, continuity and discreteness” I propose an interpretation of the Bragg law without wave.

In 1935, Linus Pauling and Bright Wilson Jr also did. They needed a quantization of the linear momenta. It was a so splashing failure that I had pleasure to reproduce them in the paragraph 8.5 of the handbook.

By the Scherrer law, I could confound an international crook in an international trial. http://impostures.deontologic.org/index.php?topic=133.0

With corpuscles, no more Scherrer law.

The very idea that non-directional measurement is critical for quantum mechanics is very plausible. In the situation of, say, classical mechanics, as I explained in many other places, an observable may be initial position, state is vectoral displacement, and the result of measurement is the sum of observable and state – resulting position. It does not matter do you follow governing equation for the state, that’s applied displacement, or the result of measurement. In the quantum mechanical situation properly described in geometrical algebra terms the state is operator, rotation in geometric algebra terms, and evolution of the result of measurement is fully different compared with evolution of state. For example, Schrodinger equation is equation for the state which when applied to observable gives the result of measurement. The confusion between operands and operators leads to misunderstanding of the whole QM architecture. States (or wave functions) are operators acting on observables. That makes all the witchcraft of conventional QM fully unacceptable.

@Xavier Oudet.

Remember that the theory from the Montgolfier brothers was false. Sure, the montgolfière flew, but they thought it was electrostatic instead of aerostatic.

Maybe your numerical success is not due to your erroneous corpuscularist doctrine, but simply by avoiding some unnecessary complications.

Their weird macroscopic observer and "measurement" have no place in microphysics theory.