The question touches a non relativistic gap in quantum mechanics. If something like a specific locatable object called "Electron" exists which spans an atomic shell, then it must follow accelerated paths. During acceleration it emits "Bremsstrahlung". But the complete combination of this Bremsstrahlung exactly cancels out.

The gap in quantum Mechanis is either a missing dynamic component or an extended shapeless cloud electron model with individual spatial distribution of mass and charge. (The model of an electron capable of holding kinetic and potential energy like an elastic cloud of mass and charge)

An indication for that gap is the missing detailed model of the dynamics of state transitions in atomic shells. (What is the complete detailed time behaviour of the wave function, which exactly leads to the emission of a radiation quant.)

Personally I don't think it makes sense to look after relativistic effects as long as non relativistic effects remain unknown.

Based on your question (and on the assumption "the authors admitted that the mass of a particle is spread over the space"), I can pose a similar one. In a double slit experiment, if you shoot one electron when both slits are open at every 10 seconds, say. Assuming that the electron is in a superposition of following both paths simultaneously, since it has electric charge, shouldn't it interact with itself then? If it does, how that would affect the interference pattern? Such effect should be very small, though. Since the predictions of QM assuming that the electron is free, match well with experiments.

Dear Sofia,

we understand the wave function as a probability distribution for the location of an electron considered as a point particle with mass and charge. But this implies a radiationless particle movement.

The probabilistic wave function precisely describes states, but is not fully appplicable to state transitions.The probabilistic electron point model does not describe the oscillatory behaviour of the wave function for creating a photon during a state transition. A model of an extended electron with electromagnetic interaction capabilities beyond spin can close that gap.

Wolfgang Konle : " the oscillatory behaviour of the wave function for creating a photon during a state transition".

See Schrödinger, sept 1926, Physical Review.

Erwin Schrödinger. An Undulatory Theory of the Mechanics of Atoms and Molecules. Phys. Rev. 28, 1049 – Published 1 December 1926.

Abstract (http://journals.aps.org/pr/abstract/10.1103/PhysRev.28.1049)

The paper gives an account of the author's work on a new form of quantum theory.

§ 1. The HamiltonHamiltonian analogy between mechanics and optics.

§ 2. The analogy is to be extended to include real "physical" or "undulatory" mechanics instead of mere geometrical mechanics.

§ 3. The significance of wave-length; macro-mechanical and micro-mechanical problems.

§ 4. The wave-equation and its application to the hydrogen atom.

§ 5. The intrinsic reason for the appearance of discrete characteristic frequencies.

§ 6. Other problems; intensity of emitted light.

§ 7. The wave-equation derived from a Hamiltonian variation-principle; generalization to an arbitrary conservative system.

§ 8. The wave-function physically means and determines a continuous distribution of electricity in space, the fluctuations of which determine the radiation by the laws of ordinary electrodynamics.

§ 9. Non-conservative systems. Theory of dispersion and scattering and of the "transitions" between the "stationary states."

§ 10. The question of relativity and the action of a magnetic field. Incompleteness of that part of the theory.

With alas two absentmindedness :

Forgot to come back under the relativistic frame, so his beating frequencies are alas fantasy. Feynman commited the same blunder.

Forgot the fact established in 1868 by Gustav Kirchhoff: the emission and absorption lines are the same; so the physics of emission or absorption of a photon by an atom is one.

Both blunders are easy to correct.

The beat of intrinsic frequencies (de Broglie or Dirac-Schrödinger) is a universal phenomenon with wide applications.

Dear Sofia,

I am not a specialist in Quantum Optics. But I know that Quantum Optics describes the interaction of atoms and molecules with electromagnetic radiation. But I also know that it is an extension of Quantum Mechanics which remains based on the wave function model with the statistical distribution of point particle with mass, charge and spin.

The remaining question is: "Is this statistical wave function description complete or does it hide properties of the electron?"

The point model enforces, that the mass distribution and the charge distribution is identical. What would be the consequence if this is not strictly true. If instead temporary deviations between mass and charge distribution are possible and provide additional degrees of freedom.

Does a repelling 'force' towards equal distribution of mass and charge exist? Is this 'force' actually that strong that deviations between mass and charge distribution are forbidden or is even an oszillatory relation between mass and charge distribution possible ?

Dear Sofia,

let's only assume, that our knowledge about the properties of atoms and molecules in combination with radiation is not complete. Allowing deviations between electron mass- and charge distributions in dynamic situations simply adds new degrees of freedom to our model.

The theory of relativity suggests that the influence of movement on mass and charge is different. Consequently as soon as any kind of movement is involved in the nature of atomic shells, there can't be an absolutely rigid coupling between the mass- and the charge distribution.

The question "where is the electron" implies, that we think to know what an electron is and that we only expect information about its location. But actually we only have a very limited model about the nature of atoms, molucules, and their interactions in combination with radiation.

I think that questioning the rigid coupling between mass and charge could be a small but promising step towards a more complete model.

But this requires a new QM-approach with a small perturbation of the mass/charge coupling.

For 1923 we know that mass and the intrinsic frequency are almost synonyms, as the Broglian frequency is mc²/h, involved in all interferences of say an electron, with itself.

For 1930, we know a second intrinsic frequency, 2mc²/h, involved in every electromagnetic interaction, for instance the Compton scattering, or the Rauch and Bonse experiments with neutrons and magnetic field.

So you hope to dissociate these two aspects of the same wave ?

It is only a hypothesis, that interactions of atomic shells temporarily can lead to a deviation between the mass and the charge density of the according wave function. As far as I know, we currently cannot prove that this hypothesis is wrong. The additional degree of freedom, base of that hypothesis, is related to the width of spectral lines we expect to be emitted from stimulated extremely cold matter and to the fact that absolutely precise "zero width spectral lines" do not exist.

I think this hypothesis is also related to the key point of the question "..the authors admitted that the mass of a particle is spread over the space..".

I also think, that the mass and the charge strongly belong together. But we speculate about a scenario in which quantum effects and the Heisenberg uncertainty is dominant. Why should mass and charge exactly have the same uncertainty? Is a kind of absolute equality within that uncertainty actually possible?

" Heisenberg uncertainty " is just the re-labelling of the properties of the Fourier's transform, already known a century before this fraudulous re-labelling.

Each time we obtain a spectrum in a arc or a spark, the temperature of the vapor or plasma is far from the 0K.

Low temperature spectra lines are absorption lines, in the rarefied gas.

Dear Sofia,

I have a crazy answer about where is the electron during its movement, please see this:

Research Proposal Cosmological constant problems

Best Regards,

Mazen

he short answer is, we do not know exactly. The problem with thinking that the the electron closer to the nucleus has more kinetic energy than when it is further away (when in the same level) is that you are thinking everything happens instantaneously. We know it cannot, because the electron does not radiate energy and spiral into the nucleus. My explanation is that this does not happen because the action associatd with the motion has to change by a discrete number of h for it to radiate or change energy. You might ask why? My answer is because of the wave nature of motion. If you ask why, in my guidance wave interpretation, it is because the wave is complex, except at the antinodes, so until the next crest, say, turns up, the electron does not know whether it has accelerated, therefore it does not know whether to radiated or not. If the wave antinode has not moved, the wavelength is constant, so it must be at the same energy. Where the electron is then becomes irrelevant because in this interpretation it is the wave function that determines the energy. After all, the Schrödinger equation requires energy to be conserved.

Sofia, my interpretation is not quite Bohmian. It has the physical wave, but the term exp(2πiS/h) is the phase and that is complex, except when S = h or h/2, when, from Euler's maths, it becomes momentarily real. I do not see why you can get rid of a complex number simply by multiplying it by something that is not there. The travelling particle cannot have a zero current or it would never get anywhere. I also require the phase velocity to equal the particle velocity, which means the wave transmits energy, which is what waves do. Finally, excited states ARE metastable. Phase tethering can hold them almost indefinitely. I outlined this in an ebook "Guidance Waves" ( http://www.amazon.com/dp/B00GTB8LJ6) if you are interested.

Best wishes, Ian

Never a massive "particle" has its group velocity equal to the phase velocity. Their product is c².

Louis de Broglie, 1923.

Jacques, yes de Broglie may well have said that, but the reason I say that is that is that I am asking the wave to cause the diffraction. It cannot do that if it has long since been and gone, through being superluminal - although then it might be going back in time and won't turn up until the particle has long since gone. Worse still, define a frame of reference where it is stationary and the wave front is travelling at infinite velocity. Personally, I hate infinities. You don't know the wave cannot travel with the particle.

Sofia, see Maeda, H., Norum, D. U. L., Gallagher, T. F. 2005. Microwave manipulation of an atomic electron in a classical orbit. Science 307:1757-60. I seem to recall a very excited state of lithium could be maintained for 20 minutes, and probably could have gone on longer had they wished. The problem is to stop the excited state from being nudged, because that is the cause of knocking it from its metastable position.

@ Ian Miller. From the intrinsic frequency and from the theorem of the harmony of phases, L. de Broglie deducted the wavelength of a moving massive particle.

As this result is not relativist, this is the only one they did not throw into the Memory Hole. The de Broglie wavelength is still daily verified. For instance Leybold sells an electron Debye-Scherrer apparatus for the classrooms, and we are many to have practiced Laue diffractograms under a powerful electron microscope.

Also the mechanics of the Compton scattering relies on the de Broglie phase velocity.

Article The Zitterbewegung : key of the electron-photon scattering u...

Sure, in the first paper of de Broglie in 1923, the phase velocity had to be infinite in its frame; this means that the electron is everywhere in phase with itself.

See also the refraction on a diopter: when the incidence is normal, the phase velocity is infinite on the diopter plane.

However, since the electron wave equation from Dirac, in 1928, the situation is deeply renewed : two components of the solution are orthochronous, and two are retrochronous. This implies that the Dirac-de-Broglie ground noise is bidirectional in microtimes. A revolutionary situation, not yet assimilated, for ninety years.

I recommand you to have enough refreshing sleep.

In my opinion, it depends on how much you depend on physical causes. If you don't, then maths willed you come up with a number of what others might term non-physical answers.

PS I have just got up from such a refreshing sleep

Sofia, no, it is not a scattering experiment. The concept, as I understand it is that external nudges (stray fields from passing atoms, etc) will tend to unsettle the electron and momentarily its wave length changes, and then it is unstable, and falls to a lower level. As I understand it, the microwave radiation is intended to provide a reverse nudging force that returns the wave of the excited state to its stationary state level.

Best wishes,

Ian

OK Sofia, but since scattering is not one of my prime interests, it will be merely if accidental

I am accused of incoherence by the most bellicose user of researchgate.net.

Coherent, well, but coherent with what? Some years ago, inspired by the Nicene Creed, I published a Carbocentrist Creed.

Here follows a Göttingen-Københavnist Creed:

https://www.researchgate.net/project/Transactionnal-microphysics-for-the-dumbs

Dear Sophia,

the question if scattering experiments experience atomic shells as smooth unities or as accidentally present hard objects impressively illustrates the key point of your question.

It seems that QM based on the strict assumption that a wave function is a probability distribution of an absolutely rigid point particle cannot differentiate between these two alternatives.

It may be helpful to extend the wave function to a probability distribution of a particle with intrinsic properties. But it must be ensured, that the intrinsic properties are completely independent from properties describable with the original concept of the wave function. A step into this direction could be allowing differences in mass and charge distribution caused by collisions with particles or photons. This would allow storing energy and releasing it via damped oszillations.

We assume that there is mainly (long range) charge/charge interaction at collisions which instantly displaces the massless charge and then also displaces the mass but with an according delay caused by a finite recombination force (like a spring constant). This force accelerates the mass, which is also subject to (short range) mass/mass attraction . The charge is massless but its movement is damped by the emission of radiation and it is subject of electromagnetic interactions. In this model a large variety of mass distributions can oszillate symmetrically around the center of gravity, accelerated by the recombination-, repellent-, and attracting forces.

Specifying the the recombination forces of the mass/mass and mass/charge displacements (in terms of spring constants or with another displacement dependencies) should be sufficient. In that model every point of the charge field attracts every point of the mass field with a force dependent on the displacement. Additionally the mass attracts ittself and tries to shink to a point. But the repellent force of the charge inflates the particle to the observed size.

What remains is the mapping of that model to the quantized world with integer multiples of the quantum of action. The result is a model for a particle with quantized radiation and collision properties.

In 1941, J.A. Wheeler and R. Feynman proved that the whole mass of the electron comes from its electromagnetic interactions with all other charges of the Universe.

http://authors.library.caltech.edu/11095/1/WHErmp45.pdf

The problem remains for the muon and the tauon.

My personal view is that Wheeler and Feynman proposed, not proved. It also has Machian concepts and I have problems in believing an absorber is needed to get emission. We see light from stars over 10 billion years ago. I refuse to believe the emitters "knew" someone would see them that far into the future. (Yes, the paper is technically not about light, but rather action at a distance, but I feel the same concept applies. Others may well disagree.) I also do not believe a mechanism for determining the electron mass can be correct less there is a way to include the muon and tauon.

It remains that a photon "travels" at null proper time.

Like it or hate it, it remains.

Jacques, the emitters and the absorbers do not, and according to the link, the absorber is the cause of the emission. It is the motion of the absorber in the frame of reference of the emitter that is relevant, not the frame of reference of the photon.

Without any authorization from the official church, my eyes perceive the same colors and the same illumination, whichever the astigmatism is corrected or deteriorated, or other defects of vergence.

And the photosensitive molecule is the cis-retinal, coupled to an opsin, and its longer axis is 1.8 nm.

So, without any authorization from the official church, the photons converge, each onto a cis-retinal. Now compare the size of the absorber to the size of the photon when in the air.

It seems that the photon cannot read the official handbooks and cannot listen the authorized professors. You may conclude that the photon is wrong and heretic.

Like a hen who has found a knife, but much more aggressive.

Meanwhile, the initial hypothesis of a small test-body remains a weird dream: " when a charged particle P approaches a hydrogen atom ". Wheeler and Feynman had proved in 1941 that a charged particle has at least an electromagnetic mass. If it has a mass, it has a fuzzy extension, an intrinsic frequency (two intrinsic frequencies), and if moving, a wavelength. Only at high energies requiring an accelerator, a "charged particle" can become smaller than the hydrogen atom. You cannot record the feelings of the charged particle, you only can organize a scattering experiment, and record the statistical results.

These experiments were made in the 1920 years and following. The stakes were the gas tubes and their technology. For instance at the M.I.T. they use an on-the-shelf thyratron to make the students record the Ramsauer-Townsend transparency effect.

The more the linear momentum of the incoming charged particle is precisely defined, the longer it is, rated in number of wavelengths.

Only in your dreams, the small test-body.

No Jaques, they did not prove. They only presented maths that said that provided the underpinning premises are correct. You cannot prove them in logic unless you can show that no other premise can possibly be there, and that is essentially impossible, because it requires what you do not know. But yes, observationally it has a fuzzy extension.

one cannot locate a cloud in a cloud.

https://www.researchgate.net/project/Transactionnal-microphysics-for-the-dumbs

Article Fifteen surreptitious, copenhaguist and corpuscularist postu...

Let us take again the apparatus sold by Leybold, for demonstrating in the class-room a Debye-Scherrer diffractogram by electrons impacting a target of metallic powder. Assume an acceleration tension of 150 V, so the electron de-Broglie wavelength is 1 Å. Assume that the dispersion of energies of the electrons is in the range of 0.3 V, that is 1/500. So each electron is defined on 500 wavelength, that is a 0.5 µm long. Even much more.

And you call that "a particle" in the meaning of  "a corpuscle"? Surreptitiously thought and taught as far smaller than a hydrogen atom...

Sofia, when I said "observationally it has a fuzzy extension" I meant that scattering experiments, etc, are consistent with that, and indeed the Uncertainty Principle requires it, at least in my opinion. To say it has a specific size means you have to be able to measure it, and so far, as I understand, you cannot. Caveat: I am not an expert in that; my response was mainly about the logic issue.

No, no, Ian, we can produce fast particles. We usually produce them in accelerators. There is something else that the uncertainty principle doesn't permit: precise localization of a particle.

Sofia, the speed of a particle should not affect the size of the electron, other than for an observer in a different frame of reference. If you put the frame of reference around the particle, which you often do for quantum effects, the size should be the same. My reference to the fuzziness is that a point on the surface must be uncertain with respect to the centre of mass, therefore it cannot have a precise surface and must be fuzzy.

Sofia, you can have a point on a surface. I interpreted the issue as, if the electron is a particle, does it have size and if so is it a definite size. I then argue that is not so. Whether it is a wave packet is another issue. My personal view is it is a particle but of fuzzy size.

Ian, what's the benefit of assuming a "fuzzy" size of the electron? Why not assuming that it is a combination of mass and charge with a magnetic moment and an angular momentum, capable to oscillate. If mass is glued to mass and to charge, specifying the glue properties allows modelling any internal properties of the particle. Formulation of a QM version of such an electromechanic model is surely possible.

Wolfgang, apart from discussions like this, not a lot. Personally, I simply regard it as an entity with mass, charge and a magnetic moment. That is all I need. My discussion have been mainly on logic, not on more details.

heisenberg`s uncertainty does not allow to handle an electron like a point/grain of dust: it were determined. e- is a cloud of unseparable energy.

Paul,

Heisenberg's uncertainty definitively allows handling a "wave function" which directly describes a charge density and a mass density. It also allows defining an energy operator, which calculates the state energy from the "glue" properties and the charge and mass densities and from the kinetic energy according to the time derivative of the mass density.

The eigenvalues of this energy operator will then provide Heisenberg compatible states for the mass and the charge distribution.

In the basic state of the particle, the "glue" properties define the size of spheres in which the mass and the charge is mainly concentrated. These spheres can be very tiny, which leads to the standard model or they can have a considerable extension which may lead to new properties of atoms.

It is probable, that the smallest possible eigenvalue resulting from this electron-model is larger as typical spectrum energies, but new transient states also can be helpful for calculating interactions.

One has to choose which kind of electrons we consider:

Either those ones who grow in the theoretical and corpuscularist books (but do not exist elsewhere),

Either those that are bound to a nucleus and form an atom. These ones are as big as the atom itself. It is well described by the solutions of the Schrödinger equation, modernized Pauli, modernized Dirac.

Or do you consider the free electrons, as those ones involved in a Compton scattering?

Their length, rated in number of wavelength, depends on their definition in frequency.

Their width depends on the respective diameters of the emissive and absorbing reaction, on the distances from these ends, and on the wavelength.

All that is detailed in the handbook.

Of course, such a question is hopeless when remaining inside of the cage of the corpuscularist sect.

dear Wolfgang, You are right, but it is not to handle like a grain (like I said).

Sofia, yes, of course you treat an electron mathematically as a point but that does not make it a point; it merely means the dynamics permit the omission of any size.

The electrons in an atom are not as big as an atom. The wave function is, but the Schrödinger equation clearly states there is a kinetic energy, and proper quantisation shows there is radial momentum. That the distribution can often be represented as a static electric distribution is a consequence of the Hellmann Feynman theorem, but that does not mean the electron is that size, but as the theorem shows, it is the energy distribution that is that size.

Sofia,

Feynman, R. P. 1939. Phys. Rev. 56: 340-43.

Sofia, do you think that there is another way solving your problem "where is the electron" as having a closer look at the structure of an electron?

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

Jacques Lavau. If something has a spatial extension at least this is the structure. But the important question is "what are new possible interactions" if we allow structural parameters.

Considering structural parameters of electrons is only a proposal for a deeper analysis of interactions between atoms, electrons and radiation. May be you have a better proposal.

I have already explained so many things, above.

The Quebeckers have many Newfies stories, pejorative.

We have Belgian stories.

A Belgian says to another Belgian :

"Do you know the story of the guide at the museum of Cairo? He showed two skulls. He said that the big cranium was the skull of Cleopatra when adult, and the small was the skull of Cleopatra when she was a child.

- No, I did not know your story. Please tell it.".

What do you reproach to the solutions of the Schrödinger equation, mordernized by Pauli, next modernized by Dirac?

The chemists have an intensive use of them. Are they wrong?

At excited states, the electron has frontiers of phase, where its density is null. What do you reproach to these frontiers?

They were mapped for the N2 molecule, but most of the links pointing on the images are now dead.

Just to be perverse, in my opinion the wave functions the chemists use, where the valence electron occupies a wave function corresponding to the excited states of hydrogen, are wrong. Instead, the ground state is composite, and has no nodes. See . I. J. Miller 1987. The quantization of the screening constant. Aust. J. Phys. 40 : 329 -346. The title is perhaps a little misleading, but sometimes you don't want to go completely off left field if you want to get published. I have a better explanation in my ebook "Guidance Waves" (these are modified pilot waves) and if that is correct, ALL chemical computations, other than that for hydrogen, are wrong, because there is a quantum effect most have not noticed.

References:

http://tel.archives-ouvertes.fr/docs/00/44/01/90/PDF/thesis_DrStefanHaessler.pdf

http://iramis.cea.fr/spam/MEC/ast_visu.phpnum=101&keyw=Atto%20Physique&lang=fr , http://iramis.cea.fr/spam/Phocea/Vie_des_labos/Ast/ast.phpt=fait_marquant&id_ast=1550 ,

http://iramis.cea.fr/Phocea/file.php?file=Ast/1550/CP-Photographie_electron__3_-vCNRS.pdf ...

Of course, these results are reproduced in the handbook, Transactional Quantum Microphysics, Principles and Applications.

@Sofia,

isn't it the same if the electron has an extension? The fact that you are asking the quenstion `where is the electron` is an indication that the theory is not complete.

I had the idea of considering possible deviations between mass and charge densities as a student during learning QM but I never had the time and the opportunity for a deeper investigation of that approach. My professors opinion was that this approach is far beyond computational capabilities. But this was in the year 1977.

Dear Wolfgang,

In experiments testing the electron radius appears as smaller than 10-16cm. In an atom, the radius of which is 108 times bigger (10-8cm), we take the electron as a point. Now, in an atom, the electron can be found at different points. All these points form a cloud around the nucleus. The cloud may be spherical or have other forms, depending on the quantum numbers of his cloud - see the picure.

Now, the words "extension of an electron" have no meaning. I told you above what happens.

As to whether the theory is complete, the answer depends on the level at which we pose the question. To my question can answer the experiment. I am sure that there are experiments that test the possible positions of the electron in the atom, but I suppose that if in such an experiment the electron was found at a certain position R, an extremely small time before, the electron was not at R, but in another place inside its cloud. This is why I suppose that a charged particle approaching the atom, would feel in the beginning a force from a sphere of the atom radius, i.e., that the electron is everywhere in the cloud. When approaching even more, it probably should feel a force from a certain point in the cloud. But I am not sure, because QM doesn't say that the electron has, in a given trial of the experiment, a fixed position inside the cloud. So, if the charge comes closer to the atom, I don't know what it would feel.

"In experiments testing the electron radius appears as smaller than 10-16cm". Do not hesitate to show the experiment, when you'll find one. While we have hundreds of experimental proofs that never an electron can transmute into something corpuscular at the microphysical scale, the corpuscular believing is hegemonically taught almost everywhere, but never experimentally validated.

Besides the spectrography, besides the Ramsauer-Townsend resonant transparency, besides the phonon-electron collisions, etc., the corpuscular ideation has another problem with the frontiers of phase, with null density: when you spend half of your life in the bed of your concubine Zeinab and half of your life in the bed of your concubine Zobeid, and considering you change of bed and room every 4 zeptoseconds, how will you never, never be in the lobby separating their two rooms? According to the corpusculist mythology.

Etc.

I see no problem with nul density. If the electron spends a zeptosecond at A, and then at B, and goes between the two, there will be a probability of finding it anywhere in between. The only problem is, what does "find" mean?

Take a comparison: a guitar string is excited in two bellies and a central node. Are you sure a magical, goblinic, and poltergeist corpuscle will jump from one belly of the string to the other and return?

In an excited mode of an electron around a nucleus or several nuclei, no corpuscle either, just stationary waves.

Dear Sofia,

First, I accept the concept that there is no defined trajectory, but if you accept that the electron is a particle, it has to go from A to B. I regard it as always being in existence but you cannot say which path it follows. I cannot prove that, of course, but it is logical.

I have my own interpretation of QM, which I call "Guidance Waves". This is similar to de Broglie/Bohm in concept, but I add two additional requirements. One is that if the wave causes the diffraction effect in the 2-slit experiment, then the phase velocity has to equal the expectation particle velocity so the wave get there at the same. Therefore from some fairly simple maths, the wave transmits energy and the square of the amplitude represents the energy of the particle's motion. The second is from Euler's complex number theory, the wave becomes real, not complex, at the antinode. (If anyone wants to argue maths with Euler, be my guest, but don't argue with me - Euler for me is mathematically correct.)

Why I find this important is that for carrying out calculations of the stationary state, and in particular for molecules, is the calculations become very straightforward. Thus finding the bond energy of the hydrogen molecule requires no more than mental arithmetic. To find the bond length, a pocket calculator is probably desirable because you have to take a square root. What I am most proud of currently is that the calculation of the Sb2 molecule agrees with observation to within about 3 kJ/mol, with no validation or empirical correction, and the only input is the quantum numbers. I have to admit not all are quite so good - the size difference between H and I mean HI disagrees with observation by about 12 kJ/mol, and for some reason boron, sodium and bismuth all give erroneous covalent bond energies, probably because these also give aberrant ionization energies, i.e. for these elements something else is going on in the atomic orbitals.

Sofia,

I agree the electron is not a tiny billiard ball, and I have posted elsewhere why it cannot be, and yes it has a wave function, nevertheless it also has a momentum, and instantaneously you can measure a position, which could be regarded as a centre of mass, e.g.on a photographic plate, each electron is indicated by a point. In the two-slit experiment, every time you measure, the electron has gone through one slit, and from weak measurements, it has been shown the photon does too. One slit only. That is why I believe a wave goes through both, and there is a separate wave and particle. So no, the expectation velocity of the electron does not focus on midway between slits. The electron goes through one or the other slits.

The wave travels with the particle; the antinode travels, the same way a wave travels across the sea. I realise you ,may not be interested in chemistry, BUT the reason I put that there is that when one offers an alternative interpretation of QM, there has to be a reason for it. The alternative has to do what the previous versions do, at least to the extent that is experimentally verified, and it has to do something else. My something else is the stationary state, and I put it there just to show I am not arm-waving.

Sofia, I do not expect instant responses. Look after yourself before worrying about responding.

Ian Miller. When they come to shore, the waves of a vessel also exhibits a difference of speeds:

the phase speed is superior to the group speed.

Jacques, Indeed.

Even the deadliest enemies of Louis de Broglie must use his wavelength when they proceed to any interference experiment with an electron.

The tactical trick is that they hide from the students that it comes from the Relativity and the Theorem of Harmony of phases, of de Broglie.

The de-Broglie phase velocity is the intersection between the electron framework and our macroscopic framework.

If you teach students the refraction law from Snellius and Descartes, if you sketch the fate of the front waves in the two media before and after the diopter plane, you state that the phase velocity on this plane is supraluminic, even infinite at normal incidence.

Dear Sophia, we can describe an electron in an atom as a (standing) wave or as a probability distribution of a particle position. Your illustration clearly addresses the aspect of multimode standing waves. Therefore we can ask: "Is it possible that standing electron waves show interference patterns like standing electromagnetic waves?" An implication of that imagination is that negative values for the probability distribution must be allowed. Regions with a negative electron probability density then would have a positve charge density.Because we cannot allow a negative mass density, phenomena like interference become theoretically possible only if we abandon the strict coupling of mass and charge density in the description of electrons.

They cannot obtain negative probability, as they rise the Schrödinger solution to the hermitian square, positive defined.

So the Schrödinger equation is energically un-Schrödinger-ized.

Territorial animals like the others...

That the phase velocity is supralumic, as Jacques asserts, is dependent on asserting the energy term = mc^2. I regard this as wrong. That is a sort of potential energy that is never available. I interpret it as the energy associated with the motion, and is twice the kinetic energy, on the assumption that the phase velocity has to equal the particle velocity so it can give the diffraction effects. This brings in the difficulty of where is the second half of the energy - I put it as associated with the wave, which is why I consider the square of the amplitude to equal the energy associated with the wave. In short, I put a specific value to what Bohm called the quantum potential. Obviously there is an assumption in this, namely the value of the phase velocity, but I think that is preferable to the assertion the wave goes at infinite velocity when the particle is stationary, as that makes little sense, or the assumption that in the 2 slit experiment the wave front has long gone before the particle gets there.

I have confused the recommendation button with the "Read more" button...

Unwilling!

Your assertions are full of confusions, but confusion seems to be the standard hallmark of the customers of RG.

You have no theoretical way to obtain the wavelength of an electron in move, without its intrinsic frequency, and the phase velocity.

In any electron radiocrystallography experiment, we confirm the Broglian wavelength.

The Dirac-Schrödinger intrinsic frequency 2 mc²/h has been measured in relativistic conditions:

http://aflb.ensmp.fr/AFLB-331/aflb331m625.pdf

In 1926, Erwin Schrödinger has proved that around a nucleus, any stationary state of its electronic cloud are stationary waves. Of course, his deadly enemies disagree, as they stick to the corpuscularist delirium.

Hi, Wolfgang,

The density of probability of the electron is |Ψ|2. It can't be negative.

Hi Sofia,

exactly, the description via a probability density is restrictive. A direct description with mass- and charge density would be less restrictive, and could allow new types of standing waves.

Gauge restrictions(sum of mass and charge) and extremely high energy equivalent of mass and charge density deviations are numerical challenges. But then solving HΨ=EΨ with Ψ=(M,Q) should be sufficient.

"In experiments testing the electron radius appears as smaller than 10-16cm". Do not hesitate to show the experiment, when you'll find one.

When I was a youngster, in 1964, also I was told this corpusculist fairy tale. But they never could exhibit a confirming experiment.

I don't think the size of the electron is relevant to the issue of where it is. Either it occupies a discrete position or it does not. All attempts at locating a position give the result that it is a single entity in a discrete position, thus it gives what can be considered as a point on a photographic plate. It is never observed in two places at the same time.

Dear Sofia,

the Wikipedia Text " Orbitons are one of three quasiparticles, along with holons and spinons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero.[1] The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital location and the holon carrying the charge, but in certain conditions they can become deconfined and behave as independent particles. "

states a possible separation between mass, charge, and spin of an electron, but without specifying the interaction between these three quantities.

Therefore I hope that physicists with a profound background get the time and the motivation investigating appropriate models for the interaction between these three quantities, apply the model, and compare the result to experiments.

" In an atom, at a given time, the electron occupies a given position? "

Erwin Schrödinger gave the answer in 1926:

Erwin Schrödinger. An Undulatory Theory of the Mechanics of Atoms and Molecules. Phys. Rev. 28, 1049 – Published 1 December 1926.

Abstract (http://journals.aps.org/pr/abstract/10.1103/PhysRev.28.1049)

Though in our modern time, the Schrödinger equation is ferociously disfigured and un-Schrödinger-ized, by the winning sect.

" on a photographic plate the electron is observed on a single point, is due to the collapse ".

Again a concentrate of blunders.

The grain of silver halogenure which is reduced is not of infinitesimal size, it is made of tens of atoms, at least. So the absorbing reaction is not of infinitesimal size; it has a finite size. The impacting electron has no reasons to concentrate on a smaller size than the size of the absorbing reaction.

All the hodge-potch from the sect for about 1925-1927 is founded on the confusion of a crowd of individual waves, with one of these individual waves.

One individual wave has only one emitter, and only one absorber.

While their myth of "wave function" is moulded on the crowds of many individual waves, coming from many emitters and going to many dispersed absorbers. It has very little in common with any individual wave : only the equation of evolution, but not any boundary conditions.

The grammar was unambiguous. A crowd of waves, from a crowd of emitters, to a crowd of crowds of potential absorbers, does not share the boundary conditions with one individual wave.

Moreover, what is imagined by the Göttingen-Københavnist sect and their heirs does not share the same "time": they believe in a Newtonian and universal time.

It was precisely SDW who put in evidence the ravages due to this believing in the Newtonian universal time, and is starring at https://www.agoravox.fr/tribune-libre/article/exemple-de-l-impasse-gottingen-193976

" Superposition " is a collective hallucination, when you pretend to apply it to the transfer, of say, one electron.

Things are far more complicate before the transfer and after the transfer, in the ground noise.

We do not practice any more the same physics. It is already obvious for years. One of them must be wrong; or maybe both are wrong.

Meanwhile, on Earth, nobody could find any experiment validating the assertion: "In experiments testing the electron radius appears as smaller than 10-16cm" .

But as it is an article of faith, this does not need any kind of experimental validation, among the believers of the True Faith...

Lavau,

We live in the epoch of the Internet and public media. Experiments are published there. It is exceptionally simple to find. But, one has to take the trouble and seek.

Good bye!

Sofia,

the problem is that while we not fully understand what an electron is, the question "where" is not fully defined.

The observed "split" of the electron in an orbiton , a holon, and a spinon in a cold solid state environment at least indicates that the "compact electron model" is not complete.

May be the electron is something like a flexible cloud of charge which carries a circular current and hosts a dancing tiny mass...

@ Wolfgang Konle

Above all, the theory of the electron must be compatible with the whole bundle of experimental facts:

the properties of the electrical contacts,

the collisions electron-phonon,

the fineness and the liability of all the spectral rays,

the diffraction of the electron on crystalline lattices, either on Laue or Debye-Scherrer protocols,

the interference experiments, even with the Aharonov-Bohm refinement,

the electronic capture,

its Dirac-Schrödinger frequency 2mc²/h proved in 2005 in relativist conditions,

the Ramsauer-Townsend resonant transparency effect,

the properties of the synchrotron and Brehmstrahlung emissions,

...

The theory of the electron must also be compatible with some well established theoretical facts:

the success of the method of the beating between final and initial state, used by Schrödinger in 1926, to obtain the emission or the absorption of a photon,

the four components of the Dirac's wave equation of the electron,

the success of the beating method for the properties of the synchrotron radiation,

the success of the beating method for the properties of the Compton scattering,

...

A new theory must either replace these results by some better ones, either integer these known facts.

Sorry, Jacques,

but your statements with an arbitrary mix of ancient and newer general approaches/experiments are not at all helpful because the investigation of a very detailed extension of a theory requires new specific approaches.

But what are the experimental facts you prefer to discard?

Pure bluff: " It is exceptionally simple to find. "

Never SDW has found any experiment proving her " the electron radius appears as smaller than 10-16cm". And she will never find any.

It is just an old extrapolation, based on a cascade of "IF".

I suppose I have to add my tuppence worth. There is no clear interpretation of QM. I have my own, which I call a Guidance Wave because it is like the pilot wave in that I assume there is a real wave, but there are two major differences. The first is, the wave is not entirely complex - that comes from Euler's complex number theory - and it is real at the antinode. I then assume that if the wave is to guide or pilot the particle, its phase velocity has to equal the particle velocity (leaving aside uncertainty) so it arrives at the slits at the same time. That means that the wave actually transmits energy, and the antinode defines the particle energy. Position now becomes somewhat irrelevant. The advantage of this is it permits a different way of calculating stationary states, and something like the chemical bond, in which I am particularly interested, has its properties defined by simple (at least until the number of electrons gets large) analytical expressions. In the unlikely event that anyone is interested you can read about it here ( http://www.amazon.com/dp/B00GTB8LJ6 )

Some awkward facts if this is correct. The hydrogen molecule properties require only mental arithmetic; the atomic orbitals are different in nature from what all the text books say (that was published in Aust J Phys and despite the data correlations, ignored) and if that is correct, then ALL computations other than hydrogen are wrongly based because they use the wrong orbitals. Good agreement with observation is only obtained through "validation", which is effectively setting a whole lot of constants by comparison with observation. Density functional theory has been claimed to have up to fifty such constants, so agreement should be obtained.

Now, if this is correct (and I am sure there will be disagreement, as there should be) then position of the electron is irrelevant to the stationary state.

" At high energies, and if the wave-packet is tight, we can take the wave-packet as a classical object".

However, the Lorentz transform does not concentrate the width of the "wave-packet", only its length. What may change in diameter are the new absorbing reactions with higher energies. So was proved with the "on partons scattering".

Dear Ian Miller

Your statement " ..the wave is not entirely complex.. " touches the very basics of wave theory related to Fourier- and Laplace-transformations.

The other statement " the atomic orbitals are different in nature from what all the text books say " is not at all helpful without description of the difference.

Dear friends,

I am grateful to everybody who finds my question interesting and wishes to contrbute knowledge and suggestions.

Now, I would like to communicate two things, quite puzzeling:

1. I have a proof that the electron (or any other particle) cannot have a continuous trajectory. I mean, if the evolution of a particle is described by a traveling wave-packet, the wave-packet can have a group velocity. But, inside the wave-packet, there is no such thing as a particle following some smooth trajectory, with a well-defined derivative (velocity) at each point.

2. I have a proof that the concept of particle wih well defined position at each time, is impossible, even if it is not required that the sequence of positions describe, during the time, a continuous trajectory, i.e. even if we admit that the particle jumps from one position to another.

I plan to publish these proofs. Of course, it is quite absurd to tell the conclusions of not yet published proofs. But my intention in doing this, is to remind that an object which does not have a well defined position at each time, is not a particle. A particle is localized at each time.

The above proofs rule out Bohm's interpretation, but this is not big bravery. The issue is that my question "where is the electron" becomes meaningless. The electron is not localized at each given time. It seems that, before a macroscopic measurement, the thing traveling inside our apparatus is a strange creature bearing no similarity with anything from our macroscopic world.

I'll do my best to tell details of my proofs even before publishing them - they are no big secret.

With kind regards,

Sofia

Wolfgang Konle The concept of the orbitals is they are sums of components, each of which must have one quantum of action per period. Hydrogen 1s has two for the two degrees of freedom, therefore the period is two cycles, and these are required to maintain the Uncertainty Principle. The remaining action can be assigned to one period in one solution. The orbitals "explore" all options, so the s electrons try that, and also the excited hydrogen solutions, which gives a period of 4 "nominal cycles". P orbitals explore those, and also try the three available options, giving a periodic time of 12. Where you end up with this for atoms is given in I. J. Miller 1987. The quantization of the screening constant. Aust. J. Phys. 40 : 329 -346. If you follow the above, you will see that in a chemical bond, the zone between the two nuclei must change this "screening constant" (using what others will label the term Z in the usual expression but it has nothing to do with screening and more to do with the nodal structure of the wave) because there cannot be nodes between the nuclei without getting an anti bond.

I apologise for not highlighting your name. This wretched system seems determined to change the n to an h, and I cannot change a link on my computer once it has changed itself.

Dear Sofia D. Wechsler

Announcing proofs about properties of electrons in atoms is courageous. That something like "particles following smooth trajectories" or "particles with well defined positions at each time" cannot exist is a direct conclusion derivable from the Heisenberg uncertainty relation.

Would you admit to the possibility, that within an atomic shell this kind of Heisenberg uncertainty is only applicable to the mass of electrons and charge and magnetic moment (spin) can be described like standing waves which are in a not absolutely rigid interaction with the mass probability density.

Dear Sofia,

Even if you didn't reply to my comments (I didn't know why) I continue to reply to your questions, because I like this questions very much!

Anyway, If we thinking based on our experience, what actually we see?

We observe the electron in discontinuous positions and times, and therefore we have to recognize its existence in a discontinuous way. So between this moments, there is no evidence of its existence. Hence, in my opinion, the earliest model of this motion is the discontinuous motion through the disappearance and appearance model.

With kind regards,

Mazen

Dear friends, and dear Mazen,

I applogize if I missed some comments of yours. It happens because I am so busy and with so many problems on my head, not because I neglect somebody.

Now, please take into account that we cannot observe one and the same electron more than once, because the measurement disturbs it.

But, as I said, I have a proof indicating that the "particle", electron or another particle, cannot have a position, no matter at which time. The position is only a result emerging at the macroscopic measurement, not a property of the "particle" before the measurement. ( This is why I place the word particle between quotation marks, because it is a misleading word - a particle is considered a localized object, having a position at each time and time.)

My proof, goes in general as follows (trying to avoid equations): for two particles, p+ and p-, entangled in a certain way, I show that if at a certain time t1 they have the positions A+ and A- respectively, then at a later time t2 > t1, they should have the positions B+ and B-. But the wave-function forbids the result |B+>|B->, i.e. no measurement yealds this result. On the other hand, the result |A+>|A-> is a possible result, it can appear in the experiment at the time t1.

In all, if "particles" have positions, then one of the possible combinations of positions for p+ and p- at t1, is A+ and A- respectively. But these positions impose an impossible pair of positions at t2.

With kind regards to all the friends,

Sofia

Dear Sofia ,

Thank you for your reply, and I wish you good health and happiness,

you said:

" for two particles, p+and p-, entangled in a certain way, I show that if at a certain time t1 they have the positions A+ and A- respectively, then at a later time t2 > t1, they should have the positions B+ and B- "

but as I know If you measure an entangled property like position, you destroy this entanglement, so you can't maintain the entanglement after the measurement at time t1.

With kind regards,

Mazen

Dear Mazen,

For testing that the response |A+>|A-> is a valid response, I perform a set of experiments in which I place detectors at A+ and A-. Since the wave-function has a component |A+>|A->, I get indeed in part of these tests a joint detection of the particle p+ is at A+ and the particle p- at A-.

For testing the result |B+>|B-> I move the detectors to the positions B+ and B-. The entangled wave-function of which I speak, does not admit a component |B+>|B->. So, despite the fact that if the particle p+(p-) was at A+(A-) at t1, its pair-particle p-(p+) should go to B-(B+) at t2, the wave-function written for both particles at t2 does not admit a component |B+>|B->.

Kind regards,

Sofia

Dear Sofia ,

I didn't understand exactly your experience in your last comment, but anyway I agree with you that it is impossible to have a path for the particle, but I disagree with you in your second point, that the particle didn't have a well-defined position at each time, I agree with you that it does not always have a well-defined position at each time, but it has it in a discontinuous way.

With kind regards,

Mazen

@Mazen Khoder. I have never seen any individual wave with "a discontinuous" propagation.

@Jacques,

neither did I. But there is a problem.

You see, objectively, a quantum system (what we name, non-rigorously, "particle") can be tested only once, because the test destroys its wave-function. Therefore, we have no possibility to say whether a discontinuous propagation exists, or not.

But we can something else: that a discontinuous propagation is a violation of the energy conservation. Energy cannot disappear from the universe, and reappear. A type of particle "from the shelf" (not virtual) has a precisely defined energy, s.t. ΔE = 0. Therefore, by the uncertainty principle, its life-time has to be infinite, ΔT → ∞.

P.S.(In the case of an unstable particle, I speak of the total energy of the disintegration components.)

Dear Jacques,

The wave function is always continuous because it gives us the probability of existence during the continuous space and time, but the motion of the particle itself is discontinuous.

With kind regards,

Mazen

Dear Sofia ,

For the problem of energy conservation, I suggest a solution,

please see this paper:

https://www.researchgate.net/publication/325881106_Cosmological_constant_problems

With kind regards,

Mazen

But what could be the intrinsic physical laws of your goblinic, poltergeist, fantasmagoric, and discontinuous "particle" ?

Sure, Landau and Lifshitz wrote the same fantasmagoric assertion as you did, and I included it in the howlers collection in the handbook (it is so funny) :

At the end of page 12, beginning of 13, 3rd edition, 1975: “Let measure at intervals Δt the successive coordinates of an electron. Generally, the results will not materialize a regular curve. On the contrary, the most precise the measurements are, the most the results are chaotic, with bounces, as the notion of trajectory is invalid for an electron. A more or less continuous trajectory is obtained only if we measure the coordinates of the electron with low precision, for instance the droplets of fog in a Wilson chamber. But, if conserving the precision of the measurements, we reduce the intervals Δt, neighboring measures will give neighbor results, of course. However, the results of a series of successive measures, though in a small portion of space, will be dispersed in chaos, with no alignment on a regular curve. Particularly, when making Δl approach zero, the results of the measures will not at all align in a straight line.”. End of quote.

The authors are prisoners of the confusion between the fate of an individual electron and the properties of a crowd of electrons, whose we never master the initial conditions nor the final ones. Each electron from the crowd has chaotic initial and final conditions, under the sway of the Broglian ground noise, that we will never rule.

When they teach their chaotic trajectory of a mad dog, it is a shameful bluff; never any such experiment, under such corpuscularist ideation, will be made. They just bet that never any student would dare to ask proofs. The conservation of the momentum applied to a relativist particle issuing from the accelerator and/or a collision forbids the erratic behavior postulated by Landau and Lifshitz; the law of the physical optics, from Fresnel (1819) forbids it too.

My dear Mazen,

Regrettably, you should forget about the possibility that I read articles. It is so unreal that I have no words to say. The amount of material on my desk is a mountain.

If you have a solution, describe it in your own words. Just tell us what is that solution, in a couple of lines. Leave to me the job of asking additional questions if necessary.

With kindest regards,

Sofia

Jacques,

when people give you advices, do you bother to consider them? Look how you write:

"goblinic, poltergeist,fantasmagoric, and discontinuous "particle" ?"

What is this style? First of all, you offend Mazen. Why? Did he do any harm whatsoever to you? Can't you be polite? What's the problem? "Goblinic, poltergeist and fantasmagoric" are physical arguments? Do they help in any way? I'll tell you what they do, they make the reading difficult.

I am not sure whether I understood what displeases you about Landau and Lifshitz. Can't you put it more clearly? Neither am I sure on what they are trying to say. What is sure is that there is no such thing as measuring a quantum object twice. A measurement corrupts the wave-function. But, it's not clear to me whether this is their message. As to measuring with low precision - weak measurements, the method embraced by the Bohmians - I doubt its benefit. I also doubt the suggestion of Landau and Lifshitz

"if conserving the precision of the measurements, we reduce the intervals Δt, neighboring measures will give neighbor results, of course."

Measuring with precision the position leaves the linear momentum totally undetermined, and reducing Δt, won't help, the linear momentum would be still totally undetermined.

"never any such experiment, under such corpuscularist ideation, will be made."

Which experiment, Jacques? Our hands are tied. I repeat, we can't measure a quantum system twice. We can do all sort of indirect experiments. The conclusions of some of them, simply lock horns, although the experiments are corectly done. We do fishing in troubled waters.

"They just bet that never any student would dare to ask proofs."

Would you stop accusing all the great scientists of being cheaters? Nobody is interested to cheat. People tell what is known to them, that's all. And the world is not just students, there are enough highly experienced scientists. One cannot rely that others won't ask proofs. Also, no serious scientist is impressed by the names of Landau and Lifshitz - when something is not clear people ask questions and criticize. But YOU, would you ever become polite?

In 1925-1927, the Knabenphysiker in Göttingen had an excuse for shouting their "Me, Myself, and I, and MY measurement, and MY psychism, and MY information, and MY uncertainty...": they had just escaped to the butchery of the world war by the benefice of their age.

In the 21st century, in 2018, we do not more have this excuse. Now we know that we came about fourteen milliards of years too late, to edict that the physical laws must wait that a Göttingen-Københavnist deigns to lean his/her sublime attention on the physical state of some absorber...

The physical transactions between emitters, absorbers and the space in-between have never waited for us. Even when we now repeat "Measurement! Measurement! Measurement! ...".

Not mobilized, the Knabenphysiker :

Pascual Jordan: born in 1902, in Hanover.

Werner Heisenberg: born in 1901, in Würtzburg.

Wolfgang Pauli: born in 1900, in Wien.

Max Born: born in 1882 in Breslau (Wroclaw), was University professor in Berlin from 1914 to 1919. Not mobilized in the war.