In quantum mechanics particles are described by states. A single particle's state assigns a complex number to every position  in space the particle could occupy. The squared modulus of that complex number is the probability density to find the particle there.  In other words, the probability of finding the particle in an infinitesimal volume around x is |psi(x)|^2 time the volume, where psi(x) is the complex number representing the value of the state psi at position x.

When there are two particles, then the state assigns a complex number to every pair of positions x and y that particles 1 can 2 can both occupy. So if both particles move in 3d space, the state will be a function in pairs of 3d vectors, that is, it will be a function of 6 variables.

The state of one particle could conceivably be described in terms of waves. The state of two particles clearly cannot. If you are learning quantum mechanics, and the book  you are reading says something about wave description of particles, discard the book. There are analogies between one particle quantum mechanics and wave problems, but they are largely formal. They had a certain importance in the historical development of quantum mechanics, but now this whole set of ideas is far more a hindrance to understanding than it is anything else.

In quantum mechanics particles are described by states. A single particle's state assigns a complex number to every position  in space the particle could occupy. The squared modulus of that complex number is the probability density to find the particle there.  In other words, the probability of finding the particle in an infinitesimal volume around x is |psi(x)|^2 time the volume, where psi(x) is the complex number representing the value of the state psi at position x.

When there are two particles, then the state assigns a complex number to every pair of positions x and y that particles 1 can 2 can both occupy. So if both particles move in 3d space, the state will be a function in pairs of 3d vectors, that is, it will be a function of 6 variables.

The state of one particle could conceivably be described in terms of waves. The state of two particles clearly cannot. If you are learning quantum mechanics, and the book  you are reading says something about wave description of particles, discard the book. There are analogies between one particle quantum mechanics and wave problems, but they are largely formal. They had a certain importance in the historical development of quantum mechanics, but now this whole set of ideas is far more a hindrance to understanding than it is anything else.

The idea is not that particle can jump to different space points, but that we are restricted in tools: we only can measure if particle is in some area? We should prepare measurement and after that we will kill particle from it's previous existence - this is quantum way!

That way of speaking alludes to the 'collapse of the wavefunction'. This is related to a set of interpretations, but not all of them. Particularly, the idea that matter can instantaneously jump between different places sounds bizarre!

   For difference between the behavior of quantum particles and that of light waves, see E.R. Jones et al: "Path integrals, matter waves, and the doublé slit", Eur. J. Phys. 36, 2015.

As far as I know that the wave property of the fundamental particles is related with associated energy which transfers by motion of particles.

``However to blame Max Born that he was so dump and "simply guessed or accidentally found his interpretation without really knowing the true meaning of what he is actually doing when he was working on the state vector or wave function" is breathtakingly snotty.''

Overall, I entirely agree: that kind of remark should surely come from someone who has found something at least equivalent to the Born interpretation of quantum mechanics.

Nevertheless, even the greatest ideas do not come, like Minerva, clad in full armour from their father's head. In the case of the Born interpretation, it is notable, for example, that in Born's paper the probability to observe a particle at x is claimed to be |psi(x)| (sic)! It is only in a footnote that the correct formula is stated, attributed, if I remember right, to Heisenberg!

Ideas evolve, initial errors often abound, and that is why the study of the history of science is so full of surprises. On the other hand, if we do not have a thorough understanding of the theory as it stands, we are surely far better off learning it from present day textbooks, which have had time to present things in the clearest and in the most accurate fashion, than to resort to historical texts.

The physical meaning is that, when trying to localize any object, whether ``fundamental particle'' or not, the result is a diffraction pattern, where the role of the wavelength is that of the de Broglie wavelength, when the size of the localization region becomes of the order of the de Broglie wavelength. This wavelength is proportional to Planck's constant and inversely proportional to the object's momentum. So, when this wavelength is very small, with respect to the length scales one uses, diffraction effects are negligible and wave properties that depend on quantum effects are hard to observe; when  this wavelength does become comparable, to the length scales one uses then such effects can be detected-just like any diffraction effect.

As your statements and questions are formed, they use lots of surrepticious postulates. These postulates are usually admitted by the tribal community, but none are confirmed by experiments.

You have postulated that a "particle" is a goblinic and poltergeist corpuscle.

You have postulated that the undulatory and deterministic formalism is just a magic cloak, that when squared, gives the probability of apparition of the goblinic and poltergeist corpuscle.

Etc. A list of the postulates we do not more admit : http://jacques.lavau.perso.sfr.fr/Physique/postulates.html

Landau and Lifchitz also taught that in the bubble chamber, the particles practiced such a zigzagodromy. I can give you the page number for the french edition, not for an english nor russian edition : §1, fourth or fifth page of the paragraph.

Hawking and Mlodinow also taught that an electron in its journey between the wehnelt and the screen or IC to groove, could explore up to Jupiter and back... The collection of howlers is rich.

I heard this came from Richard Feynman who took the point of view that it was easy to deal with the particle-wave duality: "An electron is a particle, period.  A photon is a particle, period (Feynman defended Newton's theory of light as corpuscles).  Anything resembling a wave is a wave of probability resulting from the Copenhagen interpretation of quantum mechanics".  It's an answer to your question.

Thanks for your encouragement, Georgi Pekov Vasilev. Beyond the necessary critics of what is presently reigning, time to building :

Why the transactionnal re-interpretation of quantics was unavoidable (in french, no translation available) :

http://deontologic.org/quantic/index.php?title=Interpr%C3%A9tation_transactionnelle and

http://deontologic.org/quantic/index.php?title=Quantique,_un_d%C3%A9m%C3%AAlage_linguistique_pr%C3%A9alable

An english version exists for Zitterbewegung, Bragg, Compton.

http://jacques.lavau.perso.sfr.fr/Physique/Zitterbewegung_Bragg_Compton_english.html

And the book for popularization is almost finished :

http://jacques.lavau.perso.sfr.fr/Physique/Microphysique_contee.pdf

Wave property signifies a different state of any object. The wave-particle duality theory says the particle nature changes completely into wave nature while the speed of any object approaches the speed of light.

This approach is a kind of relativity approach where the characteristic of object changes with the speed of the respective object.

As said in the question "particle can instantaneously jump from one place to another", this process can't be instantaneous, until the particle nature changes into the wave nature. As my best knowledge the wave nature is an instantaneous property of any object behalf of its particle state. This rigid explanation would be much spectacular if you observe any very fast moving train having a long distance with you. Then as the outcome, in your retina the body of the train will visualize as wave. But proper visualization is much required.

Dear Georgi Pekov Vasilev,

Reading your question, I thought of wave–particle duality and de Broglie matter waves and looked again at de Broglie’s Nobel lecture from 1929 at http://nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf.

In his last paragraph de Broglie comments: Thus to describe the properties of matter as well as those of light, waves and corpuscles have to be referred to at one and the same time. The electron can no longer be conceived as a single, small granule of electricity; it must be associated with a wave and this wave is no myth; its wavelength can be measured and its interferences predicted. It has thus been possible to predict a whole group of phenomena without their actually having been discovered. And it is on this concept of the duality of waves and corpuscles in Nature, expressed in a more or less abstract form, that the whole recent development of theoretical physics has been founded and that all future development of this science will apparently have to be founded.

From my own theoretical and practical experience of industrial and scientific optics, I find the whole theory of matter waves and the way they can build wave groups with the properties of matter (including fundamental particles) entirely plausible.

So in terms of your question “What is the physical meaning of the wave property of the fundamental particles?” I refer you to the 1929 Nobel paper from de Broglie and in particular his last paragraph as given above. The matter waves and group waves (the particles) have to be regarded as real waves. The diffraction effects achieved with electrons are one example of experimental proof and there are many others. However this still leaves open the question as to the origin of matter waves and their physical form.

From my own research, I have a model built on the de Broglie theory of wave-particle duality and the matter wave has its own distinct path orbiting in a local space (e.g. the matter waves of planet Earth orbit the sun, and the mattes waves of the electron orbit the nucleus of an atom, etc.). The associated particle and/or body exhibits “gravity” like behaviour, without the need for a theory of gravity. The matter wave in this model is electromagnetic radiation (light waves).

This is just one example of a possible theory, but it does illustrate the potential of reviewing the accepted fundamentals of physics and developing different perspectives, without altering the fundamentals of physics themselves. The retention of an objective view of physics plays a significant role with such work and results in the development of plausible alternative perspectives of physics.

http://nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf

The quantum mechanical waves are modulations of the Compton oscillation of the metrical scale of spacetime. This oscillation is a consequence of the cosmological expansion, which takes place in the scale of spacetime. See further: http://www.amazon.com/The-Progression-Time-expansion-universe/dp/1456574345

To the question of ``virtual' particles. I believe the Casimir effect, which has indeed been experimentally verified, results from a perfectly straightforward computation in quantum electrodynamics. The calculation can be interpreted using zero-point energy and virtual particles, but it need not be viewed in that light. What it tells us is  that, if you perform a correct computation in QED, experiment confirms it. If instead you try to use concepts like virtual particle to make a qualitative theory, I would not be  too sure about the quality of the predictions.

The only meaning of the wave function is that it is a mathematical encoding that enables the quantification of uncertainty of information about reality available to an observer. Reality cares nothing about wave-functions.

@ Mike York. Unless it cares nothing about "corpuscular aspects" nor the holy duality of the Göttingen-København sect...

Richard Feynman proudly boasted that he and nobody else understood nothing in quantum mechanics. Well, raised in a corpuscularist tribe, he took the right means to understand nothing. See for instance "Space-Time approach to Non-Relativistic Quantum Mechanics" where he reinvents the wheel, but far less practical.

Jacques, I have no idea what you mean. Instead of an irrelevant "appeal to authority", why don't you explain what you mean yourself.

@Mike York : I will not repeat at each post... It is so tedious to repeat all the time, all the time, all the time... You had all the necessary links just above :

https://www.researchgate.net/post/What_is_the_physical_meaning_of_the_wave_property_of_the_fundamental_particles/2

I didn't ask for links Jacques. I asked you what you meant. If it is too tedious for you to explain the broad idea in 100 words or less, then it is too tedious for me to follow your links. 

No "corpuscular aspects" exist. Period.

But the howlers exist, and lots of group thinks exist, too.

The following was unavoidable.  If I re-discovered the transactions in microphysics eighteen years ago, anybody who uses his/her brain can find the solution too, even against all the censures and repressions against it.

Originally the series of experiments by Devisson and Germer (1927) proved that electrons have a wave nature. These experiments were performed to establish de Broglie hypothesis (1924). In his Ph.D. thesis de Broglie proposed that light has particle like properties and electron has wave like properties. Electron waves were called matter-waves. He also introduced the concept of de Broglie wave length. λ=h/p=h/(mv).

The wave function associated with a particle of mass m and energy E is however a different thing. It is a complex valued function written as ψ(x,t). By mod squaring it, ie calculating |ψ(x,t)|2= ψ(x,t)* ψ(x,t), we get a real quantity, which is the probability density  of finding the particle at position x. In quantum mechanics time dependence of the wave function is in the form of a pure phase. This phase goes away while calculating probability density.

@Biswajoy Brahmachari. But Louis de Broglie was too timid to achieve his reasoning. He did not unify the wave with the electron, he merely thought that the wave was only a pilot for the maintained corpuscle. So of course he never more succeeded in anything. Only Erwin Schrödinger had the guts in 1926 (loosing the relativistic frame, alas), and later in 1930, 1932 and 1933, after P.A.M. Dirac had found the right wave equation for the electron, with four components.

Who knows these papers of Schrödinger, 1930, 1932, 1933 ? Heavily censured by the winning pack. Only Dirac mentions these results in his Nobel lecture, in 1933. Only Dirac had the guts to mention that.

A moving wave package tends to disperse. Describing a particle as a single phase and single frequency wave is nonsense. So the only way to be able to describe a particle as a wave package is to describe it as a continuous  location density distribution that has a Fourier transform and that on its turn describes a discrete set of locations. The set is continuously regenerated such that the location density distribution is rather constant. In that way the "wave function" gets no time to disperse. At the same time it behaves as a detection pattern that can show as an interference pattern. However, this package does not contain waves!. With the help of highly sensitive detection equipment, such as a night vision device, you will see at low dose rates a hail storm of point-like particles that when the conditions are proper over long integration times will look like interference patterns.

Neither elementary particles nor photons are waves!!!

Photons are constituted out of strings of shape keeping fronts. They have a frequency and in free space they have a fixed speed. They follow geodesic paths. The one dimensional shape keeping fronts are solutions of the homogeneous second order partial differential equations, which describe the behavior of the field that carries the photons. That field is NOT the electromagnetic field!!!

http://www.e-physics.eu/#_What_image_intensifiers

@Jacques Lavau: ``Who knows these papers of Schrödinger, 1930, 1932, 1933 ?'' Do you mean, for Schrodinger 1930, Schrödinger, E. (1930). Über die kräftefreie Bewegung in der relativistischen Quantenmechanik. Akademie der wissenschaften in kommission bei W. de Gruyter u. Company?

This is cited 443 times, according to Google Scholar: the censors do not seem to be terribly efficient...

The wave property of particles is a physical reality reflected say in the diffraction 

properties of ordered crystals. The square modulus of  the wave function gives probability density or intensity.

However in the copenhagen interpetation the wave function itelf is a mathematical

artifact with no physical meaning.

While the particles remain particles, the probability of finding them is dictated by a wave. Alternatively it is possible to think that the wave guides the particle. In this case there are two separate things, the wave and the particle.

The answer to the question can easily fill a book. Currently there is no consensus in the community of experts working in the foundations of quantum mechanics, but in the physics community at large the Copenhagen interpretation is prevalent.

There are basically two attitudes: the epistemic camp which contends that the wavefunction is just a mathematical tool to compute probabilities, and the collapse of the wavefunction is simply an information update, and the ontic camp which believe the wavefunction is very real. In the epistemic corner you can count Copenhagen, consistent histories, qbism, while in the ontic camp you have Bohmians, objective collapse, and many worlders. There are many other interpretations but they have a very small body of proponents.

Here are my argument for why I believe the ontic camp is misguided: the wavefunction caries no energy or momenta and this does not sound like anything real. Also there are several distinct mathematical representations. One can describe for example the hydrogen atom in ordinary complex quantum mechanics or in a much less known fancy quaternionic quantum mechanics and both of them yield the very same predictions. However, the actual wavefunctions are very different. Who is to say that one is real and the other is not? (both cannot be real at the same time).

Dear Christian,

Thank you for your kind words. I can reply to your arguments but that would lead to a long back and forth. Instead I invite you to read my blog dedicated to quantum mechanics http://fmoldove.blogspot.com/ where I already have many posts explaining my position and we can discuss there. By the way, I work in QM foundations.

I don't think of them as particles that have wave properties.  I think of them as waves that are spacially localised when they are captured.  But we should not think of the wave's existence as having the same logical status as the particle's existence.   On capture, their logical status changes.  Collaspe doesn't just involve a step in topology, it also involves a step in existential logic.

The particle is a particle because its position corresponds to a pure position eigenstate.  The waves are generally mixed states.  Pure and mixed states are logically distinct.  The pure states do not need to be unitary and their operators do not need to be self-adjoint.  But the mixed states do.  So there is a necessary / possible unitarity in the system.  This necessary / possible situation is known to Mathematical Logicians as a modal logic.

This unitary modal logic also means that the square root of minus one is necessary in mixed states and not necessary but possible in pure states.  And if we then study the logical status of the square root of minus one in Elementary algebra, we find that this number's existence merely satisfies Elementary Algebras axioms, whereas, existence of all rational numbers are provable from those axioms. That is to say, complex numbers and probability amplitudes are logically independent of Elementary Algebra and rational numbers and eigenvalues are logically dependent in Elementary Algebra.  Note that Elementary Algebra is the system on which quantum mathematics rests.  This lack of provability is why I regard probability amplitudes as conceptually inferred and not witnessable.

Steve Faulkner

Article The logical difference in quantum mathematics separating pur...

Article Logical independence of imaginary and complex numbers in Ele...

@Juan Weisz. "While the corpuscles remain corpuscles", indeed ! But do corpuscles exist ? It is a concept internal to MACROphysics. Can we extrapolate it to microphysics ? And where is the experimental validation of this extrapolation ?

@Hans van Leunen. I have a challenge for you. Please explain how, in your views, we can evaluate the mean size of the cristallites, by radiocristallography.

Exemple in http://deonto-ethics.org/resources/Corrige_expertise.html, access by http://deonto-ethics.org/impostures/index.php?topic=133.0

Or pages 87-88 of http://jacques.lavau.perso.sfr.fr/Physique/Microphysique_contee.pdf

So I confounded an international crook in an international trial.

Dear Dr Vasiliev,

A possible answer can find in the paper: Einstein-de Broglie relations for wave packet: the acoustic world. The model also applies to the electromagnetic world (the world of electromagnetic waves).

Best regards,

Ion

@F. Leyvraz. When you write "waves", of course you silently mean macroscopic waves, having many emitters, and at least as many absorbers (probably much more, if the temperature of the source is high), dispersed between many more potential absorbers.

Excepted the mathematical laws of propagation, these macroscopic waves have little in common with individual waves, each photon, or each electron, or so. An individual wave has only one emitting reaction at its beginning, and only one absorbing reaction at the other end.

So what is the problem with the two correlated photons ? Two individual waves and a tie between one emitter and two absorbers ? Whichever "delayed choice" experimental trick you manage, it remains plain vanilla for transactionist physicists.

I think Abanto is on the right track. In my own work I have found that an oscillating metrical spacetime scale would explain the wave function as well as non-local action. With the scale of spacetime as a fifth dimension there is also an explanation to the inertial force if the Lorentz transformation is replaced by Voigt's transformation.

Dear Johan, in your model where does energy come from?

Dear Alfredo, in my model all energy comes from the cosmological expansion of the scale of spacetime. Since the scale of spacetime expands the second gets longer and longer, which induces energy that equals Einstein's Critical Density and explains the cosmological Dark Energy. There is an equal but negative energy due to the spatial expansion that acts like a Cosmological Constant. Thus an oscillating spacetime scale can induce both positive and negative energy. I think all energy in the cosmos comes from a cosmological scale expansion, which we experience as the "progression of time".

Dear Christian, We have been trying to understand the cosmos without first understanding what causes time to progress.  I think this is impossible; since the progression of time is the most fundamental aspect of existence it cannot be ignored. It turns out that if the four dimensional geometry of cosmos were to expand not only in space but also in its temporal coordinate the resulting cosmos model would agree with all our observations. This would mean that the four dimensions of general relativity would not suffice to model the universe; we also need the scale of existence as a fifth dimension. This would also mean that our traditional 4D world may be energized via this fifth dimension, the expansion of which is the progression of time.

@Jacques Lavau: To my mind, there is a great advantage in knowing what one means before one starts to talk. So if we must talk about particles and waves, I should start out with concepts that are clear in the minds of most, something one might call ``clear and distinct ideas''.

So I think of a particle as a classical particle, that is, a billiard ball, a top, or anything else of the kind that strikes your fancy. Of course, a top is not elementary (it has parts), but we roughly know what a ``point particle'' in that case does. Two particles bounce off each other, particles are localised, and when we do not know where a particle is, we add up the *probabilities* of its having arrived at a given position through various paths.

Similarly, a wave, as we know it from classical mechanics, is a collective excitation of several particles. Light, of course, is an unpleasant exception, since we have no idea as to ``what vibrates'' but sound, water waves, shock waves and even some peculiar phenomena such as second sound are recognisably similar: they are collective oscillations of many-particles. They show interference phenomena, meaning that if a wave passes at the same time through various paths, we must add amplitudes: that is wholly straightforward, though I may have expressed it poorly. On the other hand, we always observe a wave as an extended and continuous phenomenon: the amplitude of a wave is a continuous variable, whereas the presence of a particle is a yes/no phenomenon.

Now to quantum mechanics: quantum objects are, in the above sense, neither waves nor particles. Nothing surprising there, in fact: they are quantum objects, neither classical waves, nor classical particles. But it is hard to form a clear idea of anything unless we connect it to something else, that is more familiar.

An electron (or a photon) definitely has particle characteristics: it is either there, or it is not. One cannot meaningfully measure (I believe) a continuously variable amplitude of an electron at a given position. On the other hand, in the two-slit experiment, single electrons show interference, which is very much a wave property. In my opinion, it is clearest to avoid the word particles and wave, and talk only about quantum systems. As a personal preference, I still believe the particle mode of speech to be preferable to the wave metaphor: the failure of waves to describe many-particle systems: indeed, in my opinion waves must of necessity exist and propagate in the three-dimensional space we live in, else we lose any intuition of what a wave might be. But I do agree that the latter is a private opinion.

Dear Johan and Christian:

If we assume that the First Law of Thermodynamics is true, but energy oscillates in time and space, could this conjecture explain the oscillations of the spacetime?

@F. Leyvraz. Alas you are lost in the contradictions between dead ends.

However, tiny CO molecules capture huge infrared photons, provided they have the right frequency. Excellent detectors use it :

https://www.researchgate.net/publication/241318487_Carbon_monoxide_measurements_aboard_commercial_Airbus_aircraft_technical_validation_and_first_scientific_results_of_the_MOZAIC_III_programme

So any theory that does not respond to such facts is wrong, is good for the garbage can.

Extrapolating corpuscles or macroscopical waves to microphysics is a dead end, we know that for years and years.

Extrapolating the macroscopical time and its macroscopical only-one-arrow to microphysics is a dead end, we have a lot of experimental proofs for that.

Extrapolating the macroscopical space and the ultrafine topology we were taught at school, to microphysics is a dead end too... Ultrafine topology does not exist in the experimental works. At low energies, no one went smaller than one atom. At low energies, no one saw an electron to become smaller than an atom. No one saw a visible or UV or X photon becoming smaller than an atom. Excepted in the Mössbauer effect, a matter of frequency resonance again, as for the capture of infrared 2143 cm-1 photon by a CO molecule.

Article Carbon monoxide measurements aboard commercial Airbus aircra...

Dear Jacques, you note: "However, tiny CO molecules capture huge infrared photons, provided they have the right frequency."

What if the wavelengths of photons do not have anything to do with their physical size? If the photon is similar to a material particle it has both a Compton oscillation and a deBroglie wave. The deBroglie wave, which is generated by its motion in space, can be quite longer the Compton wavelength. This would mean that a photon actually moves slightly slower than the "speed of light" c.

@Johan Masreliez.

However the plane polarization of light exists. And on enough kilometers so bees can use it.

And in atomic physics, the selection rules specifiy more dipolar electric photons than magnetic ones.

So the corpuscular nature of light does not exist. Just use the experimental facts known in the 19th century... Corpuscular photons could only carry helicity, not any plane polarization.

Have you ever practiced radiocrystallography ? Interferometry ? Gratings ? Coherent optics ?

What do you do of the vibrational rest frequency of the molecule CO ? Without it, how the emitted photon could find the resonating molecule ?

Dear Christian, I was making reference to Johan's previous post; he used the word "oscillation" this way (my italics): "Dear Alfredo, in my model all energy comes from the cosmological expansion of the scale of spacetime. Since the scale of spacetime expands the second gets longer and longer, which induces energy that equals Einstein's Critical Density and explains the cosmological Dark Energy. There is an equal but negative energy due to the spatial expansion that acts like a Cosmological Constant. Thus an oscillating spacetime scale can induce both positive and negative energy."

``However, tiny CO molecules capture huge infrared photons, provided they have the right frequency. Excellent detectors use it ''

No argument. And there is no difficulty in reproducing this result using traditional quantum mechanics. It is difficult to visualise if you think of the photon as a wave, but if you use the quantum formalism, no problems arise. It also fits nicely with the claim I have often been making on such threads, that trying to visualise how quantum systems behave is treacherous business: ``visualise'' no matter how abstract, will eventually boil down to what our eyes can perform. But truly quantum behaviour, by definition, cannot be seen, since it involves the interaction of two quantum particles, to the *exclusion* of large classical systems (such as a pair of eyes would unavoidably be).

You can, of course, attempt to visualise Hilbert space. Or you can use, for instance, wave metaphors to understand *one-particle* behaviour. All that is fine. But you should not confuse the map with the territory, the metaphor with the system. At the end of the game, some phenomena must first be calculated, in order, only then, to be understood qualitatively. (Note that this is not limited to quantum mechanics: could any honest person, I ask, claim to understand a heavy asymmetrical top's motion, before having first computed it?).

@ F. Leyvraz.

Sure, the formalism of the mathematical phenomology, as it is  hegemonic, is correct. And it is strictly deterministic and strictly undulatory. However it contradicts the Göttingen-København semantics that are taught to the students before the formalism, for three generations, and that completely wrap the formalism, and the sudents too. Here I intervene.

 @Pierre Ferreira do Prado. There is nothing to save in the Bohr's mythology, and yours attempts do not save anything, either.

There is no scientific ground to "There are no absorbers, only artillery of corpuscles, wrapped in a magic cloak of statistics", nor to magical duality.

Another common phenomenon is only explained in waves, never in corpuscles : the electrical contacts. The air or oxyde layer is narrower than the phase wavelength of the electron at the Fermi level. That's all folks. No magic, no holy duality, no fairy tales.

Neither any need to put a copenhaguist physicist in the middle of the picture, repeating "Measurement ! Measurement ! Measurement !".

Particles are not constituted of waves. Packages of waves disperse when the package moves. Instead the pattern of possible detection locations can be described by a continuous location density distribution and in addition that distribution possesses a Fourier transform. As a consequence the swarm of locations possesses a displacement generator. This means that at first approximation, the swarm moves as one unit. Another consequence of the existence of the Fourier transform is that the location density distribution can take the form of an interference pattern. This is not a wave, but instead it is still a pattern.of potential detection locations. This becomes observable when image intensifying devices are used in order to observe low dose rate images.

@Hans van Leunen. You have again used the postulate : "There are no absorbers. Only artillery of corpuscles".

The true nature of the Quantum Mechanical (QM) wave functions is an old, fundamental, question, which currently is being ignored because nobody had found an explanation-until now. The cosmos expands not only in space but also in time, making the second longer when the meter grows. The new Scale Expanding Cosmos model not only agrees with all our observations, but also explains Dark Energy and Dark Matter. This new model implies that the world is five-dimensional (5D) rather than four-dimensional (4D), the fifth dynamic dimension being the scale of 4D spacetime. Thus, the cosmos expands by incrementally increasing the scale of all existence. This process had no beginning or end. Modeling this by General Relativity (GR), assuming an oscillating scale at the Compton frequency, allows derivation of QM from GR. The deBroglie/Bohm “pilot function” may be derived directly from the geodesic relation of GR. The wave functions are phase modulations of  Compton waves in the scale associated with particles. Thus, the QM wave functions are real physical waves and not just probability waves.

http://www.amazon.com/Progression-Time-expansion-powers-universe/dp/1456574345/ref=asap_bc?ie=UTF8

That there is a wave property that acompanies particles is a well established fact

ie. P=h/lambda . But the physical origin of lambda is not understood

If one asks what process might be working one comes up with an energy transition

amounting to twice the kinetic energy (non relativistically); which might only be due to

a transition between positive and negative energy states in dirac theory, discarding the rest mass. But there is certainly no consensus about that.

ie. that there is a frequency

that as the particle moves along marks the desired value of lambda, for the distance of a full oscilation. 

After calculating this frequency the equivalent energy is mvv

It is possible to generate a mathematical test model in which something that is similar to the squared modulus of the wave function acts as the location density distribution of the landing positions of a stochastic hopping path. If that location density distribution owns a Fourier transform, then it can act as a wave package. However. wave packages disperse when they move. Not this location density distribution. It is continuously regenerated from the location swarm. At the utmost it can create a detection pattern that looks like an interference pattern.

During my career I was involved in the design of image intensifying devices. At low dose rates they produce images of point-like objects. They never show waves.

http://www.e-physics.eu/#_What_image_intensifiers

My Paper in quantum gravity:

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.93.084017

which can also be downloaded from my paper directly from my research gate profile:

 https://www.researchgate.net/publication/301230112_Canonical_reduction_for_dilatonic_gravity_in_3_1_dimensions

adds yet another meaning to the quantum mechanical wavefunction, namely the field of the gravitational dilaton, a particle originating from Kaluza-Klein theory representing dilations of space-time.

Article Canonical reduction for dilatonic gravity in 3 + 1 dimensions

@Hans van Leunen ·: you are still unconscious that your sensing device is an absorber, and that the human scale is not the appropriate scale to treat about photons and electrons.

I repeat again and again and again the definition of a photon :

A photon is the successful electromagnetic transaction between three partners :

This transaction transfers by electromagnetic means a quantum of looping h, has a fuzzy beginning and a fuzzy end, at both apex ; The energy and the linear momentum it transfers depends on the frame, depends on its frequency, as seen from the emitter, as seen from the absorber.

Jaques,

In a mathematical model the equivalent of a photon is a string of solutions of a homogeneous second order partial differential equation. Its constituents have the form of a one-dimensional shape and amplitude keeping front.

Several different processes can generate and annihilate photons.

 @Hans van Leunen ·: You are free to live in mathematical models gathered on the shelf.

Do your mathematical models predict that a Yagi antenna on the roof pinches the EM field to its profit ? And that several Yagi antennas interfer together ?

And a CO molecule still pinches the EM field when it has precisely the resonant frequency. Do your mathematical model predict such facts ? And so on with all the absorption spectroscopy, including colorimetric methods in analytical chemistry.

Jaques,

Do your models explain why electric charges and color charges exist? A foundation model can do that.

Do not expect that foundation models explain high level features. They don't. And it is foolish to require such a capacity.

Since nothing at the foundation level can be observed, the model that is used to investigate this level is necessarily a pure mathematical or a philosophical model.