Dear Sofia,

I expect that you need to look in more detail at the nature of the transition induced by the 'impacting' electron. I would want to work out the energy of the slow electrons (e.g. in eV) and perhaps even consider the chemical composition of the photographic plate emulsion, then consider whether at that energy the 100 m/s electron would a) attach itself to form a negative ion, or b) excite - and possibly dissociate - the molecule in passing (or do something else). Then it may be possible to examine in more detail how the wave packet is absorbed.

Regards - Paul

Dear Paul and Franz,

Yes, the energy of the electron that I described was too small. I corrected the question by assigning a group velocity of 1000Km/s. The electrons are still non-relativistic. Their energy in eV is of the order of magnitude

(1/2) x 10-27 x 1016/(1.6 x 10-12) ≈ 3eV.

As far as I see in all sort of tables, e.g. in Wikipedia, dissociation energies of molecules are of this order of magnitude.

https://en.wikipedia.org/wiki/Bond-dissociation_energy

But the time needed to this wave-packet, 1mm width, to cross a surface is 10-9s. It's a short time, however I think that the reaction of dissociation is quicker.

I DON'T KNOW HOW MUCH TIME TAKES THE DISSOCIATION, this I expect to learn from people which answer my question.

Dear Sofia,

"The most elementary steps into which any sequence of chemical reactions can be broken have a common time scale dictated by the rapidity of nuclear rearrangement. This fundamental chemical time scale ranges from 10 femtoseconds to 10 picoseconds. "

The above is from the attached review. Though a bit dated, it's a good introduction. (The attached .PDF should open OK in Adobe - my IT guy has loaded a Firefox-related PDF program that overrides Adobe, but if there's any problem opening the file, try the link, to the same article).

However, the question remains as to whether it's nuclear rearrangement or - if meaningful - electronic rearrangement that's most important for your question. Presumably, nuclear motions can be treated on a semi-classical basis - one step up (so to say) from the Born-Oppenheimer Approximation. As for the electronic 'rearrangement', does the Uncertainly Principle hide the electron dynamics, or can one derive a transitional wave function to establish the dynamics in detail?

Interested to see your conclusions.

Best - Paul

https://www.google.com/search?q=molecular+dissociation+reaction+time&ie=utf-8&oe=utf-8&rls=org.mozilla:en-GB:official&client=firefox-a&channel=fflb&gfe_rd=cr&ei=E5UcVpyOBZPj8wfs0pOADQ

Paul, thanks for information.

Now, just a remark, the words "nuclear arrangement" are not good, maybe you wanted to say "rearrangement of nuclei". Chemical reactions are not nuclear reactions. In fact, what is rearranged are the electron shells, the nuclei are not modified.

Again, thanks for the material, I will read it and return to you.

Sofia,

Thanks for pointing that out - I was just lazily repeating the phrase used by the the authors of the article. As primarily a chemist I am very well aware that chemical and nuclear reactions are on vastly different energy scales.

Paul

Very odd, you concept of "empty waves". How could you obtain an electronic wave that is NOT the electron itself ?

10-9s is a very long time compared to the broglian periods of each electron in atoms and molecules, say about 8.093 . 10-21 s. But you are no more concerned by the spatial characteristics of the original bunch of electrons, only by the characteristics of the one or two or three or zero real electrons reaching the photographic plate.

The incoming wavelength is of the same order as the diameters of the postulated absorbing molecule or salt. Are you deceived by the cross section of your photographic emulsion ?

I am confused: why should it matter, in which time the electron crosses the whole photographic plate? After all, it will cross, presumably, one molecule after the other. Once the electron has left a molecule behind, it is quite unlikely to dissociate it. So I guess the relevant time is, how fast does the electron cross a molecule? But this time should presumably be comparable, or even shorter than, the time needed for the electrons in the molecule to move around, since the energy of the incoming electron is comparable to the energies of the electrons in the molecule.

Jacques,

the concept of full/empty waves is discussed for a long time, and it is basic in the de Broglie - Bohm mechanics. An empty wave, in the de Broglie-Bohm mechanics, passes through fields, beam-splitters, is deflected, etc., according to the properties of the particle, however, does not impress a detector. A full wave behaves in the same way, but impresses a detector.

So, please first of all get familiar with these things.

Also, you ask,

"But you are no more concerned by the spatial characteristics of the original bunch of electrons"

READ my question, I said that the wave-packet is Gaussian. As to your question

"Are you deceived by the cross section of your photographic emulsion ?"

my question is about full/empty waves, not about deceptions.

To Prof. El Nashie,

My dear friend,

I don't examine here the set theory, neither the concept of particle. The quantum theory doesn't accept the concept of "particle", it accepts only the concept of "wave-packet". Very well! But this wave-packet seems to be, most of it, inactive on a detector. See below!

If it takes ~ 10-9s to cross an emulsion surface, though the dissociation reaction takes, say, less than 10-15s, then it seems that only a small volume from all the wave-packet participates in the dissociation activity. To put it in length units, multiplying the presumed dissociation time of 10-15s by the velocity of 1000km/s, one gets 10-9m = 1nanometer. But the width of the wave-packet is 1mm.

So, from the wave-packet width of 1mm, only a length of 1nanometer DOES SOMETHING. The rest of the wave-packet seems to pass through the photographic plate doing nothing.

Now, we use the terminology of EMPTY WAVE exactly for a wave that does not act on a detector, and FULL WAVE if it yes acts on a detector. The empty wave is deflected by fields, beam-splitters, etc., but doesn't impress a detector.

This is why I ask whether we have here evidence that most of the wave-packet is, what we call EMPTY.

Asking otherwise, what does the rest of the wave-packet (1mm - 1nanometer)  to the plate? Does it have any effect?

THIS is what I asked.

@Sofia D. Wechsler.

The problem with de Broglie and Bohm is that they remained corpuscularists, still believing that a corpuscle should exist, which WAS the electron, just guided by a wave that was NOT the electron... So they remained with both feet trapped in a concrete boot of 200 kg.

So there are two cases for your "empty wave".

Either no electron so no wave at all.

Or the electron misses the purposed detector : either it was absorbed before, or it will be absorbed farther.

After your drastic beam-splitter, no more bunch of electrons exists any more in the meager beam. They are individualist fermions. The width and length of the original bunch has no more relevance in the meager beam ; only those of each individual electrons for this kind of absorbing target.

Jacques,

1) First of all, you are wrong about what exits the beam-splitter. The beam-splitter modifies only the intensity of the wave-packet, not its form and dimensions.

2) It seems that you didn't read my explanation to Prof. El Naschie.

My discussion of the experiment is purely according to the standard QM. But I encounter a fact that seems rather to speak in favor of full/empty waves, which is not accepted by the standard QM. So, the problem is whether something is wrong.

We know the so-called "collapse", by which a whole wave-packet delivers the energy to ONE point (one molecule) of the photographic plate. The collapse concept is ALIEN to the QM, but we have to admit that a SINGLE-PARTICLE wave-packet cannot deliver more than a SINGLE quantum of energy.

Now the phenomenon I described in the experiment doesn't look like the collapse. Imagine this big wave-packet impinging on the plate, then passing through the plate while doing nothing most of the time, and only for an interval less than 1 femtosecond we have a reaction. Then most of the wave-packet is what we call EMPTY WAVE.

THIS we don't expect. Going with the QM we don't expect to fall on something that the QM doesn't accept, i.e. empty waves.

It seems you are living under illusions. When you emit a burst of electrons, they never become a wave, with a phase. They are fermions, each in a different state, all with slightly different energies, momenta, frequencies, directions and phases. Your gaussian shape is only statistical for the burst.

If your beam splitter stops or diverts most of the electrons elsewhere, on the meager beam your initial burst is only sampled by very few electrons, say just one electron. How such a meager sampling could conserve the initial bulk (length, duration and width) of the original burst ?

Jacque,

I don't know illusions, I know what says QM. The solution of the Schrodinger equation is a wave-packet. A Gaussian wave-packet is a very common product.

As to your question

"How such a meager sampling could conserve the initial bulk (length, duration and width) of the original burst ?"

I repeat, a beam-splitter doesn't modify the form of the wave-packet. Beam-splitters are linear devices. As to the wave-packet form, it is independent of the intensity. These are two different things.

I am just a voluntary, not a paid director. Not paid, I will let you go and get stuck in your theoritical, standardized and unexperimental dreams.

EOT.

No. The statement that one electron per wavepacket is transmitted says nothing about the average time it takes the electron to pass through the plate, these are independent quantities. So the implication of the second paragraph is incorrect. The ``destruction'' of a molecule by an electron depends on the binding energy of the molecule in question and the initial and final states.  The time required has a distribution, that can be calculated-for molecules the calculation can be very complicated, for simpler, two-body systems, more tractable. There isn't any such concept as an ``empty wave'' or a ``full wave''. It's known from standard quantum mechanics that waves can be described as coherent superpositions of particles and vice versa. The energy density of a wave, in a given mode,  is proportional to the average number of quanta in that mode,  and the proportionality coefficient is hbar ω, where ω is the frequency of the wave mode in question. The number of quanta is an average and there is a distribution, that characterizes the ``shot noise''-that has been studied in detail for many systems. A search for ``electron shot noise'' is useful. This is a standard exercise in quantum mechanics, though there does exist a classical description: The relevant calculation was done by Bethe and Bloch, cf. for instance, http://www.kip.uni-heidelberg.de/~coulon/Lectures/Detectors/Free_PDFs/Lecture2.pdf

Dear Sofia,

I never heard the terms full or empty waves.

If you speak from a wave packet you may think about that part between these packets.

In  general you made a difference between chemical and nuclear reactions. I would say you are thinking about a chemical reaction. I am not sure if one single electron or even a packet can start a chemical reaction. 

An electron (or a wavepacket thereof) certainly can start a chemical reaction-that's what a chemical reaction is, of course--it is described by the interactions of electric charges.

Stam,

what are you saying there?

1) My question says clearly that the average number of energy quanta per wave-packet is 1. No need for a lecture about how to find the average number of quanta.

2) About the ``destruction'' of a molecule by an electron depending on the binding energy, and the complicated calculus of reaction-time, there are TABLES which give average reaction times. No need to recalculate that.

3) Also, you introduce things that I didn't say:

"average time it takes the electron to pass through the plate".

Which "electron"? Standard QM doesn't know "electron", it knows wave-packet. However, we have "reaction-time". It's calculated, it's tabulated.

4) But the main point: you say

"There isn't any such concept as an ``empty wave'' or a ``full wave''. It's known from standard quantum mechanics . . ."

Why don't you read previous explanations of mine? Please do it! The wave-packet needs a long time to cross the plate, but the reaction time is short. Then, what happens here? Most of the wave-packet crosses the plate while doing nothing? So, most of the wave-packet behaves as an empty wave.

Isn't known to you that for explaining measurements we need the postulate of collapse, which is outside the QM? I point here to a problem that seems similar, but not identical, with the collapse. Don't you see? So, what you give us a lecture about things that we already know?

I am sorry, no intention to offend you, I appreciate you very much and you know it. But, please read what is already written.

Sofia

The statement that the wavepacket requires a long time to cross the plate (or anything for that matter) is misleading-that's the point. Precisely because the wavepacket has finite extent it's not possible to state, in an unambiguous way, that ``part'' of it does something-either all of it does something or none of it does, there's just a probability that this occurs. The statement about part of the wavepacket doing something is a classical notion and it isn't appropriate for a quantum wavepacket, precisely, because it can't be given any meaning by an experiment, thought, or real. 

 And everything the wavepacket does can be described within quantum mechanics, there isn't any consistent way or any need to introduce any notion beyond quantum mechanics: just projection operators and evolution operators suffice. 

Ah, Stam,

There is an average time for the interval needed for a wave-packet to cross the plate. And you know that from other phenomena. For instance, the length of the wave-packet of a down-conversion photon is of the order of magnitude of its coherence time, ~ 100fs, times the light velocity, i.e. 3 x 10-3cm = 30μm. You see?

There is no absolute length, but is has an order of magnitude.

As to your saying that "everything the wave-packet does can be described within quantum mechanics", I absolutely agree, but the reaction-time is much shorter by many orders of magnitude. What does the wave-packet in all the remaining time while crossing the plate?

What the projection operators help here?

(You know that the issue of full/empty waves is not trivial. You know that closing the eyes and saying that the QM gives all the answers is not true! Does the QM tell us how the collapse works? Is the QM able to manage without this postulate which is outside the QM? I am just pointing to something that "smells" like the collapse, but is not identical to it. Both the average time-length of the wave-packet and the average reaction-time, are calculated within the QM.)

Kind regards!

The question, precisely, is, what is the procedure for deciding that the wavepacket has crossed the plate, vs. the procedure for deciding the wavepacket has taken part in a reaction. If the wavepacket has reacted, it hasn't crossed the plate-the wavepacket that can be detected afterwards is the result of subsequent reactions, not the ``same'' wavepacket. It's possible only to state that one wavepacket has reacted and one wavepacket has crossed the plate, but it's not possible to give meaning to the statement that these are the ``same'' wavepacket. Indeed, they aren't.

``Collapse'' is just a word-it must be given content. The statement that there's been a measurement can be given content, by a description of the measurement device, in terms of the dynamical variables. And then it's perfectly clear what does it mean to perform a measurement, namely, to couple the system in a specific way to a device, whose description is given beforehand. And it's possible to describe what this entails, within the formalism of quantum mechanics. One can ``call'' the result of having performed a measurement on the system, ``collapse of the wavefunction''-it doesn't matter, as long as the mathematical description is well-defined, which it is. 

Stam,

Your last post is good. Please see the answer.

The wave-packet has a finite average duration. Indeed, we may place an aperture on the source and open it periodically and for a definite interval of time. We can record all these times.

The distance aperture-plate is also known to us, s.t. given the group-velocity and the wave-packet duration, we have no problem in estimating approximately when does the wave-packet touch the plate.

Now, did the wave-packet impress the plate or not, it is stopped by the plate. Beyond the plate we have NOTHING. Also, the standard QM tells us that the question of WHEN the reaction of impressing the plate takes place (if it occurs indeed) is meaningless. The reaction, if it occurs, takes place during the interval of time that the wave-packet illuminates the plate. This is all that the standard QM is able to tell us. If we record this time for every wave-packet, we are bound to find for each one of them a different delay after the respective wave-packet touched the plate.

The issue is that the time interval during which the wave-packet illuminates the plate (which is equal with the wave-packet duration in time) is much longer than the reaction duration. So, most of the volume of the packet impinges on the plate, is absorbed, but DOES NOTHING. Only a tiny volume does something. This is why it seems that most of the packet behaves as an empty wave.

The description isn't precise and that leads to confusion. There's a wavepacket that illuminates a plate. Either it provokes a reaction or it doesn't. The fact that, IF the reaction occurs, it takes a much shorter time than the duration of the illumination isn't in contradiction with anything.

Ah, Stam,

The question is WHAT does the rest of the wave-packet? The rest of the wave-packet behaves as am empty wave. But standard QM does not admit empty waves. 

There isn't any ``rest of the wavepacket''-it's not possible to make any experiment or calculation that can describe this consistently. This is confusion stemming from trying to use classical concepts in quantum physics, where they aren't applicable. The ``whole'' wavepacket is, always, involved. An empty wave is the vacuum state, since the occupation number of quanta is equal to zero, so, of course quantum mechanics ``admits'' it.  For, in order to measure the time of the reaction, one needs to be able to probe such a time-and this is impossible with a wavepacket that doesn't have this property. The fact that one is illuminating for a certain time doesn't imply that the wavepacket one is using has that coherence time. And if it does and it's possible to determine that a reaction has occurred, its duration isn't simply related to the coherence time of the outcoming wavepacket. 

Stam,

You too don't understand the concept of empty wave. It's not vacuum. You give explanations on things that you don't understand properly. That's not good.

Let me give an example to elucidate the things. When a wave-packet is split at a beam-splitter into a reflected and a transmitted beam,

(1) |input> → ir|refl> + t|tran>

(r and t are real) and we place detectors on both these outputs, you know that in each single trial of the experiment, only one of the beams produces a detection, either |refl> or |tran>. But none of them has occupation number 0, none is vacuum. These two beams interfere. A beam with occupation number 1 doesn't produce interference fringes with a beam with occupation number 0. You know this.

Well, adepts of the full/empty wave hypothesis called the beam that doesn't produce detection, "empty wave". It doesn't have occupation number 0, when passing through fields it is deflected and influenced exactly as the respective type of particle is supposed to be.

Let me show what you misunderstood: Asher Peres proposed to describe the transformation (1) as "entanglement with vacuum",

(2) |1>input → ir|1>refl |0>tran + t|1>tran |0>refl

That means, if you get a detection on the transmitted branch, you simultaneously get nothing (vacuum) on the reflected branch. So, the combination |1>refl |0>tran passes undetected; this combination was called empty wave.

It doesn't mean that this combination has no effect. It has remarkable effects, though in INTERFERENCE experiments - see the description of Sciarrino's experiment in my last article on RG (it's a small paragraph), and see also the well-known non-destructive detection experiment of Elitzur and Vaidman. If you don't understand something, I invite you to ask questions.

The polemic whether the empty wave hypothesis is true lasted for years in the literature. Where you were? It stands at the base of the de Broglie - Bohm mechanics.

Best regards.

Occupation numbers have fluctuations, they aren't sharply defined across trials-that's what matters. If the experiment is sensitive to the number of individual photons, or electrons, that's what's, conventionally,  called shot noise in the literature.  Once more, what something's called is irrelevant, what it means is what matters. What's not at all clear, however, is just what the ``empty wave hypothesis'' is, that's *different* from ordinary quantum mechanical interference, not what's the same. Insofar as de Broglie-Bohm mechanics is equivalent to ordinary quantum mechanics, the point would be to highlight what can be more easily or readily shown in this formulation,  than in the other formulations. However the discussion seems to focus on issues such as ``part of a wavepacket'', that aren't meaningful in any consistent formulation of quantum mechanics.  In particular, in any consistent formulation the answer to the last question in the main text is, surely, No. So the ``empty wave hypothesis'' can't have anything to do with it. If it does make any statement about ``part of the wavepacket'', it *can't*, also, make correct statements about interference effects in quantum mechanics. Why isn't it just synonymous to the usual statement that the system could have been in that state, but wasn't? 

Stam,

The experiment is NOT sensitive to number of photons, and there is no matter of shot noise here. Please look at formula (2) in my previous answer.

About "part of the wave-packet", I already told you that we can calculate WHEN a certain wave-packet impinges on the plate, and we can record the time at which the plate is impressed. Also, if it seems to you problematic, we can use a series of devices and "chop" the wave-packet, s.t. we can get parts of the initial wave-packet.

Now, you also say

"Insofar as de Broglie-Bohm mechanics is equivalent to ordinary quantum mechanics, the point would be to highlight what can be more easily or readily shown in this formulation, than in the other formulations."

I lost you here. What you want to say? Can you put it more clearly? By the way, the de Broglie - Bohm (dBB) mechanics is not equivalent to QM, it contains additional hypotheses with which the QM disagrees - you know that. It would be EXCEPTIONAL if we could say which one is correct, the QM, or the dBB.

You see, the full/empty wave hypothesis is more general than the dBB mechanics, because it's just a hypothesis without any accompanying mathematics. And if you'd spend a few minutes to read my interpretation of Sciarrino's experiment in terms of full/empty waves, you'd see how well it goes.

But I am not an adept of this hypothesis. I just honestly admit that it is very appealing, and I don't know yet if it is correct or not. Nobody knows! Believe me, it is not simple to dismiss this hypothesis. In the Discussion section of my last article on RG, I show what difficulties we have to face if we refute this hypothesis.

My kindest regards!

Sophia D. Wechsler believes in "a beam-splitter doesn't modify the form of the wave-packet. Beam-splitters are linear devices". It is a catechist statement on fictitious knowledge-waves, as taught by the heirs of the Göttingen-København sect. Physical waves as physical electrons behave differently than the fictitious catechist waves. Either an electron passes the obstacle and finds an absorber on the intended target, either it finds another absorber behind the intended target, either it is blocked or scattered elsewhere. Only the fictitious knowledge-wave keeps the original bulk of original burst of electrons. No one of the real electrons does. Though dissidents of the hegemonic sect, Bohm and de Broglie shared the believing that the electronic waves were not the electrons, but were some magical guides to electronic corpuscles. As dead-end as the hegemonic one.

Dear Jacques,

As a native-English speaker, with awareness of the QM history to which you refer, your last contribution is nevertheless somewhat opaque (especially the two open-ended uses of "either").

Would you mind re-explaining it, not only for non-native English speakers, but for me too, please?

With interest, as well as best regards - Paul 

Jacque,

First of all please explain what is

"catechist statement on fictitious knowledge-waves, as taught by the heirs of the Göttingen-København sect."

Most of all, what is "knowledge-waves"? I don't believe in "knowledge waves", I don't even know what is that.

So far we don't know what is the wave-function, but, as long as it doesn't meet a classical obstacle, it behaves as WAVE. At the encounter with a classical apparatus of measurement, the apparatus truncates this WAVE, what occurs is the so-called "collapse" that we don't exactly understand. This is the view of the standard QM, which is the most spread view about QM since it is confirmed by all the experiments.

The standard QM doesn't accept the concept of particle, in our case electron, or "real electron" of which you speak. To convince yourself, try to explain Sciarrino's experiment. Do you know it? If not, it is described in the section 5 of my article on RG entitled "Why is QM nonlocal - Bell's Inequalities, etc."

Not only that you can't explain this experiment in the way you suggest, but neither can you explain the Pfleegor and Mandel experiment, nor different other interference experiments. If you want to give ideas about QM, you have to try if your ideas can explain ALL the types of quantum experiments. Only if you succeed, your can consider your ideas correct. And, I am telling you from the beginning that with what you said, you won't succeed.  

About myself, please don't explain to people what I believe in. I am alive, I can explain by myself. By the wave you said false things about me.

A wavefunction can't encounter any obstacle, classical or quantum, because it doesn't describe a wave in spacetime. A wavefunction, as solution of the Schrödinger equation, is a means to an end: the calculation of a probability density in phase space. From that density all observables are constructed. The wavefunction and the probability density are defined in phase space, not spacetime, so the obstacles there describe constraints on the states, not on the trajectory itself.  The probability density  allows  the calculation of observables in spacetime in this indirect way. A way to perform calculations in spacetime  directly is in the path integral formalism. For non-relativistic quantum mechanics this works with particle trajectories, appropriately weighted. The transition amplitudes are then constructed from such superpositions. In the path integral formalism one doesn't deal with operators, but with classical quantities-quantum effects are described as the result of interference in spacetime, expressed through the phase factors,  and not as interference in phase space.

Particles can be described within quantum mechanics: the subtle point is that the position operator and momentum operator, on unbounded domains, don't have normalizable eigenstates, so wavepackets must be used, to describe, e.g. scattering states; for bound states there isn't any problem: but a particle in a bound state, which is  an eigenstate of the Hamiltonian, that's a sum of non-commuting operators, while it does have definite energy, doesn't have, either definite position, or definite momentum. The corresponding densities are, however, readily calculable. 

Stam,

The wave-function can calculate also other things than density of probability - very interesting things, worth to be studied (but this is another talk). As to observables, they are not constructed from the DENSITY of the wave-functions. Don't forget that observables have associated operators which are independent of any wave-function, all the more of the absolute square of those.

Now, a wave-function  \psi (r, t)  is not defined in space-time? What are r and t? (The phase-space is of r and p.)

You also say,

"Particles can be described within quantum mechanics"

What is "particle"? Standard QM knows only equations (Schrodinger, Dirac, etc.), Hilbert spaces, wave-functions, observables, operators, correlations. In the 2nd quantization we have also occupation number, fields. But, particle? What is that? Asher Peres was saying that particle is a click in a counter.

Position operator and momentum operator are concepts of the QM, but what is "particle"?

My kind regards.

No big need of new and heavily instrumented experiments to sort out lots of surrepticious postulates. When you use the concept of "wave function", then invoque an act of God for "collapse", you surrepticely use the postulate of only orthochrone causality - which is valid and proved in macrophysic, but never validated in microphysics.

Just consider these experimental facts, daily used in industry : the convergence of big Infrared photons on a gas molecule, say O3 or CO, which is tens millions times smaller. 3 Å of small axis, 4,7 Å big axis for CO molecule. Just impossible under the only orthochrone causality. Not physicists but electronicians think to the main fact : it is a resonance in frequency phenomenon. And the causality flows equally from the emittor of the photon as from the absorber to the emitter.

For 1928, P.A.M. Dirac has put in evidence that two of the four components of the electronic wave are retrochrone, with negative energies and negative frequencies. They are not yet integrated in the "standard QM"... 1928 ! In his Nobel lecture in 1933, Dirac recalls that the Zitterbewegung found by E. Schrödinger gives exactly the right spatial equidistance to explain the Compton Scattering as a Bragg diffraction. 1933...

http://jacques.lavau.perso.sfr.fr/Physique/Zitterbewegung_Bragg_Compton_english.html is out of date, as it does not integrate the Dirac information : Schrödinger found it eighty years before me. It is ferociously censured by the hegemonic group think.

Erratum : as it does not integrate..

Jacques,

Did you try your theories on the experiments I said? I won't consider your posts before you do that. You can't apply your theories only on what you like. A theory about QM has to explain ANY QM experiment.

"Orthochrone" and "retrochrone" are not part of what we talked until now. They won't explain Sciarrino's experiment. If you jump from topic to topic, enjoy yourself, but I am busy. I can attend only a serious and focused talk.

As to God, He has to be respected, so I think, but in science we don't work with Him. Collapse is not an act of God, it is a deed of our macroscopic apparatuses which are unable to cope with the quantum superposition. We don't know for the moment to explain the collapse, because we can't explain a macroscopic apparatus with the QT. Our (I hope) temporary lack of explanation doesn't make the collapse "divine".

Let's return to youy initial questions.

In the transaction between the final absorber in the photographic plate (say a halogenure of silver), the emitter (say an emissive cathode in a electronic gun) and the intermediate medium, there is no physical mean to keep as pertinent the initial bulk and duration of the burst of electrons. There is no physical reason to think "wave packet time" of the initial burst for the absorption of one electron.

The story of "empty waves" is a cock and bull story ; no electron, no wave, that's all. But no electron absorbed in the photographic emulsion does not imply that there is no electron passing through the plate without been captured there. Otherwise, the electronic microscopy by transmission could not work, and it works well.

Jacques,

I made it clear that I won't talk with you if you are not able to explain Sciarrino's experiment.

All the best, and end of talk. 

The spatial coordinate of the wavefunction is a phase space coordinate-it labels the state of the system, whose the position is r, or x. The time coordinate labels the action of the evolution operator. This is Hamiltonian mechanics, where conjugate variables are coordinates of the space of states of the system.  Lagrangian quantum mechanics is the path integral formalism. 

The wavefunction is defined up to a phase, so not all functionals of the wavefunction are observables. Only appropriate invariants are, one of them being the density and, thus,  its moments. 

A particle is, typically, defined, in non-relativistic quantum mechanics, as a wavepacket, because only a wavepacket has a well-defined center of mass, that can be identified with the position of the particle. The point is that, in quantum mechanics, the distribution of the position, |ψ(x,t)|2, is not a δ-function, it has finite width and this expresses the uncertainty principle. This width depends on Planck's constant. 

More precisely this wavepacket is defined in phase space, so describes an object, that has high probability of being in a state of a given position. This can then be translated into a statement about localization in space; time here is the label of the evolution operator.

Stam,

The word particle just doesn't correspond to a concept of QM, it is a misuse. The correct expression is "quantum system", but people are lazy and prefer something short. There is another concept, but not of it we talk here: "type of particle", i.e. rest-mass, spin, lepton/barion/etc. number, charge, etc. To attribute the position of "the particle" the center-of-mass is risky, why not at the most probable position in the packet? I don't understand why do you try to justify the use of a problematic work. "Particle" is in Bohm's mechanics - you know that.

You make some association, so it seems, between "particle" and δ-function. But δ-function is an idealization, and a problematic one because if at a given time a quantum system occupies a well-defined position, immediately after, it occupies whole the space - you know that. We work sometimes with δ-functions indeed, but it is not a realistic thing.

Now, what you said about phase-space I don't exactly understand. I know that the phase-space has 6 dimensions for each single-system, 3 dimensions for position and 3 for linear momentum.

Well, maybe we'll clarify later.

Best regards.

Words have meaning, but there are many words that have equivalent meaning, so, as long as the mathematical properties attached to the words ``quantum system'' are the same as those attached to the word ``particle'', it's a question of taste, which one uses. One isn't any more ``correct'' or ``incorrect'' than the other. In non-relativistic quantum mechanics in any case the only notion is that of states in a Hilbert space and their superpositions. It's only in relativistic mechanics that  rest-mass and spin are appropriate labels, since they are the Casimirs of the Poincaré group, of which particles can be  defined as irreducible representations. All other labels refer to ``internal'' symmetry groups. 

In classical Hamiltonian mechanics and in the canonical formulation of quantum mechanics the dynamics is defined on the phase space. In this space a point describes the state of the mechanical system. In fact, while in classical mechanics, this space is finite dimensional, though, containing an infinite number of points, for a finite number of degrees of freedom, e.g.  a finite number of particles, in quantum mechanics this space is an infinite dimensional Hilbert space: the position and momentum operators and the Hamiltonian, that act on the functions that are elements of this space, do not admit finite dimensional representations.  (Their exponentials, however, do admit finite dimensional representations and, thus, can act on finite dimensional spaces.) And one way to understand this is by realizing that the transition amplitudes, between any two states involve a sum over the contribution of all intermediate states. This is an infinite sum, in general. This infinity can be countable-if the spectrum of the Hamiltonian is discrete-or uncountable, if it's continuous (absolute or singular). 

The map from phase space to spacetime was first described by Wigner and is known as the Wigner transform. It provides the correspondence between phase space and spacetime, in the canonical formalism and is a standard tool in theoretical and experimental studies. 

There do exist physical systems, whose space of states is finite-dimensional in quantum mechanics, namely spin systems of a finite number of particles, when studying the spin part of the dynamics.

@Paul G. Ellis 

May be you have to consider that you knowledge of "awareness of the QM history" could be plagued by some falsifications you were not aware of.

In

Michelangelo de Maria, Francesco La Taena. Schrödinger's and Dirac unorthodoxy in Quantum Mechanics. Fundamenta Scientiae, Vol. 3 n° 2, pp. 129-148. 1982. Pergamon Press,

de Maria and La Taena have pinpointed that Werner Heisenberg reconstructed the Solvay Conference

> following the logic of the " victors " who are allowed to modify

> history as much as it suits them : he did not even mention

> Schrödinger's or de Broglie's opposing lectures nor the bitter

> discussion that took place. He simply asserted that on that occasion

> the "orthodox" interpretation received "its crucial test", and

> concluded :

> «Since the Solvay Conference of 1927, the Copenhagen interpretation has

> been fairly generally accepted and has formed the basis of all

> practical applications of quantum theory».

And Van der Waerden also is guilty of some falsifications, lies by omissions.

Physics is considerably more than textual analysis, so what people's personal opinion is  doesn't matter, beyond history of physics, which is distinct from physics-what does matter, for physics, are the impersonal calculations that anyone can do and check and the impersonal experiments that, also, can be done and are done by any interested research group-they require some material resources, of course. 

Also, precisely because it's the impersonal results, the ideas, that matter, the exact text isn't important, or relevant. 

A lot of confusion has been caused by the term ``interpretation''. That term might have had some significance, historically, but it's irrelevant, actually. What matters is understanding what solving the Schrödinger equation means and all the mathematically equivalent ways of obtaining the same results and how observables can be constructed. These are mathematical statements that don't admit any ambiguity and don't require any interpretation-they are themselves well-defined and lead to well-defined thought and real experiments. They may well have required a lot of effort ninety years ago, but this effort has been accomplished and it's possible to understand what they mean with a lot less effort and build on them.

@ Stam Nicolis. Your assumption that "presently hegemonic " implies "therefore correct and free of blunders" is contradicted:

Once more, it doesn't matter *who* claims something, *what* is claimed does. So there's no point in compiling a list of quotations-especially if the list contains one's own pronouncements and just cites more known names out of context. That's the difference, once more, between physics and rhetoric: content matters in the former, form matters in the latter. And these issues don't have anything to do with the description of the interference effects that affect a wavepacket travelling across a photographic plate. 

@ Stam Nicolis. The repetitive tune of "Classical/quantic" is a rhetoric trick, designed to claim "ourselves" as "we are the modern for ever after, and the non believers are just retired cavalry colonels...".

Transionnists, we already do not make the same physics, do not explain/avoid the same things, do not predict the same effects. Though we share the same equations of evolution, which are correct. You do not share the same conditions to limits. You deny the final conditions, we don't.

@Jacques Lavau: there is, as already sufficiently pointed out by Stam, no issue of modern versus traditional in quantum physics. The purpose of quantum mechanics is simply to explain a (large) number of related phenomena by means of a straightforward mathematical formalism. This formalism makes essentially perfect predictions (there are, to my knowledge, no instances of experiments contradicting quantum mechanics) for an extremely broad range of phenomena.

On the other hand, this formalism has not been easy to explain in terms of pictures. In particular, it contradicts a well-established set of pictures derived from Newtonian mechanics. This involves in particular that to every particle we can assign unambiguously an arbitrarily precise position and velocity, and that this arbitrarily precise knowledge can be used in order to predict deterministically future positions and velocities also to arbitrary precision.

These ideas are in fact not obviously true even for classical systems, but they do, of course, follow from Newton's equations. They should not, however, be viewed as necessities of though, just the pictorial expression of the consequences of Newton's equations being ordinary differential equations of second order.

The formalism of quantum mechanics is different, involving a concept of interference. This interference, however, does not take place in physical space, but in what is known as configuration space, that is, in an abstract space describing all the possible ways in which the various particles which constitute the system can be arranged. The fact that Quantum mechanics considers waves in configuration space is, in fact, the major difference between it and preceding theories by de Broglie (the Bohm theory does have that same feature, which is, of course, what makes it nonlocal).

If I understand her right, Sofia Wechsler is searching for such a picture in this question. It is a very worthwhile pursuit, though I am not sure I truly understand what that picture is. But denying the formalism of quantum mechanics has so far always led to contradiction with experiment.

If you have some formalism which explains a large number of quantum effects and which is yet not formally equivalent to quantum mechanics, it would be good to know...

Dear F. Leyvraz,

My last article shows that we can explain all the predictions of the QM I terms of full/empty waves. Full/empty waves is a generalization of de Broglie's ideas, i.e. there is no difference between these two types of waves, except that full waves produce a click in a counter, while empty waves don't. But they interfere as if there were no difference between them. So, they can explain why in the 2slit experiment we get a detection only behind one slit, but in absence of any obstacle/detectors, we get an interference pattern at some distance from the screen with slits.

Everything would be fine, the full/empty waves model that I describe would excellently reproduce the QM prediction for single particle experiments or for entanglements, if there weren't problems with the relativity.

What my article says is that we are really at a crisis (although I don't use this term). With full and empty waves, we can obtain all the QM predictions as long as we don't compare conclusions of observers in relative movement.

Then, the question is what to do, to refute the idea of empty and full waves or to admit that relativity shouldn't be used in QM?

I show in my article that in any case we come to big problems (e.g. influence from the future). A crisis!

Fundamentally, the TIQM lets aside some habits of the Special Relativity, as we do not prohibit advanced waves. The mechanisms that yields some handshakes (and mainly no handshake) involve as well retarded and avanced de Broglie-Dirac-Schrödinger waves.

@ Remi Cornwall. "the spatial extent of the wave" near an absorber has much to do with the physical properties of this absorber. Mutatis mutandis for the emitter. Obviously for its diameter, but largely also for its length. The more fuzzy is the difference of levels between initial and final state of the absorber (resp. emitter), the shorter can be the photon absorbed (resp. emitted).

Oups ! English rule ! --> the shorter can be the absorbed (resp. emitted) photon.

@ Remi Cornwall : "the frequency determining the electron's energy". Error !

1000 km/s is 0.33 % of c. These electrons are non relativistic. So the increase of intrinsic Dirac-Schrödinger electronic frequency, as seen in the frame of the photographic plate is negligible. This frequency remains very near of 2mc²/h. The so small frequency shift plays no role in the absorption mechanism : it is an electron, not a photon.

@ Remi Cornwall. You have explained your believings, believings I do not share.

An electron does not have per se any definite size.

Brutally said : an electron has the (fuzzy) size of the orbital it occupies.

And in metals, conduction electrons extend each on several tens of interatomic distances. Like it or not. And they rebounce on phonons, that are sampled on many thousands of metallic ions.

In a dye molecule, the delocalized electron has a molecular size.

And worse : for 1928, the electron has four components, two of them are retrochrone, with negative energy and negative frequency. Like it or not.

"point-like" does not tell you anything on what electrons are. It only express the limitations and inadequacies of the concept of "space", and the inadequacy of our inherited notions of topology for it in microphysics.

Dear Sofia D. Wechsler, the problem we must face it knowing: the effective frontal area of the electron and speed, the effective frontal area of the molecule in the absorber plate, the average density of molecules in the absorber plate and the thickness of the absorber plate. See: https://www.researchgate.net/publication/268503521_Teora_QEDa_-_El_tomo_y_su_ncleo?ev=prf_pub

And https://www.researchgate.net/publication/228574979_Speed_of_atomic_particles_and_physical_constants?ev=prf_pub

The calculation is probabilistic in theory collisions. See the work of my remembered Dr. R.P. Feynman.

Cheers

Book Teoría QEDa - El átomo y su núcleo.

Article Speed of atomic particles and physical constants