The author asks

"can the collapse of the wave function be considered a dynamical process?"

and defines what he has in mind

"Dynamics is described by the time dependence of observables, i.e. operators. It is governed by Heisenberg's equation of motion, an equation that is equivalent to the Schrödinger equation."

Going with Heisenberg's picture may be a complication when the quantum object passes through all sort of devices that split the wave-packet re-joins some parts of it. So, the desire of the author to stay in this picture may be expensive in terms of effort. No experimental result predicted in one picture may be different than predicted in the other picture, so, the desire to work with the more convenient utility is normal.

But, the author says

"the collapse of the wave function cannot be said to be due to a wave packet interacting with a detector, because the wave packet does not change in time, it never gets close to a detector, if it is far from all of them initially."

This is one more argument for not working this way. Some tools are mathematically elengant, but do not give us the possibility to feel the ground beneath our feet. When we perform a measurement, we perform it on what impinges on the detector, and the distribution of the results is encapsulated in the wave-function as it is at the input of the detectors.

"the quantum objects are neither waves nor particles but something different -- that's why their description is by operators."

The quantum object is something that travels in our apparatus. Obviously, it is some form of matter in a very general sense, but something not understood to us. Operators and all the apparatus of QM is for predicting what we get at the output of our macroscopic apparatuses, and let's keep in mind that the macroscopic measurement is a brutal intervention on the "thing" traveling in the apparatus, s.t. let's be careful with declarations about that "thing".

Now, about the question on dynamical evolution within this or that picture. Imagine a microscopic particle producing a tiny current in an apparatus, and the current is amplified and moves a pointer on a dial. Where is the original particle when the pointer moves? We forget about it and follow the movement of the pointer. In other words, we pass from the description of the quantum object to the description of the movement of a classical object. So, which dynamical evolution? We simply get out from the quantum domain.

Schrödinger very early proved that his picture and the one of Heisenberg-Born-Jordan are mathematically equivalent.

Article Über das Verhältnis der Heisenberg‐Born‐Jordanschen Quantenm...

It is a mere unitary transformation applied both to the wave function and the operator of an observable. By this operation, the dynamics is transferred to the matrices, but that is false to say the wave function doesn't change. It changes whenever there is a measurement, to reflect the new initial conditions.

@Massé: "Schrödinger very early proved that his picture and the one of Heisenberg-Born-Jordan are mathematically equivalent. "

I guess I did state that ('It is governed by Heisenberg's equation of motion, an equation that is equivalent to the Schrödinger equation.')

"By this operation, the dynamics is transferred to the matrices, but that is false to say the wave function doesn't change. It changes whenever there is a measurement, to reflect the new initial conditions."

I think I stated that correctly as well, without mentioning the unitary transformation. ('It does not change in time, only on measurement.')

And of course, you can delay this change as long as you can delay the Heisenberg cut. In any case, the wave function reflects only the initial conditions, not the dynamics. And changes of the wave function correspond to the choice of new initial conditions, following measurements that changed your knowledge on the system. (A funny thing with quantum measurements is, however, that they only change your knowledge on the system, they do not increase it, if you knew the wave function before measurement, because that is already maximal knowledge. Classical measurements increase knowledge.)

Then all have been said. The dynamics is about the observables. It makes no difference how the observables and their evolution are represented, up to a mathematical equivalence.

But does the transfer exist?

Transferring a photon, an electron, or proton, of neutron, of helium nucleus, or helium atom, ions, so on.

Cathodic tubes work. Electronic microscopes work. The transfer of energy by radiation from the Sun works. Engraving the integrated circuits works...

Do the transfers exist?

In 1916, Albert Einstein proved that the transfer of a photon in a gas was perfectly directional.

Please explain me where in the Heisenberg picture, is the frequency of the transferred photon, where are the changes of intrinsic frequencies of the emitter and the absorber, where are the length of coherence of the interfering photon or the interfering electron, so on.

And why can we proceed to some radiocrystallographic experiments with electrons instead of the usual X-rays?

Dear Kassner,

I think that you have forgotten the interaction picture (IP) which is not equivalent to the Schrödinger's (SP) and Hamilton's(HP) pictures when the operators are acting at different times (this is very important if the evolution must be compatible with relativity). The problem is that the unitary transformations U(t) which could make equivalent SP to HP depend of time.

In any case if you have a great difficulty in one of these pictures you must have it also in the others.And your question, which obviously you hope to respond no

can the collapse of the wave function be considered a dynamical process?

Obviously is non sense (at least for me). You must employ the interaction function or if you assume simultaneity the Schrödinger picture close to the measuremente event.

@Baldomir: "The problem is that the unitary transformations U(t) which could make equivalent SP to HP depend of time."

That is not a problem. We know how to deal with time-ordered exponentials.

Moreover, the interaction picture is also mathematically equivalent to the Heisenberg and Schrödinger pictures.

Of course, I do not argue in favor of one or the other of these pictures as they are all mathematically equivalent. Rather my argument is that these different pictures suggest different visualizations and call into question any absolutist assignment of meaning to a concept such as the wave function. Its meaning is different in different pictures, so it may not be appropriate to make absolute statements regarding its dynamics -- in particular, if in one of the pictures it does not have a dynamics.

I do not understand your remark about nonsense. In the Heisenberg picture, the interaction is carried by the operators, so it does not matter that the wave function may be zero in the interaction region. It simply is not involved in the interaction.

@Lavau: "Please explain me where in the Heisenberg picture, is the frequency of the transferred photon, "

Of course, it is in the same place as in the Schrödinger picture -- it is a difference of eigenvalues of the photon Hamiltonian (up to a factor of hbar).

There is no use arguing against the Heisenberg or Schrödinger pictures. They both are working formulations of quantum mechanics. The calculations give the correct results in both. They just are suggestive of slightly different interpretations.

Kassner,

No you are wrong the Interaction Picture is not equivalent to the other two if the time is different for the operators.

The notion of time for Heisenberg is his human macro-time. "Me, myself and I" as the other teens.

So he cannot deal with the duration of an emission, the duration of an absorption, the length of coherence of a photon or any other individual wave. Then his tribe has to censure energetically lots and lots and lots of experimental facts in optics.

So they are unable to size the shaking mirror involved in the Elitzur and Vaidman contrafactuality hoax.

https://www.agoravox.fr/culture-loisirs/culture/article/contrafactualite-penrose-elitzur-155565

Hello Kassner,

First, here is in quantum physics no such requirement that you mentioned, that "interpretations of quantum mechanics should be compatible with both the Schrödinger and Heisenberg picture." Physical theories must agree with Nature, if not, Nature is the not wrong side!

You did mention the picture of Feynman, I would include the Feynman Diagrams too. There are other pictures as well, where the question you post out does -- not -- appear. It seems to be an artifact of the formulation, the picture. In reality, the Universe exists for billions of years, and never suffered a "halt"; although computer science says it must, we do not see it. Physical theories should support what we see.

Cheers, Ed Gerck

It is an error to identify the dynamics of observables with the dynamics of operators. An observable is represented by an operator in all pictures, and in the Schrödinger picture the operator doesn't evolve. An observable is defined by the action of an operator on a wave function. It doesn't matter which of them evolve and which is fixed, the dynamics is their relative motion. The choice of the picture is no other than the choice of a referential.

Hello,

RG again is not allowing edits in posts. Refined posts seem to have less value in RG than new (and incorrect) posts. Please edit my post above to read, "First, there is in quantum physics no ...".

Cheers, Ed Gerck

Dear K. Kassner

Thank you for this nice question, which triggers thinking

I will try to answer the question in a non traditional way. Taking the EPR paradox can give us some clues about what is going on between the two entangled particles and the effect of measurement process. The two entangled particles even if they are non local relative to our space time (measurement space time), they might be local relative to their space time. If we assume complex transformations between our space time and the quantum particles' space time then the non locality will be justified for such particles relative to our space time, however it will be conserved relative to the particles space time. I have a paper which tries to solve this paradox and it reached to a result that non locality is only happened relative to ours (the classical observers), while in the quantum particles space time the locality is conserved relative to the particles' frames. Returning to your question; there should be a relation between the wave vectors of the entangled particles and the detectors. "if the detectors are not aligned, the propagation vectors of both particles would change simultaneously (because of their closeness to each other in their space-time), wherein the change proceeds in such a way that the projections of the paths of both particles at our (measurement space time) form a single straight path that corresponds to a single new value of propagation vector of both particles at their space-time". This rule governs the relation between the measurement and the particles' wave vectors; so it is a dynamical process. Please see the paper for more information if you are interested.

Article Solving the instantaneous response paradox of entangled part...

@Baldomir: " No you are wrong the Interaction Picture is not equivalent to the other two if the time is different for the operators."

I do not know what you mean by the qualification "if the time is different for the operators". If you are talking about correlation functions, then this is not a discussion about the interaction picture.

Otherwise, if you really mean the interaction picture, which is unitarily connected with the Schrödinger picture and hence equivalent to it by construction, then I would ask you to reconsider your statement after having checked, how familiar you are with the following concepts: time-ordered exponentials and Feynman's disentanglement theorem.

I happen to have worked with all three pictures a long time ago and I know how to do the fully time dependent case. The equivalence of the three pictures remains, if you do everything correctly. If you remain unconvinced, I may post (after Christmas...) an exposition how the interaction picture is defined in the time dependent case, what time-ordered operators are needed and how to prove the equivalence with the Schrödinger picture (and, mutatis mutandis, the Heisenberg picture).

Dear Kassner,

What I wanted to say is that if you have equations with operators depending of different times, although they were defined in the Heisenberg or Schrödinger pictures, this doesn't mean that they can hold in an interaction picture.

Dear Kassner,

Let me try to explain me a little bit more explicitally.

The word picture suggest that quantum mechanics is the same in every picture that you represent it. This in general is the same because it is possible to choose unitary transformations among them. Most of the textbooks of Quantum Mechanics explain the form to pass from one to another. Going from Heisenberg to Schrödinger (or vice verse) is quite simple because in one the dependence of time is for operatos while for the other is on the states. But the interaction picture works with both, the interaction Hamiltonian term evolves in time while the operators do it with its free part. In principle this representation can be different then to the other two if the times are chosen to be different when they depend of the points that you apply the interaction (which in the case that we have spoken where in the device or where the collapse happen).

It is very difficult (and wasteful time) to write here formulae and therefore to explain me only with words, I hope that you can follow my interpretation and why I told you to be wrong when you were reduce your analysis to the SP and HP when the interaction played a fundamental role in this issue.

The author asks

"can the collapse of the wave function be considered a dynamical process?"

and defines what he has in mind

"Dynamics is described by the time dependence of observables, i.e. operators. It is governed by Heisenberg's equation of motion, an equation that is equivalent to the Schrödinger equation."

Going with Heisenberg's picture may be a complication when the quantum object passes through all sort of devices that split the wave-packet re-joins some parts of it. So, the desire of the author to stay in this picture may be expensive in terms of effort. No experimental result predicted in one picture may be different than predicted in the other picture, so, the desire to work with the more convenient utility is normal.

But, the author says

"the collapse of the wave function cannot be said to be due to a wave packet interacting with a detector, because the wave packet does not change in time, it never gets close to a detector, if it is far from all of them initially."

This is one more argument for not working this way. Some tools are mathematically elengant, but do not give us the possibility to feel the ground beneath our feet. When we perform a measurement, we perform it on what impinges on the detector, and the distribution of the results is encapsulated in the wave-function as it is at the input of the detectors.

"the quantum objects are neither waves nor particles but something different -- that's why their description is by operators."

The quantum object is something that travels in our apparatus. Obviously, it is some form of matter in a very general sense, but something not understood to us. Operators and all the apparatus of QM is for predicting what we get at the output of our macroscopic apparatuses, and let's keep in mind that the macroscopic measurement is a brutal intervention on the "thing" traveling in the apparatus, s.t. let's be careful with declarations about that "thing".

Now, about the question on dynamical evolution within this or that picture. Imagine a microscopic particle producing a tiny current in an apparatus, and the current is amplified and moves a pointer on a dial. Where is the original particle when the pointer moves? We forget about it and follow the movement of the pointer. In other words, we pass from the description of the quantum object to the description of the movement of a classical object. So, which dynamical evolution? We simply get out from the quantum domain.

Hello All,

Interesting question and debate. I do not have much time to expand here for now, but in addition to my humble opinion, which does not bring anything valuable to the discussion, that wave function collapse is not a satisfactory concept at all, I would like to point towards a rather interesting paper I came across by chance: "A grasp of identity" by Seglar and Pérez, Eur. J. Phys. vol. 36 035016 (2015). It contains an interesting discussion.

I hope to have more time to discuss your question soon.

Best,

Henni

No, since it is supposed to happen instantaneously, i.e. in no time.

How long lasts the process that you corpuscularist say "click" ?

Let us take for example a photon of wavelength = 0.5 µm,

and a length of coherence of 0.5 m, that is 1,000,000 periods.

At any end, emission or absorption in the frame of the laboratory, it lasts 0.5 m / c = 1.668 ns.

Your "click" represents which part of this timelaps?

However a photon always transfers one quantum of looping h.

At what time of this transfer do you place your "click"? At the beginning? At the middle? At the end?

Contrary to what is often claimed, the paths integral of Feynman is not another picture. It works only in the Schrödinger picture, and is but a way to represent the propagation of any linear classical wave. Schrödinger derived his equation heuristically from the Hamilton-Jacobi equation, that already contains the action and a principal function that has been identified with the phase of the wave function.

No, Feynman did not describe a wave - he pretended that there were no waves - but a dream of waves, exorbitant from any physical law. This famous work of Feynman was reinventing the wheel, but less practical, with heaps of unuseful mathematical fatigue.

Why? Just because of american arrogance: what is not published in english is thought not being, for american physicists. So Feynman simply ignored the periodic character of any quanton that has a mass, its two intrinsic frequencies:

Broglie frequency for all of them: m.c2/h, proved in 1924 (published in french).

Dirac-Schrödinger electromagnetic frequency for fermions, such as the electron : 2.m.c2/h, proved in 1930 (published in german).

This fact (the Broglie intrinsic frequency) drastically reduces the alternative paths to mathematically explore, as they very very quickly become unphysical: the interferences become destructive.

Now there is an implicit frequency in the Feynman text, but is not the good one, it is much lesser, not relativistic, not intrinsic: The original paper of 1948, “Space-Time approach to Non-Relativistic Quantum Mechanics” is at pages 321 to 341 of the gathering by Julian Schwinger “Selected Papers on Quantum Electrodynamics”, Dover Ed.

The hypotheses Feynman used are not explicit, and are buried deep under the Lagrangian formalism. Indeed the merit of Taylor, Vokos and O'Meara is precise­ly to have them put in evidence; only then their unrealism is obvious.

Quotation:

This fundamental and underived postulate tells us that the frequency f with which the electron stopwatch rotates as it explores each path is given by the expression:

f=(KE−PE)/h.

So with this inappropriate tool, Feynman explores much much broader paths than necessary, much much broader than the physical real paths.

Now this frequency, implicit by Feynman, explicit by these authors – thanks to them – is totally fictitious, immensely variable, and milliards of times slower than the real, intrinsic frequency. And Feynman, internee in the group-think coming from the copenhagists pack, strongly believed that the electron wave was only fictitious, just a magic trick for calculation; corpuscularists, they believed in corpuscles, just endowed with magic powers. Fictitious and unrealistic frequency for a supposed-fictitious wave. The result is that all the paths that Feynman and his readers could imagine were far too slack and un-stringent, are exorbitant from any physical law, and their calculation had to embrace gigantic spaces for a null result. Not surprising they had to struggle with heaps of diverging integrals, though condemned to give zero.

Figures in line at http://citoyens.deontolog.org/index.php/topic,887.0.html

if observation does collapse the wave, what about A Creator Who started Big-Bang (name it Fiat Lux)? He must have observed the universe at the beginning!?

@Baldomir: "What I wanted to say is that if you have equations with operators depending of different times, although they were defined in the Heisenberg or Schrödinger pictures, this doesn't mean that they can hold in an interaction picture."

That is not the same as saying that the interaction picture is not equivalent to either the Schrödinger or Heisenberg picture.

In fact, as soon as the Hamiltonian becomes time-dependent, it takes different forms in the Schrödinger and Heisenberg pictures. Of course, also the interaction picture with time-dependent operators is more complicated than the one with originally time-independent ones. (The interaction part of the Hamiltonian becomes time dependent even in the case where both the interaction-free part of the Hamiltonian and the interaction part are time independent in the Schrödinger picture, provided interaction part and zeroth-order part do not commute.)

My point is simply that in all cases it is possible to define a Heisenberg picture and an interaction picture and that these are related to the Schrödinger picture by unitary transformations, hence equivalent.

@Pistea: "If observation does collapse the wave, what about A Creator Who started Big-Bang (name it Fiat Lux)? He must have observed the universe at the beginning!?"

That is a question outside of the realm of physics. If there was a Creator, she may have created the physical laws as well. Before she did that there was no concept of observation. So these are muddy waters.

@Sofia:

'Operators and all the apparatus of QM is for predicting what we get at the output of our macroscopic apparatuses, and let's keep in mind that the macroscopic measurement is a brutal intervention on the "thing" traveling in the apparatus, s.t. let's be careful with declarations about that "thing".'

That is not true for all measurements. When we measure one out of a pair of entangled particles, we measure the other one, too. Without any brutal intervention. In fact, an observer at the other end of the setup, possibly light years away, has no means of determining by further measurements on the second particle that we have measured it before.

'Now, about the question on dynamical evolution within this or that picture. Imagine a microscopic particle producing a tiny current in an apparatus, and the current is amplified and moves a pointer on a dial. Where is the original particle when the pointer moves? We forget about it and follow the movement of the pointer. In other words, we pass from the description of the quantum object to the description of the movement of a classical object. So, which dynamical evolution? We simply get out from the quantum domain.'

No. First, the quantum domain is not limited. Quantum mechanics holds for macroscopic objects, too. Second, it is obvious what I mean by dynamics from the context of my question. We have dynamical equations that describe the evolution of the system. These are either the Schrödinger equation or the Heisenberg equation. One describes dynamical evolution of the wave function, i.e. the quantum state of the system, the other describes dynamical evolution of the observables of the system, whereas the state is only given by the initial conditions.

@Sofia:

"The so-called collapse does not happen instantaneously, "

Yes, it does in standard quantum mechanics.

" it is a continuous process of passing from quantum evolution to classical evolution."

No. That is your own interpretation, and, frankly, nonsense.

"However, in this process appears a non-deterministic part - as shown below.

If the wave-function is of the form

(1) |ψ> ~ |a> + |b>"

If by any measurement process, you measure the property a, then the rule to collapse the wave function is to apply the projection operator |a> -> |a> -> |a>/ √

These are the rules of standard quantum mechanics.

@Masse: " Contrary to what is often claimed, the paths integral of Feynman is not another picture. "

That is a defensible point of view. It is difficult to point out the unitary transformation from the wave function description to the path integral one.

But Feynman's path integrals constitute a new approach to quantum mechanics. Completely different from the Heisenberg one and the Schrödinger one. Apparently inspired by the double slit experiment. There is the folklore that Feynman asked himself the simple question how to describe a situation with infinitely many slits without intervening blocking material. That must lead to propagation in free space -- and led him to path integrals.

A major advantage of path integrals is that they do not care whether your description is Newtonian or relativistic. So Feynman's approach allows a generalization to relativistic descriptions more easily than the other two.

And I believe, there is no fourth formulation of quantum mechanics. So Feynman's work really stands out.

@Klaus,

How many times shall I say that

NON-PERFORMED MEASUREMENTS HAVE NO RESULTS

"If by any measurement process, you measure the property a, then the rule to collapse the wave function is to apply the projection operator |a>

@Kassner: my opinion here is an irony just because of the latest utopies in physics. if cosmos were an unlimited infinity, a creator could have created a limited infiniy (infinite limited sets do exist- think at al numbers between zero and one- [0;1] is a larger set than a countable one; it has the cardinality of continuum!. this is an error first made by Immanuel Kant, who claimed that an infinite set needn`t be created even due to its infinity... and, outside of a limited infinity, the laws could as well exist... why not? again: this are ironies, but can you contradict this?

Dear Kassner,

I have just seeing your answer now and I don't remember very well the details of the discussion, but you argumented using only the Heisenberg and Schrödinger pictures only and you want to distinguish them. This is Ok because, even if it is possible to translate one in another, in fact they use different information for being applied. But I tought that this was a poor form to treat the problem of your question:

Is the collapse of the wave function a dynamical process?

because the collapse is directly related with measurement and therefore with the interaction. On the other hand, I understood that you divided the wave function in one part related with the measurement and another which could survive far away. This is for me impossible.

Coming back to the interaction picture, I have to say that there are important subtleties (it is the picture which allows to pass from QM to QFT in a natural form).

1. You need to be able to separate the Hamiltonian in two terms (not always so simple), where the interaction term is plays the role of giving the transitions between the eigenvalues of the another part of the Hamiltonian (free Hamiltonian).

2. The transitions (scattering, decays etc) are events very different that wave-packet spreading associated to the wave function vector in the Schrödinger's picture.

3. At difference of what happens in Heisenberg picture, in the interaction picture the states depend on time as if they were free states following a Schröding's equation. This is distinguishes clearly the free time from the interaction time which is very important for keeping the Lorentz's relativistic transformations.

4. The evolution unitary operator although it follows a Schrödinger's equation is much more complex and in fact (in the case that the interaction term can be considered much smaller than the free one), the formal solution to this equation is an infinite Dyson's series, where the time is well ordered associated to potential operators.

Thus, you can see that although these are considered to be just "pictures" of quantum mechanics, it is clear that the concepts and even some results are not easily translated from one to the another. The important for your question is the interaction picture if you want to consider the collapse of a wave function for all that I have told you and for this problem I think that it is, from the physical point of view, not equivalent to the other two: Schrödinger and Heisenberg.

The squared modulus of the wavefunction equals a location density distribution of the swarm of hop landing locations that result from the hopping around in a stochastic hopping path of the point-like elementary particle. A stochastic process generates these hop landing locations. At the instant of the detection of the particle the stochastic process changes its operation mode. Consequently, the Location density distribution collapses. See: Article Stochastic control of the universe

@Daniel,

What you talk about? Klaus reads only what is convenient to him, that is clear to me. But, what about you? You don't read my posts?

A measurement is impossible without the intervention of a classical (big, massive) object. You and Klaus debate about the unitary part of the measurement, which only transforms the wave-function but doesn't damage it. It is the interaction with a macroscsopic object that decides the result of the measurement, i.e. which picks from the spectrum of eigenvalues, ONE of them.

In this interaction we "appended" the tiny quantum particle to a classical (massive) object. You know the Feynman paths integral. When the quantum particle is "appended" to a macroscopic object, the action in the phase of the wave-function becomes undefined. The phases of all the paths, except one, mutually cancel out. It is the same thing as we explained to Ulrich Mutze. So, we are forced to pass from the quantum description to the study of the path which remains, i.e. a classical trajectory.

For Klaus this is a nonsense. If he denies the process described by Feynman and so widely known, that's his bussiness - he may deny whatever he wishes..

Also, I have to continue the description of the experiment showing that the part of the wave-function on which there is no detector, does not disappear - I was very busy a few days.

Dear Sofia,

My discussion with Kassner was only related with the interaction picture that I think that he has forgotten to introduce in his question and for measuremets it is the more convenient because it is separated the free and interacted Hamiltonians for the calculations (which can be very difficult) and in fact it corresponds to the natural representation for gluing QM and QFT.

I agree with most of your with respect to him, but I don't understand your last post devoted to me.

You write:

A measurement is impossible without the intervention of a classical (big, massive) object.

This is not true in general or it doesn't needs to be true. For instance, the shift of a phase due to Bohm-Aharonov effect on the electronic spectra or the Compton scattering wavelength.

I agree that the action is the important object to compare if the quantum behaviour or the classical ones are going to be related. This is one old discussion where I have remembered the formalism of Feynman for the concept of trajectories.

One big problem in all that we are discussing here is that the quantum states are not real because they are not gauge determined.

Dear Sofia,

The molecules of hydrogen (2 p+ +2e-) are macroscopic objects? Actually these are in fact quantum big objects which changes their phase (liquid-gas) when the charged particles pass through the liquid of the bubble-chamber depending of the entering particles. But the relation of the actions depends of the velocity and mass of the incident charged particle, not only of the tested particles.

But the experiments with spectra are much more accurate as it happens with the ones of Aharonov-Bohm. For instance

https://arxiv.org/pdf/1103.1607.pdf

or the direct scattering of particles of similar sizes where the Compton length is not too big

https://arxiv.org/pdf/hep-ph/0204197.pdf

Dear Sofia,

One particle scatters with a molecule of H2 and no with all the liquid phase of H2. The bubbles are obtained by the change of phase liquid-gas and it is obtained after the particle has scattered the molecule and therefore transfered part of its energy. Thus the series of bubbles only give us trajectories for calculating energies and momenta.

Happy New Year 2018 !!!

Hi everyone,

IMHO, no one has yet said the key word: phenomenology. Collapse of the wave function is a nice piece of phenomenology, introduced by von Neuman in place of a full electrodynamical theory of photodetection (say). There is no need for collapse after Glauber and Kelley and Kleiner. Moreover, collapse is impossible in principle in any approach based on Heisenberg equations, notably in quantum field theory. And, again IMHO, today theoretical physics as theory of this world IS quantum field theory, and not elementary quantum mechanics of 1930's.

Why collapse outlived its necessity? The main reason is, it indeed picks up a lot of general features of measurement, and of interaction in general, notably decoherence. Another reason is pedagogical: a lecturer starting a paper in elementary quantum mechanics from Fock spaces risks empty audience.

It is a pity that the wavefunction is so misunderstood by nearly all physicists. The same holds for the photon, for gravity for electric charge, for color charge, for relativity, for space, for time and many fundamental aspects of reality.

The cause is that physics lacks a proper modeling platform and a proper foundation.

Article Structure in Reality

Dear Sofia,

Dear Sofia,

There are many things to say and which are also quite subtle to explain in a post as this one, but I would try to summarize some of them in my more clear form.

1. What I have said with respect to Ulrich is that there is not form to go from quantum mechanics to classical mechanics. The correspondence of Poisson's bracket with the quantum commutator

{A,B} ----> 1/ih [A,B]

is not a map because it has not inverse. The example that I have purposed is Newton's law which was discussed in the literature and you has helped to understand properly too.

2. I think that bubble chamber follows this idea clearly. A quantum particle cannot interact as a whole with a macroscopic body, it does it with a microscopic part of it which works quantum mechanically.

3. The bubbles are artefacts created with a metastable liquid phase very close to the the boiling critical point. Once the charged particle enters in the chamber the thermodynamic variables changes in such a form that the ionization of the molecules (usually hydrogen liquid) can vaporized and therefore create a macroscopic trajectory made with the liquid vaporized (bubbles).

4. Have we got a classical trajectory associated to the entering particle? Yes, of course we have done. But could we predict this trajectory with classical laws as Newton's one? No, because a particle with action of the order of h or less has not at all one only trajectory. This was shown by Feynman and it is very simple to be explained.

5. Quantum states are not gauge invariant physical objects as it can happen with the potentials in electrodynamics. This fail in electrodynamics is overcome introducing a new equation as a gauge condition ( Coulomb, Lorentz gauges. etc...).

Dear Plimak,

When you write:

today theoretical physics as theory of this world IS quantum field theory, and not elementary quantum mechanics of 1930's.

You do the same important mistake as the people who says that no quantum field theory (QFT) is necessary when you have superstring theory. QED has solved many different problems (renormalization, anomalous magnetic moment, etc..) but Classical Electrodynamics is still a fruitful theory that nobody could substitute by QED. For instance go to the question

https://www.researchgate.net/post/Are_magnetic_and_electric_fields_made_by_different_photons

In the same form that Classical Mechanics (CM) is needed although Relativistic Mechanics (RM) contains it.

It is in the peculiar confluence of special relativity and quantum mechanics(QM) that a newset of phenomena arises, without avoiding the existance of others as the measurement theory in QM: Particles can be born and particles can die. It is this matter of birth, life, and death that requires the development of a new subject in physics, that of quantum field theory. But nobody can study QFT without having a good trening in QM and RM and less to think that the all the problems can be solved better by the most general theories that using they more particular ones.

Dear Sofia,

The particles don't interact with the bubbles at all. Obviously the bubbles are macroscopic and made with the molecules of the liquid.

http://hst-archive.web.cern.ch/archiv/HST2000/teaching/resource/bubble/bubble.htm

4- I said associated to the quantum particle entrance. No a quantum trajectory which doesn't exist. A trajectory in QM cannot be defined !

5. I have written:

"Quantum states are not gauge invariant physical objects as it can happen with the potentials in electrodynamics."

Obviously the fields are gauge invariants (curvatures instead of connections from the geometrical point of view).

Sofia, I think that we have discussed enough about this question and we deserve a rest !!!

K. Kasser, no. The paths integral is a mere mathematical representation of the propagation of a classical wave. The "trajectories" are not trajectories, but paths along with the phase of the wave function changes according to the wave equation. By summing them through classical superposition, the complex amplitude is obtained. The result of the paths integral is the phases and amplitudes as a function of space at a given time, that is, a wave function that is then interpreted as a probability amplitude according to Born. To every classical linear wave equation of first order in time can be associated a Lagrangian and an action. Conversely, to any Hamiltonian and the corresponding Lagrangian is associated a linear wave equation. I urge you to really study what is the paths integral, and not simply to repeat like a parrot the rubbish that is heard everywhere.

L. I. Plimak, it is true the collapse is not "necessary," but if it isn't in the interpretation, it must be replaced by something else that is as much problematic. A single example: in David Böhm's interpretation, there is a statistical ensemble of trajectories, but a non-local potential must be introduced, and the problem isn't solved. So "collapse" can loosely stand for the measurement problem, or quantum non-locality.

@Baldomir and @all:

I have written up a short note about the equivalence of the three pictures in quantum mechanics for arbitrary time dependent Hamiltonians to settle that issue, and I discuss a little the philosophy behind my statement that an interpretation of quantum mechanics should be compatible with all pictures (and the Feynman path integral approach, in which the wave function is a derived rather than a fundamental concept, point particles being at the basis of the conceptual picture).

The wave collapse is a dynamical process. It can be seen as the evolution of the reduced state of the observer. Obviously, the final state depends on the interaction beween the observer subsystem, say "1", and the observed subsystem, say "2". I have described this in an article (currently having the form of a presentation)

Conference Paper Quantum Systems' Measurement through Product Hamiltonians

If the joint system is driven by a Hamiltonian built of a finite sum of multipliers (mutually commuting operators) in the product form, then the maximal available in subsystem "1" information about the state of "2" is the diagonal of its density matrix.

This corresponds to the questioned wave collapse, not being it - this is only the info available by the observer "1" while the whole system evolves all the time in the deterministic way (according to the Schr\"odinger equation).

It is very interesting (for me at least), that for non-commuting factors, the result of observations is more informative.This could be interpreted as a less total collaps. In particular, a suitably chosen example shows, that the evolution the reduced state of subsystem "1" contains the whole information about the state of the system.

It is worth to add, that according to my proposal the intermediate quantum observations are also modelled. For this am I am using three-partite systems with product Hamiltonians, without any direct interaction between the observed and the observing subsystems. The calculated examples show that then the subsystems cannot see each other if suitable factors of their interactions with the third party commute.

I think that the proposed fashion of the quantum measurement answers the main topic of the current question.

Regards, and . . . Happy New Year 2018, Joachim

K. Kassner, still wrong. Through a canonical transformation, the paths integral can be formulated in the momentum representation as well, where now the paths are in the momentum space, that is, "point particles" in space lose all meaning. Moreover, by applying the paths integral to small consecutive time steps, the whole evolution of the wave function can be calculated, exactly like with a wave equation. The Schrödinger equation has been derived from the Hamiltonian, just like the paths integral, passing by the Lagrangian with the well known Legendre transformation, and they both result in a probability amplitude. Mathematically, there is no difference at all between the Schrödinger equation and the paths integral. Globally, there is nothing more and nothing less in the paths integral formulation. You never back your assertions, that is not a good practice. Even in the presence of a would be intergalactic genius, everything in science must be backed.

@Massé: " The paths integral can be formulated in the momentum representation as well, where now the paths are in the momentum space, that is, "point particles" in space lose all meaning. Moreover, by applying the paths integral to small consecutive time steps, the whole evolution of the wave function can be calculated, exactly like with a wave equation."

I do not doubt that you can do all these calculations. Point particles in momentum space however are a fully reasonable concept in the Feynman formulation, where the restrictions of Heisenberg's uncertainty principle do not apply to the particles.

What I was talking about is the physical picture behind Feynman's path integrals. This picture is not about wave functions.

Feynman diagrams talk about particle interactions all the time -- even in momentum space. And they come from the same physical picture.

Since the Feynman formulation of quantum mechanics covers the complete field, you can of course map it to the Schrödinger equation. But you can also map it to the Heisenberg picture.

I do not know what you mean by "backing my assertions". I just report my knowledge -- do you want citations of scientific papers? That would take some effort and time and considerably slow down the discussion.

@Domsta: "The wave collapse is a dynamical process."

If that is true, and from glancing at your presentation, I am not yet convinced, you should be able to answer questions such as the following:

How much time does the collapse take? How does it propagate through space? (I.e., if I perform a measurement here, how long does it take for the collapse to arrive at some observer on the other side of the sun? Is there a dynamical description of the details of the collapse?)

What is the difference between the dynamical description of the collapse in the Heisenberg and Schrödinger pictures?

@ Kassner

You are asking: " How much time does the collapse take? "

The answer is: All the time since the instant when the interaction is ON.

Strict expressions for one of the simplest cases is given as formula (3.10), more precisely, by the whole page 20 of my presentation. The availble information on the part "2" by part "1" varies from "nothing" at instant t=0, and during all the time till \infty it cumulates in the form of the function \rho_1^{(t)} [ \rho_2 ], t>0, where rho_2 is the initial state of part "2". It is seen from the formulas, that only the diagonal \rho_2(x,x) of the density matrix is restorable by the observer which "knows" only own states (by assumption), since only the diagonal determines the evolution of the reduced state of "1" . My suggestion is to interpret this restriction of access to the information as collapse of the wave-function (more generally - of the state) of the observed subsystem (indeed, it cannot be seen by "1" in a more detailed form!).

Note, that if the starting state is pure, determined by a wave function \psi_2, then the diagonal equals \rho_2(x,x) = |\psi(x)|^2 which is in accordance to a postulate, that after measurement the state is a mixture of pure states with determined position spread with probability density |\psi(x)|^2 . Let me stress, however, that according to the presentation - in cases with non-commuting factors of the interaction, a more reach information about the observed system is available for the observer.

K. Kassner, you are not without knowing that in the Schrödinger equation, there is a term representing interaction too. You are not able to make any distinction between the Schrödinger picture and the paths integral, and for a good reason, they are mathematically identical, not even up to a unitary transformation. I'm really fed up with all this mythology about the paths integral. Feynman is not Hercules, he didn't stifle snakes in his cradle. Actually, the connection between the Lagrangian formalism and the short wavelength approximation is known from the very beginning of the Hamiltonian formalism, and is already explicit in the Fermat principle. The Hamilton-Jacobi theory makes it even clearer. It is not by worshipping a puppet that one can learn all that.

Part of the so-called collapse is the symmetry breaking - I will describe it though in the Schrodinger picture, for simplicity. Assume a wave-function comprising three wave-packets

(1) |ψ> = (1/√3)( |a> + |b> + |c>)

Assume that on the path of each wave-packet, there is an ideally absorbing detector, respectively A, B, C. The interaction with the detectors begins as

(2) |Φ> = (1/√3)( |Ae>|Bg>|Cg> + |Ag>|Be>|Cg> + |Ag>|Bg>|Ce>).

where th subscript 'e' indicates excited state and 'g' ground state, or non-excited.

However, at a certain time, two of the three detectors return to the ground state. The symmetry between the three wave-packets is broken. First of all, WHY? Second, which "dynamical process", in whatever picture, includes this passing from a symmetric wave-function to an asymmetric outcome? (Please do not propose hidden variables - there are no such things.)

@Sofia

The statement "... at a certain time, two of the three detectors return to the ground state": Is ithis an assumption, or is this a real fact.

Moreover, the system has not defined by the promised SE, since there is no hamiltonian given. However, if one assumes that the distinguished states e and g are stationary, then the evolution of the state is given by

(1/√3)( |Ae>|Bg>|Cg> eif_A t+ |Ag>|Be>|Cg> eif_B+ |Ag>|Bg>|Ce> eif_C t),

where f_A, f_B and f_C are proportional to the differences of the energies between the exited and ground states for detectors A, B and C respectively. Mathematically this is a pseudoperiodic function, but no change of the type of state g to e nor e to g happens.

Obviously, the evolution will be different if some interaction between detectors is present. Simply, without any further description no more can be said. In particular within the presented model there is no reason for the return of the detectors to their ground states ever.

Regards, Joachim

@Joachim,

"The statement "... at a certain time, two of the three detectors return to the ground state": Is ithis an assumption, or is this a real fact."

The conclusion that two of the three detectors return to the ground state is my conclusion from the experimental fact that those two detectors don't click. You see, a click comes from the following process: a change of state occurs in the detector, usually a small change. Though, the detector is monitored by an amplifying circuitry. So, if we get no click, it means that the amplifying circuitry saw nothing.

I believe that we can assume that the amplifying circuitry works correctly and reports exactly what it "sees". I rely on the fact that if in the initial wave-function is of the form

(1') |ψ'> = α|a> + β|b> + γ|c>

the clicks in the detectors appear with the correct probabilities, |α|2, |β|2, |γ|2. So, if the amplification works correctly, the input to the amplification - i.e. the state of the material in the detector - is as reported. That means, in every trial of the experiment, two of the detectors return to the background state.

For me to follow you properly in continuation, please tell me what is SE.

"However, if one assumes that the distinguished states e and g are stationary, then the evolution of the state is given by

(1/√3)( |Ae>|Bg>|Cg> eif_A t+ |Ag>|Be>|Cg> eif_B+ |Ag>|Bg>|Ce> eif_C t)"

The state 'e' is not stationary. If, for instance, the studied quantum particle is charged, it ionizes the material, s.t. if the material is placed between the plates of a capacitor, we get a small current. The amplification circuit detects this current. As to the exponential factors that you proposed, you can introduce them in the excited state, as they bring no contribution in the probabilities of the clicks in the detectors.

"Obviously, the evolution will be different if some interaction between detectors is present."

We have enough a complicate situation. We need reliable responses from detectors. Of course the detectors are isolated as far as we can from the environment, not to speak of the isolation from one another.

"In particular within the presented model there is no reason for the return of the detectors to their ground states ever."

I presented no model, only what the experiment tells us. If a detector is in the excited state, this state is detected. I am not going to discuss inefficient detectors - as I said, we have enough a complicated phenomenon to try to understand.

@ Sofia

Thanks for your answer.

1. SE= Schrodinger Equation

2. No exited stationary state can be changed without interaction with some other subsystem

3. Neglecting interaction of the devices with the environment implies neglecting the collapse

4. The fact of dealing with measurement without strict definition makes the problem unsolvable; my proposal is to consider the observed evolution as the evolution of the reduced state of the measuring system via the corresponding partial trace (never opposed till now as the correct description of what the distinguished (interpreted as the measuring/observing) subsystem passes through . How it is seen from my examples, the final reduced state of the measuring subsystem is also a mixture. THUS: if we agree with a slightly less controversial postulate, that mixed states are in the real world displayed as an realization of a random state, then we come - seemigly - to an interpretation easier acceptable by the community.

5. Obviously, my proposal does not give the full answer on what causes that we observe the particular device clicking the success.

6. Returning to your example:

- My proposal (which follows an old idea of many other researchers investigating the decoherence) explains when the final reduced state of the detectors become a mixture. For this it sufficies to add suitable interaction between them and the environment (any outer subsystem), which is necessary to change the reduced state from the initial pure state.

- I have no idea why the mixture of the pure states displays probabilistically, which in fact is the well known interpretation of the QM.

Finally, please note that the proposal does not use the probabilistic interpretation for pure states!

Regards, Joachim

PS. I am interested in the (many times repeated) description of the quantum events: If we measure the energy, then the system enters in the mixture of stationary states corresponding to the eigenvalues of the energy(=Hamiltonian)). HOW DO WE TELL THE SYSTEM THAT WE MEASURE ITS ENERGY? This question is important since - as it is basic - every pure state possesses expansions into eigenstates of many other operators not just the Hamiltonian. Note, please, that my proposal answers this question referring to the interacting Hamiltonian: if the terms of the interaction commute with the self-evolving parts, then ideed the final state is the mixture of the eigenstates of the own Hamiltonians. If the factors do not commute, then the limit reduced state of the observer and/or the observed part become mixtures of another families of the pure states. Therefore I claim, that my proposal somehow explaines the way we are telling the system what observable is currently measured. JoD

Dear @Joachim,

"2. No exited stationary state can be changed without interaction with some other subsystem"

The detectors can't be in a stationary state but in an evolving state. I gave you an example. Why should we discuss things that cannot be? An ionized particle passing through a material inside a capacitor generate ions and a current appears. When the particle leaves the detector, the detector is reset. Which stationary state?

"3. Neglecting interaction of the devices with the environment implies neglecting the collapse"

I am not sure if we understand each other. A detector reacts to the passing of a particle through it, but we don't do experiments in which a detector is influenced by another detector. You said such a thing in your previous post "the evolution will be different if some interaction between detectors is present." Could it be that we have here a problem of language? Please have a look at the respective statement in your former post.

"4. The fact of dealing with measurement without strict definition makes the problem unsolvable; my proposal is to consider the observed evolution as the evolution of the reduced state of the measuring system via the corresponding partial trace"

If you have a proposal, elaborate it into an article, and tell us. By the way, you use the words "without a strict definition". It's not strict definition, it's rigorous theory that we need. As a theory of measurement we have what von Neumann gave us, the quantum part of the measurement process. But we do measurement with classical apparatuses and read the result on a classical dial, or recorded in the memory of a computer - classical objects. I right now encouraged a friend to ask a question on these issues.

Please permit me a small joke: a child was seeking a lost coin on a street under a gas lamp. A fellow asked the child "it's here that you lost the coin?", and the child answered "no, I lost it in another place". The the fellow asked "then why do you seek here?". The child answered "because here is light".

People seek the explanation of the so-called "collapse" with the tools of the quantum formalism because they don't have other tools. But the "collapse" occurs when we input the observed system in a classical apparatus, and the result is displayed classically.

"my proposal is to consider the observed evolution as the evolution of the reduced state of the measuring system via the corresponding partial trace (never opposed till now . . . "

Wait a bit, slow down! Which reduced state of the measuring system? The observed system is inside the masuring apparatus and they evolve together. They are not spacely separated and don't evolve independently. Before speaking of a reduced state, are you able to describe the joint evolution? It would already be a progress.

"6. . . . My proposal . . . . explains when the final reduced state of the detectors become a mixture."

In the final state of the detector, in each particular trial, we get a well defined result. Did you ever see on a dial, in a given trial of the experiment, that the pointer points to a mixture of results? The pointer points to one result.

Dear Sofia,

For the sake of completness - I have already put the proposal in the form of a presentation linked to in my first answer. It uses just the QM rules in terms of the SE, without usage of the von Neumann postulate. Instead, it is shown by stricly calculated examples of evolution of the reduced dynamics, that the final state (in some cases at least) coincides partly with the postulate - namely, that the state becomes a mixture of suitable states. This allows to interpret the results of quantum measurements as random events with calculated probabilities.

> "The detectors can't be in a stationary state but in an evolving state. I gave you an example. " Note, that this was your assumption in the example, that the detectors after the passage of the measured particles form a pure state linearly combined by product pure states |egg+geg+gge>/\sqrt{3}. Your example, that the exited particle causes changes around its trajectory is obviously a result of existing interaction with the surrounding matter. Thus you didn't present an evidence that he stationary pure state chages by itself.

> "The observed system is inside the masuring apparatus and they evolve together." Perfectly right! but the pointer is showing its own state after some time of joint evolution of the observer (let this be the pointer) and the system under observation. No contradiction. But seeing just the pointer, you cannot state what is the joint state of the pair pointer-system. My calculations in the presented conference article show examples to what extend the features of the system are reflected in the evo;ution of the pointer. Usually it is not pure, thus the results are random (in your example of the three detectors, it is not hard to add a reasonable interaction of the triple with the environment, that the resulting reduced state of this tri-fold pointer will end with probability 1/3 in each of the possible three states: |egg>, |geg> or |gge> (strict calculations performed accordin to section 2 of the paper are currently in preparation).

> "The pointer points to one result. " ... but at random with suitable probabilities every one from the mixture. Thus the question is not how the mixtrure appears, but how the system chooses the particular resulr from the mixture. This seems to be a simpler question than the undefinite choce of the basis of the prefered observable.

Let me ask again: Can anyone answer, please, how the system knows which observable is measured by the pointer?

Best regards, Joachim

Addendum to my last answer:

If the possible states of the detectors correspond to mutually orthoganal wave functions |1>, |2> and |3>

and if the outer world state is decribed by a wave functions |\psi(x)> with continuous parameter x (this could be the position of a disturbing particle),

and if the Hamiltonian of the system detectors+particle is given by

H(j,x) = w_j + v_j x, j=1,2,3, x real,

and if the joint system starts from a state decribed by the product wave function (a |1> + b |2> + c |3> ) |\psi(x)>,

then

1. The initial density matrix equals r_(i,j) ,

with r=[a^2, ab, ac; ba, b^2, bc; ca, cb, c^2]

2. After time t the reduced state of the detectors equals (use page 20 of the presentation): r_(j,k)(t) = r_(j,k) c_(j,k) where

c_(j,k) = exp[it(w_k - w_j)] \int_R exp[it(v_k - v_j)x] |\psi(x)|^2 dx

3. Under additional assumption that the impact of the perturbing world is different for different states |1>, |2> and |3> (i.e. v_j \ne v_k for j\ne k), then the off-diagonal integrals approach zero and the reduced state of the detectors in the limit as t goes to infinity becomes

r(infty) =[a^2, 0, 0; 0, b^2, 0; 0, 0, c^2].

Thus under the assumptions of the proposition above, the limit state is a mixture of the pure states |1>, |2> and |3> with probabilities a^2, b^2 and c^2, rspectively (just for simplifying the typesetting, it is assumed that a, b, c are real). Obviously, by the normalization condition, a^2 + b^2 + c^2 = 1.

Any comment is welcome!

Joachim

Dear @Joachim,

I see no link to your former comment. However,

"the final state (in some cases at least) coincides partly with the postulate - namely, that the state becomes a mixture of suitable states."

No, Joachim, the postulate doesn't speak of a mixture of states, but of reduction to one state.

"this was your assumption in the example"

I wouldn't take for sure that the excited state is stationary. You see, the passage of a charged particle causes ionization, causes excitation of part of the atoms without ionizing them, in short a couple of phenomena. After the particle exits the detector the excited atoms decay by emitting photons, in short, a situation far from stationarity. But, for the monitoring amplification system what is relevant is the micro-current.

"the pointer is showing its own state"

Which state of pointer? The pointer is a macroscopic object. We are out of the QM.

"My calculations in the presented conference article show examples to what extend the features of the system are reflected in the evolution of the pointer. Usually it is not pure, thus the results are random . . ."

If you'd give the link to the article, I'll try to comment. But, I am telling you from the beginning, if the final result you present is a mixture of states of the pointer, you didn't solve the symmetry breaking. I repeat, in a single trial of the experiment we get a single position of the pointer - symmetry breaking.

I don't want to ellude you, the symmetry breaking is considered as cause by the fact that macrocopic objects, as a pointer or as the cat of Schrodinger, cannot be in a superposition of states. However, which one of the eigenvalues of the measured operator is choosen, is considered to be absolutely stochastic, because there are no hidden variables.

". . . how the system knows which observable is measured by the pointer?"

Let's take a Stern-Gerlach (SG) experiment. You pass, say, electrons polarized in the direction x, through an SG apparatus with the magnetic field in the direction -z. So, you get two beams, one polarized z, the other polarized -z. You let the beams land on a photographic plate. The z-polarized electrons will land in the upper half-plane of the plate, and the -z polarized ones, on the lower half-plane. Is there any problem?

Dear Sofia, the link has been supplied with my first answer to this thread; it is

Conference Paper Quantum Systems' Measurement through Product Hamiltonians

I wish you good reading; perhaps our points of view become at least a little bit closer.

Before next detailed answers, let me share just one remark about the sentence: "if the final result you present is a mixture of states of the pointer, you didn't solve the symmetry breaking." Afterwords I am not saying, that I am explaining the symmetry breaking; my idea is that the explanation of the changes of pure states to mixtures via the partial trace is not using the von Neumann postulate and brings us closer to the phenomenon of breaking symmetry. Namely we become rid of the mysterious instantenous changes of pure states into another pure states, just by fact of performing the measurement of some observable. In my fashion, measurement is a dynamical process of changes of the reduced states of the observer, which then consequently becomes a mixture. And the probabilities of the mixture are explained by the properties of the interaction. As a side effect we obtain a rigorous definition of the measurement. Of course, there is a lot of work to perform to adopt this structure of notions to the widely spread ideas about the quantum measurement, which I find inconsistent.

Once more - many thanks for you answers!

Best regards, Joachim

Dear @Joachim,

I will read your article, it "sounds" interesting what you say. Just, a bit of patience, because a friend of mine put me to read half of a book. So, I will do my best.

From my point of view von Neumann-Lüders postulate should be replaced by a symmetry breaking postulate.

With best regards from me too, and Happy New Year!

Dear @Sofia,

Many thanks for the time devoted to reading the article and for the comment put within my page on RG. Hopefully after some time our points of view become closer. It would be nice if I can adopt the presented considerations to the physical system suggested in your comment. I shall try it, as well as some other cases.

Please accept my good wishes for the New Year!

With best regards, Joachim

Dear @Joachim,

I warmly recommend a new question posted by a student

https://www.researchgate.net/post/Is_there_is_any_hybrid_model_between_classical_mechanics_and_quantum_mechanics

Just, please see the question, would you? It is a challenge for the mathematicians of QM.

About your article, I added one new comment, please see it.

With best wishes for the New Year!

Dear @Sofia,

Thanks for the link.The question posed by @Manoj Sithara looks like a "lost link of the chain". Even if it does not lead to New Mechanics, it is certainly a need to answer the question. Of course, it requires deep understanding the Feynman paths and the related problems, some of them barrely touched in this thread.

The comment is interesting, still under careful reading:) Thank you for it.

Regards

If collapse is just a change in information then it is not

a dynamical process of anything real.

Dear Juan,

My point of view can be explained as follows (with many, however simplifications): every experiment and/or observation of the reality is oriented toward information about the reality. The collapse is just an imagination of the following human activity: We think that a particle is/should be described by a wave function - and in some places our image is correlated to the observations. Sometimes, suddenly we see that the particle appears is some exact point. In order to explain this we say that the (imagined) wave functions has been changed into the (imagined) point. Thus we have got another information about the particle: the information that it is a wave function has been changed into the information that it has became a particle. Since up to now, nowbody has seen the wave function neither the particle, hence everything we are talking about within QM is our imagination (call it (mathematical) model) of the observed world, which - obviously - is real, but seen only partially. The changes of the world are reported by the observer(s) as changes of the information about the world.

Best regards, Joachim

Dear @Joachim and @Juan,

Everybody here forgets a physical fact. The wave-function whether ontic, or epistemic, or describing information - whatever we want to say about it, is the best mathematical representation of something traveling in our apparatus. We don't know from which kind of material is built that "something", because it seems to have strange properties. However, there is a relationship between it and the wave-function that nobody denies: there where that material is present, the wave-function is non-zero, and vice-versa.

So, this language of "information" is not always correct.

What I am trying to say is that in some experiments, the "information" that we get after the so-called "collapse", may ellude us.

For instance, in which-way experimets performed on the wave-packets of a so-called "single particle wave-function", we know that only one of the wave-packets produces a detection. So, we say that the respective wave-packet carried a particle, and the other wave-packets disappeared, (or we have to do with many worlds).

But it is not true. Nothing disappears, more subtle experiments show this. Also, there is no particle - see my article

Deleted research item The research item mentioned here has been deleted

The so-called "single-particle" wave-function can have an observable effect in a couple of places simultaneously, the places being distant from one another. A particle can have an effect in one single place.

Best regards.

Joachim

I agree with your general point of view.

Except that in some experiments you see points on a screen that build up

in time, which for me is indicating particle impingment.

Now when you see the shadow of these points building up then you get

the probability density predicted by the wave function.

In this case both things seem to make sense, but if I had to sacrifice one of

the two I would keep the particle and sacrifice wave. You cannot have the shadow without the points.

Talk to experimental physicists, its not all imagination.

Best regards, Juan

there is not merely a point and its shadow: the line between them must be included in that shadow too!?

Dear @Joachim and @Juan

The process of measurement is a brutal intervention on the wave-function. As we usually work with absorbing detectors, part of the wave-function is absorbed.

On a photographic plate, in each trial and trial all the wave-packet impinging on the plate is absorbed. However, the quantum of energy carried by the wave-packet is only ONE. It is indivisible, s.t. it cannot be shared between the molecules at different places on the plate. Thus, only one molecle gets it.

That does not mean that we have a particle. That means that the wave-function is nonlocal. Even the single-particle wave-function is an entanglement - an extanglement with the vacuum. Look at this

|ψ> = α|1;a>|0;b>|0;c> + β|0;a>|1;b>|0;c> + γ|0;a>|0;b>|1;c>.

And, as any other entanglement, it displays a nonlocal constraint. In any detection, the number of energy quanta delivered should be 1. E.g. a quantum delivered in the region of the wave-packet |1;a> is accompanied by no quantum delivered in the regions b and c. The three regions are controlled by nonlocal constraints, the wave-packets do NOT behave independently one from another.

So we don't have a particle, we have nonlocal correlations.

@Daniel Baldomir

Can't see where we disagree, apart from wording. For every problem, there is a minimal approach allowing one to write a comprehensive dynamical theory. QED is a minimal approach for electromagnetic measurements, etc. As to QED versus CED, have a look at PRA, 50, 2120 (1994) and 92, 022122 (2015).

@Claude Pierre Massé

Conceptually, collapse is replaced by decoherence; dynamically, by any suitable dynamical approach (cf. the above comment on Dr. Baldomir's post).

As to "quantum nonlocality", its full title in the realm of physics is " quantum nonlocality ". Can't see where collapse can be squeezed in, except as phenomenology.

The shadow is formed by the points, there is no line in between.

Do not agree with the wave function been absorbed and becoming

a point. It is just pure particle and pure probability density which guides particles.

Thus the wave and the particle are two different things.

the shadow of a 3-dimensional thing isn`t the 2-dimensional projection (on a wall, for instance), it is a cone. try to move the wall and you will get an other 2-dimensional projection, dear Juan.

I dont mean literaly a shadow as a figure formed when you block the rays of the sun.

Perhaps the pattern formed by the points is a better term.

The pattern gives an idea of the density of points within some small area,

relate this to probability density.

physicists calculate probability by squaring amplitude. so they locate (uncertainty principle not to be ignored) a particle. now please try the inverse: square-root of amplitude. you would get 2 results (plus and minus). where is the particle now? NOT in 2 different places (apropos 2-slit experiment).

Dear @Juan,

I propose you to see a very interesting thread

https://www.researchgate.net/post/Is_there_is_any_hybrid_model_between_classical_mechanics_and_quantum_mechanics?

The question discussed here, may loose any meaning in view of the problems presented there.

@Sofia: " You made a logical mistake. It's not the wave-function |ψ> that passes into |a> , it's only a part of the wave-function. If you destroy the wave-packet |b>, e.g. by sending it to an absorber, the remaining part of the wave-function can be characterized in continuation by a state |a>/ √ , iff the operator that you measure on it is the one whose eigenfunction is |a>. Otherwise, "unperformed measurements have no results". "

No. I made no logical mistake. I just applied the rules of quantum mechanics. These are to do the projection in the Hilbert space. Of the entire state. There are no diverse wave packets to consider. Just project the state. All of it.

I am not talking about unperformed measurements. If a detector at x measures a quantum particle, that affects the wave function everywhere, not only at the position of the detector. That is standard qm.

@Domsta: " My suggestion is to interpret this restriction of access to the information as collapse of the wave-function (more generally - of the state) of the observed subsystem (indeed, it cannot be seen by "1" in a more detailed form!). "

Sorry for the late response, but even before resuming courses I do not always have the time to read stuff here.

I looked at your presentation and, while it is interesting, I do not think it says much about the collapse proper.

In fact, I once posted a more detailed description along the lines of yours (but only in words) in a project on RG maintained by Sofia Wechsler. Unfortunately, RG requires you to update your projects all the time (apparently they do not consider that a project can ever be finished) and if you don't, you are pestered with requests. Anyway, Sofia redid the presentation of her project and erased my comment - so I will not do more than short comments on projects anymore. Let me repeat my description and I hope, here it will last longer.

When doing a measurement, you have to couple your apparatus to the system of interest. Then they evolve together, and if the measuring apparatus is to serve its purpose, the state arising will be a superposition of product states, in which the system is in an eigenstate of the observable to be measured, while the apparatus takes on a "pointer state", uniquely (or not uniquely, in the case of a non-ideal measurement) identifying the eigenstate. In the case of a mixed initial state, you have a mixture of such superpositions after the time needed for a measurement has passed. But the system and the measuring apparatus are still coupled. To obtain information about the system alone, you should trace out the apparatus degrees of freedom. That corresponds to your trace over one of the systems, but in my description it is only the apparatus that gets traced out, because I want to get information about a system state only. This is the Heisenberg cut, but not yet the collapse, because what this trace will give you is just a mixed state (to perform it, one has to go to the density operator description), with the density operator being diagonal in the eigenstates of the measured observable and the diagonal elements giving the probabillities for the corresponding measured values. Now such a density operator can be interpreted very much like a classical probability density, with the eigenstates the possible system states and the probabilities given by the diagonal elements (and with obvious generalization to the continuous case). The final step is the read-off of the pointer variable. This involves an interaction between the observer and the apparatus, which we may however treat classically, because both are macroscopic. During the Heisenberg cut, information is normally lost, because we may move from a pure to a mixed state. During the read-off, information is gained. All the probabilities but one become zero, and the probability corresponding to the measured value becomes one. This is a collapse of probabilities known from classical physics. If it is interpreted as the collapse of the wave function, that is of course not a dynamical process and it will not take time accordingly. On the other hand, I think that the Heisenberg cut together with the collapse of classical probabilities should be considered the collapse of the wave function. Then the latter will still not be a dynamical process.

Your general answer about the time of the collapse makes sense in your view. But I believe that you cannot just omit taking the trace from being an essential part of the collapse (although the final determination of a single measured value may be argued to be more essential, but that is definitely not dynamic). However, one cannot consider taking this trace as part of the dynamics of the microscopic system.

@Massé: " You are not able to make any distinction between the Schrödinger picture and the paths integral, and for a good reason, they are mathematically identical, not even up to a unitary transformation."

And that is wrong.

Since you want me to "back up things", I simply quote Feynman's thesis (1948), where he introduced the path integral approach. Starting on page 48, in the chapter "The role of the wave function" he discusses the possibility that there are quantum mechanicals systems not describable by a wave function but still accessible to his approach.

I quote:

"It is not unreasonable that it should be impossible to find a quantity like a wave function which has the property of describing the state of the system at one moment, and from which the state at another moment is derived. In the more complicated mechanical systems (e.g. the example, (44.2)) the state of motion of a system at a particular time is not enough to determine in a simple manner the way that the system will change in time. It is also necessary to know the behavior of the system at other times; information which a wave function is not designed to furnish. An interesting, and at present unsolved, question is whether there exists a quantity analogous to a wave function for these more general systems, and which reduces to the ordinary wave function in the case that the action is the integral of a Lagrangian. That such exist is, of course, not at all necessary. Quantum mechanics can be worked entirely without a wave function, by speaking of matrices and expectation values only. In practice, however, the wave function is a great convenience, and dominates most of our thought in quantum mechanics."

He then goes on to discuss how his method may be applied to systems that do not have a wave function in certain time intervals. (For simplifying the discussion, he assumes them to have one at time -∞ and +∞, but he leaves no doubt that his approach may be used also in the case, where there is never a wave function.) It is, moreover, clear, that he considers matrix mechanics as more general than the Schrödinger equation. Again, this is true when the system does not have a (one-time) Hamiltonian but an action principle is still available.

In fact, the motivation for Feynman to develop his path integral approach was to apply quantum mechanics to the Feynman-Wheeler absorber-emitter theory of electrodynamics, which is nonlocal in space and time (the electromagnetic field is "integrated out", so one obtains an effective action at a distance). In that theory, the action is not the integral of a one-time Lagrangian, and there is hence no (one-time) Hamiltonian either, so there is no obvious way of applying the Schrödinger picture. But there is an action integral, with the integrand depending on more than a single time, so Feynman's approach is applicable, because it does not nead a Hamiltonian. But if there is no initial wave function, you cannot use it to construct a wave function.

Anyway, it seems that you have your knowledge about Feynman's approach from secondary literature or from a teacher who knew only the modern variant (that you can find in Wikipedia, for example), in which the wave function is directly expressed via a path integral. But this is not the original version, nor does it exhaust the approach. (Of course, today the case with an action coming from a Lagrangian is the one that is almost exclusively used.)

The basic quantity calculated in Feynman's approach is a propagator. That is, as I stated before, a Green's function, not a wave function. It can be turned into a wave function via multiplication with an initial wave function and integration over all of space. Whicn is not possible, if you do not have an initial wave function. Still, you can use Feynman's approach to calculate transition probabilities.

Now what is contained in that basic quantity? It contains the action in the exponential of which the path integral is taken. What kind of action? The action of the classical system that we wish to quantize. So in the case of a single particle, for which we have a Lagrangian (and a Hamiltonian, then), this is the action of the classical (point) particle. It is not the action of a wave, nor is it an operator. Just the time integral of the classical Lagrangian. So the ontological entity behind the formalism is a point particle, not a wave (function). However, the wave is also there in the formalism. We add up, via the path integral, phase terms (the exponential of the action multiplied by the imaginary unit) -- these are waves, the sum of which produces a probability amplitude. But the picture of a particle taking all possible paths to produce these interfering waves is present and a sound one. It is also used all the time when doing perturbation theory in the Feynman approach.

The basic path integral in Feynman's approach is one between a fixed initial point and a fixed final point, just as in the action principle. The expression for the wave function is also usually written just as a path integral. But it is not a basic path integral, it is one where the initial point "slides" through all of space. It is actually a spatial integral of a basic path integral, but usually the integral over space is absorbed into the path integral notation.

"@Sofia: " You made a logical mistake. It's not the wave-function |ψ> that passes into |a> , it's only a part of the wave-function. If you destroy the wave-packet |b>, e.g. by sending it to an absorber, the remaining part of the wave-function can be characterized in continuation by a state |a>/ √ , iff the operator that you measure on it is the one whose eigenfunction is |a>. Otherwise, "unperformed measurements have no results". "

"@K. Kassner: "No. I made no logical mistake. I just applied the rules of quantum mechanics. These are to do the projection in the Hilbert space. Of the entire state. There are no diverse wave packets to consider. Just project the state. All of it."

You did not apply the rules of QM, as the collapse postulate is not part of QM. In the QM, everything evolves according to the Schrodinger equation. Things don't appear out of nothing, and don't disappear into nothing. Thus, if you place a detector on a part |a> of the wave-function, you can describe the process by introducing a loss-factor describing the absorption. The part |a> of the wave-function is reduced in intensity, while the other part, |b>, remains. If the quantum of energy carried by the wave-function is delivered to the absorber, the part |b> won't be able to deliver energy, it becomes an "empty wave". Though, as Hardy proved in an article dedicated to "empty waves", these have observable effects.

Of course, a fellow like you who "doesn't have the obligation" to read articles, cannot know what was proved, and insists on his own theories.

You attribute to the nonlocality of the wave-function properties that it doesn't have. The fact that the wave-packet |b> won't trigger a detection together with the wave-packet |a> is not because because something disappears, this is your theory, but because there is no component |a>|b> in the wave-function. Did you look at the wave-function, or this too it's not your obligation? A joint detection is allowed by a joint probability, i.e. by the absolute square of the amplitude of |a>|b>. There is no joint amplitude in the wave-function |a> + |b>. The two wave-packets are connected by the relationship 'OR', not 'AND'.

But if you don't have the obligation to read, and place your theories against whatever was proved and acknowledged, I don't enjoy speaking to a wall, neither have time for this. From my part, believe in whatever abra-cadabra of things that disappear into nothing, and ignore even the wave-function.

If your logic say that you can argue against material that you don't read, then please by kind and don't mention my name and my material. Say whatever you like about other people, if they permit.

Good day to you!

The following is an answer to some issues raised in another question (asking about the possibility to derive the quantum state vector from classical mechanics). But it contains some material relevant to the present question, too, so I post it here as well.

@Sofia: "You did not apply the rules of QM, as the collapse postulate is not part of QM. In the QM, everything evolves according to the Schrodinger equation."

My dear Sofia, this is complete nonsense. Some minimal statement about the results of measurements must be part of qm, otherwise you could not make any predictions. As long as everything evolves according to the Schrödinger equation, you cannot predict anything, because there never is a decision between different possible measurement results.

The collapse postulate is part of standard qm.

In some non-standard interpretations of qm, it is replaced by other hypotheses, such as, e.g., the entrance of the observer into a subbranch of the wave function. Which leads to a collapse-like behavior of the accessible branch as well.

K.Kasner,

The collapse of the wave function is a particular interpretation of a particular theory that tries to describe (not explain) quantum physics. The wavefunction is an artificial concept that hides most of what it represents. Other theories are possible in which the wavefunction is replaced by a stochastic process. Such theory reveals what the wavefunction hides and it shows why observers notice a collapse of the wavefunction when the object in question interacts with something.

Article Stochastic control of the universe

@van Leunen: The collapse of the wave function is part of standard quantum mechanics, i.e. quantum mechanics including a minimal interpretation. As I said, there are interpretations that replace it by something different to get the same results.

There has been a series of papers some thirty to twenty years ago that showed that stochastic processes cannot reproduce quantum mechanics (that is, classical stochastic processes without the effects that the concept of probability amplitudes brings in that the wave function represents). In fact, the ultimate proof that stochastic processes cannot reproduce quantum mechanics (as long as they are local) is given by Bell's inequalities.

@K.Kassner,

The Hilbert Book Model proves the contrary. Stochastic processes that own a characteristic function do control the generation of all discrete objects that exist in universe.

https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project

Please notice the challenge http://www.e-physics.eu/#_Challenge

discrete objects/space are very well handled by using distributions on set functions.

@van Leunen: "The Hilbert Book Model proves the contrary."

I doubt it. Does it refer anywhere to the proofs? If not, it probably simply misses the point. If you do not know the proofs, then you are likely wrong, because then you can hardly have addressed their point.

The proofs are provided in the Wikiversity Hilbert Book Model Project.

https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project/Stochastic_Location_Generators

Wave function collapse, that means the retarded wave send from emitter collapse to the absorber. The advanced wave send from absorber collapse to the emitter(If you accept the concept of advanced wave). This means wave collapse to the target. None can offer a formula to describe the collapse process. Wave function collapse is a wrong concept. Wave is only looks like collapse but never collapse.

The correct answer is that the wave is time-reversal returned. There are time-reversal waves which satisfy time-reversal Maxwell equations (for photon) corresponding to the retarded wave and the advanced wave. Hence there are 4 waves instead of 1 or 2 waves! These 4 waves completely balanced out or canceled, hence wave do not transfer energy! However the retarded wave and advanced wave are superposed, which produced the mutual energy flow. Mutual energy flow can carry energy from the emitter to the absorber. There is time-reversal mutual energy flow which is the results of the superposition of the two time-reversal waves. The time-reversal mutual energy flow is responsible to bring half photon back form the absorber to the emitter, in case a race condition happens. For example if a emitter send a retarded wave this wave energy has been received by two absorbers, each get a half photon. This photon will be returned to emitter by time-reversal mutual energy flow.

Mutual energy flow do not decrease with distance. The energy transferred by the mutual energy flow are equal at any surface between the emitter and the absorber.

All the wave are canceled and the energy is transfer by the mutual energy together look very like that the wave is end from emitter has collapsed to the absorber.

This theory is started from the mutual energy principle and self-energy principle, which are applied as new axioms to replace the Maxwell equations. Since Maxwell equations need to be remedy by adding 4 new time-reversal Maxwell equations (which is not Maxwell equations). The concept about the mutual energy and mutual energy theorem is introduced by Shuang-ren Zhao in 1987. Recently this theorem is developed to as two principles the self-energy principle and the mutual energy principle, which solved the wave-particle duality paradox. For details please see:

http://www.openscienceonline.com/journal/archive2?journalId=726&paperId=4042

S. Ren Zhao,

The wave function is not a solution of the wave equation.

The square of the modulus of the wavefunction describes the location density distribution of the swarm of hop landing locations where the corresponding particle has been, is or will be. It is the Fourier transform of the characteristic function of the stochastic process that generates the hop landing locations.

It is surprising that in this thread reference to the notion of `ensemble' is

made only once, because, evidently, everyone followed the usual textbook interpretation of the wave function as a description of an individual object (rather than as a statistical description of an ensemble of such objects).

This is surprising the more so because the ensemble interpretation has been experimentally corroborated already a long time ago (for instance by Tonomura et al, American Journal of Physics 57, 117-120, 1989).

Hence, projection can be understood as a selection of a subensemble, based on observed pointer positions of measuring instruments (at least, Einstein was right on this score). Whether you want to call this a ``dynamical process'' is a matter of taste.

For separate elementary particles the wavefunction is not composed. In all higher order modules the wavefunction is composed.

In the Hilbert Book Model the superposition of the components does not take place in configuration space. Instead it takes place in Fourier space. The reason is that the wavefunction represents a location density distribution. For elementary particles this is the squared modulus of the wavefunction. The location density distribution describes the production of a stochastic process, which owns a characteristic function that equals the Fourier transform of the location density distribution. Elementary particles are elementary modules. Composed modules are also governed by a stochastic process. This stochastic process also owns a characteristic function, but this characteristic function equals a dynamic superposition of the characteristic functions of the stochastic processes of the components of the composed module. With other words, the wavefunctions of components "superpose" in Fourier space. The superposition coefficients may install internal oscillations.

For more details, read "Structure in Physical Reality"; http://vixra.org/abs/1802.0086 (15 pages)