Dear Sofia,

You can find the answer to your question in section 3.3.4 (formula (3.31))

of my book (W.M. de Muynck, Foundations of quantum mechanics, an empiricist approach, Kluwer, 2002).

Maybe I earlier told you that I believe that von Neumann's projection postulate is just mathematics, and that `conditional preparation' (i.e. selection of a subensemble on the basis of selecting a unique pointer position of the measuring instrument) should be taken into account instead.

In general the abovementioned formula describes a density operator, depending on the interaction of the object and a microscopic part of the measuring instrument (often referred to as a probe).

Greets, Willem

Willem Marinus de Muynck

Dear Prof. de Muynck,

First of all, how are you? It's a lot of time that we didn't talk.

Now, how shall I read your book? We are under Korona, shops are closed. I hope that in your country the situation is better.

About von Neumann's postulate, the situation is not simple - I have an article that proves that it is impossible to ignore the collapse,

Preprint The quantum mechanics needs the principle of wave-function c...

see section 4. Simple experiments are discussed showing that denying the collapse we run into contradictions with different predictions of the quantum mechanics.

However, admitting that the test of one particle collapses the other, we again run into contradictions. Suppose that Alice's lab and Bob's lab recede from one another such that by the lab-time of Alice (Bob) it's she (he) who measures first. I suppose that you are familiar with this situation, so, I'll tell in brief.

- If Alice measures and gets H, the collapse principle says that at the time of this event by her lab's time-axis, Bob's photon becomes polarized H, although it was not yet tested.

- However, by Bob's lab's time-axis, it's him who measures first. Until this event, no change should occur in the wave-function, no collapse. After Bob tests its photon and gets C, the collapse postulate says that Alice's photon becomes C-polarized although it was not yet tested.

It's a contradiction. Then, what is the truth?

With kind regards and wishes of health,

Sofia

Dear Sofia,

It is too bad that I did not send you the prepublication version of my book (which Springer does not mind because it is sufficiently different from the published one,

but essentially contains the same). Please send me your email address (mine is still [email protected] ).

In the meantime I will try to answer your reply.

Hope all is well with you!

I am still going (be it less strong than I would like it to be).

Regards,

Willem

Dear Sofia,

Most answers to your questions are discussed in my book, the prepublication version of which I hope to send you as soon as I have got your email address.

Here I want to add some insights not explicitly dealt with in the book. It is mainly about what I use to refer to as the `classical paradigm', referring to the classical

custom of omitting all reference to measuring instruments in textbooks of classical mechanics, but unfortunately being continued in textbooks of quantum mechanics.

This is unfortunate because humans are not able to see the (sub)microscopic objects quantum mechanics is dealing with. As a matter of fact we need measuring instruments to bridge the gap between the human observer and these objects. Such a measuring instrument needs to have a pointer allowing to attribute numerical values to the observable which is measured.

Omitting here a number of important issues having to await further explanation, I here restrict myself to von Neumann's projection postulate, which you still seem to consider as important. As a matter of fact, in my book you will see that, contrary to von Neumann's suggestion, his projection postulate has not been proven by him. As a matter of fact, in the last chapter of his `Mathematische Grundlagen der Quantenmechanik (1932)' he is discussing a quantum mechanical interaction between object and measuring instrument. But in the very last paragraph of that chapter he tells us that he is leaving (a general) discussion to

the reader. My advice to you is to have a look at sect.~3.3.4 of my book.

Regards,

Willem

Nothing happens with "entanglement". Since two wave functions of two geometric elements representing particles are strictly connected by known Clifford translation, see Sec.6.1 of "The Geometric Algebra Lift of Qubits and Beyond", measurement of one simultaneously gives the result of not made measurement of the second one.

As there is no Hamiltonian of interaction and the two Hilbert spaces specifying the properties of the two particles do not overlap, nothing will happen to the other particle after one of them is measured. See- Robert B. Griffiths, “Nonlocality claims are inconsistent with Hilbert space quantum mechanics”, Phys. Rev. A 101, 022117 (2020).

Actually, an entangled state is a statistical description of an ensemble of measurements and, being time- and space-independent, the notation specifies four, not two, particles. At the level of one single measurement, you either have |H>1 |H>2 or |V>1 ||V>2 but not both at the same time. This is the root cause of the misinterpretation for "quantum nonlocality".

For photons, see a recent book titled "The Physical Reality of Applied Quantum Optics".

Andre X Vatarescu

Oh, Andre, I don't see myself having the force to read a book. However, the nature doesn't suffer of double personality. The behavior of entangled photons, as of entangled particles possessing rest-mass, has to be the same at a partial measurement.

I disagree with Griffiths about nonlocality, but I agree with you that the measurement of one of the particles does nothing to the other one, as long as the latter is not yet measured. Well, when the latter is measured, combinations of results for which the amplitude of probability is zero, are suppressed due to destructive two-particle interference. It's easy to prove. So, as long as the second particle is not tested, there is nothing to suppress.

Best regards!

Reply to S. D. Wechsler,

You can have two-particle interference if you have a global wavefunction which is time- and space- independent as is the case with the statistical measurement of an ensemble of identical events. But it is you who decides to formulate a global wavefunction. The ensemble experiment is put together by a long sequence of single measurements and in each and every measurement only one pair of photons is present. Therefore, the "entangled" state is not present during the single and individual measurement. Thus, there are no entangled photons if only because the quantum Rayleigh scattering replaces the original photons with spontaneously emitted ones which can go in any direction. Search for "Quantum Rayleigh annihilation of entangled photons". The same correlation function is obtained with single and independent photons as for mathematically entangled photons.

If there is an interaction between measurement operations, you should specify the Hamiltonian of interaction and the common physical Hilbert space where that interaction takes place. As the photons move away from each other, their Hilbert spaces which describe the photonic properties become disconnected and the measurement is projected onto a mathematical Hilbert space for comparison purposes of the synchronized measurements.

Justo Pastor Lambare

No, the state (2) is another measurement, along other axes.

As to the formalism of QM, everybody knows it. But the formalism does not answer my question, it tells us what we get if BOTH particles are tested.

Justo Pastor Lambare

Maybe Sofia, unwillingly, moved to considering states as operators acting on observables - the point of view I believe is the only correct one and that I've followed in my researches for some years, see soiguine.com

Dear Sofia, the short answer is: nothing happens, imho. After photons stop interacting, the pair of photons "collapses locally", prior to any measurement, to a non-entangled state defined by the initial entangled state, i.e., present in the representation of the entangled state as a superposition of non-entangled states. But it is (or seems) impossible to know this non-entangled state. More detail about this approach can be found in a preprint "On the EPR paradox and local causality principle", especially in section 4 (5 pages), which I recently posted on ResearchGate.

Kind regards, Zbigniew

Justo Pastor Lambare

Confusing between states and tests is too silly, I don't do such confusions.

The quantum formalism makes predictions ONLY for measurements results. It takes no responsibility for what isn't measured yet. There is also a famous dictum (and article) of A. Peres "Unperformed experiments have no results". What happens with the particle not yet tested is an unperformed experiment.

Of course, we are displeased with the QM silence, and would like to fill in this gap. However, the situation with one particle measured and another one not yet, is likely to be a non-quantum state. The tested particle passed through a detector and interacted there with a big number of particles of the detector, so big that the ensemble of perturbed particles is macroscopic. On the other hand, the not yet tested particle is likely to be still a quantum object since it didn't interact with anything.

This is the question asked here, what can be said about the state of the not yet tested particle. Does it collapse on a definite state, in consequence of the measurement of the pair-particle, or does it remain in an undefined state as before the measurement of its pair-particle?

Justo Pastor Lambare

No, Justo, what you say quarrels with the relativity. For making the discussion simple and efficient please first read the following:

Article Hardy’s paradox made simple – what we infer from it?

You'd see that if the not yet tested particle collapses, a contradiction appears.

The so-called "Hardy's paradox" should be taught in universities at the courses of quantum mechanics. Unfortunately, it is not done.

Justo Pastor Lambare

The quantum formalism says what I said, not what you said. I repeat, QM takes no responsibility on not measured systems.

As to those facts that the problems with the relativity were there for a long time, that does not solve these problems.

If you really read the article I recommended - I am not convinced of that - you could see that reasoning according to one moving frame, the particle p- should collapse (albeit not tested) on the state |u->. According to another moving frame, the particle p+ should collapse (albeit not tested) on the state |u+>. Thus, returning to the lab frame, the two particles should have been before reaching the beam-splitters, in the joint state |u+>|u->. But such a state is forbidden.

Justo Pastor Lambare

You go too far, too quickly. My article is correct but cannot be published because it is not entirely original. The contradiction it describes was already presented in another article, by other authors - though in a much more complicated form. There was a whole debate around this contradiction, with the participation of the best minds in QM.

There is no conflict between QM and relativity. I repeat (how many times I said it already?), unperformed experiments have no results. The test of one particle does nothing to the pair-particle.

Justo Pastor Lambare

No so-called "interpretation" solves all the paradoxes.

About beliefs, they are good in the church. Science goes with proofs, not with beliefs. Hooft's theory for which he got the Nobel prize has nothing to do with my question. You have to decide whether you try to answer my question, or deal with another domain. For another domain I advise you to open a question/thread of yourself.

In science there are two types of people: 1) librarians; 2) researchers. The first type are able only to cite what other say. The second, know what others say, but try do find new facts, eventually to say something tottaly new.

they are disentangled by the measurement process, or better decoherent. this is not to be confused with determinism.

I'm puzzled about this discussion. First, a singlet is described but then three polarized photons example, Hardy's paradox, presented as a previous understanding of the problem.

Then someone gets angry by a scientific discussion!

The problem posed by Sofia is simple enough to merit a cool discussion. Because simple does not mean easy to discuss... Let's try to find out...

I have developed a theory called QED-Physical (QED-P) that produces an explanation for the physical basis of quantum entanglement. This is a testable hypothesis, and I need help finding experimenters who will perform this test. Please email me at [email protected] if you would like a copy of I fist paper in a series of Perryview journal articles. Abstract is as follows:

The QED – Physical (QED-P) theory presented in four previous papers [1,2,3,4] is integrated with QED into a single theory in this paper, since both are based on the same Dirac Equation four current c( α ,I). QED couples this four vector with an external electromagnetic (EM) field, and uses covariant perturbation theory to produce results that are very accurate computationally [5], except for the electron self energy, which is infinite. The reason for QED’s accuracy is its Dirac Equation velocity operator, c α , with highly usual properties compared to classical velocity vectors. QED could not produce highly accurate answers without the 4 by 4 complex matrix c α as the electron “velocity operator. QED-P starts with the same Dirac Equation four current used so successfully in QED, and the discrete internal spatial and time coordinate operators (ISaTCOs) are derived in QED-P to give the electron internal structure a very specific, but highly, non classical geometric description with no ad hoc assumptions.

However, one should ask what new physical measurements are predicted by QED-P that are not determined by the very accurate QED? Although the answer is none yet, due to the very rapid fluctuation of the ISaTCOs with a period of ~ 1.4 10-21 sec. This induced electron field fluctuation is in addition to any vacuum fluctuation that exists without the electron field present.

This paper presents a highly speculative, but testable, experiment in which the ISaTCO rapid fluctuations may be confirmed indirectly as the physical basis of field Quantum Entanglement (QE).

To James H. Wilson,

Does your theory require global wavefunctions or states which are space- and time- independent, and as such can be be used anywhere, at any time and in any context?

There's a manuscript titled "Quantum Rayleigh annihilation of entangled photons" which is under consideration by Optics Letters and which can be found on this website. The correlation function which is alleged to be of a quantum nature can be derived without entangled states.

Andre X Vatarescu In the geometric algebra scheme replacing conventional quantum mechanics the wave function (not confusing word "state") is operator acting on observables. In that scheme wave functions may be constructed as special solutions of Maxwell equations also written in geometric algebra terms. That wave functions when subjected to modifications like Clifford translations or Hopf fibrations instantly change their values everywhere through 3D space and forward and backword in time. That particularly gives physically feasible demonstration of what is called entanglement. Some details may be found in my "Instantly Propagating States", Journal of Applied Mathematics and Physics, 2021, 9, 468-475

decoherence or disentanglement

To Andre: In my theory of electron called QED-P, only the Dirac Equation is assumed to be correct. There are no other assumptions. QED uses the Dirac velocity operator cxalpha, and calculates very accurate electron properties, such as the anomalous magnetic moment. Therefore, in my theory, QED-P, the derived internal space and time operators are also highly accurate, and suggest a reason for Quantum Entanglement 

To Andre: In my theory of electron called QED-P, only the Dirac Equation is assumed to be correct. There are no other assumptions. QED uses the Dirac velocity operator cxalpha, and calculates very accurate electron properties, such as the anomalous magnetic moment. Therefore, in my theory, QED-P, the derived internal space and time operators are also highly accurate, and suggest a reason for Quantum Entanglement 

To Andre: In my theory of electron called QED-P, only the Dirac Equation is assumed to be correct. There are no other assumptions. QED uses the Dirac velocity operator cxalpha, and calculates very accurate electron properties, such as the anomalous magnetic moment. Therefore, in my theory, QED-P, the derived internal space and time operators are also highly accurate, and suggest a reason for Quantum Entanglement 

To Andre: In my theory of electron called QED-P, only the Dirac Equation is assumed to be correct. There are no other assumptions. QED uses the Dirac velocity operator cxalpha, and calculates very accurate electron properties, such as the anomalous magnetic moment. Therefore, in my theory, QED-P, the derived internal space and time operators are also highly accurate, and suggest a reason for Quantum Entanglement 

To Andre: In my theory of electron called QED-P, only the Dirac Equation is assumed to be correct. There are no other assumptions. QED uses the Dirac velocity operator cxalpha, and calculates very accurate electron properties, such as the anomalous magnetic moment. Therefore, in my theory, QED-P, the derived internal space and time operators are also highly accurate, and suggest a reason for Quantum Entanglement 

To James Wilson,

How do you model light - matter interactions with your theory?

To Alexander Soiguine,

How do you model light - matter interactions with your theory?

This is an interesting question.

Preprint A Heuristic View on the Composition of Space

Preprint A New View on the Composition of Matter

Andre X Vatarescu

When light is written as (proportional to ) g-qubit its action on matter is what is defined as measurement (in my theory), generalized Hopf fibration. See my works/books. RG and soiguine.com.

Alexander Soiguine

I had a look at your website and I like your quotations:

We all say so, and so it must be true Rudyard Kipling, The Jungle Book Truth never triumphs, but its enemies eventually die Max Planck

I am trying to approach the "quantum miracles" from a physical perspective of light-matter interactions. The attached four-page manuscript was revised according to requests made by a topical editor of Optics Letters. Let's see what they make of it.

Andre X Vatarescu

Though you are acting in the terms of conventional quantum mechanics, the general ideas are plausible. Light can play the role of wave function, something external to measured elements, elements of matter, observables. When a measurement, interaction of wave function with the matter elements, takes place, all formulated in my terms, the "quantum miracles" would get feasible, logically consistent explanations.

Maybe you will find something additionally interesting to quotations in the Technology section of my website.

Alexander Soiguine

How would you solve the following problem?

A single photon comes across a multitude of electric dipoles, and it is certain to be absorbed by an oscillating dipole. The dipole emits spontaneously a photon into an arbitrary direction. Therefore, the photon cannot propagate in a straight line inside a dielectric medium. Yet, the dominant approach in Quantum Optics is to have the photon propagate undisturbed through dielectric devices and components. This miraculous approach is based on global functions which display no space or time dependence leading to quantum nonlocality of remote measurements of two photons which had a common past.

The question is: How does the photon evade absorption by the dipoles?