I dont think you will get very many answers this way, because von Neuman is very mathematical, and the measurement problem

lies outside QM proper, although recieving more attention. Your best bet, if you have the contacts, is to directly converse with experimental groups working in the area of the quantum, or perhaps quantum optics.

If parts a and b are physically separated, and you put a detector in part a, you block beam a, but not beam b, simple as that. If your source is sufficiently coherent and monochromatic you can further divide beam b and get interference.

Thats my comon sense.

States don't disappear in quantum mechanics. What does occur is that, if |a> and |b> are eigenstates of the Hamiltonian, the states α|a>+β|b> are, also, states of the quantum system.

If the system is prepared in the state |a>, it will always be found in the state |a>; and likewise for the state |b>. If its initial state isn't known, it can, only, be described as a linear superposition of all possible states and, in that case, the statement that the classical apparatus yields a measurement consistent with the system being in state |a> implies that, from that point on, any subsequent measurement will find it in state |a>, an eigenstate of the Hamiltonian and, thus, the evolution operator-and the reason is, simply, that the measurement selected that particular eigenstate.

To find it, subsequently, in state |b> one needs an apparatus that is sensitive to some other property of the system.

Stam,

I would appreciate an answer to my question. I asked what said von Neumann, not what YOU say. If you have his book, please be so kind, LOOK in it and tell me what HE said, i.e. HIS WORDS.

The situation that raises questions in the measurement theory, is when the wave-function is a superposition of eigenstates of the measured operator, for instance |ψ> = α|a> + β|b>. My question is clear: in the trials in which one gets the result a, did von Neumann say something about what happens with the component |b> of the initial wave-function? Did he say or didn't? In particular, did he say that the component |b> disappears, or didn't he refer to |b>?

People sometimes take the liberty to re-interpret the von Neumann reduction postulate in a way that von Neumann didn't say. This is why I ask what HE said, I mean HIS words.

My Juan,

I asked what von Neumann said in his book. Nobody knows better what von Neumann said in his book, than the book itself. So, why should I ask experimenters? I ask if somebody has the book, or, in a less precise case, if somebody has an exact citation from his book.

My question comes exactly because different people take the liberty to interpret von Neumann as they understand, instead of citing him exactly. For instance about the measurement of a quantum system with a macroscopic apparatus, some people claim that von Neumann said that an entanglement appears between the eigenstates of the system, and states of the macroscopic apparatus. I found in different sources that von Neumann spoke of a MICROscopic apparatus, i.e. which is also a quantum system.

Also, some people interpret the collapse postulate in the sense that for an initial state |ψ> = α|a> + β|b> of the tested system, in the trials in which the outcome is a, the part |b> of the initial state disappears. I don't think that von Neumann said such a thing. But I don't have the book, s.t. I don't really know if he said or not.

(Unfortunately, the Technion library is very far from me and the library of my town is not scientific. To travel to Technion I have to exchange 4 busses in each direction and wait in buss stations long time. It's very difficult for me.)

Dear Sofia,

Perhaps you can get the book from this link:

Book The Mathematical Foundations of Quantum Mechanics

With best regards.

The words-of von Neumann, or whoever-are, simply, irrelevant; their meaning only matters. And it's this meaning, that's the content of my answer. Physics is different from textual analysis!

When the result is la>, it's nothing else-that's the state of the system, one among the possible states the system may be found in. And, if this state is an eigenstate of the evolution operator, then no other state is, ever, produced; if the state |a> isn't an eigenstate of the evolution operator, then there is a probability to find the system in a state that's not |a>, since the state is a superposition of states, that define a basis.

So the only issues that matter are: (a) Is the system prepared in an eigenstate of the evolution operator-or not? (b) Does the measurement apparatus define an operator, that commutes with the evolution operator-or not?

The rest is a completely straightforward application of linear algebra-that is only complicated by the fact that the Hilbert space of states can be infinite dimensional.

My Stam,

The situation is as follows: there are people who take the liberty to attribute to von Neumann things that he NEVER said.

von Neumann was an extremely clear mind, but these people say, behind his name, wrong and misleading things. The situation is more severe, but I'll tell you some later, in a private message.

This is why I asked what exactly von Neumann wrote. Moreover - I suppose that you know the Lating saying "traductori - tradittori" (please correct me if the grammar is wrong) - enough for me that I have to read the English translation as I don't know German. I hope to God that this translation is of high fidelity. This is why I don't speak of meaning - for the moment - I want his exact words. About the meaning I can discuss after I see what the fellow said, exactly.

With kindest regards, and again,

HAPPY NEW YEAR!

Technical texts aren't scripture! Nor does the fact that anyone appeals to von Neumann-or any other ``famous'' name-imply anything about whether the statements made by the people-or by von Neumann or the authority appealed to-are correct, or not. That's why it's utterly futile to focus on the text and not the meaning in scientific issues.

The only thing that does matter is that the system that's found, in some instant, in an eigenstate of the evolution operator, remains in that eigenstate; while the effect of a measurement can be straightforwardly be described by expressing the measurement in the basis of the evolution operator.

Stam, my kind friend,

You know how much I appreciate your wisdom (and also wide education). You are not the only one who protests against this custom to stick to what said the "great masters". No matter how deep was their clarity of mind, they weren't saints. In some respects they may have been wrong. Even Einstein was wrong with respect to "God does not play dice". The science advances, and that's exactly what happens, different things in what they said turn out to be more complicated or totally different.

But many, many people have the custom to stick to what the great pioneers said, when it's convenient, i.e. when coincides with those people's view. And it's even worse, sometimes people take the liberty to "interpret" what said the great masters in a way coinciding with their own theories.

I want to say that some of these peope are not at all beginners.

I said that I'll send you a message and as I have some problems of myself, I didn't have time to do it. I appologize, and I am doing this now.

With kindest regards!

The original is written in German and is accessible as "Ueber die Grundlagen der

Quantenmechanik"

https://gdz.sub.uni-goettingen.de/id/PPN235181684_0098?tify={%22pages%22:[5],%22view%22:%22export%22}

You can buy the book https://www.bookdepository.com/search?searchTerm=Mathematical-Foundations-of-Quantum-Mechanics-John-Von-Neumann&search=Find+book

John von Neumann doubted long between Projective Geometries and Hilbert spaces as platform for modelling quantum physics. I think finally he selected Hilbert spaces. See: https://plato.stanford.edu/entries/qt-nvd/

In my youth as a student I studied many of his books and papers and I chose quaternionic Hilbert spaces as subject of the paper that closed my study at TUE in 1970. In 2009 I restarted this investigation, which resulted in the Hilbert Book Model Project. See: http://vixra.org/author/j_a_j_van_leunen.

The HBM uses a huge set of quaternionic Hilbert spaces that all share the same vector space. Each elementary particle owns a private separable Hilbert space that floats over a background separable Hilbert space. See:

https://www.opastonline.com/wp-content/uploads/2018/11/tracing-the-structure-of-physical-reality-by-starting-from-its-fundamentals-atcp-18.pdf for more details.

I have to admit that in particle physics we are still in a rather primitive stage, a particle may be some kind of floating around singularity, which dresses itself up surrounded by fields and other virtual phenomena, a real kind of ghost.

Instead of investing our time in seeing what some theorist sais about it, with a theory that sais something at the cost of minimalism (try not to say anything very specific) , just bone up on the latest solid results. Hilbert was brillant in his field (math) but ultimately must remain silent about grass root physics. So must we if we simply do not know.

Maybe someone can help us out?

My Juan,

I claim that those things that we do not understand are just under our nose. The Nature is so simple - but so smart - that there are things that we do not see because we look for complications. What can help us is ONLY our research. And more experiments are needed about certain specific things.

I'd also like to tell you that QM formalism is an absolute ruler over the quantum world. It does not admit to share its power with anybody else. All the tentatives to supplement QM with additional assumptions (e.g. particles and trajectories a la Bohm), failed. I think that also the GRW (Ghirardi-Rimini-Weber) interpretation (spontaneous localization of the wave-function) is not correct. Leaving aside the fact that it is not relativistic and the trials to make it relativistic are complicated - a heap of ad hoc assumptions and formulas, there are things on which this theory just stammers.

With kind regards

Sofia,

I share your view on simplicity of reality. Also John von Neumann made it far too complicated.Scholars of the early twentieth century did not recognize that the wavefunction stands for the activity of a type of stochastic process. That process generates a discrete distribution and not a continuous function. Measurements show that this process is a combination of a Poisson process and a binomial process. The binomial process implements the spatial spread of the wavefunction. This knowledge is applied in the Optical Transfer Function (OTF) and in the Detective Quantum Efficiency (DQE) characterization of the imaging quality of image intensifier devices. The process produces a coherent hop landing location swarm. A location density distribution describes that swarm and equals the square of the modulus of the wave function. It acts as a detection probability distributions. This last thing was already known by Hilbert and von Neumann.

That buisness of absolute ruler is of course unscientific, because nothing in science can be considered carved in stone.

However the rules, vague as they are, have been tested for about 100 years, which is not really a long time yet.

I think the rules are vague and flexible enough, so that no one can easily question them yet.

So probably a future theories will just adorn this a bit, not really change it that much. Much like SR has modified Newton,

but Newton is still nearly correct.

Juan,

You appear to deny that physical reality owns a structure and its own rules. It applies its own mathematics and in that language it writes is own laws. In that sense Sofia is correct. Physical reality is an absolute ruler. The fact that humans make a mess from their rules has no effect on what reality is or does.

Hans

On the contrary, when you think that the rules are ironclad and cannot be changed, then you are probably wrong.

So science has to keep a certain open mind, flexibility.

Saludos, Juan

Reality has structure, properties and behavior. It applies its own rules. We (humans) have science. We can observe reality.

Our professor had a simple explanation for the phenomenon of a collapsing wave function:

What's collapsing after a measurement is only the uncertainty region of the phase space. After a measurement a certain region of the phase space can be found as non accessible for the measured particle. This non accessible part of the phase space vanishes after the measurement, ergo the remaining phase space collapses.

Actually this collapse is hard to call from an experimental point of view.(or people would have had an answer by now)

For some time a particle may remain in the state it collapsed to, so during this time we could say there is no superposition.

On the other hand we could say that there is not enough time for the particle to transition to another state, so the rest of the states are inconsequential but not unexistant.

The well definition of a state depends on the lenghth of time a particle remains in it.(uncertainty principle)

The time a particle remains in any partially measured state depends on the forces acting on the particle or more generally on the system model, which describes the evolution of the particles state. The analogy to the Kalman Filter algorithm should be taken into account.