Maybe I would not yet quite use the term consistent or closed. Closure is a math concept. I would call QM consistently verified experimentally, by quite a large mass of different experiments, constantly repeated. The empirical support is comparatively good, compared to other topics in Physics, even excelent.

There are those still concerned with a philosophy of QM ; the reason or interpretation. But the factual basis is there, but resists belief , due to its strange nature. Perhaps we need time, to come to terms with it.

Juan,

I am asking what are the definitions. People use these words giving them hazardous meanings.

Next, I am asking whether QM satisfies the consistency and closeness.Or, at least, if until now we have a reason to doubt any of these properties.

So, I expect a focused answer.

With kind regards.

Possible meanings of closure,

Cannot go beyond, the topic is settled. (Cannot yet say of QM)

In math, math operation has closure if some result of a math operation takes you into the same kind of math object

ie. multiply two real nos, get a real nos. Fails with integers under division.(Irrelevant here)

Consistency,

An experiment in this topic is not in contradiction with another experiment.

Here you may have a possible deficiency. One experiment gives you waves, another particles.

This difficulty could be apparent or not. There are different opinions.

Complete

You can answer any reasonable question,

Well, not even the theory of numbers is so, less so in QM

consistency in axiomatic structure

One axiom does not contradict another.

Here people have been clever enough to avoid mayor problems in QM, but limits what they say.

Dear Juan,

About closed theory I have a more precise definition: I think a theory is closed when one can add nothing to it, i.e. any hypothesis one would try to add, would lead to a contradiction. (That has nothing to do with closed sets.)

But this definition is impractical. People can suggest all sort of additional hypotheses, the number of options being of the power of continuum. Could you suggest a more practical definition?

The fact that the two most elaborated interpretations of QM, Bohm's one and the GRW one, failed because they were based on adding new assumptions to QM, makes me think that QM seems to be closed (according to my definition). But, two assumptions that failed do not cover all the possible additional assumptions that can be made. As I said, my definition is not operative.

With kind regards

I would accept closure in a sense that means that the essential ideas that are used, in given historical context (today),

are a relatively stable set, in a sense that means there are variations in the interpretation, but all essentially go back to the same

set of ideas going around; nothing revolutionary going on.

Gradually this may change, for example ideas of Quantum Field Theory seeping in to the body of the quantum. In particular the

statistics of the particles Fermi or Boson playing a more significant role in the theory. For example the Schrodinger equation by

itself seems to say almost nothing about this.(that is what I do now). However as to clear up the philosophy of QM, clear up mystery, there is nothing yet in sight. If anything mystery might yet deepen.

Dear Juan,

The Bohm interpretation added to the QM a substructure of particles and trajectories. As I repeatedly said, I proved that it leads to contradiction with QM.

The GRW we already discussed, it is at odds with the relativity. (By the way I am reading these days their basic article and I have plenty of objections - I don't even recommend it).

The Bose and the Fermi statistics are not assumptions needed, they were proved. I believe that it also was proved that fermions should have spin N/2 and bosons integer spin, and their wave-functions should be anti-symmetrical, respectively symmetrical.

But I don't refer in my question to QFT which categorically is not a closed theory. I refer only to the relativistic and non-relativistic QM, i.e. QM with wave-functions not field operators.

Now, I want to tell you what I am interested in fact. I would like to check if QM is complete (closed). I expect proposals of additional assumptions. I'd like to find out which can be the most general additioal assumption one may add to QM. If even this assumption is rejected by QM - i.e. a contradiction appears - it would mean that QM is a complete theory.

Sofia D. Wechsler claimed:

"As I repeatedly said, I proved that it leads to contradiction with QM."

And as I repeatedly said, your proof is errorneous, it contains a big loophole. As it should, given that dBB theory obviously exists and is proven to be equivalent to quantum theory in quantum equilibrium states.

For the details of the discussion about this proof, see https://ilja-schmelzer.de/hidden-variables/showthread.php?tid=4654

Dear users,

The problem that I posed is a quite ambitious one, and whoever can give a good proposal, is great. Whatever is known about QM, is that no experiment until now, contradicted the standard QM. But until now contains no guarantee for the future. In short, we have no rigorous proof that QM is consistent (no experiment contradicts it), neither that QM is complete (i.e. any new hypothesis added to QM would lead to a contradiction).

Personally, I don't see how can be proved that the standard QM is consistent. I think that for such a proof one should perform all the possible experiments. But the set of all the possible experiment is of the power of the continuum.

What I think that yes can be proved is that the standard QM is complete. I believe that the proof should be done in two steps: a) proposing an assumption orthofonal to all the axioms of the standard QM, and showing that it is the most general such assumption; b) proving that this assumption leads to a contradiction.

Dear Sofia D. Wechsler

Consistency is a purely mathematical property of a theory, namely that one cannot derive as A, as not A from the theory. So, if one assumes that mathematics itself is consistent (which cannot be proven given Goedel's theorem), to prove the consistency of physical theories is possible, usually even trivial. In reality, this often makes no sense because many physical theories contain infinities, thus, are already known to be wrong because of this. So, i n particular, quantum field theories are shown to be consistent only in some exceptional cases, like free particles which do not interact and some particular low-dimensional theories.

But the mathematics of quantum theory is consistent, what makes field theories problematic are the infinite numbers of degrees of freedom.

In principle, it makes also sense to talk about inconsistency of some interpretations. As an example of an inconsistent interpretation I would name many worlds. This is also a logical problem.

So, consistency has nothing to do with experiments. A theory may be completely consistent but have nothing to do with the real world and fail every experimental test.

That QM is complete cannot be proven. There are known hidden variable theories, and these hidden variable theories are consistent too.

Dear Sofia,

Yes, as you know very well, Quantum Mechanics is an "incomplete" theory because the so called problem of measuement. That is to say, how the superposition of states associated to a particle must project in one only state due to measurement on a given device. The problem is obviously not easy and I don't pretend to solve it at all. It seems to me that what is missing is to formulate a correspondance between a given base of the Hilbert space of states |x>i (i=1,2,.....N) decaying in only one |x>. What is the reallistic form to to it ? The latter suggestion is difficult if we think that the states are not well determined physical objects, but without a rule of this kind the problem will be remain.

You might want to modify Dirac type of theory to deal with many particles, and I see QM as a whole mostly at odds with relativity., as well as better explaining the measurement part, as Daniel says.

My wise Daniel,

I have to object to what you say,

"Quantum Mechanics is an "incomplete" theory because the so called problem of measuement. That is to say, how the superposition of states associated to a particle must project in one only state due to measurement on a given device."

Please see, it's not the "problem of the measurement", but the "problem of the measurement with a macroscopic apparatus". Such an apparatus is OUTSIDE the QM formalism. Of course, you can argue that QM has to explain ALSO what happens with a quantum superposition at the encounter with such an apparatus, and I am not sure that I would have a definite reply.

HOWEVER! I have HARD WORDS to say about the quantum community. I don't think that it's QM to be blamed for the lack of explanation of the macroscopic measurement. It's not exactly QM to have the duty to explain, it's the quantum community that has the duty to explain. The nature does not give us everything on a silver tray. We have MINDS. If our minds are not able to explain difficult things, should we jump to the conclusion that QM is incomplete, or it simply means that we are UNCAPABLE?

You know me so well. You know that my efforts are in the direction of explaining things. It seems to me that the issue of completeness is an issue of axiomatization. I think that one systematic way to deal with it is as follows: a) find a general hypothesis that could be added to the set of axioms of QM - this hypothesis has, of course, to be orthogonal to all the others; b) prove that QM leads, under this additional hypothesis, to a contradiction.

Do you see another way? Or, can you propose such a general hypothesis? By general hypothesis I mean something with the least constraints. For instance, local hidden variables are constrained by the requirement of being local. Bohm's hypothesis of continuous trajectories is constrained by the requirement of continuity of the trajectories. Both these hypotheses failed exactly because their constraints. Non-local hidden variables is a more general hypothesis, but it is impractical. (If you'd ask me I will give details.) Non-continuous trajectories e.g. jumping from one wave-packet to another, between distant regions, might be a candidate, but I am not sure because I see some problems.

With kindest regards

Juan my friend,

Standard QM (including relativistic QM) has no problem with the relativity, and needs no modifications. Again, I don't speak of quantum FIELD theory, but of the theory operating with wave-functions. Please recall that standard QM takes no other responsibility than predicting measurement results. I have to mention here Peres' proof that "Unperformed experiments have no results".

What yes have problems with the relativity are the interpretations. Both dBBI and GRW are at odds with the relativity. About the latter, I explained you. Though, I have to talk with Ghirardi, I believe that the problem of the GRW may be fixed, though, with a conceptual modification. (To tell you frankly, Ghirardi is a very wise physicist and a kind fellow, but whenever I write to him he complains that he is not young and is over-burdened.)

With kindest regards

Dear Sofia,

I'm one user of QM and not a maker of it. For me QM is enough in certain cases and others I need to use QFT when the degrees of freedom are much higher (infinite in most of the cases). This problem was shown by many people and it is well known (starting with the paper of Einstein-Rosen-Podolsky) and I'm not at all original. So, for me, the problem of measurement (with macroscopic devices if you want) in QM is just a formal problem which doesn't prevent to use this theory . What I wanted to say is sinthesized in your sentence:

Of course, you can argue that QM has to explain ALSO what happens with a quantum superposition at the encounter with such an apparatus, and I am not sure that I would have a definite reply.

Dear Daniel,

My question refers to the QM (relativistic or not), i.e. the one working with the wave-function not with FIELDS. So, QFT is OUTSIDE my question. (I wouldn't even dare to ask whether QFT is a complete theory, because I would not know how to define completeness for it. Look at the Standard Model, could we take responsibility and say that it is complete?)

Now, what's between the EPR paradox and QFT? I don't understand what you are trying to say.

On the other hand, your reply is as if I came to you with some pretention. But I didn't. Did I ever do such a thing?

You see, I think that QM is complete. I also think that the macroscopic measurement can be explained by QM - with the microscopic part of the measurement the QM formalism has no problem, as it preserves superposition. And I am trying to find the explanation, or, better said, to push the explanation as far as possible.

But, let me say another thing: in very old times, people who were unable to explain some phenomena in the nature, invented gods. In our times, in face of the measurement problem, which is indeed a very difficult one, people invent "interpretations" based on additional hypotheses. Though, what I see, is that those interpretations fail, one after another.

With kindest regards

Dear Sofia,

I don't agree that QM is complete (EPR doesn't belongs to a complete theory) and clearly the Standard Model isn't too. I only have told you about QFT (generalizes QM for fields) for saying that some times uses it because I cannot use QM and never for working with the Standard Model, but with Many-Body Theory. But always as user and not as a maker

My dear Daniel,

It is your full right to agree or not agree with a certain statement.

Along with this, the Standard Model belongs to the QFT domain and formalism (Lagrangians, fields), not to QM which works with the Schrodinger equation, or Dirac, or Klein-Gordon. So, I repeat that my question does not refer to QFT.

About the EPR paradox, it is not a proof of incompleteness of QM. This paradox has a clear solution, the Copenhagen Interpretation of QM, i.e. the standard one. The standard QM predicts only results of measurements, while "unperformed experiments have no results", an operator that cannot be measured doesn't have a value. Sorry, it's quantum mechanics here, not classical mechanics. As you know, in standard QM the position operator and the linear momentum operator, don't commute, s.t are not measurable together, therefore standard QM does not predict that they have values, IN PRINCIPLE.

EPR thought the contrary, i.e. that each particle involved in their thought-experiment should have both these well-defined values, one of the values measured, the other deduced as it could not have been directly measured. This is why EPR asked if QM is complete. Unfortunately, both Einstein and Podolsky died before Peres' proof that "Unperformed experiments have no results". So, they did not get an answer to the question. But Nathan Rosen lived to see Peres' proof.

So, it is not that QM is incomplete, i.e. some observables may have values even if not accessible experimentally. It is that a quantum object does not have, IN PRINCIPLE such values.

Sofia,

Relativity has no wave function and no uncertainty principle. Therefore, minimally the theories are hard to compare.

Maybe we dont agree on the meaning of contradiction.? on comparison?

I reiterate that with standard relativistic QM, you cannot go to many particles.

You dont think that this is a deficiency?

Regards, Juan

Juan,

What kind of a statement is "Relativity has no wave function and no uncertainty principle"? Of course it doesn't have, that's trivial. The relativistic QM has. Wow!!!!!! Wait a bit! Please tell me, could it be that Hardy's paradox is not known to you? It is the best argument that dBBI trajectories are not Lorentz-covariant). If you don't know, I recommend my very short article Article Hardy’s paradox made simple – what we infer from it?

As to many particles, I also don't understand what is your proble. Are you not aware of the GHZ experiment using entanglements of 3 or 4 particles?

However, I again repeat, I speak of the QM that works with wave-functions, not fields. QFT works with fields, i.e. another formalism, and I am no expert in it.

Kindest regards

Dear Sofia D. Wechsler

You wrote "dBBI is in contradiction with the relativity". This is misleading. dBB is in contradiction not with relativity, but with the spacetime interpretation of relativity, which rejects the possibility of existence of a hidden preferred frame. The Lorentz ether interpretation of the same theory of relativity is not in any conflict with dBB.

QFT is conceptually the same as QM. The wave function becomes a wave functional on the space of field configurations, which is an infinite-dimensional space. This makes the mathematics much more problematic. But one can always regularize the theory, so that a field configuration is approximated by a finite number of degrees of freedom, then the standard QM formalism works without further modifications.

QM does not explain some experiments that it should.

Add the wave medium is REAL and waves in the medium have a speed much greater than the speed of light.

John,

WHICH experiments does not explain QM? I already said, you make all sort of declarations in a misty way. Explain yourself!Otherwise, it's just words in the air.

With best regards

Ilja Schmelzer

My question is about QM. If you want to deal with QFT open a thread by yourself. You probably have time to chat about everything, but I don't have, s.t. ask in your threads about A and get answers about B.

About the existence of a preferred frame, you prove it!!!! The supreme judge in physics is the experiment, see the experiments of Gisin.

For the rest, as I already said, I am revolted by your style of talking with me, and not willing to continue with you.

GOOD BYE.

Sofia Sarcasm is not needed, I think you evade the issue.

ddB is so unimportant to me, that I do not even bother to combat it. Not my fight!

For the reasons I gave relativity is mostly at odds with any QM, maybe meaningless to compare.

I tried to tell Ilya an alternative for the mesurement problem not using trajectories, I will repeat it if you like.

Juan my friend,

Ilja's problems are not within the topic of this question - s.t. I believe that he should solve his problems elsewhere. This thread is meant for solving my question.

Now, you see, I have the feeling that QM (relativistic and not relativistic - but not QFT, QED, QCD) is a complete theory, so much so that any additional axiom one would be tempted to add, would lead to a contradiction. But I am not absolutely sure. (About QFT nobody can guarantee that the Standard Model is closed - do you recall the mass gap problem? It's a prize on it. And, please believe me, judging the QM is enough bother.)

You see, the problem is the macroscopic measurement, as daniel said. So, the question is, can we find a hypothesis which would replace the collapse principle? If QM is complete, there is no such hypothesis. We remain with the collapse and it's the duty of the quantum community to explain how the collapse works, within the set of axioms of the QM.

By the way, I sent you a message, please be kind and read it.

With warm regards

Sofia D. Wechsler

you have a real antagonistic tone, I see why Ilja responds as he does.

I said experiment that QM not explain NOT you misstatement (or deliberate rephrasing?). I guess you have to know something of the field - I don't want to educate such as you.

quantum eraser, quantum entanglement, Afshar's experiment Hodge experiments (several depending on how you count them).

Nothing is that clear in QFT, but in general the wave function is converted to a field operator, which in turn has eigenvalues and eigenstates as usual. The worst in QFT is perturbation techniques, with infinities, etc.

Sofia D. Wechsler

On second thought. Your non-collegiality manner is something I do not want to deal. I'm done with you.

Yes, Juan,

But, as I said, there is enough trouble with QM. One doesn't learn mathematich beginning from the differential calculus, but from simple algebra. In physics when we tackle a problem, we begin from the simplest cases, solve them (if we can), and only after that we go to more complicated cases.

(I am telling you frankly, if we were given the possibility to live twice, in the second part I would have learnt thoroughly the general relativity. I find it much more attractive than dicovering new particles. I would have looked for worm-holes.)

With kindest regards

John Hodge

"I said experiment that QM not explain NOT you misstatement (or deliberate rephrasing?)"

I don't understand what you say. What you mean by "QM not explain NOT"? It's a language problem here.

I have no reason to rephrase, I told you repeatedly that when you make a statement you have to prove it, otherwise it has no convincing effect. But I force nobody to talk with me. So, good luck!