# Jiri Soucek

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• #3335

Dear Matthew Leifer,

Thank you very much for your comments. These are very helpful for me. In general I agree with your remarks but some points are to be discussed.

In general, it is clear that QM must be an applied probability theory and it is clear that this probability theory cannot be the Kolmogorovian probability theory.

1. The first point is the concept of a probability theory. I think that this concept requires the following two properties.
(i) The probability theory excludes the use of the concept of an observable and of the concept of a measurement so that any general probability theory (as an example the so-called quantum probability theory) are not probability theories in this sense. (The general probability theories are something like the general statistical schemas.) The probability theory is only about events and its probabilities and on the probability distributions interpreted as states of a system.
(ii) The probability theory requires the concept of an individual state, i.e. the state of an individual system (in a given time instant). Thus to each system there must be associated the (finite) set of its possible individual states. Then the state of an ensemble of systems is the density matrix defined on the set of individual states.
At the end there are only two “true” probability theories: the Kolmogorov theory and the quadratic probability theory. At least I think so.

2. The relation to the operationalism. I agree with you but not completely. QMand the modified QM are empirically equivalent (i.e. at the operationalism level they are equal) but they are different on the theoretical level. For example, in the modified QM the individual superposition principle is false, the Bell’s theorem cannot be proved and the Bell nonlocality cannot be proved. So that empirically equivalent theories may be theoretically very different. (See may paper in the topic “The absolute and relative truth in quantum theory …” in this conference.)

3. Let us assume that we want to be realist. At first we must consider the concept of an individual state of a measuring system since it is exactly what we observe in an experiment: the individual state of an individual measuring system.
What is the set of individual states? (The idea that pure states are individual states is excluded by the possible non-unique decomposition of the state into pure states – see the attached paper.) Thus the set of individual states is a subset of the set of pure states. There are clear reasons that different individual states must be orthogonal. For example: if the system is in an individual state, it cannot be found in another individual state.
Assuming this we obtain that the maximal set of individual states must be identical to a certain orthogonal bases of the Hilbert space of the system.
But this is exactly the starting point of the modified QM: we assume that each system is associated with some particular bases containing all individual states.
The idea that each system is associated to a particular orthogonal bases is completely comfortable with the concept of a probability theory – this orthogonal bases is the set of all individual states.

As a conclusion I would like to state that there is an interpretational work inside the modified QM and also in the probability approach to the QM. I think that this matter should be discussed in more details later.

#3333

Dear Shan,

I have a comment and a critical remark to your argumentation.

I shall consider the property (C1) in the more complete formulation:
(C1x) the wave function of a physical system is a complete description of the individual system.
You write “The first approach is to deny the claim (C1), and add some additional variables …”.
I think that there are two possibilities how to deny (C1):
(ii) to deny that every wave function is a description of the individual system.

The second possibility is usually overlooked but it is the bases of the modified quantum mechanics (QM). The modified QM is systematically overlooked. The main idea of modified QM (see attached paper) is that for each system there exists exactly one special orthogonal bases composed from individual states (= states of individual systems) and there are no other individual states. This can be called the psi-hybrid option.

In the paper it is proved that QM and modified QM are empirically indistinguishable so that the modified QM should be considered as equivalent to QM. It is also shown that the measurement problem can be simply solved in the modified QM.

I would like only to remark that your list of possibilities how to deny some claim from (C1)-(C3) is incomplete since one possibility is missing and this possibility may be a key to the solution of the measurement problem.

#3320

Dear Matthew,

1) The very idea of the ontological models is based on the assumption that there exists only one probability theory – the standard Kolmogorov theory. But from 2008 there exist two probability theories – the Kolmogorov (linear) probability theory and the new quadratic probability theory published in arXiv:1008.0295v2 where the probability distribution is the quadratic function f(x,y) of two elementary states x and y. Then the choice of the Kolmogorov probability theory in the definition of the ontological models is unjustified.

2) I think that QM cannot be modelled in the linear probability theory since this probability theory does not allow the reversible time evolution (see the first attached paper).

3) The ontological model based on the linear probability theory seems to me to be completely un-natural. On the other hand using the quadratic probability theory there is a completely natural model for the “real” QM (i.e. QM based on the real numbers instead on complex numbers). In fact, the quadratic probability theory with the reversible evolution is almost identical to the “real” QM. This is described in the section 2 in the first attached paper. This results can be generalized, in some extend, to the complex QM (see section 3 of the first attached paper).

4) You have mentioned the “Dirac-von Neumann interpretation with its explicite collapse upon the undefined primitive of measurement”. I agree with you that the “undefined primitive of measurement” is the basic problem of QM. I think that the first step in the solution of the measurement problem is to give the axiomatic formulation of QM which does not contain the masurement among its axioms. Exactly this is done in the modified QM (see the second attached paper).

jiri soucek

#3318

Dear Shan,

I am suprised that you consider the psi-epistemic view together with the idea that all observables have pre-existing values.
I understand the psi-ontic view as the standard assumption that each pure state represents the possible state of an individual system. For me the psi-epistemic view means that not all pure states represent the possible state of an individual system – possibly, no pure state represent an individual state.
In this situation the assumption that each observable has a pre-existing value is not a good idea.
The set of individual states can be quite small. One can expect that two individual states must be orthogonal since the system in certain individual state cannot be found in another individual state. This implies that the set of individual states should be a particular orthogonal bases.
These ideas are basis of the modified quantum mechanics introdused in the attached paper. In this theory the collapse problem can be solved along lines proposed in your paper – as an update procedure.
I would like only to remark that your argument of the impossibility of the psi-epistemic view based on the Kochen-Specker theorem is not clear.

jiri soucek

#2908

Dear Ken,

I understand your question QM/GR. But there is also the simpler problem: how to make sense of QM and SR in the same consistent framework. Up to now, QM and Special Relativity cannot be considered in the same framework since QM is not local (at least this is the general opinion). At the moment there are not many proposals for the local QM. One of them is the Consistent History approach and another is the modified QM which I have proposed in the section nonlocality and relativity. At each case there is a preliminary problem of QM/SR before looking at the QM/GR problem.

Jiri Soucek

#2903

Dear Robert,

I think You use the different concept of the probability theory than me. You say that in CH approach the time symmetric formulation of probability is used. OK, but in my concept of the probability theory this is impossible, since in my concept of the probability theory the evolution is strictly uni-directional. It is clear that we use different concepts of the probability theory. I think this is the point.
But nevertheless, there are similarities. In the extended theory of probability, the basic concept is the concept of a context. The context is a maximal set of mutually compatible events. In each context the extended probabiity is reduced to the standard probability. Each experiment must be associated with certain context: only events from this context can be observed in a given experiment. Thus the context can be understood as an analog of your framework. But I need much more time to study the CH approach.

Jiri Soucek

#2902

Dear Dieter,

in my study I only tried to analyze the nonrealism option using the concrete model. The nonrealism possibility exists already 50 years, but it was not explored. Thus the question is old, only the proposed solution is new.
The realism is equivalent to the von Neumann axiom (the wave function represents the individual state) hence in each nonrealism model the von Neumann axiom must be false and then also individual superposition principle must be false. I did not take the psi-epistemic position but the psi-hybrid position (some wave functions represent individual systems). In my analysis I have found the suprising fact that many old problems can be relatively simply solved in the modified QM (as expected, nobody believes that this is possible).
Your expectation that this needs the new empirical evidence cannot be satisfied in this case since the modified QM and the standard QM give the same predictions. The fact that two very different theories can give the same prdictions is strange but it seems that it is true (i.e. these theories are empirically indistinguishable). This implies that neither the von Neumann axiom nor the anti-von Neumann axiom have some empirical consequences – but the explanation power of these theories is different.
There is a question if the psi-epistemic variant can be realized (no-go theorems). If modified QM is consistent (I hope it is) then this is an example of the psi-epistemic model.
Your opinion that the wave function is nonlocal (I agree) is the kernel of the classical argument against von Neumann: the nonlocal wave function cannot represent the individual cat which is local (it can perhaps represent the ensemble of cats). The classical argument is, of course, the old Einsten`s example.
I think that the nonrealism option should be studied seriously since the opposite option, the nonlocality, was not fruitful.

#2877

Dear Dieter Zeh,

I think there is one old hypothesis which was not analyzed yet: the nonrealism option from the dichotomy nonlocality vs. nonrealism. The nonlocality option was analyzed in many studies in last 50 years but there are only few papers that analyze the nonrealism option in some concrete explicit models. I think that such non-equilibrium is very bad. In fact, the nonlocality option did not show much success – old problems rest unsolved. I think that this is a mistake since the nonrealism option could offer new perspectives and new possibilities to solve old problems.
I tried to develop ecplicit proposals in this direction (cited in the attached notes) and perhaps something interesting can be found there.

I would like to comment Your opinion expressed in the reply #2212 that a proposal containing possible changes in some building blocks of QM like superpositon principle, for example, should be well justified. I try to do this. In attached notes I hope I have proved that (i) the predictions of modified QM are the same as predictions of the standard QM and (ii) the nonrealism option implies the necessity to abandon the individual superposition principle (“the superposition of individual states represents an individual state”) – here the term individual state means the state of the individual system (i.e. the ontic state). This means that without the possibility to change something in the superposition principle the nonrealism option is not realizable. I hope that the abandonment of the superposition principle in my papers on the modified QM (i.e. using the anti-von Neumann axiom) can be in this way justified. Your opinion on this matter would be very helpful for me.

#2837

Dear Matthew,

I would like to comment your effort to consider seriously the psi-epistemic position. I think that there are not only two options but three options – besides the psi-ontic and psi epistemic positions there exists also psi-hybrid position introduced in my paper on modified QM. This psi-hybrid position means that some wave functions represent individual states and others represent states of ensembles. Typically the set of individual states forms the orthogonal base of the Hilbert space. The psi-hybrid position offers more advantages and less disadvantages then the two other positions. Details can be found in attached papers.

#2804

Dear professor Zeh,

You have written “I think that every individual proposal that does not explicitely postulate the superposition principle … should at least indicate how it would justify the well established general applicability … of this most important principle of quantum mechanics.” My comment. In fact, there are two superposition principles. The individual superposition principle applicable to individual states (i.e. states of individual systems, i.e. ontic states) and the collective superposition principle applicable to collective states (i.e. states of ensembles, i.e. epistemic states). In the psi-ontic situation the collective superposition principle implies the individual superposition principle but this may be false in the situation which is not psi-ontic. (In such a situation Your statement might be partially a prejudice.) The collective superposition principle is generally considered as true. My proposal (http://vixra.org/pdf/1503.0109v1.pdf), the modified QM is not psi-epistemic but it is psi-hybrid, i.e. ontic-epistemic which means that some wave functions describe individual (ontic) states (typically individual states form the orthogonal base of the Hilbert space) while other wave functions describe collective (epistemic) states. In this situation the collective superposition principle holds, while the individual superposition principle does not hold (in fact, the anti-superposition princople holds). This is consistent position since the experimental proofs of the superposition principle are always concerned with ensembles. QM is a probabilistic theory and predicts only probabilities which can be tested only on ensembles. Moreover, I think that considerations concerning individual states cannot be experimentally tested since the standard QM and the modified QM have the same experimental consequences.

My position with respect to the locality: I think that locality should be an axiom of QM (especially with respect to Special Relativity). I hope that I have proved that my proposal, that the modified QM is local.

My position in Your taxonomy: 3b`4 – this means 3b, psi-hybrid but not psi-epistemic and completely local. I hope I have been able to show the locality of the modified QM.

#2781

Dear Robert,

But I cannot agree with Your position with repect to the probability theory. The Kolmogorov probability theory cannot be the model for QM since it does not offer any possibility for the reversible time evolution. The evolution in the standard probability theory is strictly uni-directional. This is exactly the advantage of the extended probability theory that it offers the comfortable way how to describe the time reversible evolution. I am sure that the possibility to represent QM as a probabilistic theory needs the use of the extended probability theory.
To the concept of the observation. It is the fact that axioms for the concept of the observation in the modified QM are quite different from the axioms for the concept of the measurement in the standerd QM. In the modified QM the measurement proces is the standard internal QM proces of the special type. But the external observation proces in the modified QM is something completely different from the external measurement proces in the standard QM. In each theory the external proces of the obseervation must be defined (at least implicitely) – without this no physical information can be obtained. The external proces of the observation (perhaps hidden) must be assumed. In fact, the concept of the observation makes possible to cut the von Neumann chain. The second basic difference consists in the fact that the measurement is related to the ensemble while the observation is related to the indvidual system.

#2742

Dear Matthew,

I am afraid that the problem with the superposition may be harder. In fact, the superposition problem must be consider as a part of the problem of the which way information. The problem stays in the fact that the existence resp. not existence of the which way information can influence the real physical processes. The superposition is only one side of this problem. I am almost sure that there exists only one rational explanation which is based on the concept of a context introduced in my paper attached below. This explanation is based on the following considerations: there are incompatible events, which cannot be observed simultaneously in the given experiment; events observable in the given experiment make together the context of this experiment (the experimental setting defines the context); thus the existence (resp. not existence) of the which way information defines the context of the eperiment; thus with the which way information we observe different events then in the situation when the which way information is not available. Then when we have not available the which way information we can observe the interference. This means that the phenomenon of the interference is primarily associates with the context of the experiment. All this is explained in details in my paper on the extended probability theory and quantum mechanics attached to this note. In conclusion I think that the problem of interference is only a part of the larger problem of understanding well the role of the which way information (of information in general) in quantum physics.

#2707

Dear Robert,

You have written “The consistent histories approach was initiated in order to deal with probabilities in the quantum context, and I think it has solved the problem–while I allow that there may be alternative or better approaches.”
I think that the consistent description of probabilities in quantum mechanics needs more. Probability approach to quantum mechnaics must at the first step to explain why it is possible that the real physical outputs depend on the “which way information” !! This means that real physics depends on the things like the information !! This is shocking !! I have been trying to do this in arXiv:1008.0295. In this approach I have tried to build the extended probability theory appropriate for the describing quantum mechanics. I hope I have arrived at the point to understand the point of the problém. But this theory is not complete. The details can be found in http://arxiv.org/pdf/1008.0295.pdf.

#2705

Dear Robert,

You have written “Can quantum mechanics and special relativity be combined into a single coherent theory?” But this is neccesary !! The reality cannot be inconsistent !! The microworld is described by the quantum mechanics and the special relativity. Without the consistency of these two theories the quantum theory cannot exists. But it exists and this means that in real applications QM and special relativity are mutually consistent. To achieve this consistensy is the task for theorists. But this means that the discussion of quantum nonlocality (or Bell nonlocality) is impossible !! The problem is how to find the possibility for the quantum theory to be local. I have tried to do this in the paper attached to this note.

#2704

Dear Robert,

You have written “Is measurement essential to any formulation of quantum mechanics, or can measurements be described using fundamental quantum principles that make no reference to measurements?”. I comment that if measurement should be the part of the quantum theory, than you will need something as the concept of the observation. observation means that some “observable” systems can be observed and its individual state can be “observed”. This is clear for classical systems. Without the observation the measurement problem cannot be solved. The possibility to observe the individual state of some systems is necessary for any solution of the measurement problem. I have tried to solve this in https://ijqf.org/wp-content/uploads/2015/06/201503.pdf . I think that the measurement problem can be solved only in the theory like the modified quantum mechanics. In the standard quantum mechanics there is no progress in the solution of this problem.

#2698

Dear Robert,

You have writen “how shall we understand quantum correlations as in EPR-Bohm?”. This is the basic question. If any local quantum mechanics could be possible, it must at the first place to give the local explanation of the EPR correlations !! Of course, the first goal is to exclude the derivation of Bell inequality. But the local explanation of EPR correlations is necessary !! I tried to do this in http://vixra.org/pdf/1502.0088v1.pdf but this needs to be checked. The goal to create the local quantum mechanics is the main problem of quantum physics !!

#2695

Dear Carlo

Quantum theory is about the ensembles and about the individual outcomes of measuring systems. But I think that in quantum mechanics there are less real events than in clsxsical mechanics but there are more real events than in the classical statistical mechanics. The reason is the fact that quantum mechanics is reversible probabilistic theory while classical statistical mechnics is the irreversible probabilistic mechanics. This is the main difference !!! Thus quantum mechanics has features that cannot be found in the classical statistical mechanics. Details of my opinions can be found in https://ijqf.org/wp-content/uploads/2015/06/201503.pdf.

#2617

Dear Robert

to the locality: I agree with You that QM must be local – in the sense that locality must be among axioms. Then possible derivation of Bell inequalities (BI) gives the inconsistency of QM. Thus for me the problém is how to make local QM consistent. I have red your paper, but I was not able to understand the argumentation – Your interpretation seems to me to be too complicated. For me the most difficult problem in local QM is the local explanation of EPR correlations – how the result of Alice` measurement can be transported immediately to Bob – one possibility is the pre-determination of individual results, but this means the hidden parameters and then BI. In standard QM this is the nonlocality of the Collapse rule. I have proposed the possible solution (in http://www.nusl.cz/ntk/nusl-177617) – perhaps You have found the another way how to obtain the local explanation of EPR. In each case I think that to obtain the local QM one must modify standard QM.

to the non-realism: the point is in the concept of the individual state. Following von Neumann, each pure state is individual state (“ensemble in the pure state is homogeneous”). I called this the von Neumann axiom and I think that it is the hidden assumption in standard QM and that it is the main error in QM which must be rejected and substituted by the anti von Neumann axiom: two different individual states must be orthogonal. This then gives the starting point of the modified QM. The main point is the following: the individual state of the measuring system does not imply the individual state of the measured system. There is a fine interplay between collective properties (of ensembles) and individual properties (of individual systems). I have shown that both standard QM and modified QM have the same experimental consequences (quantum predictions are only probabilistic and related to ensembles) – thus the choice between realism and non-realism cannot be experimantally resolved. In modified QM there is nothing classical, only the set of individual states is the small subset of the set of pure states.

to the observation: this concept can be introduced in the non-realistic QM, but not in standard realistic QM. This made possible to solve the measurement problém. I have introduced also the intermediate vetrsion of “minimally non realistic QM” (“http://vixra.org/pdf/1504.0117v1.pdf&#8221;), where only anti von Neumann axiom is introduced without the introduction of the concept of the observation. The concept of the observation serves exactly for the task to cut the von Neumann chain.

In general I believe that QM is the probabilistic theory and in each probabilistic theory the state means the probabilistic distribution (the density operator in QM) and the probabilistic distribution is associated with ensemble but not with the individual system. I agree also with You that the evolution of the individual state is stochastic, but the evolution of the probability distribution is smooth.