Is the Devil in h?

This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of the latter. The main casualty of Bell’s model is that it straightforwardly contradicts Heisenberg’s uncertainty and Bohr’s complementarity principles generally. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as such. The original Einstein-Podolsky-Rosen (EPR) argument assumed the Heisenberg’s principle without questioning its validity. Hence, the arguments of EPR and Bell differ crucially, and it is necessary to establish the physical ground of the aforementioned principles. This is the quantum postulate: the existence of an indivisible quantum of action given by the Planck constant. Bell’s approach with hidden variables implicitly implies rejection of the quantum postulate, since the latter is the basis of the reference principles.

Modeling Combination of Question Order Effect, Response Replicability Effect, and QQ-Equality with Quantum Instruments

We continue to analyze basic constraints on human's decision making from the viewpoint of quantum measurement theory (QMT). As has been found, the conventional QMT based on the projection postulate cannot account for combination of the question order effect (QOE) and the response replicability effect (RRE). This was an alarm signal for quantum-like modeling of decision making. Recently, it was shown that this objection to quantum-like modeling can be removed on the basis of the general QMT based on quantum instruments. In the present paper we analyse the problem of combination of QOE, RRE, and the famous QQ-equality (QQE). This equality was derived by Busemeyer and Wang and it was shown (in the joint paper with Solloway and Shiffrin) that statistical data from many social opinion polls satisfies it. Now, we construct quantum instruments satisfying QOE, RRE, and QQE. The general features of our approach are formalized with postulates which generalize {\it Wang-Busemeyer} postulates for quantum-like modeling of decision making. Moreover, we show that our model closely reproduces the statistics of the famous Clinton-Gore Poll data with a prior belief state independent of the question order. This model successfully removes the order effect from the data to determine the genuine distribution of the opinions in the Poll. The paper also provides a psychologist-friendly introduction to the theory of quantum instruments - the most general mathematical framework for quantum measurements. We hope that this theory will attract attention of psychologists and will stimulate further applications.

Bell Model with Hidden Variables and Bohr Quantum Postulate on the Existence of Indivisible Quantum of Action Given by Planck Constant H.

This note is a part of my efforts for getting rid of nonlocality from quantum mechanics (QM). Quantum nonlocality is two faced Janus, one face is apparent quantum mechanical nonlocality (assigned with projection postulate), another face is nonlocality of Bell's model with the hidden variables. This paper is directed against the latter. The main casualty of Bell's model is that it contradicts to the Heinsenberg's uncertainty and Bohr's complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the {\it quantum postulate}: the existence of indivisible quantum of action given by the Planck constant. Bell's model by contradicting to the basic principles of QM implies rejection of this postulate. Thus, it contradicts not only to the QM-formalism, but also to the fundamental feature of the quantum world that was initially discovered by Planck.

Two Faced Janus of Quantum Nonlocality

This paper is a new step towards understanding why “quantum nonlocality” is a misleading concept. Metaphorically speaking, “quantum nonlocality” is Janus faced. One face is an apparent nonlocality of the Lüders projection and another face is Bell nonlocality (a wrong conclusion that the violation of Bell type inequalities implies the existence of mysterious instantaneous influences between distant physical systems). According to the Lüders projection postulate, a quantum measurement performed on one of the two distant entangled physical systems modifies their compound quantum state instantaneously. Therefore, if the quantum state is considered to be an attribute of the individual physical system and if one assumes that experimental outcomes are produced in a perfectly random way, one quickly arrives at the contradiction. It is a primary source of speculations about a spooky action at a distance. Bell nonlocality as defined above was explained and rejected by several authors; thus, we concentrate in this paper on the apparent nonlocality of the Lüders projection. As already pointed out by Einstein, the quantum paradoxes disappear if one adopts the purely statistical interpretation of quantum mechanics (QM). In the statistical interpretation of QM, if probabilities are considered to be objective properties of random experiments we show that the Lüders projection corresponds to the passage from joint probabilities describing all set of data to some marginal conditional probabilities describing some particular subsets of data. If one adopts a subjective interpretation of probabilities, such as QBism, then the Lüders projection corresponds to standard Bayesian updating of the probabilities. The latter represents degrees of beliefs of local agents about outcomes of individual measurements which are placed or which will be placed at distant locations. In both approaches, probability-transformation does not happen in the physical space, but only in the information space. Thus, all speculations about spooky interactions or spooky predictions at a distance are simply misleading. Coming back to Bell nonlocality, we recall that in a recent paper we demonstrated, using exclusively the quantum formalism, that CHSH inequalities may be violated for some quantum states only because of the incompatibility of quantum observables and Bohr’s complementarity. Finally, we explain that our criticism of quantum nonlocality is in the spirit of Hertz-Boltzmann methodology of scientific theories.

Summoning, No-Signalling and Relativistic Bit Commitments

Summoning is a task between two parties, Alice and Bob, with distributed networks of agents in space-time. Bob gives Alice a random quantum state, known to him but not her, at some point. She is required to return the state at some later point, belonging to a subset defined by communications received from Bob at other points. Many results about summoning, including the impossibility of unrestricted summoning tasks and the necessary conditions for specific types of summoning tasks to be possible, follow directly from the quantum no-cloning theorem and the relativistic no-superluminal-signalling principle. The impossibility of cloning devices can be derived from the impossibility of superluminal signalling and the projection postulate, together with assumptions about the devices’ location-independent functioning. In this qualified sense, known summoning results follow from the causal structure of space-time and the properties of quantum measurements. Bounds on the fidelity of approximate cloning can be similarly derived. Bit commitment protocols and other cryptographic protocols based on the no-summoning theorem can thus be proven secure against some classes of post-quantum but non-signalling adversaries.

Rhetoric, logic, and experiment in the quantum nonlocality debate

This paper argues that quantum nonlocality (QNL) has not been rigorously proven, despite the existence of recent Einstein-Podolsky-Rosen-Bohm (EPRB) experiments that are claimed to be ‘loophole-free’. First, readers are alerted to rhetorical arguments, which are unfortunately often appealed to in the QNL debate, to empower readers to identify and reject such arguments. Second, logical problems in QNL proofs are described and exemplified by a discussion of the projection postulate problem. Third, experimental issues are described and exemplified by a discussion of the postselection problem. The paper concludes that QNL has not been proven and that locality cannot be excluded.