arXiv subjects

Andrei Khrennikov

Publications and source records attributed to Andrei Khrennikov.

At least 73 records · Page 4Linked to original sources

arXiv2017

The present situation in quantum theory and its merging with general relativity

We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena - a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the most widely known (but, e.g., Bohmian mechanics is also a part of QT). The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement. We compare the QFT and QM based measurement theories by presenting both theoretical and experimental viewpoints. Then we discuss two basic mathematical constraints of both QM and QFT, namely, the use of real (and, hence, complex) numbers and the Hilbert state space. We briefly present non-Archimedean and non-Hilbertian approaches to QT and their consequences. Finally, we claim that, in spite of the Bell theorem, it is still possible to treat quantum phenomena on the basis of a classical-like causal theory. We present a random field model generating the QM and QFT formalisms. This emergence viewpoint can serve as the basis for unification of novel QT (may be totally different from presently powerful QM and QFT) and general relativity GR. (It may happen that the latter would also be revolutionary modified.)

quant-ph↗

arXiv2017

Outline of a unified Darwinian evolutionary theory for physical and biological systems

The scheme of a unified Darwinian evolutionary theory for physical and biological systems is described. Every physical system is methodologically endowed with a classical information processor what turns every system into an agent being also susceptible to evolution. Biological systems retain this structure as natural extensions of physical systems from which they are built up. Optimization of information flows turns out to be the key element to study the possible emergence of quantum behavior and the unified Darwinian description of physical and biological systems. The Darwinian natural selection scheme is completed by the Lamarckian component in the form of the anticipation of states of surrounding bio-physical systems.

physics.gen-ph↗

arXiv2017

Quantum probability updating from zero prior (by-passing Cromwell's rule)

Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a straightforward implication of how Bayes's rule works). Relatedly, hypotheses with a very low prior cannot be updated to have a very high posterior without a tremendous amount of new evidence to support them (or to make other possibilities highly improbable). Cromwell's rule appears at odds with our intuition of how humans update probabilities. In this work, we report two simple decision making experiments, which seem to be inconsistent with Cromwell's rule. Quantum probability theory, the rules for how to assign probabilities from the mathematical formalism of quantum mechanics, provides an alternative framework for probabilistic inference. An advantage of quantum probability theory is that it is not subject to Cromwell's rule and it can accommodate changes from zero or very small priors to significant posteriors. We outline a model of decision making, based on quantum theory, which can accommodate the changes from priors to posteriors, observed in our experiments.

q-bio.NC↗

arXiv2017

Automaton model of protein: dynamics of conformational and functional states

In this conceptual paper we propose to explore the analogy between ontic/epistemic description of quantum phenomena and interrelation between dynamics of conformational and functional states of proteins. Another new idea is to apply theory of automata to model the latter dynamics. In our model protein's behavior is modeled with the aid of two dynamical systems, ontic and epistemic, which describe evolution of conformational and functional states of proteins, respectively. The epistemic automaton is constructed from the ontic automaton on the basis of functional (observational) equivalence relation on the space of ontic states. This reminds a few approaches to emergent quantum mechanics in which a quantum (epistemic) state is treated as representing a class of prequantum (ontic) states. This approach does not match to the standard {\it protein structure-function paradigm.} However, it is perfect for modeling of behavior of intrinsically disordered proteins. Mathematically space of protein's ontic states (conformational states) is modeled with the aid of $p$-adic numbers or more general ultrametric spaces encoding the internal hierarchical structure of proteins. Connection with theory of $p$-adic dynamical systems is briefly discussed.

q-bio.BM↗

arXiv2017

A Quantum-like Model of Selection Behavior

In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory.

econ.GN↗

arXiv2016

Quantum epistemology from subquantum ontology: quantum mechanics from theory of classical random fields

The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be inaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity - the quantum state ("wave function"). The correspondence PCSFT to QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle - by using the formalism of classical field correlations.

quant-ph↗

arXiv2016

Towards better understanding of QBism

Recently I posted a paper entitled "External observer reflections on QBism". As any external observable, I was not able to reflect some features of QBism properly. Therefore comments which I received from one of its creators, C. Fuchs, are very valuable - to understand better the views of QBists. Some of QBism features are very delicate and to extract them from articles of QBists is not a simple task. Therefore I hope that the second portion of my reflection on QBism (or better to say my reflections on Fuchs' reflections on my reflections) might be interesting and useful for other experts in quantum foundations and quantum information theory (especially by taking into account my previous aggressively anti-QBism position). In the present paper I correct some of my previously posted critical comments on QBism. At the same time better understanding of QBists views on some problems leads to improvement and strengthening of other critical comments.

quant-ph↗

arXiv2016

After Bell

We analyze foundational consequences of recently announced loophole free tests of violation of Bell's inequality. We consider two interpretations of these remarkable experiments. By the conventional one "Einstein was wrong and Bohr was right, there is spooky action at a distance, quantum realism is incompatible with locality." However, we show that it is still possible to treat quantum mechanics without appealing to nonlocality or denying realism. We hope that this note will attract attention of the experts in quantum foundations and convince them to come with their own comments on the final Bell's test.

quant-ph↗

arXiv2016

Secure cloud computations: Description of (fully)homomorphic ciphers within the P-adic model of encryption

In this paper we consider the description of homomorphic and fully homomorphic ciphers in the $p$-adic model of encryption. This model describes a wide class of ciphers, but certainly not all. Homomorphic and fully homomorphic ciphers are used to ensure the credibility of remote computing, including cloud technology. The model describes all homomorphic ciphers with respect to arithmetic and coordinate-wise logical operations in the ring of $p$-adic integers $Z_p$. We show that there are no fully homomorphic ciphers for each pair of the considered set of arithmetic and coordinate-wise logical operations on $Z_p$. We formulate the problem of constructing a fully homomorphic cipher as follows. We consider a homomorphic cipher with respect to operation "$*$" on $Z_p$. Then, we describe the complete set of operations "$G$", for which the cipher is homomorphic. As a result, we construct a fully homomorphic cipher with respect to the operations "$*$" and "$G$". We give a description of all operations "$G$", for which we obtain fully homomorphic ciphers with respect to the operations "$+$" and "$G$" from the homomorphic cipher constructed with respect to the operation "$+$". We also present examples of such "new" operations.

cs.CR↗

arXiv2016

Reflections on Zeilinger-Brukner information interpretation of quantum mechanics

In this short review I present my personal reflections on Zeilinger-Brukner information interpretation of quantum mechanics (QM). In general, this interpretation is very attractive for me. However, its rigid coupling to the notion of irreducible quantum randomness is a very complicated issue which I plan to address in more detail. This note may be useful for general public interested in quantum foundations, especially because I try to analyze essentials of the information interpretation critically (i.e., not just emphasizing its advantages as it is commonly done). This review is written in non-physicist friendly manner. Experts actively exploring this interpretation may be interested in the paper as well, as in the comments of "an external observer" who have been monitoring the development of this approach to QM during the last 18 years. The last part of this review is devoted to the general methodology of science with references to views of de Finetti, Wigner, and Peres.

quant-ph↗

arXiv2016

Testing boundaries of applicability of quantum probabilistic formalism to modeling of cognition

Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and finances. To distinguish such models from genuine quantum physical models, they often called quantum-like (although often people simply speak about, e.g., "quantum cognition"). These novel applications generate a number of foundational questions. Nowadays we can speak about a new science - foundations of quantum-like modeling. At the first stage this science was mainly about comparison of classical and quantum models, mainly in the probabilistic setting. It was found that statistical data from cognitive psychology violate some basic constraints posed on data by classical probability theory (Kolmogorov, 1933); in particular, the constraints given by the formula of total probability and Bell's type inequalities. Recently another question attracted some attention. In spite of real success in applications, there are no reason to believe that the quantum probability would cover completely all problems of, e.g., cognition. May be more general probability models have to be explored. A similar problem attracted a lot of attention in foundations of quantum physics culminating in a series of experiments to check Sorkin's equality for the triple-slit experiment by Weihs' group. In this note we present a similar test in the cognitive experimental setting. Performance of this test would either give further confirmation of the adequacy of the quantum probability model to cognitive applications or rejection of the conventional quantum model. Thus this note opens the door for a series of exciting experimental tests for the quantum-like model of cognition.

q-bio.NC↗

arXiv2015

Randomness: quantum versus classical

Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is elaboration of a consistent and commonly accepted interpretation of quantum state. Closely related problem is clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. The second part of this review is devoted to the information interpretation of quantum mechanics (QM) in the spirit of Zeilinger and Brukner (and QBism of Fuchs et al.) and physics in general (e.g., Wheeler's "it from bit") as well as digital philosophy of Chaitin (with historical coupling to ideas of Leibnitz). Finally, we continue discussion on interrelation of quantum and classical randomness and information interpretation of QM.

quant-ph↗

arXiv2015

External observer reflections on QBism

In this short review I present my personal reflections on QBism. I have no intrinsic sympathy neither to QBism nor to subjective interpretation of probability in general. However, I have been following development of QBism from its very beginning, observing its evolution and success, sometimes with big surprise. Therefore my reflections on QBism can be treated as "external observer" reflections. I hope that my view on this interpretation of quantum mechanics (QM) has some degree of objectivity. It may be useful for researchers who are interested in quantum foundations, but do not belong to the QBism-community, because I tried to analyze essentials of QBism critically (i.e., not just emphasizing its advantages, as in a typical QBist publication). QBists, too, may be interested in comments of an external observer who monitored development of this approach to QM during the last 16 years. The second part of the paper is devoted to interpretations of probability, objective versus subjective, and views of Kolmogorov, von Mises, and de Finetti. Finally, de Finetti's approach to methodology of science is presented and compared with QBism.

quant-ph↗

arXiv2015

"Social Laser": Action Amplification by Stimulated Emission of Social Energy

The problem of the "explanation" of recent social explosions, especially in the Middle East, but also in Southern Europe and the USA, have been debated actively in the social and political literature. We can mention the contributions of P. Mason, F. Fukuyama, E. Schmidt and J. Cohen, I. Krastev to this debate. We point out that the diversity of opinions and conclusions is really amazing. At the moment, there is no consistent and commonly acceptable theory of these phenomena. We present a model of social explosions based on a novel approach for the description of social processes, namely, the quantum-like approach. Here quantum theory is treated simply as an operational formalism - without any direct relation to physics. We explore the quantum-like laser model to describe the possibility of Action Amplification by Stimulated Emission of Social Energy (ASE).

physics.soc-ph↗

arXiv2015

Unuploaded experiments have no result

The aim of this note is to attract once again attention of the quantum community to statistical analysis of data which was reported as violating Bell's inequality. This analysis suffers of a number of problems. And the main problem is that rough data is practically unavailable. However, experiments which are not followed by the open access to the rough data have to be considered as with no result. The absence of rough data generates a variety of problems in statistical interpretation of the results of Bell's type experiment. One may hope that this note would stimulate experimenters to create the open access data-base for, e.g., Bell tests. Unfortunately, recently announced experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km was not supported by open-access data. Therefore in accordance with our approach "it has no result." The promising data after publication is, of course, a step towards fair analysis quantum experiments. May be this is a consequence of appearance of this preprint, v1. But there are a few questions which would be interesting to clarify before publication (and which we shall discuss in this note).

quant-ph↗

arXiv2015

Reality without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics

First, this article considers the nature of quantum reality (the reality responsible for quantum phenomena) and the concept of realism (our ability to represent this reality) in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different (from quantum mechanics) theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, "the statistical Copenhagen interpretation," is nonrealist, insofar as the description or even conception of the nature of quantum objects and processes is precluded. The second, by A. Khrennikov, is ultimately realist, because it assumes that the quantum-mechanical level of reality is underlain by a deeper level of reality, described, in a realist fashion, by a model, based on the pre-quantum classical statistical field theory (PCSFT), the predictions of which reproduce those of quantum mechanics. Moreover, because the continuous fields considered in this model are transformed into discrete clicks of detectors, experimental outcomes in this model depend on the context of measurement in accordance with N. Bohr's interpretation and the statistical Copenhagen interpretation, which coincides with Bohr's interpretation in this regard.

physics.hist-ph↗

arXiv2015

A Macroscopic Behavioral Violation of No Signaling In Time Inequalities

In this paper we applied the no-signaling in time (NSIT) formalism discussed by Kofler and Brukner to investigate temporal entanglement between binary human behavioral unconscious choices at t1 with binary random outcomes at t2. NSIT consists of a set of inequalities and represents mathematical conditions for macro-realism which require only two measurements in time. The analyses of three independent experiments show a strong violation of NSIT in two out of three of them, supporting the hypothesis of a quantum-like temporal entanglement between human choices at t1 with binary random outcomes at t2

q-bio.NC↗

arXiv2015

Unconditional quantum correlations do not violate Bell's inequality

In this paper I demonstrate that the quantum correlations of polarization (or spin) observables used in Bell's argument against local realism have to be interpreted as {\it conditional} quantum correlations. By taking into account additional sources of randomness in Bell's type experiments, i.e., supplementary to source randomness, I calculate (in the standard quantum formalism) the complete quantum correlations. The main message of the quantum theory of measurement (due to von Neumann) is that complete correlations can be essentially smaller than the conditional ones. Additional sources of randomness diminish correlations. One can say another way around: transition from unconditional correlations to conditional can increase them essentially. This is true for both classical and quantum probability. The final remark is that classical conditional correlations do not satisfy Bell's inequality. Thus we met the following {\it conditional probability dilemma}: either to use the conditional quantum probabilities, as was done by Bell and others, or complete quantum correlations. However, in the first case the corresponding classical conditional correlations need not satisfy Bell's inequality and in the second case the complete quantum correlations satisfy Bell's inequality. Thus in neither case we have a problem of mismatching of classical and quantum correlations. It seems that the whole structure of Bell's argument was based on unacceptable identification of conditional quantum correlations with unconditional classical correlations.

quant-ph↗