Consciousness is widely perceived as a phenomenon that poses a special explanatory problem for science. The problem arises from the apparent rift between immediate first-person acquaintance with consciousness and our inability to provide an objective/scientific third-person characterization of consciousness. In this paper, I outline a theory of perceptual consciousness called the 'Quantum Uncertainty Reduction (QUR)1 Theory of Access and Phenomenal Consciousness'. The theory offers a functional solution to the hard problem of consciousness in terms of quantum information (...) processing in a Bayesian brain-inspired information processing system. I argue that the central aspect/step of information processing, namely, quantum uncertainty reduction, gives rise to qualitative properties of phenomenal and access consciousness. (shrink)

I argue that intrinsic quantum uncertainty informs the elemental life experiences of random play and compassionate sorrow. These experiences, like Niels Bohr’s quantum ontology, point toward unscripted novelty, fresh variation, and far-flung sympathetic interconnections. And in doing this, they allow the inner and outer feeling experiences to grow back together. As we feel the world sensibly—that is, touch it with our sense organs—it touches back in a way that engenders feeling-laden or sympathetic understanding.

Quantum uncertainty relations have deep-rooted significance in the formalism of quantum mechanics. Heisenberg’s uncertainty relations attracted a renewed interest for its applications in quantum information science. Following the discovery of the Heisenberg uncertainty principle, Robertson derived a general form of Heisenberg’s uncertainty relations for a pair of arbitrary observables represented by Hermitian operators. In the present work, we discover a temporal version of the Heisenberg–Robertson uncertainty relations for the measurement of two observables (...) at two different times, where the dynamical uncertainties crucially depend on the time evolution of the observables. The uncertainties not only depend on the choice of observables but also depend on the times at which the physical observables are measured. The time correlated two-time commutator dictates the trade-off between the dynamical uncertainties. We demonstrate the dynamics of these uncertainty relations for a spin-1/2 quantum system and for a quantum harmonic oscillator. We also present the dynamical uncertainty relation in terms of entropies, where the temporal entropic uncertainties are restricted by a time-dependent complementarity factor. The temporal uncertainty relations explored in this work can be experimentally verified with the present quantum technology. (shrink)

Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation follows from the following stronger statement: Of all parallelograms with given sides the rectangle has the largest area.

I present results of recent work in the field of quantum optics and relate this work to discussions about the theory of quantum mechanics and God's divine action in the world. Experiments involving atomic decay, relevant to event uncertainty in quantum mechanics, as well as experiments aimed at elucidating the so–called Schrödinger’s–cat paradox, help clarify apparent ambiguities or paradoxes that I believe are at the heart of renewed attempts to locate God within our constructed physical theories (...) and tend to narrow the gaps proposed as an opening for divine action. Some problems arise because of imprecise use of nonmathematical language to force quantum mechanics into an intuitive “classical” framework. (shrink)

In many real-life situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. To estimate y, we find some easier-to-measure quantities x1, … , xn which are related to y by a known relation y = f. Measurements are never 100% accurate; hence, the measured values equation image are different from xi, and the resulting estimate equation image is different from the desired value y = f. How different can it (...) be? Traditional engineering approach to error estimation in data processing assumes that we know the probabilities of different measurement errors equation image. In many practical situations, we only know the upper bound Δi for this error; hence, after the measurement, the only information that we have about xi is that it belongs to the interval equation image. In this case, it is important to find the range y of all possible values of y = f when xi ∈ xi. We start the paper with a brief overview of the computational complexity of the corresponding interval computation problems: Most of the related problems turn out to be, in general, at least NP-hard. In this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether “hypothetic” physical devices can compute NP-hard problems faster than in exponential time. Most of the paper's results were first presented at NAFIPS'2003 [30]. (shrink)

Economic forecasting is famously unreliable. While this problem has traditionally been blamed on theories such as the efficient market hypothesis or even the butterfly effect, an alternative explanation is the role of money – something which is typically downplayed or excluded altogether from economic models. Instead, models tend to treat the economy as a kind of barter system in which money's only role is as an inert medium of exchange. Prices are assumed to almost perfectly reflect the 'intrinsic value' of (...) an asset. This paper argues, however, that money is better seen as an inherently dualistic phenomenon, which merges precise number with the fuzzy concept of value. Prices are not the optimal result of a mechanical, Newtonian process, but are an emergent property of the money system. And just as quantum physics has its uncertainty principle, so the economy is an uncertain process which can only be approximated by mathematical models. Acknowledging the dynamic and paradoxical qualities of money changes our ontological framework for economic modelling, and for making decisions under uncertainty. Applications to areas of risk analysis, forecasting and modelling are discussed, and it is proposed that a greater appreciation of the fundamental causes of uncertainty will help to make the economy a less uncertain place. (shrink)

In talking about the compatibility of quantum observables, discussions often center on the question of whether the corresponding operators commute—even though commutativity is a coarse-grained notion that largely fails to capture the salient “nonclassical” features of quantum theory. Often, too, such discussions involve the issue of whether the operators in question satisfy a Heisenberg-like inequality, of the form ΔA·ΔB≥r>0—even though such inequalities are specific to unbounded operators and (for this and other reasons) are typically not a useful way (...) to discuss joint uncertainty in quantum mechanics. In the present paper we emphasize a simpler dichotomy, in which operator pairs (A, B) are classified according to whether or not states can be found with arbitrarily small dispersions in both A and B. If A and B cannot be made arbitrarily dispersionless simultaneously, then we call A and B an uncertainty pair. Otherwise, we call A and B a certainty pair. An interesting feature of uncertainty pairs in particular is that they are stable, in the sense that if A and B form an uncertainty pair, then slight enough perturbations of A and B must also form an uncertainty pair. This stability, obvious in the finite-dimensional case, follows in general from an operator inequality derived herein. A consequence of this inequality is that perturbed position and momentum operators X+δX and P+δP cannot share an eigenvector unless |δX|·|δP|≥ℏ/2. (Here vertical bars denote the operator norm.) This, despite the fact that (as we show) arbitrarily slight perturbations of X and P can fail to satisfy a Heisenberg inequality—a fact which raises interesting measurement issues in its own right. (shrink)

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of self-locating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, (...) but we argue that the temptation should be resisted. Applying lessons from this analysis, we demonstrate (using methods similar to those of Zurek's envariance-based derivation) that the Born rule is the uniquely rational way of apportioning credence in Everettian quantum mechanics. In doing so, we rely on a single key principle: changes purely to the environment do not affect the probabilities one ought to assign to measurement outcomes in a local subsystem. We arrive at a method for assigning probabilities in cases that involve both classical and quantum self-locating uncertainty. This method provides unique answers to quantum Sleeping Beauty problems, as well as a well-defined procedure for calculating probabilities in quantum cosmological multiverses with multiple similar observers. (shrink)

The Cramér–Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show that the identification of the mean quantum potential, an important notion in Bohmian mechanics, with the Fisher information, leads, through the Cramér–Rao bound, to an uncertainty principle which is stronger, in general, than both Heisenberg and Robertson–Schrödinger uncertainty relations, allowing (...) to experimentally test the validity of such an identification. (shrink)

I argue that the overly simplistic scenarios discussed by Pothos & Busemeyer (P&B) establish at best that quantum probability theory (QPT) is a logical possibility allowing distinct predictions from classical probability theory (CPT). The article fails, however, to provide convincing evidence for the proposal that QPT offers unique insights regarding cognition and the nature of human rationality.

It is shown that the time operatorQ 0 appearing in the realization of the RCCR's [Qμ,Pv]=−jhgμv, on Minkowski quantum spacetime is a self adjoint operator on Hilbert space of square integrable functions over Σ m =σ×v m , where σ is a timelike hyperplane. This result leads to time-energy uncertainty relations that match their space-momentum counterparts. The operators Qμ appearing in Born's metric operator in quantum spacetime emerge as internal spacetime operators for exciton states, and the condition (...) that the metric operator should possess a ground exciton state assumes the significance of achieving minimal spacetime4-momentum uncertainty in fundamental standards for spacetime measurements. (shrink)

Quantum measurement is a physical process. A system and an apparatus interact for a certain time period, and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy–time uncertainty relation, to find that it needs an external (...) system that switches on the interaction between the system and the apparatus. In such a sense this model is not closed. Therefore to treat a measurement process in a fully quantum manner we need to consider a “larger” quantum apparatus which works also as a timing device switching on the interaction. In this setting we prove that a trade-off relation, \, holds between the energy fluctuation \ of the quantum apparatus and the measurement time \. We use this trade-off relation to discuss the spacetime uncertainty relation concerning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus. (shrink)

It is demonstrated that in quantized general relativity one is led to Jordan-Fock type uncertainty relations implying the occurrence of cut-off lengths. We argue that these lengths (i) represent limitations on the measurability of quantum effects of general relativity and (ii) provide a cut-off length of quantum divergences.

Uncertainty relations and complementarity of canonically conjugate position and momentum observables in quantum theory are discussed with respect to some general coupling properties of a function and its Fourier transform. The question of joint localization of a particle on bounded position and momentum value sets and the relevance of this question to the interpretation of position-momentum uncertainty relations is surveyed. In particular, it is argued that the Heisenberg interpretation of the uncertainty relations can consistently be carried (...) through in a natural extension of the usual Hilbert space frame of the quantum theory. (shrink)

The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral “in finite limits”). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present paper is to express this (...) variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is δS≳ℏ, whereS is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is |∫ ′ t″ (δS[q]/δq(t))Δq(t)dt|≃ℏ, where the paths [q] and [Δq] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as Δ(Equation) Δ(Path) ≃ ℏ. This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement. (shrink)

It is shown that the uncertainty principle has nothing directly to do with the non-localisability of position and momentum for an individual system on the quantum logical view. The product Δ x· Δ p for localisation of the ranges of position and momentum of an individual system→ ∞ , while the quantities Δ X and Δ P in the uncertainty principle $\Delta X\cdot \Delta P\geq \hslash /2$ , must be given a statistical interpretation on the quantum (...) logical view. (shrink)

We explore the different meanings of “quantum uncertainty” contained in Heisenberg’s seminal paper from 1927, and also some of the precise definitions that were developed later. We recount the controversy about “Anschaulichkeit”, visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg’s programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg’s work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and (...) rigour, and between shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance. (shrink)

In the existing expositions of the Károlyházy model, quantum mechanical uncertainties are mimicked by classical spreads. It is shown how to express those uncertainties through entities of the future unified theory of general relativity and quantum theory.

A century after the advent of quantum mechanics and general relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion of relativistic locality include the Bell’s inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava–Lifshitz gravity. Here, we explore a recent proposal for a “real ensemble” non-local description of quantum mechanics, (...) in which “particles” can copy each others’ observable values AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has quantum mechanics as a fixed point, where all particles with the same values for a given observable have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per value of the observable, as well as systematic deviations from quantum mechanics, decay as \ time)\, where \. Interestingly, this convergence is controlled by the absolute value of energy, suggesting a possible connection to gravitational physics. Finally, we discuss different issues related to this theory, as well as potential novel applications for the spectrum of primordial cosmological perturbations and the cosmological constant problem. (shrink)

It is assumed that experiments yield results that are not isomorphic with reality, but represent a distorted image of reality. Reality is related to observation via a communication channel of finite capacity. Quantum uncertainties are due to the bound on the amount of information available. Use is made of recent results from information and communication theories.

This paper considers the relationship between quantum uncertainty and the problem of God. Among the issues considered are the existence and essence ofGod, divine action, human freedom, and personal identity. In recent discussions concerning the relative merits of science and religion, thinkers like Ian Barbourand John Haught have suggested several such credible, albeit tentative, connections between the two on the basis of the epistemological limit imposed upon human knowledge by the Heisenberg Uncertainty Principle.

Prologue: Stormclouds : London, April 1900 -- Quantum of action: The most strenuous work of my life : Berlin, December 1900 ; Annus Mirabilis : Bern, March 1905 ; A little bit of reality : Manchester, April 1913 ; la Comédie Française : Paris, September 1923 ; A strangely beautiful interior : Helgoland, June 1925 ; The self-rotating electron : Leiden, November 1925 ; A late erotic outburst : Swiss Alps, Christmas 1925 -- Quantum interpretation: Ghost field : (...) Oxford, August 1926 ; All this damned quantum jumping : Copenhagen, October 1926 ; The uncertainty principle : Copenhagen, February 1927 ; The 'Kopenhagener geist' : Copenhagen, June 1927 ; There is no quantum world : Lake Como, September 1927 -- Quantum debate: The debate commences : Brussels, October 1927 ; An absolute wonder : Cambridge, Christmas 1927 ; The photon box : Brussels, October 1930 ; A bolt from the blue : Princeton, May 1935 ; The paradox of Schrödinger's cat : Oxford, August 1935 -- Interlude: The first war of physics : Christmas 1938-August 1945 -- Quantum fields: Shelter Island : Long Island, June 1947 ; Pictorial semi-vision thing : New York, January 1949 ; A beautiful idea : Princeton, February 1954 ; Some strangeness in the proportion : Rochester, August 1960 ; Three quarks for Muster Mark! : New York, March 1963 ; The 'God particle' : Cambridge, Massachusetts, Autumn 1967 -- Quantum particles: Deep inelastic scattering : Stanford, August 1968 ; Of charm and weak neutral currents : Harvard, February 1970 ; The magic of colour : Princeton/Harvard, April 1973 ; The November revolution : Long Island/Stanford, November 1974 ; Intermediate vector bosons : Geneva, January/June 1983 ; The standard model : Geneva, September 2003 -- Quantum reality: Hidden variable : Princeton, Spring 1951 ; Bertlmann's socks : Boston, September 1964 ; The Aspect experiments : Paris, September 1982 ; The quantum eraser : Baltimore, January 1999 ; Lab cats : Stony Brook/Delft, July 2000 ; The persistent illusion : Vienna, December 2006 -- Quantum cosmology: The wavefunction of the universe : Princeton, July 1966 ; Hawking radiation : Oxford, February 1974 ; The first superstring revolution : Aspen, August 1984 ; Quanta of space and time : Santa Barbara, February 1986 ; Crisis? What crisis? : Durham, Summer 1994 -- A quantum of solace? : Geneva, March 2010. (shrink)

In this short paper, we propose a special class of quantum systems with implicit quantum uncertainties without any probability structure followed by the dynamical behavior of the systems. When a system is deterministic or random, it does not capture the essence of freedom of choice (FOC), which is the ability to make decisions followed by one’s preferences, free from both deterministic and random outcomes. The proposed special class of quantum systems contains non-deterministic yet non-random outcomes, and so (...) they open the possibility of having FOC within the systems. We also examine examples of such a special class of quantum systems that do not violate the postulates of quantum mechanics. (shrink)

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The (...) second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision. (shrink)

Freely falling point-like objects converge toward the center of the Earth. Hence the gravitational field of the Earth is inhomogeneous, and possesses a tidal component. The free fall of an extended quantum mechanical object such as a hydrogen atom prepared in a high principal-quantum-number state, i.e. a circular Rydberg atom, is predicted to fall more slowly than a classical point-like object, when both objects are dropped from the same height above the Earth’s surface. This indicates that, apart from (...) transitions between quantum states, the atom exhibits a kind of quantum mechanical incompressibility during free fall in inhomogeneous, tidal gravitational fields like those of the Earth.A superconducting ring-like system with a persistent current circulating around it behaves like the circular Rydberg atom during free fall. Like the electronic wavefunction of the freely falling atom, the Cooper-pair wavefunction is quantum mechanically incompressible. The ions in the lattice of the superconductor, however, are not incompressible, since they do not possess a globally coherent quantum phase. The resulting difference during free fall in the response of the nonlocalizable Cooper pairs of electrons and the localizable ions to inhomogeneous gravitational fields is predicted to lead to a charge separation effect, which in turn leads to a large Coulomb force that opposes the convergence caused by the tidal gravitational force on the superconducting system.A “Cavendish-like” experiment is proposed for observing the charge separation effect induced by inhomogeneous gravitational fields in a superconducting circuit. The charge separation effect is determined to be limited by a pair-breaking process that occurs when low frequency gravitational perturbations are present. (shrink)

Quantum mechanics is currently being tried to be used as a probe to unravel the mysteries of consciousness. Present paper deals with this probe, quantum mechanics and its usefulness in getting an insight of working of human consciousness. The formation of quantum mechanics based on certain axioms, its development to study the dynamical behavior and motions of fundamental particles and quantum energy particles moving with the velocity of light, its insistence on wave functions, its probability approach, (...) its dependence on uncertainty principles will all be critically discussed. The result of this discussion will be presented. Its limitations in unraveling the form, function and biological nature of consciousness will be presented. The alternative probe available and being used – the translation of Upanishadic insight and Advaita philosophy into cognitive science elements in delineating the definition, form and function of Consciousness will be given. The usefulness of this modeling and analysis in understanding the consciousness, mind and its functions in cognitive science and theory of human language acquisition and communication will also be presented. The physic-chemical nature of ideas, senses, thoughts, feelings, utterances will be grossly dealt with. The functions of consciousness and mind, in knowledge and language acquisition and communication will be dealt with. (shrink)

In this paper we critically analyze the situation of quantum mechanics in discussions on free will. It starts describing how the uncertainty principle and the measurement problem pose a challenge to determinism. Next, we present positions supporting and rejecting correlation between quantum phenomena and free will. Finally, we will place all these issues into the context of five key questions set out by Robert Kane: the Compatibility, Significance, Intelligibility, Existence and Determinist Questions.

This chapter contains sections titled: * Introduction * The Two-Slit Experiment and Wave-Particle Duality * Heisenberg’s Uncertainty Principle * Schrödinger’s Cat * The Einstein-Podolsky-Rosen Experiment * Interpretation: Quantum Reality? * Critical Realism in Science and Theology * Determinism, Human Free Will, and Divine Action * Consonance with Christian Doctrine * References * Further Reading.

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an (...) infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action. (shrink)

Everettian accounts of quantum mechanics entail that people branch; every possible result of a measurement actually occurs, and I have one successor for each result. Is there room for probability in such an account? The prima facie answer is no; there are no ontic chances here, and no ignorance about what will happen. But since any adequate quantum mechanical theory must make probabilistic predictions, much recent philosophical labor has gone into trying to construct an account of probability for (...) branching selves. One popular strategy involves arguing that branching selves introduce a new kind of subjective uncertainty. I argue here that the variants of this strategy in the literature all fail, either because the uncertainty is spurious, or because it is in the wrong place to yield probabilistic predictions. I conclude that uncertainty cannot be the ground for probability in Everettian quantum mechanics. (shrink)

We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle can be considered as an extension of the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a physical system needs to exhibit during its dynamics in order to be observable. Second, there is constant vacuum fluctuation along a classical trajectory. A novel method is introduced to define (...) the information metrics to measure additional observability due to vacuum fluctuations, which is then converted to an additional action through the first assumption. Applying the variational principle to minimize the total actions allows us to recover the basic quantum formulations including the uncertainty relation and the Schrödinger equation in the position representation. In the momentum representation, the same method can be applied to obtain the Schrödinger equation for a free particle while further investigation is still needed for a particle with an external potential. Furthermore, the principle brings in new results on two fronts. At the conceptual level, we find that the information metrics for vacuum fluctuations are responsible for the origin of the Bohm quantum potential. Even though the Bohm potential for a bipartite system is inseparable, the underlying vacuum fluctuations are local. Thus, inseparability of the Bohm potential does not justify a non-local causal relation between the two subsystems. At the mathematical level, quantifying the information metrics for vacuum fluctuations using more general definitions of relative entropy results in a generalized Schrödinger equation that depends on the order of relative entropy. The extended least action principle is a new mathematical tool. It can be applied to derive other quantum formalisms such as quantum scalar field theory. (shrink)

In the Copenhagen interpretation the Heisenberg inequality ΔQΔP≥ℏ/2 is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint measurement of incompatible observables. This interpretation was criticized a long time ago and has recently been challenged in an experimental way. These criticisms can be substantiated by using the generalized formalism of positive operator-valued measures, from which an inequality, different from the Heisenberg inequality, can be derived, precisely illustrating the (...) Copenhagen concept of complementarity. The different roles of preparation and measurement in creating uncertainty in quantum mechanics are discussed. (shrink)

The arguments presented by Gibbins in his Note are based on a sharp distinction between the product Δx·Δp, which refers to the ranges of position and momentum of an individual system, and the uncertainty principle ΔX·ΔP ≥ ħ/2, which expresses a statistical relation for an ensemble of systems. A critical role in Gibbins’ reasoning is played by the theorem T which states that the restriction of the dynamical variable of position x of an individual system to a finite range (...) Δx excludes the possibility of restricting the canonically conjugate dynamical variable of momentum p to a finite range Δp. (shrink)

We present a quantum mechanical analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model 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 Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles (...) of QM, Bell’s model implies rejection of this postulate as well. Thus, this hidden-variable model contradicts not only the QM-formalism, but also the fundamental feature of the quantum world discovered by Planck. (shrink)

There have been suggestions that the unity of consciousness may be related to the kind of holism depicted only in quantum physics. This argument will be clarified and strengthened. It requires the brain to contain a quantum system with the right properties — a Bose-Einstein condensate. It probably does contain one such system, as both theory and experiment have indicated. In fact, we cannot pay full attention to a quantum whole and its parts simultaneously, though we may (...) oscillate between the two. In a quantum theory of consciousness, emergent meanings arise as an inevitable consequence of Heisenberg''s Uncertainty Principle. (shrink)

The reluctant revolutionary -- The patent slave -- The golden Dane -- The quantum atom -- When Einstein met Bohr -- The prince of duality -- Spin doctors -- The quantum magician -- A late erotic outburst -- Uncertainty in Copenhagen -- Solvay 1927 -- Einstein forgets relativity -- Quantum reality -- For whom Bell's theorem tolls -- The quantum demon.

Quantum cognition is an emerging field that uses mathematical principles of quantum theory to help formalize and understand cognitive systems and processes. The topic on the potential of using quantum theory to build models of cognition (Volume 5, issue 4) introduces and synthesizes its new development through an introduction and six core articles. The current issue presents 14 commentaries on the core articles. Five key issues surface, some of which are interestingly controversial and debatable as expected for (...) a new emerging field. (shrink)

David Wallace has given a decision-theoretic argument for the Born Rule in the context of Everettian quantum mechanics. This approach promises to resolve some long-standing problems with probability in EQM, but it has faced plenty of resistance. One kind of objection charges that the requisite notion of decision-theoretic uncertainty is unavailable in the Everettian picture, so that the argument cannot gain any traction; another kind of objection grants the proof’s applicability and targets the premises. In this article I (...) propose some novel principles connecting the physics of EQM with the metaphysics of modality, and argue that in the resulting framework the incoherence problem does not arise. These principles also help to justify one of the most controversial premises of Wallace’s argument, ‘branching indifference’. Absent any a priori reason to align the metaphysics with the physics in some other way, the proposed principles can be adopted on grounds of theoretical utility. The upshot is that Everettians can, after all, make clear sense of objective probability. 1 Introduction2 Setup3 Individualism versus Collectivism4 The Ingredients of Indexicalism5 Indexicalism and Incoherence5.1 The trivialization problem5.2 The uncertainty problem6 Indexicalism and Branching Indifference6.1 Introducing branching indifference6.2 The pragmatic defence of branching indifference6.3 The non-existence defence of branching indifference6.4 The indexicalist defence of branching indifference7 Conclusion. (shrink)

Quantum mechanics studies physical phenomena on a microscopic scale. These phenomena are far beyond the reach of our observation, and the connection between QM's mathematical formalism and the experimental results is very indirect. Furthermore, quantum indeterminism defies common sense. Microphysical experiments have shown that, according to the empirical context, electrons and quanta of light behave as waves and other times as particles, even though it is impossible to design an experiment that manifests both behaviors at the same time. (...) Unlike Newtonian physics, the properties of quantum systems are not all well-defined simultaneously. Moreover, quantum systems are not characterized by their properties, but by a wave function. Although one of the principles of the theory is the uncertainty principle, the trajectory of the wave function is controlled by the deterministic Schrödinger equations. But what is the wave function? Like other theories of the physical sciences, quantum theory assigns states to systems. The wave function is a particular mathematical representation of the quantum state of a physical system, which contains information about the possible states of the system and the respective probabilities of each state. (shrink)