It is argued that the distinction between matter wave and probability wave is made clear when the problem is considered from the field-theory viewpoint. Interference can take place for each of these waves, and the similarity as well as dissimilarity between the two cases is discussed.

This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newton's bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibniz's critique, a fact which has been obscured by the conflation of two of Leibniz's arguments. The form of relationism appropriate to the Special Theory of Relativity is also able to evade the problems raised by Field. I survey (...) the effect of the General Theory of Relativity and of plenism on these considerations. (shrink)

Proposed derivations of the Born rule for Everettian theory are controversial. I argue that they are unnecessary but may provide justification for a simplified version of the Principal Principle. It’s also unnecessary to replace Everett’s idea that a subject splits in measurement contexts with the idea that subjects have linear histories which partition Many worlds? Everett, quantum theory, and reality, Oxford University Press, Oxford, pp 181–205, 2010; Wallace in The emergent multiverse, Oxford University Press, Oxford, 2012, Chapter 7; Wilson in (...) Br J Philos Sci 64:709–737, 2013; The nature of contingency: quantum physics as modal realism, Oxford University Press, Oxford, forthcoming). Linear histories were introduced to provide a concept of pre-measurement uncertainty and I explain why pre-measurement uncertainty for splitting subjects is after all coherent, though not necessary because Everett’s original fission interpretation of branching can arguably be rendered coherent without it, via reference to Vaidman, Tappenden, Sebens and Carroll and McQueen and Vaidman. A deterministic and probabilistic quantum mechanics can be made intelligible by replacing the standard collapse postulate with a no-collapse postulate which identifies objective probability with relative branch weight, supplemented by the simplified Principal Principle and some revisionary metaphysics. (shrink)

Hugh Everett III proposed his relative-state formulation of pure wave mechanics as a solution to the quantum measurement problem. He sought to address the theory’s determinate record and probability problems by showing that, while counterintuitive, pure wave mechanics was nevertheless empirically faithful and hence empirical acceptable. We will consider what Everett meant by empirical faithfulness. The suggestion will be that empirical faithfulness is well understood as a weak variety of empirical adequacy. The thought is that the very (...) idea of empirical adequacy might be renegotiated in the context of a new physical theory given the theory’s other virtues. Everett’s argument for pure wave mechanics provides a concrete example of such a renegotiation. (shrink)

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements (...) of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

In quantum mechanics, the wavefunction predicts probabilities of possible measurement outcomes, but not which individual outcome is realised in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce (...) quantum mechanics violate Statistical Independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur-Vaidman bomb detector, and the Extended Wigner's Friends Scenario. (shrink)

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. (...) The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. Which kind of ergodic motion of particles then? It is argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. We show that this new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed. (shrink)

We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find (...) it explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation. (shrink)

Machine generated contents note: -- Series Editors' PrefaceAcknowledgementsNotes on ContributorsHow Things Are Elsewhere; W. Schwarz Information Change and First-Order Dynamic Logic; B.Kooi Interpreting and Applying Proof Theories for Modal Logic; F.Poggiolesi & G.Restall The Logic(s) of Modal Knowledge; D.Cohnitz On Probabilistically Closed Languages; H.Leitgeb Dogmatism, Probability and Logical Uncertainty; B.Weatherson & D.Jehle Skepticism about Reasoning; S.Roush, K.Allen & I.HerbertLessons in Philosophy of Logic from Medieval Obligations; C.D.Novaes How to Rule Out Things with Words: Strong Paraconsistency and the Algebra of (...) Exclusion; F.Berto Lessons from the Logic of Demonstratives; G.RussellThe Multitude View on Logic; M.Eklund Index. (shrink)

The origin of the wave properties of matter is discussed from the point of view of stochastic electrodynamics. A nonrelativistic model of a charged particle with an effective structure embedded in the random zeropoint radiation field reveals that the field induces a high-frequency vibration on the particle; internal consistency of the theory fixes the frequency of this jittering at mc2/ħ. The particle is therefore assumed to interact intensely with stationary zeropoint waves of this frequency as seen from its proper (...) frame of reference; such waves, identified here as de Broglie's phase waves, give rise to a modulated wave in the laboratory frame, with de Broglie's wavelength and phase velocity equal to the particle velocity. The time-independent equation that describes this modulated wave is shown to be the stationary Schrödinger equation (or the Klein-Gordon equation in the relativistic version). In a heuristic analysis appled to simple periodic cases, the quantization rules are recovered from the assumption that for a particle in a stationary state there must correspond a stationary modulation.Along an independent and complementary line of reasoning, an equation for the probability amplitude in configuration space for a particle under a general potential V(x) is constructed, and it is shown that under conditions derived from stochastic electrodynamics it reduces to Schrödinger's equation. This equation reflects therefore the dual nature of the quantum particles, by describing simultaneously the corresponding modulated waveand the ensemble of particles. (shrink)

A new formulation involving fulfillment of all the Kolmogorov axioms is suggested for acomplete probability theory. This proves to be not a purely mathematical discipline. Probability theory deals with abstract objects—images of various classes of concrete objects—whereas experimental statistics deals with concrete objects alone. Both have to be taken into account. Quantum physics and classical statistical physics prove to be different aspects ofone probabilistic physics. The connection of quantum mechanics with classical statistical mechanics is examined and the origin (...) of the Schrödinger equation is elucidated. Attention is given to the true meaning of the wave-corpuscle duality, and the incompleteness of nonrelativistic quantum mechanics is explained. (shrink)

It is argued that the many-worlds interpretation is by far the best interpretation of quantum mechanics. The key points of this view are viewing the wave functions of worlds in three dimensions and understanding probability through self-locating uncertainty.

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either (...) single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track (...) objective ones. But it is shown that if probability only arises with decoherence, then they must be given by the Born rule. That further, on the Everett interpretation, we have a clear statement of what probabilities are, in terms of purely categorical physical properties; and finally, along lines laid out by Deutsch and Wallace, that there is a clear basis in the axioms of decision theory as to why subjective probabilities should track these objective ones. These results hinge critically on the absence of hidden-variables or any other mechanism (such as state-reduction) from the physical interpretation of the theory. The account of probability has traditionally been considered the principal weakness of the Everett interpretation; on the contrary it emerges as one of its principal strengths. (shrink)

It’s generally taken to be established that no local hidden-variable theory is possible. That conclusion applies if our world is a _thread_, where a thread is a world where particles follow trajectories, as in Pilot-Wave theory. But if our world is taken to be a _set_ of threads locality can be recovered. Our world can be described by a _many-threads_ theory, as defined by Jeffrey Barrett in the opening quote. Particles don’t follow trajectories because a particle in our world (...) is a set of _elemental_ particles following different trajectories, each in a thread. The “elements” of a superposition are construed as subsets in such a way that a particle in our world only has definite position if all its set-theoretic elements are at corresponding positions in each thread. Wavefunction becomes a 3D density distribution of particles’ subset measures, the stuff of an electron’s “probability cloud”. Current Pilot-Wave theory provides a non-relativistic dynamics for the elemental particles (approximated by Many Interacting Worlds theory). EPR-Bell nonlocality doesn’t apply because the relevant measurement outcomes in the absolute elsewhere of an observer are always in superposition. (shrink)

The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the de Broglie–Bohm theory. However, its standard formulation is referred to the statistical ensemble of its possible trajectories. The statistical ensemble is introduced in order to establish the exact correspondence between the probability density on the spatial configurations and the quantum distribution, that is the squared modulus of the (...) wave-function. In this work we explore the possibility of using the pilot wave theory at the level of a single Bohm’s trajectory, that is a single realization of the time dependent configuration which should be representative of a single realization of the quantum system. The pilot wave theory allows a formally self-consistent representation of quantum systems as a single Bohm’s trajectory, but in this case there is no room for the Born’s rule at least in its standard form. We will show that a correspondence exists between the statistical distribution of configurations along the single Bohm’s trajectory and the quantum distribution for a subsystem interacting with the environment in a multicomponent system. To this aim, we present the numerical results of the single Bohm’s trajectory description of the model system of six confined planar rotors with random interactions. We find a rather close correspondence between the coordinate distribution of one rotor, the others representing the environment, along its trajectory and the time averaged marginal quantum distribution for the same rotor. This might be considered as the counterpart of the standard Born’s rule when the pilot wave theory is applied at the level of single Bohm’s trajectory. Furthermore a strongly fluctuating behavior with a fast loss of correlation is found for the evolution of each rotor coordinate. This suggests that a Markov process might well approximate the evolution of the Bohm’s coordinate of a single rotor and, under this condition, it is shown that the correspondence between coordinate distribution and quantum distribution of the rotor is exactly verified. (shrink)

The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a \-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton’s principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.

Why are quantum probabilities encoded in measures corresponding to wave functions, rather than by a more general class of measures? Call this question WHY BORN? I argue that orthodox quantum mechanics has a compelling answer to WHY BORN? but Bohmian mechanics might not. I trace Bohmian difficulties with WHY BORN? to its antistructuralism, its denial of physical significance to the algebraic structure of quantum observables, and I propose other cases where Bohmian antistructuralism might have an explanatory cost.

“Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in quantum correlations … and (...) for wave-particle dualism. Its meaning:- mathematically: a ratio of two measures (of sets), which are not collinear; physically: the ratio of the measurements of two physical quantities, which are not simultaneously measurable. The main innovation is in the mapping between phase and Hilbert space, since both are sums. Phase space is a sum of cells, and Hilbert space is a sum of qubits. The mapping is reduced to the mapping of a cell into a qubit and vice versa. Negative probability helps quantum mechanics to be represented quasi-statistically by quasi-probabilistic distributions. Pure states of negative probability cannot exist, but they, where the conditions for their expression exists, decrease the sum probability of the integrally positive regions of the distributions. They reflect the immediate interaction (interference) of probabilities common in quantum mechanics. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, (...) there are two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

Many epistemologists hold that an agent can come to justifiably believe that p is true by seeing that it appears that p is true, without having any antecedent reason to believe that visual impressions are generally reliable. Certain reliabilists think this, at least if the agent’s vision is generally reliable. And it is a central tenet of dogmatism (as described by Pryor (2000) and Pryor (2004)) that this is possible. Against these positions it has been argued (e.g. by Cohen (2005) (...) and White (2006)) that this violates some principles from probabilistic learning theory. To see the problem, let’s note what the dogmatist thinks we can learn by paying attention to how things appear. (The reliabilist says the same things, but we’ll focus on the dogmatist.) Suppose an agent receives an appearance that p, and comes to believe that p. Letting Ap be the proposition that it appears to the agent that p, and → be the material implication, we can say that the agent learns that p, and hence is in a position to infer Ap → p, once they receive the evidence Ap.1 This is surprising, because we can prove the following. (shrink)

A simplified derivation of the Gudder-Hemion quantum probability formula is proposed. Defining configurations as the classical (q, p) deterministic states and generalized action as the (quantum) generating function of a canonical transformation, we obtain the usual quantization rules (for arbitrary polynomial quantities) and derive the Schrödinger wave equation on the same grounds. This approach suggests a statistical interpretation of the wave function in terms of the classical canonical transformations.

Anderson localization of electromagnetic waves in three-dimensional disordered dielectric structures is studied using a simple yet realistic theoretical model. An effective approach based on analysis of probability distributions, not averages, is developed. The disordered dielectric medium is modeled by a system of randomly distributed electric dipoles. Spectra of certain random matrices are investigated and the possibility of appearance of the continuous band of localized waves emerging in the limit of an infinite medium is indicated. It is shown that localization (...) could be achieved without tuning the frequency of monochromatic electromagnetic waves to match the internal (Mie-type) resonances of individual scatterers. A possible explanation for the lack of experimental evidence for strong localization in 3D as well as suggestions how to make localization experimentally feasible are also given. Rather peculiar requirements for setting in localization in 3D as compared to 2D are indicated. (shrink)

Hugh Everett III's pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett's argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship between the predictions of pure wave mechanics and the standard quantum probabilities.

The objective of this paper is to show that, instead of quantum probabilities, wave packets are physically real. First, Cartwright's recent argument for the reality of quantum probabilities is criticized. Then, the notion of ‘physically real’ is precisely defined and the difference between wave functions and quantum probabilities clarified. Being thus prepared, some strong reasons are discussed for considering the wave packet to be physically real. Finding the reasons inconclusive, I explain how the Aharonov—Bohm effect delivers the (...) final punch. I conclude that wave packets are the quantum objects that underlie the indeterministic quantum processes and have the propensity of displaying probabilistic (or indeterministic) behavior. (shrink)

If this book were a film, it would be rated M-with a caution that 'some viewers may be disturbed by some scenes'. In CATCHING THE KNOWLEDGE WAVE? Jane Gilbert takes apart many long-held ideas about knowledge and education. She says that knowledge is now a verb, not a noun-something we do rather than something we have-and explores the ways our schools need to change to prepare people to participate in the knowledge-based societies of the future. The knowledge society is (...) an idea that is widely discussed, but not well understood. Knowledge is developing a new meaning, one that is quite different to the one our schools were built on. Because of this, knowledge society developments are a major challenge for our schools. We cannot address this challenge by adding more ideas to our existing structures. We need a completely new framework-one that takes account of knowledge's new meaning, but also gives everyone an equal opportunity to succeed. If this seems like a tall order, it probably is-however this book attempts to map out such a framework. This is a book to argue with, to agree or disagree with, but above all to read-the future of our public education system is at stake. (shrink)

The nature of quantum waves, whether they are real physical waves or, on the contrary, mere probability waves, has been a very controversial theme since the beginning of quantum theory. Here we present some possible experiments that may clarify the problem.

In discussions surrounding epistemology and rationality, it is often useful to assume an agent is rational or ideally rational. Often, this ideal rationality assumption is spelled out along the following lines: -/- 1. The agent believes everything about a situation which the evidence entitles her to believe and nothing which it does not. -/- 2. The agent believes all the logical consequences of any of her beliefs. -/- 3. The agent knows her own mind: if she believes P, she believes (...) that she believes P; and if she doesn't believe P, she believes that she doesn't believe P. -/- 4. The agent believes nothing of the form 'P and it is not the case that P.' -/- 5. If an agent's background belief-set satisfies 1-4 and if rationality requires the agent to add P to her belief-set, then the resulting belief-set will also satisfy 1-4. -/- While individually plausible, there are cases in which holding on to 1-5 generates paradox. Some resolve such paradoxical cases by granting 1-5 but arguing while ideally rational agents can exist, they can't possibly ever find themselves in such a situation: such case descriptions are epistemically incoherent. Others allow that rational agents can coherently find themselves in such odd circumstances, and argue that it's more reasonable to weaken our concept of ideal rationality and give up premise (2) above. However, this strategy has also been rejected. My aim in this paper is to defend the utility of positing an ideally rational agent in such paradoxical circumstances. I argue in such cases we should give up (2), in particular the assumption that (necessarily) if an ideally rational agent believes both P and the conditional, if P then Q, then she believes Q.. What's important is to hold on to the goal of positing ideal rationality: to maximize the amount of true or probably true information a thinker can justifiably believe in a given circumstance. Normally that will mean holding on to (2), but these unusual paradoxical cases are best handled by giving up (2). (shrink)

Probability distributions are seen to be observer dependent. The probability function ψ†ψ can be put into an observer-dependent form. This eliminates the acausal behavior of the collapse of the wave function.

Bell's theorem is believed to establish that the quantum mechanical predictions do not generally admit a causal representation compatible with Einsten's principle of separability, thereby proving incompatibility between quantum mechanics and relativity. This interpretation is contested via two convergent approaches which lead to a sharp distinction between quantum nonseparability and violation of Einstein's theory of relativity.In a first approach we explicate from the quantum mechanical formalism a concept of “reflected dependence.” Founded on this concept, we produce a causal representation of (...) the quantum mechanical probability measure involved in Bell's proof, which is clearly separable in Einstein's sense, i.e., it does not involve supraluminal velocities, and nevertheless is “nonlocal” in Bell's sense. So Bell locality and Einstein separability aredistinct qualifications, and Bell nonlocality (or Bell nonseparability) and Einstein separability arenot incompatible. It is then proved explicitly that with respect to the mentioned representation Bell's derivation does not hold. So Bell's derivation does notestablish thatany Einstein-separable representation is incompatible with quantum mechanics. This first—negative—conclusion is asyntactic fact.The characteristics of the representation and of the reasoning involved in the mentioned counterexample to the usual interpretation of Bell's theorem suggest that the representation used—notwithstanding its ability to bring forth the specified syntactic fact—isnot factually true. Factual truth and syntactic properties also have to be radically distinguished in their turn. So, in a second approach, starting from de Broglie's initial relativistic model of a microsystem, a deeper, factually acceptable representation is constructed. The analyses leading to this second representation show that quantum mechanics does indeed involve basically a certain sort of nonseparability, called here de Broglie-Bohr quantum nonseparability. But the de Broglie-Bohr quantum nonseparability is shown to stem directly from the relativistic character of the considerations which led Louis de Broglie to the fundamental relation p = h/λ,thereby being essentially consistent with relativity. As to Einstein separability, it appears to be a still insufficiently specified conceptof which a future, improved specification, will probably be explicitly harmonizable with the de Broglie-Bohr quantum nonseparability.The ensemble of the conclusions obtained here brings forth a new concept of causality, a concept offolded, zigzag, reflexive causality, with respect to which the type of causality conceived of up to now appears as aparticular case of outstretched, one-way causality. The reflexive causality is found compatible with the results of Aspect's experiment, and it suggests new experiments.Considered globally, the conclusions obtained in the present work might convert the conceptual situation created by Bell's proof into a process of unification of quantum mechanics and relativity. (shrink)

Here we report that a specific form of yoga can generate controlled high-frequency gamma waves. For the first time, paroxysmal gamma waves were observed in eight subjects practicing a yoga technique of breathing control called Bhramari Pranayama . To obtain new insights into the nature of the EEG during BhPr, we analyzed EEG signals using time-frequency representations , independent component analysis , and EEG tomography . We found that the PGW consists of high-frequency biphasic ripples. This unusual activity is discussed (...) in relation to previous reports on yoga and meditation. It is concluded this EEG activity is most probably non-epileptic, and that applying the same methodology to other meditation recordings might yield an improved understanding of the neurocorrelates of meditation. (shrink)

We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 38.2 (2000) 221-238 [Access article in PDF] Hume's Iterative Probability Argument: A Pernicious Reductio Kevin Meeker University of South Alabama In this essay I want to look afresh at David Hume's iterative probability argument, found in the section entitled "Of Scepticism with regard to Reason" in his A Treatise of Human Nature.1 Interestingly enough, after years of comparative neglect,2 this argument (...) has been basking in the glow of scholarly sunshine lately.3 But to what can we attribute its extended hiatus? The convergence of three major factors seems responsible. First, philosophers have oftentimes flung this argument into the ocean of obscurity because of its perceived inadequacies.4 Second, and on a related note, many assume that Hume himself permitted this argument to drown because it never resurfaces again in his writings. Most suspiciously, Hume's Enquiry Concerning Human Understanding, which is his popular (and preferred) presentation of the epistemological sections [End Page 221] of the Treatise, does not contain this argument.5 Last, but certainly not least, for a long time this argument sat uncomfortably with the naturalist interpretation of Hume6 that has gained ascendancy in the twentieth century. For prior to this century, Hume was almost unanimously regarded as a sceptic. Despite a few waves from those who interpreted Hume as a logical positivist earlier in this century, Norman Kemp Smith charted a new course for Humean interpretations with his emphasis on Hume's naturalism.7 And this is the current according to which most Hume interpreters set their sails today.Because the naturalist reading of Hume relies so heavily on the system he attempts to set forth in the Treatise, though, naturalists have come to see the importance of reading this argument in a naturalistically acceptable way. William E. Morris best expresses the significance of this argument from a naturalistic perspective in the following manner: If we ever are to understand Hume's view of the role of reason, it stands to reason that we should first figure out how to integrate "Of scepticism with regard to reason" into the picture. Only then will we be ready to move to a consideration of Hume's positive views about reason. These views are the least understood of any of Hume's doctrines. Gaining an adequate understanding of them is both the most pressing and the most difficult problem facing Hume studies today.8While I agree with Morris about the importance of getting a clear understanding of the reasoning of I, iv, 1, I will argue that a correct reading of this section reveals the implausibility of major naturalistic interpretations of Hume.This paper has four major sections. In the first important section, I will highlight the crucial aspects of the iterative argument that will be the focus of this paper and deal with a preliminary but important interpretive issue. In the second section, I will briefly look at Annette Baier's naturalistic reading of Hume's philosophy to show how this particular passage bears on broader [End Page 222] interpretive issues. The third main section will focus on explicating Morris' similar but more detailed interpretation. Finally in the last part I will show that while it is legitimate to characterize the argument here as a reductio (as Baier and Morris both do), the argument still yields, contrary to what naturalists have recently suggested, a very sceptical conclusion. 1. The Arguments of Section I, IV, 1 of the TreatiseHume's "Of Scepticism with regard to Reason" contains at least two important arguments. While Hume agrees that knowledge involves certainty (whereas beliefs based on probability are by their very nature uncertain9 ), the conclusion of his first argument is that "all knowledge resolves itself into probability" (Treatise, 181). His point here is simply that all of our beliefs are fallible. That is, nothing is absolutely certain; thus none of our beliefs attain the exalted status of certain knowledge. But once this consequence of our fallibility is recognized, he then argues roughly that the probability that any particular belief... (shrink)

The general properties of measurements in microphysics are studied and the three types of probabilities that, according to the authors, appear in wave mechanics are set up. Such a distinction, together with the principle of the localization of the corpuscle as was laid down at the very introduction of the theory of the double solution, provides a good grasp of certain phenomena whose explanation according to the usual theory (which makes no use of permanent localization and where the three (...) types of probabilities are intermingled) leads to paradoxical or self-contradictory situations. (shrink)

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not (...) continuous but discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wave function. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 38.2 (2000) 221-238 [Access article in PDF] Hume's Iterative Probability Argument: A Pernicious Reductio Kevin Meeker University of South Alabama In this essay I want to look afresh at David Hume's iterative probability argument, found in the section entitled "Of Scepticism with regard to Reason" in his A Treatise of Human Nature.1 Interestingly enough, after years of comparative neglect,2 this argument (...) has been basking in the glow of scholarly sunshine lately.3 But to what can we attribute its extended hiatus? The convergence of three major factors seems responsible. First, philosophers have oftentimes flung this argument into the ocean of obscurity because of its perceived inadequacies.4 Second, and on a related note, many assume that Hume himself permitted this argument to drown because it never resurfaces again in his writings. Most suspiciously, Hume's Enquiry Concerning Human Understanding, which is his popular (and preferred) presentation of the epistemological sections [End Page 221] of the Treatise, does not contain this argument.5 Last, but certainly not least, for a long time this argument sat uncomfortably with the naturalist interpretation of Hume6 that has gained ascendancy in the twentieth century. For prior to this century, Hume was almost unanimously regarded as a sceptic. Despite a few waves from those who interpreted Hume as a logical positivist earlier in this century, Norman Kemp Smith charted a new course for Humean interpretations with his emphasis on Hume's naturalism.7 And this is the current according to which most Hume interpreters set their sails today.Because the naturalist reading of Hume relies so heavily on the system he attempts to set forth in the Treatise, though, naturalists have come to see the importance of reading this argument in a naturalistically acceptable way. William E. Morris best expresses the significance of this argument from a naturalistic perspective in the following manner: If we ever are to understand Hume's view of the role of reason, it stands to reason that we should first figure out how to integrate "Of scepticism with regard to reason" into the picture. Only then will we be ready to move to a consideration of Hume's positive views about reason. These views are the least understood of any of Hume's doctrines. Gaining an adequate understanding of them is both the most pressing and the most difficult problem facing Hume studies today.8While I agree with Morris about the importance of getting a clear understanding of the reasoning of I, iv, 1, I will argue that a correct reading of this section reveals the implausibility of major naturalistic interpretations of Hume.This paper has four major sections. In the first important section, I will highlight the crucial aspects of the iterative argument that will be the focus of this paper and deal with a preliminary but important interpretive issue. In the second section, I will briefly look at Annette Baier's naturalistic reading of Hume's philosophy to show how this particular passage bears on broader [End Page 222] interpretive issues. The third main section will focus on explicating Morris' similar but more detailed interpretation. Finally in the last part I will show that while it is legitimate to characterize the argument here as a reductio (as Baier and Morris both do), the argument still yields, contrary to what naturalists have recently suggested, a very sceptical conclusion. 1. The Arguments of Section I, IV, 1 of the TreatiseHume's "Of Scepticism with regard to Reason" contains at least two important arguments. While Hume agrees that knowledge involves certainty (whereas beliefs based on probability are by their very nature uncertain9 ), the conclusion of his first argument is that "all knowledge resolves itself into probability" (Treatise, 181). His point here is simply that all of our beliefs are fallible. That is, nothing is absolutely certain; thus none of our beliefs attain the exalted status of certain knowledge. But once this consequence of our fallibility is recognized, he then argues roughly that the probability that any particular belief... (shrink)

One of our most sophisticated accounts of objective chance in quantum mechanics involves the Deutsch-Wallace theorem, which uses state-space symmetries to justify agents’ use of the Born rule when the quantum state is known. But Wallace argues that this theorem requires an Everettian approach to measurement. I find that this argument is unsound. I demonstrate a counter-example by applying the Deutsch-Wallace theorem to the de Broglie-Bohm pilot-wave theory.

A physical and mathematical framework for the analysis of probabilities in quantum theory is proposed and developed. One purpose is to surmount the problem, crucial to any reconciliation between quantum theory and space-time physics, of requiring instantaneous “wave-packet collapse” across the entire universe. The physical starting point is the idea of an observer as an entity, localized in space-time, for whom any physical system can be described at any moment, by a set of (not necessarily pure) quantum states compatible (...) with his observations of the system at that moment. The mathematical starting point is the theory of local algebras from axiomatic relativistic quantum field theory. A function defining thea priori probability of mistaking one local state for another is analysed. This function is shown to possess a broad range of appropriate properties and to be uniquely defined by a selection of them. Through a general model for observations, it is argued that the probabilities defined here are as compatible with experiment as the probabilities of conventional interpretations of quantum mechanics but are more likely to be compatible, not only with modern developments in mathematical physics, but also with a complete and consistent theory of measurement. (shrink)

A new probability interpretation of interference phenomena in the double-slit experiment is proposed. It differs from the standard interpretation (based on elementary events happening in complementary, mutually exclusive setups—arrivals of waves to the screen when one of the slits is closed) which encounters the “paradox” that the law of total probability is violated. This new interpretation is free of such difficulties and paradoxes since it is based on compatible elementary events (events happening in the same setup in which (...) happenall events considered—arrivals of quantons to the screen when both slits are open). Quantum objects—quantons—possess simultaneously particle and wave properties. Compatible statistical interpretation synthesizes in a consistent way the superposition principle for waves and the law of total probability applied to compatible events. Such synthesis is a theoretical expression of de Broglie's observation, now fully confirmed by experiments, that the interference fringes obtained on a photographic plate result from an infinite number of tiny local spots which display arrival of quantons, while the set of fringes is a statistical effect of the wave aspect. (shrink)

We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. It is argued that a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. This is also a consequence of protective measurement. If the wave function is a physical field, then the mass and charge density will be distributed (...) in space simultaneously for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wave function, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus we conclude that the wave function cannot be a description of a physical field. In the second part of this paper, we further analyze the implications of these results for the main realistic interpretations of quantum mechanics, especially for de Broglie-Bohm theory. It has been argued that de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions, which turns out to be wrong according to the above results. For a charged quantum system, both Ψ-field and Bohmian particle have charge density distribution. This then results in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which contradicts both the predictions of quantum mechanics and experimental observations. Therefore, de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is probably wrong. Lastly, we suggest that the wave function is a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles, and we also briefly analyze the implications of this suggestion for other realistic interpretations of quantum mechanics including many-worlds interpretation and dynamical collapse theories. (shrink)

Given Hugh Everett III's understanding of the proper cognitive status of physical theories, his relative-state formulation of pure wave mechanics arguably qualifies as an empirically acceptable physical theory. The argument turns on the precise nature of the relationship that Everett requires between the empirical substructure of an empirically faithful physical theory and experience. On this view, Everett provides a weak resolution to both the determinate record and the probability problems encountered by pure wave mechanics, and does so (...) in a way that avoids unnecessary metaphysical complications. Taking Everett's goal to be showing the empirical faithfulness of the relative-state formulation agrees well with his characterization of his project as one of seeking a model for observation in the correlation structure described by pure wave mechanics and seeking a measure of typicality over this empirical substructure that covaries with our empirically warranted expectations. 1 Pure Wave Mechanics and Relative States2 Everett and Frank3 Everett on the Nature of Physical Theories4 Conditions for Empirical Faithfulness5 The Empirical Faithfulness of Pure Wave Mechanics6 Conclusion. (shrink)

Following a proposal of Vaidman The Stanford encyclopaedia of philosophy, 2014) The probable and the improbable: understanding probability in physics, essays in memory of Itamar Pitowsky, 2011), Sebens and Carroll , have argued that in Everettian quantum theory, observers are uncertain, before they complete their observation, about which Everettian branch they are on. They argue further that this solves the problem of making sense of probabilities within Everettian quantum theory, even though the theory itself is deterministic. We note some (...) problems with these arguments. (shrink)

I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite frequentism, in which Gibbs’ concept of an infinite ensemble of gases is replaced by the quantum state expressed as a superposition of a finite number of decohering microstates. It is a form of finite and actual frequentism (as opposed to (...) hypothetical frequentism) insofar as all the microstates exist, in keeping with the decoherence-based Everett interpretation, and some versions of pilot-wave theory. (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)

In this paper, we propose an ontological interpretation of the wave function in terms of random discontinuous motion of particles. According to this interpretation, the wave function of an N-body quantum system describes the state of random discontinuous motion of N particles, and in particular, the modulus squared of the wave function gives the probability density that the particles appear in every possible group of positions in space. We present three arguments supporting this new interpretation of (...) the wave function. These arguments are mainly based on an analysis of the mass and charge properties of a quantum system. It is realized that the Schroedinger equation, which governs the evolution of a quantum system, contains more information about the system than the wave function of the system, such as the mass and charge properties of the system, which might help understand the ontological meaning of the wave function. Finally, we briefly analyze possible implications of the suggested ontological interpretation of the wave function for the solutions to the measurement problem. (shrink)

In this article, we give a clearer argument for the reality of the wave function in terms of protective measurements, which does not depend on nontrivial assumptions and also overcomes existing objections. Moreover, based on an analysis of the mass and charge properties of a quantum system, we propose a new ontological interpretation of the wave function. According to this interpretation, the wave function of an N-body system represents the state of motion of N particles. Moreover, the (...) motion of particles is discontinuous and random in nature, and the modulus squared of the wave function gives the probability density that the particles appear in certain positions in space. (shrink)

We show that the minimum Fisher information (MFI) approach to estimating the probability law p(x) on particle position x, over the class of all two-component laws p(x), yields the complex Schrödinger wave equation. Complexity, in particular, traces from an “efficiency scenario” (demanded by MFI) where the two components of p(x) are so separated that their informations add.

For many among the scientifically informed public, and even among physicists, Heisenberg's uncertainty principle epitomizes quantum mechanics. Nevertheless, more than 86 years after its inception, there is no consensus over the interpretation, scope, and validity of this principle. The aim of this chapter is to offer one such interpretation, the traces of which may be found already in Heisenberg's letters to Pauli from 1926, and in Dirac's anticipation of Heisenberg's uncertainty relations from 1927, that stems form the hypothesis of finite (...) nature. Instead of a mere mathematical theorem of quantum theory, or a manifestation of "wave-particle duality", the uncertainty relations turn out to be a result of a more fundamental premise, namely, the inherent limitation on spatial resolution that follows from the bound on physical resources. The implication of this view are far reaching: it depicts the Hilbert space formalism as a phenomenological, "effective", formalism that approximates an underlying discrete structure; it supports a novel interpretation of probability in statistical physics that sees probabilities as deterministic, dynamical transition probabilities which arise from objective and inherent measurement errors; and it helps to clarify several puzzles in the foundations of statistical physics, such as the status of the "disturbance" view of measurement in quantum theory, or the tension between ontology and epistemology in the attempts to describe nature with physical theories whose formalisms include subjective probabilities. Finally, this view also renders obsolete the entire class of interpretations of quantum theory that adhere to "the reality of the wave function". (shrink)