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  1. F. Tito Arecchi (2003). Chaotic Neuron Dynamics, Synchronization, and Feature Binding: Quantum Aspects. Mind and Matter 1 (1):15-43.
    A central issue of cognitive neuroscience is to understand how a large collection of coupled neurons combines external signals with internal memories into new coherent patterns of meaning. An external stimulus localized at some input spreads over a large assembly of coupled neurons, building up a collective state univocally corresponding to the stimulus. Thus, the synchronization of spike trains of many individual neurons is the basis of a coherent perception. Based on recent investigations of homoclinic chaotic systems and their synchronization, (...)
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  2. Michael N. Audi (1973). Book Review:Perspectives in Quantum Theory: Essays in Honor of Alfred Lande Wolfgang Yourgrau, Alwyn Van Der Merwe. [REVIEW] Philosophy of Science 40 (2):323-.
  3. J. E. Baggott (2011). The Quantum Story: A History in 40 Moments. Oxford University Press.
    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 (...)
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  4. J. E. Baggott (2004). Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory. Oxford University Press.
    Quantum theory is one the most important and successful theories of modern physical science. It has been estimated that its principles form the basis for about 30 per cent of the world's manufacturing economy. This is all the more remarkable because quantum theory is a theory that nobody understands. The meaning of Quantum Theory introduces science students to the theory's fundamental conceptual and philosophical problems, and the basis of its non-understandability. It does this with the barest minimum of jargon and (...)
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  5. Jeffrey A. Barrett (2001). The Strange World of Quantum Mechanics Daniel F. Styer. [REVIEW] British Journal for the Philosophy of Science 52 (2):393-396.
  6. A. B. Bell & D. M. Bell (1976). Mates toE=Mc 2 and to the Heisenberg Uncertainty Relations. Foundations of Physics 6 (1):101-106.
    E=mc 2 is found to be a special case ofE=σ ±1cn, where σ is any one of four susceptibilities, namely electric, magnetic, gravitational, and elastic. Letl be length,t time,Δt time dilation, andΔl a measure of Fitzgerald-Lorentz contraction. A particle is stated to be the manifestation of a collection of susceptibilities which arise when(Δl)/1=(Δt)/t. Then(ΔE)/E=5 (Δt)/2t=±(Δσ)/σ. Corresponding to susceptibility, special energy particles are postulated which exhibitSU(3) symmetry, Related to the susceptibilities are five new Heisenberg uncertainty relations. Three new conservation laws for (...)
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  7. J. S. Bell (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press.
    This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current understanding of (...)
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  8. Henry F. Birkenhauer (1939). Causality and Quantum Physics. The Modern Schoolman 16 (2):35-37.
  9. Richard Bradley & Mareile Drechsler (2013). Types of Uncertainty. Erkenntnis:1-24.
    We distinguish three qualitatively different types of uncertainty—ethical, option and state space uncertainty—that are distinct from state uncertainty, the empirical uncertainty that is typically measured by a probability function on states of the world. Ethical uncertainty arises if the agent cannot assign precise utilities to consequences. Option uncertainty arises when the agent does not know what precise consequence an act has at every state. Finally, state space uncertainty exists when the agent is unsure how to construct an exhaustive state space. (...)
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  10. V. B. Braginsky & F. Ya Khalili (1986). How to Evade the Confrontation with the Uncertainty Relations. Foundations of Physics 16 (4):379-382.
    It is demonstrated that one can in principle register an arbitrarily small force acting on a free particle by employing only measurements of its coordinates.
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  11. G. B. Brown (1933). The Physical Significance of the Quantum Theory. By F. A. Lindemann M.A., D.Phil., F.R.S., Professor of Experimental Philosophy in the University of Oxford. (Oxford: Clarendon Press. 1932. London: Humphrey Milford. Pp. Vi + 148. Price 7s. 6d.). [REVIEW] Philosophy 8 (29):112-.
  12. Harvey R. Brown & Michael L. G. Redhead (1981). A Critique of the Disturbance Theory of Indeterminacy in Quantum Mechanics. Foundations of Physics 11 (1-2):1-20.
    Heisenberg'sgendanken experiments in quantum mechanics have given rise to a widespread belief that the indeterminacy relations holding for the variables of a quantal system can be explained quasiclassically in terms of a disturbance suffered by the system in interaction with a quantal measurement, or state preparation, agent. There are a number of criticisms of this doctrine in the literature, which are critically examined in this article and found to be ininconclusive, the chief error being the conflation of this disturbance with (...)
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  13. Grzegorz Bugajak (2011). Causality and Determinism in Modern Physics. In Adam Świeżyński (ed.), Knowledge and Values, Wyd. UKSW, Warszawa. 73–94.
    The paper revisits the old controversy over causality and determinism and argues, in the first place, that non˗deterministic theories of modern science are largely irrelevant to the philosophical issue of the causality principle. As it seems to be the ‘moral’ of the uncertainty principle, the reason why a deterministic theory cannot be applied to the description of certain physical systems is that it is impossible to capture such properties of the system, which are required by a desired theory. These properties (...)
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  14. Jean E. Burns (2002). Quantum Fluctuations and the Action of the Mind. Noetic Journal 3 (4):312-317.
    It is shown that if mental influence can change a position or momentum coordinate within the limits of the uncertainty principle, such change, when magnified by a single interaction, is sufficient to order the direction of traveling molecules. Mental influence could initiate an action potential in the brain through this process by using the impact of ordered molecules to open the gates of sodium channels in neuronal membranes. It is shown that about 80 ordered molecules, traveling at thermal velocity in (...)
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  15. Paul Busch & Brigitte Falkenbuyr, Heisenberg's Uncertainty Relation (Compendium Entry).
    This is an entry to the Compendium of Quantum Physics, edited by F Weinert, K Hentschel and D Greenberger, to be published by Springer-Verlag.
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  16. Paul Busch, Teiko Heinonen & Pekka Lahti, Heisenberg's Uncertainty Principle.
    Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the (...)
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  17. Paul Busch & Pekka J. Lahti (1985). A Note on Quantum Theory, Complementarity, and Uncertainty. Philosophy of Science 52 (1):64-77.
    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 (...)
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  18. Nancy Cartwright (1985). Book Review:Quantum Theory and Measurement John Archibald Wheeler, Wojciech Hubert Zurek. [REVIEW] Philosophy of Science 52 (3):480-.
  19. Gabriel Catren (2008). On Classical and Quantum Objectivity. Foundations of Physics 38 (5):470-487.
    We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical states is not incomplete, but rather that (...)
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  20. C. M. Caves (1994). Quantum Theory: Concepts and Methods. Foundations of Physics 24:1583-1583.
  21. Ariadna Chernavska (1981). The Impossibility of a Bivalent Truth-Functional Semantics for the Non-Boolean Propositional Structures of Quantum Mechanics. Philosophia 10 (1-2):1-18.
    The general fact of the impossibility of a bivalent, truth-functional semantics for the propositional structures determined by quantum mechanics should be more subtly demarcated according to whether the structures are taken to be orthomodular latticesP L or partial-Boolean algebrasP A; according to whether the semantic mappings are required to be truth-functional or truth-functional ; and according to whether two-or-higher dimensional Hilbert spaceP structures or three-or-higher dimensional Hilbert spaceP structures are being considered. If the quantumP structures are taken to be orthomodular (...)
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  22. R. Clifton (1995). Quantum Theory: Concepts and Methods. Foundations of Physics 25:205-205.
  23. Michael Cuffaro (2010). The Kantian Framework of Complementarity. Studies in History and Philosophy of Science Part B 41 (4):309-317.
    A growing number of commentators have, in recent years, noted the important affinities in the views of Immanuel Kant and Niels Bohr. While these commentators are correct, the picture they present of the connections between Bohr and Kant is painted in broad strokes; it is open to the criticism that these affinities are merely superficial. In this essay, I provide a closer, structural, analysis of both Bohr's and Kant's views that makes these connections more explicit. In particular, I demonstrate the (...)
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  24. Hristu Culetu (2005). Λ and the Heisenberg Principle. Foundations of Physics 35 (9):1511-1519.
    A time dependent “cosmological constant” Λ(t) is conjectured, in terms of the Gaussian curvature of the causal horizon. It is nonvanishing even in Minkowski space because of the lack of informations beyond the light cone. Using the Heisenberg Principle, the corresponding energy of the quantum fluctuations localized on the past or future null horizons is proportional to Λ1/2.We compute Λ(t) for the (Lorenzian version) of the (conformally flat) Hawking wormhole geometry (written in static spherical Rindler coordinates) and for the de (...)
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  25. George Darby (2010). Quantum Mechanics and Metaphysical Indeterminacy. Australasian Journal of Philosophy 88 (2):227-245.
    There has been recent interest in formulating theories of non-representational indeterminacy. The aim of this paper is to clarify the relevance of quantum mechanics to this project. Quantum-mechanical examples of vague objects have been offered by various authors, displaying indeterminate identity, in the face of the famous Evans argument that such an idea is incoherent. It has also been suggested that the quantum-mechanical treatment of state-dependent properties exhibits metaphysical indeterminacy. In both cases it is important to consider the details of (...)
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  26. Maurice A. De Gosson (2013). Quantum Blobs. Foundations of Physics 43 (4):440-457.
    Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by (...)
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  27. Maurice A. De Gosson (2009). The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg? [REVIEW] Foundations of Physics 39 (2):194-214.
    We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known as the “minimum volume ellipsoid” together with the notion of symplectic capacity, which we view as a topological measure of uncertainty invariant under Hamiltonian dynamics. This invariant provides a right measurement tool to define what “quantum scale” is. We take the opportunity to discuss the principle of the symplectic camel, which (...)
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  28. Willem M. De Muynck (2000). Preparation and Measurement: Two Independent Sources of Uncertainty in Quantum Mechanics. [REVIEW] Foundations of Physics 30 (2):205-225.
    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 (...)
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  29. William Demopoulos (1979). Book Review:The Uncertainty Principle and Foundations of Quantum Mechanics: A Fifty Years' Survey W. Price, S. Chissick. [REVIEW] Philosophy of Science 46 (2):336-.
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  30. Michael Dickson (2004). A View From Nowhere: Quantum Reference Frames and Uncertainty. Studies in History and Philosophy of Science Part B 35 (2):195-220.
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  31. Kenneth Eppley & Eric Hannah (1977). The Necessity of Quantizing the Gravitational Field. Foundations of Physics 7 (1-2):51-68.
    The assumption that a classical gravitational field interacts with a quantum system is shown to lead to violations of either momentum conservation or the uncertainty principle, or to result in transmission of signals faster thanc. A similar argument holds for the electromagnetic field.
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  32. F. T. Falciano, M. Novello & J. M. Salim (2010). Geometrizing Relativistic Quantum Mechanics. Foundations of Physics 40 (12):1885-1901.
    We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of (...)
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  33. Peter D. Finch (1984). The Operator Formalism of Quantum Mechanics From the Viewpoint of Short Disturbances in Nonrelativistic Classical Motion. Foundations of Physics 14 (4):281-306.
    The effect of short disturbances on nonrelativistic motion is formulated in terms of operators. Analogies with quantum mechanics are developed and some disparities noted. For the one-dimensional particle we obtain analogues of the de Broglie wave commonly associated with particle motion, Heisenberg's commutation relation, Schrödinger's equation, and the statistical interpretation. Whether these results have any bearing on quantum mechanics itself is left an open question.
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  34. E. E. Fitchard (1979). Proposed Experimental Test of Wave Packet Reduction and the Uncertainty Principle. Foundations of Physics 9 (7-8):525-535.
    A practical experiment using coincidence techniques is suggested to test the validity of the following concepts:(1) wave packet reduction and(2) the measurement-uncertainty principle for position and momentum. The suggested experiment uses the time-of-flight method to determine an electron's momentum and a coincident photon, emitted from a system excited by the electron, to determine its initial position. It is shown that this method does constitute a simultaneous measurement of position and momentum for a single system. Also, it is pointed out that (...)
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  35. Gordon N. Fleming, Correlation Coefficients and Robertson-Schroedinger Uncertainty Relations.
    Calling the quantity; 2ΔAΔB/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises, above unity, the lower bound of the UPR for each member of an infinite collection of pairs of incompatible observables. Conversely, any UPR is subject to lower bounds above unity determined by each of an infinite collection of correlation coefficients. This result generalizes the well known Schroedinger strengthening (...)
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  36. Peter Gibbins (1981). A Note on Quantum Logic and the Uncertainty Principle. Philosophy of Science 48 (1):122-126.
    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.
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  37. A. Granik (1997). Why Quantum Mechanics Indeed? Foundations of Physics 27 (4):511-532.
    Classical mechanics assumes that its laws (and specifically the second law of Newton) are independent of spatio-temporal resolutions. To see whether there is an alternative to this assumption we write the energy of a relativistic particle in a finite-difference form, e.g., ɛ=ɛ0[1-(Δx/c Δt)2]1/2. We assume that in the limit Δt→0 the energy ε has a simple pole a/Δt. We show that quantum mechanics in its different formulations (Schrödinger, Feynman, Schwinger, Klein-Gordon, and Dirac) follows in elementary fashion from this assumption. We (...)
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  38. Amit Hagar, Does Protective Measurement Tell Us Anything About Quantum Reality?
    An analysis of the two routes through which one may disentangle a quantum system from a measuring apparatus, hence protect the state vector of a single quantum system from being disturbed by the measurement, reveals several loopholes in the argument from protective measurement to the reality of the state vector of a single quantum system.
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  39. Emmanuel Haven (2011). Itô's Lemma with Quantum Calculus (Q-Calculus): Some Implications. [REVIEW] Foundations of Physics 41 (3):529-537.
    q-derivatives are part of so called quantum calculus. In this paper we investigate how such derivatives can possibly be used in Itô’s lemma. This leads us to consider how such derivatives can be used in a social science setting. We conclude that in a Itô Lemma setting we cannot use a macroscopic version of the Heisenberg uncertainty principle with q-derivatives.
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  40. Jan Hilgevoord & David Atkinson (2011). Time in Quantum Mechanics. In Craig Callender (ed.), The Oxford Handbook of Philosophy of Time. Oup Oxford.
  41. Jan Hilgevoord & Jos Uffink, The Uncertainty Principle.
    Quantum mechanics is generally regarded as the physical theory that is our best candidate for a fundamental and universal description of the physical world. The conceptual framework employed by this theory differs drastically from that of classical physics. Indeed, the transition from classical to quantum physics marks a genuine revolution in our understanding of the physical world.
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  42. V. Hushwater (1998). A Path From the Quantization of the Action Variable to Quantum Mechanical Formalism. Foundations of Physics 28 (2):167-184.
    Starting from the quantization of the action variable as a basic principle, I show that this leads one to the probabilistic description of physical quantities as random variables, which satisfy the uncertainty relation. Using such variables I show that the ensemble-averaged action variable in the quantum domain can be presented as a contour integral of a “quantum momentum function,” pq(z), which is assumed to be analytic. The condition that all bound states pq(z) must yield the quantized values of the action (...)
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  43. Toshio Ishigaki (1991). Four Mathematical Expressions of the Uncertainty Relation. Foundations of Physics 21 (9):1089-1105.
    The uncertainty relation in quantum mechanics has been explicated sometimes as a statistical relation and at other times as a relation concerning precision of simultaneous measurements. In the present paper, taking the indefiniteness of individual experiments as represented by diameters of Borel sets in projection-valued measure, we mathematically distinguish four expressions, two statistical and two concerning simultaneous measurements, of the uncertainty relation, study their interrelations, and prove that they are nonequivalent to each other and to the eigenvector condition (EV) in (...)
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  44. Max Jammer (1982). A Note on Peter Gibbins' "a Note on Quantum Logic and the Uncertainty Principle". Philosophy of Science 49 (3):478-479.
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  45. L. Jánossy (1978). Wave Mechanics and the Tunnel Effect. Foundations of Physics 8 (1-2):119-122.
    It is shown that the nonconservation of energy to the extent given by the uncertainty relation can be interpreted also as the storing of inner energyQ by a wave mechanical system. The latter formalism is, apart from its terminology, identical with the accepted one.
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  46. Andrew Khrennikov (1996). The Ultrametric Hilbert-Space Description of Quantum Measurements with a Finite Exactness. Foundations of Physics 26 (8):1033-1054.
    We provide a mathematical description of quantum measurements with a finite exactness. The exactness of a quantum measurement is used as a new metric on the space of quantum states. This metric differs very much from the standard Euclidean metric. This is the so-called ultrametric. We show that a finite exactness of a quantum measurement cannot he described by real numbers. Therefore, we must change the basic number field. There exist nonequivalent ultrametric Hilbert space representations already in the finite-dimensional case (...)
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  47. Yoon-Ho Kim & Yanhua Shih (1999). Experimental Realization of Popper's Experiment: Violation of the Uncertainty Principle? [REVIEW] Foundations of Physics 29 (12):1849-1861.
    An entangled pair of photons (1 and 2) are emitted in opposite directions. A narrow slit is placed in the path of photon 1 to provide the precise knowledge of its position on the y-axis and this also determines the precise y-position of its twin, photon 2, due to quantum entanglement. Is photon 2 going to experience a greater uncertainty in momentum, that is, a greater Δpy because of the precise knowledge of its position y? The experimental data show Δy (...)
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  48. P. T. Landsberg (1947). Discussion: The Uncertainty Principle as a Problem in Philosophy. Mind 56 (223):250-256.
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  49. P. T. Landsberg (1947). The Uncertainty Principle as a Problem in Philosophy. Mind 56 (223):250-256.
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  50. H. Margenau (1931). The Uncertainty Principle and Free Will. Science.
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