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Quantum Mechanics

Edited by Michael Cuffaro (Ludwig Maximilians Universität, München)
Assistant editors: Radin Dardashti, Brian Padden
About this topic
Summary Issues in the philosophy of quantum mechanics include first and foremost, its interpretation. Probably the most well-known of these is the 'orthodox' Copenhagen interpretation associated with Neils Bohr, Werner Heisenberg, Wolfgang Pauli, John von Neumann, and others. Beginning roughly at the midway point of the previous century, philosophers' attention began to be drawn towards alternative interpretations of the theory, including Bohmian mechanics, the relative state formulation of quantum mechanics and its variants (i.e., DeWit's "many worlds" variant, Albert and Loewer's "many minds" variant, etc.), and the dynamical collapse family of theories. One particular interpretational issue that has attracted very much attention since the seminal work of John Bell, is the issue of the extent to which quantum mechanical systems do or do not admit of a local realistic description. Bell's investigation of the properties of entangled quantum systems, inspired by the famous thought experiment of Einstein, Podolsky, and Rosen, seems to lead one to the conclusion that the only realistic "hidden variables" interpretation compatible with the quantum mechanical formalism is a nonlocal one. In recent years, some of the attention has focused on applications of quantum mechanics and their potential for illuminating quantum foundations. These include the sciences of quantum information and quantum computation. Additional areas of research include philosophical investigation into the extensions of nonrelativistic quantum mechanics (such as quantum electrodynamics and quantum field theory more generally), as well as more formal logico-mathematical investigations into the structure of quantum states, state spaces, and their dynamics.
Key works Bohr 1928 and Heisenberg 1930 expound upon what has since become known as the 'Copenhagen interpretation' of quantum mechanics. The famous 'EPR' thought experiment of Einstein et al 1935 aims to show that quantum mechanics is an incomplete theory which should be supplemented by additional ('hidden') parameters. Bohr 1935 replies. More on Bohr's views can be found in Faye 1991, Folse 1985. Inspired by the EPR thought experiment, Bell 2004 [1964] proves what has since become known as "Bell's theorem." This, and a related result due to Kochen & Specker 1967 serve to revive the discussion of hidden variables and alternative interpretations of quantum mechanics. Jarrett 1984 analyses the key "factorisability" assumption Bell uses to derive his theorem into two distinct sub-assumptions, which Jarrett refers to as "locality" and "completeness". Two important volumes dedicated to the topics of entanglement and nonlocality are Cushing & McMullin 1989 and Maudlin 2002. Among the more discussed alternative interpretations of quantum mechanics are: Bohmian mechanics (Bohm 1952, and see also Cushing et al 1996), and Everett's relative state formulation (Everett Iii 1973). The latter gives rise to many variants, including the many worlds, many minds, and decoherence-based approaches (see Saunders et al 2012). Other notable interpretations and alternative theories include dynamical collapse theories (Ghirardi et al 1986), as well as the Copenhagen-inspired Quantum Bayesianism view (Fuchs 2003). An attempt to axiomatize quantum mechanics in terms of information theoretic constraints, and a discussion of the relevance of this for the interpretation of quantum mechanics is given in Clifton et al 2003. Discussion of this and other issues in quantum information theory can be found in: Timpson 2013. Key works in the philosophy of quantum field theory include: Redhead 1995, Redhead 1994, Ruetsche 2013, Teller 1995.
Introductions Hughes 1989 is an excellent introduction to the formalism and interpretation of quantum mechanics. Albert 1992 is another, which focuses particularly on the problem of measurement in quantum mechanics.
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  1. Ernst Cassirer (1923/2003). Substance and Function. Dover Publications.
    In this double-volume work, a great modern philosopher propounds a system of thought in which Einstein's theory of relativity represents only the latest (albeit the most radical) fulfillment of the motives inherent to mathematics and the physical sciences. In the course of its exposition, it touches upon such topics as the concept of number, space and time, geometry, and energy; Euclidean and non-Euclidean geometry; traditional logic and scientific method; mechanism and motion; Mayer's methodology of natural science; Richter's definite proportions; relational (...)
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  2. Eva Cassirer (1958). Methodology and Quantum Physics. [REVIEW] British Journal for the Philosophy of Science 8 (32):334-341.
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  3. Sheldon Goldstein, Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory.
    Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...)
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  4. Sheldon Goldstein, Quantum Hamiltonians and Stochastic Jumps.
    With many Hamiltonians one can naturally associate a |Ψ|2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it is typically a jump process on the configuration space of a variable number of particles. We define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [3] and of ourselves [11]. We introduce a formula expressing the jump rates (...)
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  5. Sheldon Goldstein (1996). Review Essay: Bohmian Mechanics and the Quantum Revolution. [REVIEW] Synthese 107 (1):145 - 165.
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  6. Sheldon Goldstein, D. Dürr, J. Taylor, R. Tumulka & and N. Zanghì, Quantum Mechanics in Multiply-Connected Spaces.
    J. Phys. A, to appear, quant-ph/0506173.
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  7. Sheldon Goldstein, D. Dürr & N. Zanghì, Bohmian Mechanics and Quantum Equilibrium.
    in Stochastic Processes, Physics and Geometry II, edited by S. Albeverio, U. Cattaneo, D. Merlini (World Scientific, Singapore, 1995) pp. 221-232.
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  8. Sheldon Goldstein & W. Struyve, On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics.
    In Bohmian mechanics the distribution |ψ|2 is regarded as the equilibrium distribution. We consider its uniqueness, finding that it is the unique equivariant distribution that is also a local functional of the wave function ψ.
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  9. Sheldon Goldstein & Roderich Tumulka, Arxiv:1003.2129v1 [Quant-Ph] 10 Mar 2010.
    The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...)
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  10. Sheldon Goldstein & Roderich Tumulka, Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John Von Neumann's 1929 Article on the Quantum Ergodic Theorem.
    The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...)
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  11. Sheldon Goldstein & Roderich Tumulka, Normal Typicality and Von Neumann's Quantum Ergodic Theorem.
    We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. The QET (...)
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  12. Sheldon Goldstein & Roderich Tumulka, On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems.
    We consider an isolated, macroscopic quantum system. Let H be a microcanonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + δE. The thermal equilibrium macro-state at energy E corresponds to a subspace Heq of H such that dim Heq/ dim H is close to 1. We say that a system with state vector ψ H is in thermal equilibrium if ψ is “close” to Heq. (...)
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  13. Ravi Gomatam, Against “Position”.
    Although quantum theory is presented as a radically non classical theory in physics, it is an open secret that our present understanding of it is based on a conceptual base borrowed from classical physics, leading to the situation that all of the radical implications of quantum theory are expressed using terminology that, in other circumstances would be considered blatantly self contradictory. To give but a few examples: wave particle duality (one and the same ontological entity can be ascribed two mutually (...)
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  14. Ravi Gomatam, Quantum Realism and Haecceity.
    Non-relativistic quantum mechanics is incompatible with our everyday or ‘classical’ intuitions about realism, not only at the microscopic level but also at the macroscopic level. The latter point is highlighted by the ‘cat paradox’ presented by Schrödinger. Since our observations are always made at the macroscopic level — even when applying the formalism to the microscopic level — the failure of classical realism at the macroscopic level is actually more fundamental and crucial.
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  15. Ravi Gomatam, Book Review. [REVIEW]
    In this book, Mara Beller, a historian and philosopher of science, undertakes to examine why and how the elusive Copenhagen interpretation came to acquire the status it has. The book appears under the series ‘Science and Its Conceptual Foundations’. The first part traces in seven chapters the early major developmental phases of QT such as matrix theory, Born’s probabilistic interpretation, Heisenberg’s uncertainty principle and Bohr’s complementarity framework. Although the historical and scientific details are authentic, the author’s presentation in this part (...)
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  16. Ravi V. Gomatam, Popper's Propensity Interpretation and Heisenberg's Potentia Interpretation.
    In other words, classically, probabilities add; quantum mechanically, the probability amplitudes add, leading to the presence of the extra product terms in the quantum case. What this means is that in quantum theory, even though always only one of the various outcomes is obtained in any given observation, some aspect of the non -occurring events, represented by the corresponding complex-valued quantum amplitudes, plays a role in determining the overall probabilities. Indeed, the observed quantum interference effects are correctly captured by the (...)
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  17. Ravi V. Gomatam (1999). Quantum Theory and the Observation Problem. Journal of Consciousness Studies 6 (11-12):11-12.
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  18. Víctor Gómez Pin (1997). New Developments on Fundamental Problems in Quantum Physics, Oviedo, julio de 1996. Theoria 12 (1):203-204.
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  19. Amit Goswami (1986). The Quantum Theory of Consciousness and Psi. PSI Research 5:145-65.
  20. Gerard Gouesbet (2011). Hypotheses on the a Priori Rational Necessity of Quantum Mechanics. Principia 14 (3):393-404.
    Há um vasto número de lamentações a respeito da falta de inteligibilidade da mecânica quântica. Alguns ingredientes da mecânica quântica, contudo, podem possivelmente ser compreendidos pela referência a primeiros princípios, ou seja, a princípios (ou postulados) básicos que, para a intuição, são claros e distintos. Em particular, se nos basearmos em um primeiro princípio denominado princípio da não-singularidade, que pode ser visto como uma hipótese, afirmamos que a mecânica quântica pode ser vista como uma consequência a priori de uma exigência (...)
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  21. Martin Gough (1995). Consciousness Does Not Complete Quantum Physics. Cogito 9 (3):258-261.
  22. Elizabeth Gould & P. K. Aravind (2010). Isomorphism Between the Peres and Penrose Proofs of the BKS Theorem in Three Dimensions. Foundations of Physics 40 (8):1096-1101.
    It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the theorem.
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  23. Gilad Gour (2002). The Quantum Phase Problem: Steps Toward a Resolution. [REVIEW] Foundations of Physics 32 (6):907-926.
    Defining the observable φ canonically conjugate to the number observable N has long been an open problem in quantum theory. The problem stems from the fact that N is bounded from below. In a previous work we have shown how to define the absolute phase observable Φ≡|φ| by suitably restricting the Hilbert space of x and p like variables. Here we show that also from the classical point of view, there is no rigorous definition for the phase even though it's (...)
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  24. Gilad Gour & L. Sriramkumar (1999). Will Small Particles Exhibit Brownian Motion in the Quantum Vacuum? Foundations of Physics 29 (12):1917-1949.
    The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of a small charge and (...)
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  25. O. W. Greenberg (2000). Book Review: The Quantum Theory of Fields, Volume III: Supersymmetry. [REVIEW] Foundations of Physics 30 (7):1131-1134.
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  26. D. Greenberger (1994). The Quantum Theory of Motion. Foundations of Physics 24:963-963.
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  27. Daniel Greenberger (2001). Book Review: Conceptual Foundations of Quantum Physics: An Overview From Modern Perspectives. By Dipankar Home. Plenum Publishing Corporation, New York, New York, 1997, Xvii + 386 Pp., $167.00 (Hardcover). ISBN 0-306-45660-5. [REVIEW] Foundations of Physics 31 (5):855-857.
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  28. Daniel Greenberger (2001). Book Review: New Developments on Fundamental Problems in Quantum Physics. By Miguel Ferrero and Alwyn van der Merwe, Eds. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997. [REVIEW] Foundations of Physics 31 (3):557-559.
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  29. W. Greiner (1996). The Quantum Theory of Fields. Volume 1: Foundations. Foundations of Physics 26:1267-1270.
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  30. H. J. Groenewold (1956). Quantum Mechanics and its Models. Synthese 10 (1):203 - 209.
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  31. Stanley P. Gudder (2001). Book Review: New Trends in Quantum Structures. Anatolij Dvurečenskij and Sylvia Pulmannová. Kluwer Academic Publishers, Dordrecht, 2000, I-Xvi, 1-541, $185 (Hardcover). [REVIEW] Foundations of Physics 31 (5):863-865.
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  32. B. J. H. (1962). From Dualism to Unity in Quantum Physics. Review of Metaphysics 15 (4):676-676.
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  33. S. O. H. (1969). The Story of Quantum Mechanics. Review of Metaphysics 22 (4):754-754.
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  34. Amit Hagar & Alex Korolev (2007). Quantum Hypercomputation—Hype or Computation? Philosophy of Science 74 (3):347-363.
    A recent attempt to compute a (recursion‐theoretic) noncomputable function using the quantum adiabatic algorithm is criticized and found wanting. Quantum algorithms may outperform classical algorithms in some cases, but so far they retain the classical (recursion‐theoretic) notion of computability. A speculation is then offered as to where the putative power of quantum computers may come from.
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  35. Amit Hagar & Alexandre Korolev (2006). Quantum Hypercomputability? Minds and Machines 16 (1):87-93.
    A recent proposal to solve the halting problem with the quantum adiabatic algorithm is criticized and found wanting. Contrary to other physical hypercomputers, where one believes that a physical process “computes” a (recursive-theoretic) non-computable function simply because one believes the physical theory that presumably governs or describes such process, believing the theory (i.e., quantum mechanics) in the case of the quantum adiabatic “hypercomputer” is tantamount to acknowledging that the hypercomputer cannot perform its task.
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  36. P. Hájíček (2012). Changes of Separation Status During Registration and Scattering. Foundations of Physics 42 (4):555-581.
    In our previous work, a new approach to the notorious problem of quantum measurement was proposed. Existing treatments of the problem were incorrect because they ignored the disturbance of measurement by identical particles and standard quantum mechanics had to be modified to obey the cluster separability principle. The key tool was the notion of separation status. Changes of separation status occur during preparations, registrations and scattering on macroscopic targets. Standard quantum mechanics does not provide any correct rules that would govern (...)
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  37. P. Hájíček (2011). The Quantum Measurement Problem and Cluster Separability. Foundations of Physics 41 (4):640-666.
    A modified Beltrametti-Cassinelli-Lahti model of the measurement apparatus that satisfies both the probability reproducibility condition and the objectification requirement is constructed. Only measurements on microsystems are considered. The cluster separability forms a basis for the first working hypothesis: the current version of quantum mechanics leaves open what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. The second working hypothesis is that registration apparatuses (...)
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  38. P. Hájíček (2009). Quantum Model of Classical Mechanics: Maximum Entropy Packets. [REVIEW] Foundations of Physics 39 (9):1072-1096.
    In a previous paper, a statistical method of constructing quantum models of classical properties has been described. The present paper concludes the description by turning to classical mechanics. The quantum states that maximize entropy for given averages and variances of coordinates and momenta are called ME packets. They generalize the Gaussian wave packets. A non-trivial extension of the partition-function method of probability calculus to quantum mechanics is given. Non-commutativity of quantum variables limits its usefulness. Still, the general form of the (...)
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  39. P. Hájíček & J. Tolar (2009). Intrinsic Properties of Quantum Systems. Foundations of Physics 39 (5):411-432.
    A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be attributed to individual quantum systems without violating standard quantum mechanics, which are called intrinsic. The intrinsic properties are classified into structural and conditional. A systematic and self-consistent account is given. Much more statements become meaningful than any version of Copenhagen interpretation would allow. A (...)
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  40. T. Halabi (2013). A Conservative Solution to the Stochastic Dynamical Reduction Problem. Foundations of Physics 43 (10):1252-1256.
    Stochastic dynamical reduction for the case of spin-z measurement of a spin-1/2 particle describes a random walk on the spin-z axis. The measurement’s result depends on which of the two points: spin-z=±ħ/2 is reached first. Born’s rule is recovered as long as the expected step size in spin-z is independent of proximity to endpoints. Here, we address the questions raised by this description: (1) When is collapse triggered, and what triggers it? (2) Why is the expected step size in spin-z (...)
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  41. J. B. S. Haldane (1934). Quantum Mechanics as a Basis for Philosophy. Philosophy of Science 1 (1):78-98.
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  42. Joseph Hall, Christopher Kim, Brien McElroy & Abner Shimony (1977). Wave-Packet Reduction as a Medium of Communication. Foundations of Physics 7 (9-10):759-767.
    Using an apparatus in which two scalers register decays from a radioactive source, an observer located near one of the scalers attempted to convey a message to an observer located near the other one by choosing to look or to refrain from looking at his scaler. The results indicate that no message was conveyed. Doubt is thereby thrown upon the hypothesis that the reduction of the wave packet is due to the interaction of the physical apparatus with the psyche of (...)
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  43. Michael J. W. Hall (1989). Quantum Mechanics and the Concept of Joint Probability. Foundations of Physics 19 (2):189-207.
    The concepts of joint probability as implied by the Copenhagen and realist interpretations of quantum mechanics are examined in relation to (a) the rules for manipulation of probabilistic quantities, and (b) the role of the Bell inequalities in assessing the completeness of standard quantum theory. Proponents of completeness of the Copenhagen interpretation are required to accept a modification of the classical laws of probability to provide a mechanism for complementarity. A new formulation of the locality postulate is given, not involving (...)
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  44. N. Hall (1999). Review. The Quantum Challenge. G Greenstein, AG Zajonc. British Journal for the Philosophy of Science 50 (2):313-315.
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  45. K. Haller & E. Lim-Lombridas (1994). Quantum Gauge Equivalence in QED. Foundations of Physics 24 (2):217-247.
    We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in (...)
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  46. Francis R. Halpern (1968). Special Relativity and Quantum Mechanics. Englewood Cliffs, N.J.,Prentice-Hall.
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  47. Leopold Halpern (1987). Erwin Schrödinger's Views on Gravitational Physics During His Last Years at the University of Vienna and Some Research Ensuing From It. Foundations of Physics 17 (11):1113-1130.
    The author, who was Schrödinger's assistant during his last years in Vienna, gives an account of Schrödinger's views and activities during that time which lead him to a different approach to research on the relations between gravitation and quantum phenomena. Various features of past research are outlined in nontechnical terms. A heuristic argument is presented for the role of the zero-point energy of massive particles in counteracting gravitational collapse and the formation of horizons. Arguments are presented for the view that (...)
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  48. Stuart R. Hameroff (1994). Quantum Coherence in Microtubules: A Neural Basis for Emergent Consciousness? Journal of Consciousness Studies 1 (1):91-118.
  49. Stuart R. Hameroff & Roger Penrose (1996). Orchestrated Reduction of Quantum Coherence in Brain Microtubules: A Model for Consciousness. In Stuart R. Hameroff, Alfred W. Kaszniak & A. C. Scott (eds.), Toward a Science of Consciousness. MIT Press.
  50. Stuart R. Hameroff & A. C. Scott (1998). A Sonoran Afternoon: A Dialogue on Quantum Mechanics and Consciousness. In Stuart R. Hameroff, Alfred W. Kaszniak & A. C. Scott (eds.), Toward a Science of Consciousness II. MIT Press.
    _Sonoran Desert, Stuart Hameroff and Alwyn Scott awoke from their_ _siestas to take margaritas in the shade of a ramada. On a nearby_ _table, a tape recorder had accidentally been left on and the following_ _is an unedited transcript of their conversation._.
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