Skip to main content
SpringerLink
Log in

Quantum Theory and Locality

  • Chapter
  • First Online:
Quantum Objects

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 175))

  • 2084 Accesses

Abstract

The relationship of quantum theory and space-time theory is clarified in historical context. In particular, non-local property correlation is described in relation to various notions of locality. This lays the ground for a search for the ontology most appropriate to quantum theory and the role and nature of causation in quantum theory, where Einstein’s metaphysical views, the EPR argument, Gleason’s theorem, and the Bell-type inequalities play key roles. The fundamental principles of quantum theory, such as the Superposition principle and the Born rule, and the relevance of the theory of communication to quantum theory are also explained. It is shown that various presumptions about the above relationships are unwarranted, the most significant of these being the presumption that the failure of correlations between properties of quantum systems always to have local explanations, in Bell’s sense of locality, requires a rejection of metaphysical realism.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Nonetheless, it continues to be probed, cf., e.g. [156]. Here, Quantum mechanics with capital Q designates the standard theory of quantum mechanics, such as in the Dirac–von Neumann formulation summarized in Sect. 1.2.

  2. 2.

    Here, the former will be called simply Quantum mechanics.

  3. 3.

    Within the appropriate context in relation to relativity, of course. For a recent attempt to find fault, see [320].

  4. 4.

    They each also have issues arising from their own peculiarities such as the appearance of infinities in the latter.

  5. 5.

    More broadly, Einstein believed that the invariants of the scientific approach are: (i) “The truth of theoretical thought is given exclusively by its relation to the sum total of [the experiences of sense perception]”, (ii) “All elementary concepts are reducible to space–time concepts,” and (iii) “The spatiotemporal laws are complete” [91].

  6. 6.

    Here by event is meant an occurrence in a particular location, represented by a point in space-time, as it will here in the sequel; an explicit definition of local causal, also know as Bell locality is given in Sect. 1.4, below. Note, however, that in General relativity an event is defined as an intersection of world lines.

  7. 7.

    That is, that assume ‘local causality,’ which is defined below.

  8. 8.

    See [154], Sect. 2.5.

  9. 9.

    Contemporary results bring into question even such modest substitutes for particle trajectories as space-time tubes, as seen in Chap. 4.

  10. 10.

    See [154], Chap. 3. Arkady Plotnitsky has argued that Bohr’s approach to Quantum mechanics had already involved an informational dimension, see ([223], p. 43 and quotes therein).

  11. 11.

    The mathematical relationship involved here is specified in Sect. 1.3

  12. 12.

    Operators on Hilbert space, a theoretical novelty introduced to physics with the introduction of Quantum mechanics, are discussed in detail in the next section.

  13. 13.

    Einstein’s views on the question of the interpretation of Quantum mechanics to this effect have been carefully argued, for example, by Fine ([107], p. 61).

  14. 14.

    See Sect. 2 of [143] for a discussion of this as contrasted with the quantum theoretical case. More about the different ways of approaching quantum fields appears below.

  15. 15.

    These difficulties, which remained, are taken up in Chap. 4.

  16. 16.

    The compatibility of Quantum mechanics and Relativity has been called their “peacefully coexistence.”

  17. 17.

    Strictly speaking, the no-superluminal-signaling condition strongly associated with Relativity is not one of its basic principles. In any event, Quantum mechanics and General relativity are incompatible for other reasons.

  18. 18.

    Cf., e.g., [143]. Note also that Einstein’s signal-based rule for time attribution can be shown to provide coordinates equivalent to those given via the Lorentz transformation if some additional assumptions are made, cf. [185], Chap. 4.

  19. 19.

    Cf., e.g., [185, 307], and Fig. 1.3.

  20. 20.

    The principle that no (causal) signal may propagate faster than the speed of light is often called Einstein locality.

  21. 21.

    For discussions of the relevant spectrum of metaphysical positions see, for example, [95, 154], and [107]. Arthur Fine has called Einstein’s position “motivational realism” because, he argues, realism “is the main motive that lies behind creative scientific work and makes it worth doing” ([107], pp. 109–110).

  22. 22.

    An operator is Hermitian if it is equal to its Hermitian conjugate \(O = {O}^{\dag }\), that is, its complex conjugate transpose, as considered in the matrix representation.

  23. 23.

    Note that the inequality conditioning this commutation is exactly the negation of that defining the backward light-cone, cf. Fig. 1.4.

  24. 24.

    Interference is discussed below in Sect. 2.5.

  25. 25.

    These “matrices” are not necessarily susceptible to an explicit matrix description.

  26. 26.

    However, note that this theorem does not hold for operators in infinite-dimensional Hilbert spaces, even when there exists a countably infinite set of basis vectors. Such a decomposition does not exist in general in that case, because there may not exist a countably infinite set of eigenvectors that form a basis.

  27. 27.

    This relates to the “causal particle” concept critiqued by Falkenburg [95] and discussed in Sect. 2.3. Cloud chambers and other particle detectors are discussed later in some detail.

  28. 28.

    Entanglement is defined and characterized in Sect. 1.4.

  29. 29.

    More on the issue of wave–particle duality can be found in Chap. 3.

  30. 30.

    For Pauli, there is a “limitation of the applicability of our ways of perception, not only by the possibilities of observation but also by the possibilities of definition (caused by the laws of nature)” ([122, 317], p. 21). Note also that Pauli was less than happy with Reichenbach’s attempts to formalize these notions in logical rather than physical terms [317].

  31. 31.

    However, note that, unlike in Relativity, time in Quantum mechanics serves only as a parameter.

  32. 32.

    For more on the issue of wave–particle duality, see [154], Sect. 1.2.

  33. 33.

    This notion of particle is discussed in more detail in Chap. 4.

  34. 34.

    This is discussed in detail in Chap. 3.

  35. 35.

    This condition on quantum field operators is defined below in Eq. 1.13

  36. 36.

    Other names for quantum objects related to the particle concept that have been suggested include “quarticle” [145].

  37. 37.

    POVMs are discussed in the following chapter.

  38. 38.

    Falkenburg has identified the following characteristics, which she refers to as “informal predicates,” of classical particles: carrying mass and charge, mutually independence, exhibiting point-like behavior during interactions, being subject to conservation laws, having behavior completely determined by mechanical law, following phase-space trajectories, being spatio-temporally individuated, being able to form bound systems ([95], p. 211).

  39. 39.

    The investigation of this issue is continued in Chap. 4.

  40. 40.

    Note that for Pauli, as the causal description became less appropriate an acausal correspondence between events—a less mystically flavored version of Jungian synchronicity—became more appropriate [175, 317].

  41. 41.

    Here, the subscripts provide a label attributable by virtue of some property distinguishing to systems, such as spin or rest mass.

  42. 42.

    The products of unit vectors of Eq. 1.12 are often written in compact form: \(\vert u_{i}v_{j}\rangle _{AB} \equiv \vert u_{i}\rangle _{A} \otimes \vert v_{j}\rangle _{B}\).

  43. 43.

    This may have been overlooked because at the time many, for example Schrödinger, believed some sort of substance might be present. Reichenbach notes that here arises “the question whether the waves have thing-character or behavior-character, i.e., whether they constitute the ultimate objects of the physical world or only express the statistical behavior of such objects” ([241], p. 22). We return to this question below.

  44. 44.

    A similar example is considered in more detail in Sect. 2.3.

  45. 45.

    Measurement theory is discussed in greater detail in the next chapter.

  46. 46.

    The uncertainty principle and relations are discussed below in Sect. 2.3.

  47. 47.

    For example, the first of the two states above has unhelpful peculiarities, the most significant of which is that—despite the authors’ expectations—the correlations of measurement outcomes at distant locations they take to be characteristic of the state when the subsystems are well separated are not absolutely strict.

  48. 48.

    This assumption plays an important role in later discussions here. Also, cf. [239].

  49. 49.

    The result is then called the EPRB argument—the B standing for Bohm [24], who first used the spin singlet state for its study.

  50. 50.

    Popper’s point was later amplified in the much later GHSZ argument involving three spin-systems [123].

  51. 51.

    The relationship between the potential and actual will be taken up in greater detail in Chaps. 2 and 3.

  52. 52.

    Importantly, note that the “hidden parameters” are not necessarily truly hidden in the sense of being physically inaccessible.

  53. 53.

    An example of such a theory was introduced by Bell [16].

  54. 54.

    Bell’s general attitude was summarized by Roman Jackiw and Shimony as follows. “Bell felt Niels Bohr and Werner Heisenberg were profoundly wrong in giving observation a fundamental role in physics, thereby letting mind and subjectivity permeate or even replace the stuff of physics…Bell always maintained that what is there to be known has an objective status and is independent of being observed.” ([151], p. 83).

  55. 55.

    For a more detailed proof, see e.g. [87].

  56. 56.

    Most often, tests involve pairs of photons in the singlet state | Ψ  − ⟩ [15] of polarization.

  57. 57.

    Nonetheless, it has been argued that Bell’s sense of locality differs in important ways from that of EPR (cf., e.g. [107], p. 61). At a minimum, it can be said that the EPR conditions emphasize system properties more than measurement outcomes, although Bell also later focused on “local beables,” that is, local elements of reality rather than observables (cf. [20], Papers 8 and 17).

  58. 58.

    Indeed, the CH inequality follows from the basic properties of probabilities such as that they lie in the interval [0, 1].

  59. 59.

    For more on the relationship between interference visibilities and entanglement, see [160].

  60. 60.

    If the theory does not assume such localized states, as indeed Quantum mechanics doesn’t, then it can be expected to violate Bell-type inequalities.

  61. 61.

    Note also that conditional probability in itself does not depend in any way on causal or even temporal order.

  62. 62.

    Common causes are discussed in detail in the next chapter.

  63. 63.

    The relationship between causes and various conditional probabilities of this sort is treated in detail in the next chapter.

  64. 64.

    The state | Φ  + ⟩ is also maximally entangled. Since its introduction, the extent of the empirical value of | S | beyond 2 has served experimentalists as a figure of merit for entanglement production. More about entanglement is found in the following section.

  65. 65.

    The bounds on the probabilities and expectation values in Bell-type inequalities are the faces of extreme points in the polytopes of all classically possible correlations.

  66. 66.

    Not all such states are Bell states, that is, elements of the Bell basis as, say, | Ψ  − ⟩ and | Φ  + ⟩ are; the Bell basis for the state space \(\mathcal{H}_{4} = {\mathcal{C}}^{2} \otimes {\mathcal{C}}^{2}\) is the set consisting of the following state vectors. \(\vert {\Phi }^{\pm }\rangle = \frac{1} {\sqrt{2}}(\vert 00\rangle \pm \vert 11\rangle )\) and \(\vert {\Psi }^{\pm }\rangle = \frac{1} {\sqrt{2}}(\vert 01\rangle \pm \vert 10\rangle )\).

  67. 67.

    Entangled states of bipartite systems with components labeled A and B are typically denoted using an AB subscript, as in ρ AB , or superscript.

  68. 68.

    The entangled mixed states ρ are thus precisely the inseparable states. Nonetheless, it is sometimes impossible to tell whether or not a given mixed state is separable. The problem of determining whether a given state of a composite system is entangled is known as the separability problem.

  69. 69.

    Furthermore, the contradiction between quantum mechanical predictions and the Bell and CHSH inequalities are expressions violated only by statistical predictions of Quantum mechanics, rather than by individual events.

  70. 70.

    For example, Shimony and I noted this in the early 1990s in the course of work on the bipartite-system coincidence interference visibility (entanglement visibility), later allowing for a geometrical means of quantifying entanglement [281].

  71. 71.

    Note that the operation has been represented here for notational simplicity as a super-operator \(\mathcal{O}_{AB}\), which acts on density operators in the Liouville space—the space of statistical operators associated with the Hilbert space of state vectors for the joint system. See [153], Sect. B.3 and [106] for a short description of their relationship.

  72. 72.

    It is important to note that a LOCC operation is not necessarily a TP operation. In the case of operations on a number of copies of a quantum system for any of these classes, the adjective “collective” is added and the above acronyms are given the prefix “C,” for example, the CLOCC class is that of collective location operations and classical communication. In cases where transformations are not achievable deterministically, but rather only with some probability, they are considered stochastic operations and the adjective “stochastic” is added as well as the prefix “S,” as in SLOCC.

  73. 73.

    Here S z is defined as above, just below Eq. 1.7.

  74. 74.

    The class of completely positive trace-preserving (CPTP) linear transformations, \(\rho \rightarrow \mathcal{E}(\rho )\) often called operations, taking statistical operators to statistical operators, each described by a superoperator, \(\mathcal{E}(\rho )\), satisfying the following conditions. (i) \(\mathrm{tr}[\mathcal{E}(\rho )]\) is the probability that the transformation \(\rho \rightarrow \mathcal{E}(\rho )\) takes place; (ii) \(\mathcal{E}(\rho )\) is a linear convex map on statistical operators, that is, \(\mathcal{E}\big(\sum _{i}p_{i}\rho _{i}\big) =\sum _{i}p_{i}\mathcal{E}(\rho _{i}),\) p i being probabilities. (\(\mathcal{E}(\rho )\) then extends uniquely to a linear map.) (iii) \(\mathcal{E}(\rho )\) is a completely positive (CP) map.

  75. 75.

    For more detail on this, cf., e.g. [153].

  76. 76.

    For a discussion of quantum teleportation, see, e.g. [153], Sect. 9.9.

  77. 77.

    This quantum mechanical constraint is known as the Tsirel’son bound.

References

  1. A. Aspect, Trois tests expérimentaux des inegalités de Bell. Ph.D. thesis, Université Paris-Sud, Ph.D. thesis no. 2674; Paris, 1983; A. Aspect (Author), G. Adenier, G. Jaeger, A. Khrennikov (Translators) Three experimental tests of Bell’s inequalities by correlation measurements of photon polarization (Springer, Heidelberg, forthcoming)

    Google Scholar 

  2. A. Aspect, P. Grangier, G. Roger, Experimental test of realistic theories via Bell’s inequality. Phys. Rev. Lett. 47, 460 (1981)

    Article  ADS  Google Scholar 

  3. A. Aspect, J. Dalibard, G. Roger, Experimental realization of Einstein–Podolsky–Rosen–Bohm gedankenexperiment: a new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  4. G. Bacciagaluppi, Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference (Cambridge University Press, Cambridge, 2009)

    Book  Google Scholar 

  5. J. Barrett, S. Pironio, Popescu–Rohrlich correlations as a unit of nonlocality. Phys. Rev. Lett. 95, 140401 (2005)

    Article  ADS  Google Scholar 

  6. J.S. Bell, On the Einstein–Podolsky–Rosen paradox. Physics 1, 195 (1964)

    Google Scholar 

  7. J.S. Bell, On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447 (1966)

    Article  ADS  MATH  Google Scholar 

  8. J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987)

    MATH  Google Scholar 

  9. J.S. Bell, Indeterminism and nonlocality, in Mathematical Undecidability, ed. by A. Driessen, A. Suarez (Kluwer Academic, Dordrecht, 1997), Ch. VII

    Google Scholar 

  10. M. Bell, K. Gottfried, M. Veltman (eds.), John S. Bell on the Foundations of Quantum Mechanics (World Scientific, Singapore, 2001)

    MATH  Google Scholar 

  11. D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, 1951)

    Google Scholar 

  12. D. Bohm, A suggested interpretation of quantum theory in terms of ‘hidden’ variables I. Phys. Rev. 85, 166 (1952); II. Phys. Rev. 85, 180 (1952)

    Google Scholar 

  13. N. Bohr, Causality and complementarity. Philos. Sci. 4, 289 (1937)

    Article  Google Scholar 

  14. N. Bohr, Discussions with Einstein on epistemological problems in atomic physics, in Albert Einstein: Philosopher-Scientist, ed. by P.A. Schilpp. The Library of Living Philosophers, vol. 7, Part I (Open Court, Evanston, 1949), p. 201

    Google Scholar 

  15. M. Born, I. Born (Translator), The Born–Einstein Letters (Walker, London, 1971)

    Google Scholar 

  16. R.W. Boyd, D.J. Gauthier, P. Narum, Causality in superluminal pulse propagation, in Time in Quantum Mechanics, vol. 2, ed. by G. Muga, A. Ruschhaupt, A. Campo. Lecture Notes in Physics, vol. 789 (Springer, Berlin/New York, 2009), p. 175

    Google Scholar 

  17. P. Busch, P.J. Lahti, Observable, in Compendium of Quantum Physics, ed. by D. Greenberger et al. (Springer, Heidelberg, 2009), p. 425

    Google Scholar 

  18. E. Castellani (ed.), Interpreting Bodies (Princeton University Press, Princeton, 1998)

    Google Scholar 

  19. N.J. Cerf, N. Gisin, S. Massar, S. Popescu, Simulating maximal quantum entanglement without communication. Phys. Rev. Lett. 94, 220403 (2005)

    Article  ADS  Google Scholar 

  20. P. Cherenkov, Vidimoe svechenie chistykh zhidkostei pod deistviem gamma-radiatsii (Visible glow of pure liquids under gamma irradiation). Dokl. Akad. Nauk SSSR 2, 451 (1934)

    Google Scholar 

  21. J.F. Clauser, M. Horne, A. Shimony, R.A. Holt, Proposed experiments to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1973)

    Article  ADS  Google Scholar 

  22. R. Clifton, The subtleties of entanglement and its role in quantum information theory. Philos. Sci. 69, S150 (2002)

    Article  MathSciNet  Google Scholar 

  23. D. Collins, N. Gisin, N. Linden, S. Massar, S. Popescu, Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  24. J.T. Cushing, Foundational problems in quantum field theory, in Philosophical Foundations Quantum Field Theory, ed. by H. Brown, R. Harré (Oxford University Press, Oxford, 1988), p. 25

    Google Scholar 

  25. P.C.W. Davies, J.R. Brown (eds.), The Ghost in the Atom (Cambridge University Press, Cambridge, 1986)

    Google Scholar 

  26. L. de Broglie, La mécanique ondulatoire et la structure atomique de la matière et du rayonnement. J. Physique et du Radium 8, 225 (1927)

    Article  MATH  Google Scholar 

  27. L. de Broglie, La nouvelle méchanique des quanta, in Rapports et discussions du cinquième conseil de physique Solvay, ed. by H. Lorentz (Gauthier-Villars, Paris, 1928), p. 105

    Google Scholar 

  28. P.A.M. Dirac, The quantum theory of the emission and absorption of radiation. Proc. R. Soc. Lond. A 114, 243 (1927)

    Article  ADS  MATH  Google Scholar 

  29. P. Eberhard, Bell’s theorem and the different concepts of locality. Nuovo Cimento B 46, 392 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  30. A. Einstein, On the method of theoretical physics. Philos. Sci. 1, 163 (1934)

    Article  Google Scholar 

  31. A. Einstein, Quanten-Mechanik und Wirklichkeit. Dialectica 2, 320 (1948)

    Article  MATH  Google Scholar 

  32. A. Einstein, Physics, philosophy, and scientific progress, in Speech to the International Congress of Surgeons in Cleveland; reprinted as Phys. Today 58(6), 46 (2012)

    Google Scholar 

  33. A. Einstein, B. Podolsky, N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  34. B. Falkenburg, Particle Metaphysics (Springer, Heidelberg, 2007)

    Google Scholar 

  35. R.P. Feynman, QED (Princeton University Press, Princeton, 1985)

    Google Scholar 

  36. E. Fick, G. Sauermann, W.D. Brewer, The Quantum Statistics of Dynamic Processes (Springer, Berlin, 1990)

    Book  Google Scholar 

  37. A. Fine, The Shaky Game (The University of Chicago Press, Chicago, 1986)

    Google Scholar 

  38. W. Gerlach, O. Stern, Das magnetische moment des silberatoms. Z. Phys. 9, 353 (1922)

    Article  ADS  Google Scholar 

  39. N. Gisin, Bell’s inequality holds for all non-product states. Phys. Lett. A 154, 201 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  40. A.M. Gleason, Measures on the closed subspaces of a Hilbert space. J. Math. Mech. 6, 885 (1957)

    MathSciNet  MATH  Google Scholar 

  41. H.L. Goldschmidt, Nochmals Dialogik (ETH Stiftung Dialogik, Zürich, 1990)

    Google Scholar 

  42. D.M. Greenberger, M.A. Horne, A. Shimony, A. Zeilinger, Bell’s theorem without inequalities. Am. J. Phys. 58, 1131 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  43. D.M. Greenberger, M.A. Horne, A. Zeilinger, Multiparticle interferometry and the superposition principle. Phys. Today 46, 22 (1993)

    Article  Google Scholar 

  44. R. Haag, Local Quantum Physics (Springer, Heidelberg, 1992)

    Book  MATH  Google Scholar 

  45. W. Heisenberg, Die Entwicklung der Quantentheorie, 1918–1928. Die Naturwissenschaften 17, 490 (1929)

    Article  ADS  MATH  Google Scholar 

  46. W. Heisenberg, Physics and Philosophy (Harper and Row, New York, 1958)

    Google Scholar 

  47. D. Howard, Holism and separability, in Philosophical Consequences of Quantum Theory, ed. by J.T. Cushing, E. McMullin (University of Notre Dame Press, Notre Dame, 1989)

    Google Scholar 

  48. N. Huggett, Quarticles and identical particles, in Symmetries in Physics, ed. by K. Brading, E. Castellani (Cambridge University Press, Cambridge, 2003). Ch. 13

    Google Scholar 

  49. H.E. Ives, G.R. Stilwell, An experimental study of the rate of a moving atomic clock. J. Opt. Soc. Am. 28(7), 215 (1938)

    Article  Google Scholar 

  50. R. Jackiw, A. Shimony, The depth and breadth of John Bell’s physics. Phys. Perspect. 4, 78 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  51. G. Jaeger, Quantum Information: An Overview (Springer, New York, 2007)

    Google Scholar 

  52. G. Jaeger, Entanglement, Information, and the Interpretation of Quantum Mechanics (Springer, Heidelberg, 2009)

    Book  Google Scholar 

  53. G. Jaeger, Generalized quantum probability and entanglement enhancement witnessing. Found. Phys. 42, 752 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  54. G. Jaeger, A. Shimony, L. Vaidman, Two interferometric complementarities. Phys. Rev. A 51, 54 (1995)

    Article  ADS  Google Scholar 

  55. M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974)

    Google Scholar 

  56. N. Jones, L. Masanes, Interconversion of nonlocal correlations. Phys. Rev. A 72, 052312 (2005)

    Article  ADS  Google Scholar 

  57. R.J. Kennedy, E.M. Thorndike, Experimental establishment of the relativity of time. Phys. Rev. 42, 400 (1932)

    Article  ADS  Google Scholar 

  58. M.J. Klein, A.J. Kox, R. Schulmann (eds.), Einstein on superluminal signal velocities, in The Collected Papers of Albert Einstein (CPAE), vol. 5 (Princeton University Press, Princeton, 1993), p. 57; G. Weinstein, Einstein on the impossibility of superluminal velocities. http://arxiv.org/pdf/1203.4954v1.pdf

  59. C. Lämmerzahl, Tests theories for Lorentz invariance, in Special Relativity: Will It Survive the Next 101 Years?, ed. by J. Ehlers, C. Lämmerzahl. Lecture Notes in Physics, vol. 702 (Springer, Heidelberg, 2006), p. 349

    Google Scholar 

  60. K.V. Laurikainen, Beyond the Atom: The Philosophical Thought of Wolfgang Pauli (Springer, Heidelberg, 1988), p. 80

    MATH  Google Scholar 

  61. J.R. Lucas, P.E. Hodgson, Spacetime and Electromagnetism (Oxford University Press, Oxford, 1990)

    MATH  Google Scholar 

  62. T. Maudlin, Space-time in the quantum world, in Bohmian Mechanics and Quantum Theory: An Appraisal, ed. by J.T. Cushing (Kluwer Academic, Dordrecht, 1996), pp. 285–307

    Google Scholar 

  63. A.A. Michelson, E.W. Morley, Influence of motion of the medium on the velocity of light. Am. J. Sci. 31, 377 (1986)

    Google Scholar 

  64. A.J. Miller, S.W. Nam, J.M. Martinis, A.V. Sergienko, Demonstration of low-noise near-infrared photon counter with multiphoton discrimination. Appl. Phys. Lett. 83, 791 (2003)

    Article  ADS  Google Scholar 

  65. T. Norsen, Against ‘Realism’. Found. Phys. 37, 311 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  66. A. Peres, Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  67. M.E. Peskin, D.V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, 1995)

    Google Scholar 

  68. I. Pitowsky, Quantum Probability–Quantum Logic (Springer, Berlin, 1989)

    MATH  Google Scholar 

  69. M. Planck, Kausalität in der Natur, in Vorträge und Erinnerungen, ed. by M. Planck (Wissenschaftliche Buchgesellschaft, Darmstadt, 1975), p. 250

    Google Scholar 

  70. M. Planck, Vorträge und Erinnerungen (Wissenschaftliche Buchgesellschaft, Darmstadt, 1975)

    Google Scholar 

  71. A. Plotnitsky, Epistemology and Probability (Springer, Dordrecht, 2010)

    Book  MATH  Google Scholar 

  72. H. Poincaré, Théorie Mathématique de la Lumière, II (Gauthier-Villars, Paris, 1892)

    Google Scholar 

  73. S. Popescu, D. Rohrlich, Generic quantum nonlocality. Phys. Lett. A 166, 293 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  74. S. Popescu, D. Rohrlich, Action and passion at a distance, in Potentiality, Entanglement and Passion-at-a-Distance, ed. by R.S. Cohen et al. (Kluwer Academic, Dordrecht, 1997), also http://xxx.lanl.govquant-ph/9605004. Accessed 3 May 1996

  75. S. Popescu, D. Rohrlich, Thermodynamics and the measure of entanglement. Phys. Rev. A 56, R3319 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  76. K.R. Popper, The argument of Einstein, Podolsky, and Rosen, in Perspectives in Quantum Theory, ed. by W. Yourgrau, A. van der Merwe (Dover, New York, 1971), Ch. 13

    Google Scholar 

  77. M.L.G. Redhead, Incompleteness, Nonlocality and Realism (Oxford University Press, Oxford, 1987)

    MATH  Google Scholar 

  78. M.L.G. Redhead, A philosopher looks at quantum field theory, in Philosophical Foundations Quantum Field Theory, ed. by H. Brown, R. Harré (Oxford University Press, Oxford, 1988), p. 9

    Google Scholar 

  79. H. Reichenbach, Philosophic Foundations of Quantum Mechanics (University of California Press, Berkeley, 1944)

    Google Scholar 

  80. T. Richter, Interference and non-classical spatial intensity correlations. Quantum Opt. 3, 115 (1991)

    Article  ADS  Google Scholar 

  81. O. Rømer, Demonstration touchant le mouvement de la lumière trouvé par M. Römer de l’ Académie Royal des Science. Le Journal des Sçavans (Dec. 1676), p. 276; A demonstration concerning the motion of light. Philosophical Transactions of the Royal Society of London Vol. XII (No. 136); cf. also Y. Saito, A discussion of Roemer’s discovery concerning the speed of light. AAPPS Bull. 15(3), 9 (2005)

    Google Scholar 

  82. Y. Saito, A discussion of Roemer’s discovery concerning the speed of light. AAPPS Bull. 15(3), 9 (2005)

    Google Scholar 

  83. J.J. Sakurai (S.F. Tuan, ed.), Modern Quantum Mechanics, Rev. edn. (Addison-Wesley, Reading, 1994)

    Google Scholar 

  84. E. Schmidt, Zur Theorie der linearen und nichtlinearen Integralgleichungen. Math. Ann. 63, 433 (1906)

    Article  Google Scholar 

  85. E. Schrödinger, Quantisierung als Eigenwertproblem (1. Mitteilung). Ann. Phys. 79, 734 (1926)

    Google Scholar 

  86. E. Schrödinger, What is an elementary particle? in Interpreting Bodies, ed. by E. Castellani (Princeton University Press, Princeton, 1998), p. 197

    Google Scholar 

  87. J.S. Schwinger (B.-G. Englert, ed.), Quantum Mechanics: Symbolism of Atomic Measurements (Springer, Heidelberg, 2001)

    Google Scholar 

  88. P. Sekatski, N. Brunner, C. Branciard, N. Gisin, C. Simon, Towards quantum experiments with human eyes as detectors based on cloning via stimulated emission. Phys. Rev. Lett. 103, 113601 (2009)

    Article  ADS  Google Scholar 

  89. C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. 27, 379 (1948); ibid. 623 (1948)

    Google Scholar 

  90. A. Shimony, Controllable and uncontrollable non-locality, in Foundations of Quantum Mechanics in Light of the New Technology, ed. by S. Kamefuchi et al. (Physical Society of Japan, Tokyo, 1983), p. 225

    Google Scholar 

  91. A. Shimony, Degree of entanglement. Ann. N. Y. Acad. Sci. 755, 675 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  92. A. Shimony, Comment on Norsen’s defense of Einstein’s ‘box argument’. Am. J. Phys. 73, 177 (2005)

    Article  ADS  Google Scholar 

  93. A. Shimony, Bell’s theorem, in The Stanford Encyclopedia of Philosophy, Summer 2009 edn., E.N. Zalka, http://plato.stanford.edu/entries/bell-theorem

  94. M.P. Silverman, Quantum Superposition (Springer, Heidelberg, 2008)

    MATH  Google Scholar 

  95. P. Speziali (ed.), Albert Einstein—Michele Besso Correspondance, 1903–1955 (Hermann, Paris, 1972). As cited in J. Stachel, Einstein and the quantum: fifty years of struggle, in From Quarks to Quasars, ed. by R.G. Colodny (University Pittsburgh Press, Pittsburgh, 1986), p. 349

    Google Scholar 

  96. J. Stachel, Einstein and the quantum: fifty years of struggle, in From Quarks to Quasars, ed. by R.G. Colodny (University Pittsburgh Press, Pittsburgh, 1986), p. 349

    Google Scholar 

  97. A. Stairs, Quantum logic and the Lüders rule. Philos. Sci. 49, 422 (1982)

    Article  MathSciNet  Google Scholar 

  98. P. Teller, An Interpretive Introduction to Quantum Field Theory (Princeton University Press, Princeton, 1995)

    MATH  Google Scholar 

  99. G. ’t Hooft, What is quantum mechanics? in Proceedings of the CP905, Frontiers of Fundamental Physics (FPP8), Eighth International Symposium, ed. by B.G. Sidharth et al. (American Institute of Physics, Melville, 2007)

    Google Scholar 

  100. R. Torretti, Relativity and Geometry (Dover, Mineola, 1996)

    Google Scholar 

  101. W. Van Dam, Nonlocality and communication complexity, Ph.D. thesis, Department of Physics, University of Oxford, 2000, Ch. 9, http://www.cs.ucsb.edu/~vandam/publications.html

  102. V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  103. G. Vidal, Entanglement monotones. J. Mod. Opt. 47, 355 (2000)

    MathSciNet  Google Scholar 

  104. G. Vidal, D. Jonathan, M.A. Nielsen, Approximate transformations and robust manipulation of bipartite pure-state entanglement. Phys. Rev. A 62, 012304 (2000)

    Article  ADS  Google Scholar 

  105. K. Von Meyenn, Pauli’s philosophical ideas, in Recasting Reality, ed. by H. Atmanspacher, H. Primas (Springer, Heidelberg, 2010), p. 11

    Google Scholar 

  106. G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, A. Zeilinger, Violation of Bell’s inequality under strict Einstein locality conditions. Phys. Rev. Lett. 81, 5039 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  107. R.F. Werner, Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)

    Article  ADS  Google Scholar 

  108. L. Wessels, The way the world isn’t: what the Bell theorems force us to give up, in Philosophical Consequences of Quantum Theory, ed. by J.T. Cushing, E. McMullin (University of Notre Dame Press, Notre Dame, 1989), p. 80

    Google Scholar 

  109. C.S. Wu, I. Shaknov, The angular correlation of scattered annihilation radiation. Phys. Rev. 77, 136 (1950)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Natural Sciences and Mathematics, Boston University, Boston, USA

    Gregg Jaeger

Authors
  1. Gregg Jaeger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Jaeger, G. (2014). Quantum Theory and Locality. In: Quantum Objects. Fundamental Theories of Physics, vol 175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37629-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37629-0_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37628-3

  • Online ISBN: 978-3-642-37629-0

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation