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There are no particles, there are only fields
1. M. Schlosshauer, Elegance and Enigma: The Quantum Interviews (Springer-Verlag, Berlin, 2011).
3. W. Zurek, “ Decoherence and the transition from quantum to classical,” Phys. Today 44(10 ), 36–44 (1991): “Quantum mechanics works exceedingly well in all practical applications…Yet well over half a century after its inception, the debate about the relation of quantum mechanics to the familiar physical world continues. How can a theory that can account with precision for everything we can measure still be deemed lacking?"
4. C. Sagan, The Demon-Haunted World: Science as a Candle in the Dark (Random House, New York, 1995), p. 26: “We've arranged a civilization in which most crucial elements profoundly depend on science and technology. We have also arranged things so that almost no one understands science and technology. This is a prescription for disaster…Sooner or later this combustible mixture of ignorance and power is going to blow up in our faces.”
5. M. Shermer, “ Quantum Quackery,” Sci. Am. 292(1 ), 34 (2005).
6. V. Stenger, “ Quantum Quackery,” Sceptical Inquirer 21(1 ), 37–42 (1997). It's striking that this article has, by coincidence, the same title as Ref. 5.
7. D. Chopra, Quantum Healing: Exploring the Frontiers of Mind/Body Medicine (Bantam, New York, 1989).
8. D. Chopra, Ageless Body, Timeless Mind: The Quantum Alternative to Growing Old (Harmony Books, New York, 1993).
9. B. Rosenblum and F. Kuttner, Quantum Enigma: Physics Encounters Consciousness (Oxford U.P., New York, 2006).
10. S. Weinberg, Dreams of a Final Theory: The Search for the Fundamental Laws of Nature (Random House, Inc., New York, 1992): “Furthermore, all these particles are bundles of the energy, or quanta, of various sorts of fields. A field like an electric or magnetic field is a sort of stress in space. The equations of a field theory like the Standard Model deal not with particles but with fields; the particles appear as manifestations of those fields” (p. 25).
11. S. Weinberg, Facing Up: Science and its Cultural Adversaries (Harvard U.P., Cambridge, MA, 2001): “Just as there is an electromagnetic field whose energy and momentum come in tiny bundles called photons, so there is an electron field whose energy and momentum and electric charge are found in the bundles we call electrons, and likewise for every species of elementary particles. The basic ingredients of nature are fields; particles are derivative phenomena.”
12. R. Mills, Space, Time, and Quanta: An Introduction to Modern Physics (W. H. Freeman, New York, 1994), Chap. 16: “The only way to have a consistent relativistic theory is to treat all the particles of nature as the quanta of fields, like photons. Electrons and positrons are to be treated as the quanta of the electron-positron field, whose ‘classical' field equation, the analog of Maxwell's equations for the EM field, turns out to be the Dirac equation, which started life as a relativistic version of the single-particle Schrödinger equation.…This approach now gives a unified picture, known as quantum field theory, of all of nature.”
13. F. Wilczek, “ Mass Without Mass I: Most of Matter,” Phys. Today 52(11 ), 11–13 (1999): “In quantum field theory, the primary elements of reality are not individual particles, but underlying fields. Thus, e.g., all electrons are but excitations of an underlying field,… the electron field, which fills all space and time.”
14. M. Redhead, “ More ado about nothing,” Found. Phys. 25(1 ), 123–137 (1995): “Particle states are never observable—they are an idealization which leads to a plethora of misunderstandings about what is going on in quantum field theory. The theory is about fields and their local excitations. That is all there is to it.”
15. A. Zee, Quantum Field Theory in a Nutshell (Princeton U.P., Princeton, NJ, 2003), p. 24: “We thus interpret the physics contained in our simple field theory as follows: In region 1 in spacetime there exists a source that sends out a ‘disturbance in the field,' which is later absorbed by a sink in region 2 in spacetime. Experimentalists choose to call this disturbance in the field a particle of mass m.”
16. F. Wilczek, “ The persistence of ether,” Phys. Today 52(1 ), 11–13 (1999).
18. F. Wilczek, The Lightness of Being: Mass, Ether, and the Unification of Forces (Basic Books, New York, 2008).
19. R. Brooks, Fields of Color: The Theory That Escaped Einstein, 2nd ed. (Rodney A. Brooks, Prescott, AZ, 2011). This is a lively history of classical and quantum fields, with many quotations from leading physicists, organized to teach quantum field theory to the general public.
20. P. R. Wallace, Paradox Lost: Images of the Quantum (Springer-Verlag, New York, 1996).
21. A. Hobson, “ Electrons as field quanta: A better way to teach quantum physics in introductory general physics courses,” Am. J. Phys. 73, 630–634 (2005);
22. A. Hobson, Physics: Concepts & Connections (Addison-Wesley/Pearson, San Francisco, 2010).
23. R. Feynman, The Character of Physical Law (MIT Press, Cambridge, MA, 1965), p. 129. Feynman also says, in the same lecture, “I think I can safely say that nobody understands quantum mechanics.”
24. A. Janiak, Newton: Philosophical Writings (Cambridge U.P., Cambridge, 2004), p. 102.
25. N. J. Nersessian, Faraday to Einstein: Constructing Meaning in Scientific Theories (Martinus Nijhoff Publishers, Boston, 1984), p. 37. The remainder of Sec. III relies strongly on this book.
26.S. Weinberg, Ref. 11, p. 167: “Fields are conditions of space itself, considered apart from any matter that may be in it.”
27.This argument was Maxwell's and Einstein's justification for the reality of the EM field. R. H. Stuewer, Ed., Historical and Philosophical Perspectives of Science (Gordon and Breach, New York, 1989), p. 299.
28. A. Einstein, “ Maxwell's influence on the development of the conception of physical reality,” in James Clerk Maxwell: A Commemorative Volume 1831–1931 (The Macmillan Company, New York, 1931), pp. 66–73.
29. A. Einstein, “ Zur Elektrodynamik bewegter Koerper,” Ann. Phys. 17, 891–921 (1905).
30. I. Newton, Optiks (4th edition, W. Innys, 1730): “It seems probable to me that God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles…and that these primitive particles being solids are incomparably harder than any porous bodies compounded of them, even so hard as never to wear or break in pieces…”
31.R. Brooks, author of Ref. 19, private communication.
34. M. Kuhlmann, The Ultimate Constituents Of The Material World: In Search Of An Ontology For Fundamental Physics (Ontos Verlag, Heusenstamm, Germany, 2010), Chap. 4; a brief but detailed history of QFT.
35.The first comprehensive account of a general theory of quantum fields, in particular the method of canonical quantization, was presented in W. Heisenberg and W. Pauli, “ Zur quantendynamik der Wellenfelder,” Z. Phys. 56, 1–61 (1929).
36. E. G. Harris, A Pedestrian Approach to Quantum Field Theory (Wiley-Interscience, New York, 1972).
37.More precisely, there are two vector modes for each nonzero k, one for each possible field polarization direction, both perpendicular to k. See Ref. 36 for other details.
38.For example, L. H. Ryder, Quantum Field Theory (Cambridge U.P., Cambridge, 1996), p 131: “This completes the justification for interpreting N(k) as the number operator and hence for the particle interpretation of the quantized theory.”
39. H. D. Zeh, “ There are no quantum jumps, nor are there particles!,” Phys. Lett. A 172, 189–195 (1993): “All particle aspects observed in measurements of quantum fields (like spots on a plate, tracks in a bubble chamber, or clicks of a counter) can be understood by taking into account this decoherence of the relevant local (i.e. subsystem) density matrix.”
40. C. Blood, “No evidence for particles,” http://arxiv.org/pdf/0807.3930.pdf: “There are a number of experiments and observations that appear to argue for the existence of particles, including the photoelectric and Compton effects, exposure of only one film grain by a spread-out photon wave function, and particle-like trajectories in bubble chambers. It can be shown, however, that all the particle-like phenomena can be explained by using properties of the wave functions/state vectors alone. Thus there is no evidence for particles. Wave-particle duality arises because the wave functions alone have both wave-like and particle-like properties.”
43. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U.P., New York, 1995).
44. R. E. Peierls, Surprises in Theoretical Physics (Princeton U.P., Princeton, 1979), pp. 12–14.
45. M. G. Raymer and B. J. Smith, “ The Maxwell wave function of the photon,” in SPIE Conference on Optics and Photonics, San Diego, Aug 2005, Conf #5866: The Nature of Light.
46.Molecules, atoms, and protons are excitations of “composite fields” made of the presumably fundamental Standard Model fields.
47.The Dirac field is a four-component relativistic “spinor” field Ψi(x, t) (i = 1, 2, 3, 4).
48. R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lectures on Physics, Vol. I (Addison-Wesley Publishing Co., Reading, MA, 1963), Chap. 37, p. 2: “[The 2-slit experiment is] a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot explain the mystery in the sense of 'explaining' how it works. We will tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics.” (The italics are in the original.)
49. Nick Herbert, Quantum Reality: Beyond the New Physics (Doubleday, New York, 1985), pp. 60–67; conceptual discussion of the wave-particle duality of electrons.
50. Wolfgang Rueckner and Paul Titcomb, “ A lecture demonstration of single photon interference,” Am J. Phys. 64(2 ), 184–188 (1996).
51. A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Exawa, “ Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57(2 ), 117–120 (1989).
52. Michler et al., “ A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
53.For a more formal argument, see A. J. Leggett, “ Testing the limits of quantum mechanics: Motivation, state of play, prospects,” J. Phys: Condensed Matter 14, R415–R451 (2002).
54. P. A. M. Dirac, The Principles of Quantum Mechanics, 3rd ed. (Oxford at the Clarendon Press, Oxford, 1947), p. 9. The quoted statement appears in the 2nd, 3rd, and 4th editions, published respectively in 1935, 1947, and 1958.
55. J. von Neumann, The Mathematical Foundations of Quantum Mechanics (Princeton U.P., Princeton, 1955), p. 351.
56.The central feature of this analysis, namely how decoherence localizes the quantum, was first discussed in W. K. Wootters and W. H. Zurek, “ Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle,” Phys. Rev. D 19, 473–484 (1979).
57. M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition (Springer-Verlag, Berlin, 2007), pp. 63–65.
59. A. Einstein, B. Podolsky, and N. Rosen, “ Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47(10 ), 777–780 (1935).
60. J. Bell, “ On the Einstein Podolsky Rosen Paradox,” Physics 1(3 ), 195–200 (1964).
61. A. Aspect, “ To be or not to be local,” Nature 446, 866–867 (2007);
61. G. C. Ghirardi, “ The interpretation of quantum mechanics: where do we stand?” Fourth International Workshop DICE 2008, J. Phys.: Conf. Series 174, 012013 (2009).
62. L. E. Ballentine and J. P. Jarrett, “ Bell's theorem: Does quantum mechanics contradict relativity?” Am. J. Phys. 55(8 ), 696–701 (1987).
63. G. C. Hegerfeldt, “ Particle localization and the notion of Einstein causality,” in Extensions of Quantum Theory 3, edited by A. Horzela and E. Kapuscik (Apeiron, Montreal, 2001), pp. 9–16;
63. G. C. Hegerfeldt, “ Instantaneous spreading and Einstein causality in quantum theory,” Ann. Phys. 7, 716–725 (1998);
63. G. C. Hegerfeldt, “ Remark on causality and particle localization,” Phys. Ref. D 10, 3320–3321 (1974).
64. D. B. Malament, “ In defense of dogma: why there cannot be a relativistic QM of localizable particles,” in Perspectives on Quantum Reality (Kluwer Academic Publishers, Netherlands, 1996), pp. 1–10. See also Refs. 34 and 65.
66. Rafael de la Madrid, “ Localization of non-relativistic particles,” Int. J. Theor. Phys. 46, 1986–1997 (2007). Hegerfeldt's result for relativistic particles generalizes Madrid's result.
67. P. H. Eberhard and R. R. Ross, “ Quantum field theory cannot provide faster-than-light communication,” Found. Phys. Lett. 2, 127–148 (1989).
68.In other words, the Schrödinger equation can be quantized, just like the Dirac equation. But the quantized version implies nothing that isn't already in the non-quantized version. See Ref. 36.
69. S. Weinberg, Elementary Particles and the Laws of Physics, The 1986 Dirac Memorial Lectures (Cambridge U.P., Cambridge, 1987), pp. 78–79: “Although it is not a theorem, it is widely believed that it is impossible to reconcile quantum mechanics and relativity, except in the context of a quantum field theory.”
70. Michael Redhead, “ A philosopher looks at quantum field theory,” in Philosophical Foundations of Quantum Field Theory, edited by Harvey R. Brown and Rom Harre (Oxford U.P., 1988), pp. 9–23: “What is the nature of the QFT vacuum? In the vacuum state… there is still plenty going on, as evidenced by the zero-point energy…[which] reflects vacuum fluctuations in the field amplitude. These produce observable effects…I am now inclined to say that vacuum fluctuation phenomena show that the particle picture is not adequate to QFT. QFT is best understood in terms of quantized excitations of a field and that is all there is to it.”
72.My main source for Secs. VI A and VI B is Peter W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic Press Limited, London, 1994).
76. B. S. DeWitt, “ Quantum gravity: the new synthesis,” in General Relativity: An Einstein Centenary, edited by S. Hawking and W. Israel (Cambridge U.P., Cambridge, 1979), pp. 680–745.
77. M. Jammer, The Philosophy of Quantum Mechanics (Wiley-Interscience, New York, 1974), pp. 115–118.
79. M. O. Terra Cunha, J.A. Dunningham, and V. Vedral, “ Entanglement in single-particle systems,” Proc. R. Soc. A 463, 2277–2286 (2007): “If we want to increase the breadth of applicability of entanglement, we should think in terms of fields which are a fundamental description of nature. Particles are only a manifestation of certain special configurations of quantum fields. If entanglement is to be considered a fundamental property of nature, and even a resource to be understood and applied, one would like to understand entangled fields.”
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