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Understanding the Electron

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Information and Interaction

Part of the book series: The Frontiers Collection ((FRONTCOLL))

Abstract

Whether it is the crack and snap of an electric shock on a cold winter day or the boom and crash of a lightning bolt on a stormy summer afternoon, we are familiar with electrons because they influence us. Similarly, scientists know about electrons because they influence their measurement equipment .

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Notes

  1. 1.

    If all one can detect is the occurrence of an influence event, how can anything ever be known about the relation between those events and any internal states of the particle?

  2. 2.

    If the particle states were accessible, then we could alternatively describe the particle as a totally ordered chain of particle states.

  3. 3.

    An event z covers an event x if \(x < z\) and there does not exist any y such that \(x < y\) and \(y < z\).

  4. 4.

    As an example, given events \(p_1< p_2< p_3< \cdots < p_{12}\) along the chain \({\mathbf {P}}\), the map \(\phi \) which gives \(\phi (p_1) = \phi (p_2) = \phi (p_3)< \phi (p_4) = \phi (p_5) = \phi (p_6)< \phi (p_7) = \phi (p_8) = \phi (p_9) < \phi (p_{10}) = \phi (p_{11}) = \phi (p_{12})\) is a valid coarse-graining map.

  5. 5.

    The event x is said to be incomparable to the event y if it is true that \(x \nleq y\) and \(y \nleq x\).

  6. 6.

    The two events defining the interval are assumed to be collinear to the coordinated pair of observers. This is precisely defined in [36] in terms of projections.

  7. 7.

    Please see [36] for technical details.

  8. 8.

    Directed distance differs from distance by at most a sign, which indicates the orientation of the interval with respect to the observers \({\mathbf {P}}\) and \({\mathbf {Q}}\).

  9. 9.

    This observation was made by James L. Walsh.

  10. 10.

    It is important to note that the case where both rates are zero would result in not only zero mass but also zero energy and momentum. Such a particle would not influence anything and would therefore be unobserved.

  11. 11.

    By ‘position’ and ‘time’, we mean the directed distance and duration with respect to a defined origin.

  12. 12.

    Our initial studies of influenced particles indicate that one needs four complex numbers and that they appear to take the form of a Dirac spinor with the positive energy components representing the amplitudes for the particle to influence and the negative energy components representing the amplitudes for the particle to be influenced.

References

  1. Arfken, G.: Mathematical Methods for Physicists. Academic Press, Orlando, FL (1985)

    MATH  Google Scholar 

  2. Barut, A.O., Bracken, A.J.: Magnetic-moment operator of the relativistic electron. Phys. Rev. D 24, 3333–3334 (1981)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Barut, A.O., Bracken, A.J.: Zitterbewegung and the internal geometry of the electron. Phys. Rev. D 23, 2454–2463 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  4. Barut, A.O., Zanghi, N.: Classical model of the Dirac electron. Phys. Rev. Lett. 52, 2009–2012 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  5. Baym, G.A.: Lectures on Quantum Mechanics. Addison-Wesley (1969)

    Google Scholar 

  6. Bjorken, J.D. Drell, S.D.: Relativistic Quantum Mechanics. McGraw-Hill (1964)

    Google Scholar 

  7. Bombelli, L., Lee, J.H., Meyer, D., Sorkin, R.: Space-time as a causal set. Phys. Rev. Lett. 59, 521–524 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  8. Breit, G.: An interpretation of Dirac’s theory of the electron. Proc. Nat. Acad. Sci. 14(7), 553 (1928)

    Google Scholar 

  9. Caticha, A.: Consistency, amplitudes, and probabilities in quantum theory. Phys. Rev. A 57(3), 1572–1582 (1998)

    Article  ADS  Google Scholar 

  10. Catillon, P., Cue, N., Gaillard, M.J., Genre, R., Gouanère, M., Kirsch, R.G., Poizat, J.C., Remillieux, J., Roussel, L., Spighel, M.: A search for the de Broglie particle internal clock by means of electron channeling. Found. Phys. 38(7), 659–664 (2008)

    Article  ADS  Google Scholar 

  11. Cox, R.T.: Probability, frequency, and reasonable expectation. Am. J. Phys. 14, 1–13 (1946)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. De Broglie, L.: Recherches sur la théorie des quanta. Ph.D. thesis, Migration-université en cours d’affectation (1924)

    Google Scholar 

  13. Earle, K.A.: A master equation approach to the ‘3 + 1’ Dirac equation. (arXiv:1102.1200 [math-ph]) (2011)

  14. Feshbach, H., Villars, F.: Elementary relativistic wave mechanics of spin 0 and spin 1/2 particles. Rev. Mod. Phys. 30(1), 24 (1958)

    Google Scholar 

  15. Feynman, R.P., Hibbs, A.R.: Quantum mechanics and path integrals. McGraw-Hill, New York (1965)

    Google Scholar 

  16. Gaveau, B., Schulman, L.S.: A projector path integral for the Dirac equation and the spin derivation of space. Ann. Phys. 284(1), 1–9 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Gerritsma, R., Kirchmair, G., Zähringer, F., Solano, E., Blatt, R., Roos, C.F.: Quantum simulation of the Dirac equation. Nature 463(7277), 68–71 (2010)

    Article  ADS  Google Scholar 

  18. Gersch, H.A.: Feynman’s relativistic chessboard as an Ising model. Int. J. Theor. Phys. 20(7), 491–501 (1981)

    Article  Google Scholar 

  19. Gouanère, M., Spighel, M., Cue, N., Gaillard, M.J., Genre, R., Kirsch, R., Poizat, J.C., Remillieux, J., Catillon, P., Roussel, L.: Experimental observations compatible with the particle internal clock. Annales de la Fondation Louis de Broglie 30(1), 109–14 (2005)

    Google Scholar 

  20. Goyal, P., Knuth, K.H.: Quantum theory and probability theory: their relationship and origin in symmetry. Symmetry 3(2), 171–206 (2011)

    Article  MathSciNet  Google Scholar 

  21. Goyal, P., Knuth, K.H., Skilling, J.: Origin of complex quantum amplitudes and Feynman’s rules. Phys. Rev. A 81, 022109, (arXiv:0907.0909 [quant-ph]) (2010)

  22. Gull, S., Lasenby, A., Doran, C.: Electron paths, tunnelling, and diffraction in the spacetime algebra. Found. Phys. 23(10), 1329–1356 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  23. Hestenes, D.: The Zitterbewegung interpretation of quantum mechanics. Found. Phys. 20(10), 1213–1232 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  24. Hestenes, D.: Zitterbewegung modeling. Found. Phys. 23(3), 365–387 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  25. Hestenes, D.: Electron time, mass and zitter. “The Nature of Time” FQXi 2008 Essay Contest (2008)

    Google Scholar 

  26. Hestenes, D.: Zitterbewegung in quantum mechanics. Found. Phys. 40(1), 1–54 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Huang, K.: On the Zitterbewegung of the Dirac electron. Am. J. Phys. 20, 479 (1952)

    Article  ADS  MATH  Google Scholar 

  28. Jacobson, T.: Feynman’s checkerboard and other games. In: Sanchez, N. (ed.) Non-Linear Equations in Classical and Quantum Field Theory, pp. 386–395. Springer, Berlin Heidelberg (1985)

    Chapter  Google Scholar 

  29. Jaynes, E.T.: The evolution of Carnot’s principle. In: Erickson, G.J., Smith, C.R. (eds.) Maximum Entropy and Bayesian Methods in Science and Engineering, vol. 1, pp. 267–281. Springer (1988)

    Google Scholar 

  30. Kauffman, L.H., Noyes, H.P.: Discrete physics and the Dirac equation. Phys. Lett. A 218(3), 139–146 (1996)

    Article  ADS  Google Scholar 

  31. Knuth, K.H.: Deriving laws from ordering relations. In: Zhai, Y., Erickson, G.J. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, pp. 204–235. Jackson Hole WY, USA, August 2003, AIP Conf. Proc. 707, AIP, New York, (arXiv:physics/0403031v1 [physics.data-an]) (2004)

  32. Knuth, K.H.: Information-based physics: an observer-centric foundation. Contemporary Phys. 55(1), 12–32, (arXiv:1310.1667 [quant-ph]) (2014)

  33. Knuth, K.H.: The problem of motion: the statistical mechanics of Zitterbewegung. In: Mohammad-Djafari, A., Barbaresco, F. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering. Amboise, FRANCE, AIP, New York (2014)

    Google Scholar 

  34. Knuth, K.H.: Information-based physics and the influence network. In: Aguirre, A., Foster, B., Merali, Z. (eds.) Bit or Bit from It? On Physics and Information, pp. 65–78. Springer Frontiers Collection, Springer, Heidelberg, FQXi 2013 Essay Contest (Third Prize), (arXiv:1308.3337 [quant-ph]) (2015)

  35. Knuth, K.H.: The deeper roles of mathematics in physical laws. In press, FQXi 2015 Essay Contest (Third Prize), (arXiv:1504.06686 [math.HO]) (2016)

  36. Knuth, K.H., Bahreyni, N.: A potential foundation for emergent space-time. J. Math. Phys. 55, 112501, (arXiv:1209.0881 [math-ph]) (2014)

  37. Knuth, K.H., Skilling, J.: Foundations of inference. Axioms 1(1), 38–73 (2012)

    Article  MATH  Google Scholar 

  38. Kull, A.: Quantum mechanical motion of relativistic particle in non-continuous spacetime. Phys. Lett. A 303(2), 147–153 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. LeBlanc, L.J., Beeler, M.C., Jimenez-Garcia, K., Perry, A.R., Sugawa, S., Williams, R.A., Spielman, I.B.: Direct observation of zitterbewegung in a Bose–Einstein condensate. New J. Phys. 15(7), 073011 (2013)

    Google Scholar 

  40. Merzbacher, E.: Quantum Mechanics (1998)

    Google Scholar 

  41. Ord, G.N., Gualtieri, J.A.: The Feynman propagator from a single path. Phys. Rev. Lett. 89(25), 250403–250406 (2002)

    Article  ADS  Google Scholar 

  42. Ord, G.N., McKeon, D.G.C.: On the Dirac equation in 3+1 dimensions. Ann. Phys. 222(2), 244–253 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. Pfanzagl, J.: Theory of Measurement. Wiley (1968)

    Google Scholar 

  44. Qu, C., Hamner, C., Gong, M., Zhang, C., Engels, P.: Observation of Zitterbewegung in a spin-orbit-coupled Bose-Einstein condensate. Phys. Rev. A 88(2), 021604 (2013)

    Google Scholar 

  45. Rodrigues, Jr. W.A., Vaz, Jr. J., Recami, E., Salesi, G.: About Zitterbewegung and Electron Structure (1998)

    Google Scholar 

  46. Salesi, G., Recami, E.: Field theory of the spinning electron and internal motions. Phys. Rev. A 190(2), 137–143 (1994)

    MathSciNet  MATH  Google Scholar 

  47. Schrödinger, E.: Über die kräftefreie bewegung in der relativistischen quantenmechanik. Akademie der wissenschaften in kommission bei W. de Gruyter u, Company (1930)

    MATH  Google Scholar 

  48. Schumacher, B., Westmoreland, M.: Quantum Processes, Systems, and information. Cambridge University Press (2010)

    Google Scholar 

  49. Sidharth, B.G.: Revisiting zitterbewegung. Int. J. Theor. Phys. 48(2), 497–506 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  50. Sorkin, R.D.: Causal sets: discrete gravity. In: Gomberoff, A., Marolf, D. (eds.) Lectures on Quantum Gravity, pp. 305–327. Springer US, (arXiv:gr-qc/0309009) (2005)

  51. Sorkin, R.D.: Geometry from order: causal sets. In: Einstein Online, vol. 2, 1007, http://www.einstein-online.info/spotlights/causal_sets (2006)

  52. Thomson, J.J.: Cathode rays. The Electrician 39, 104–109 (1897)

    Google Scholar 

  53. Walsh, J.L., Knuth, K.H.: Information-based physics, influence, and forces. In: Mohammad-Djafari, A., Barbaresco, F. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering. Amboise, France, AIP Conf. Proc., AIP, New York (2014)

    Google Scholar 

  54. Wheeler, J.A., Feynman, R.P.: Interaction with the absorber as the mechanism of radiation. Rev. Mod. Phys. 17(2–3), 157–181 (1945)

    Article  ADS  Google Scholar 

  55. Wheeler, J.A., Feynman, R.P.: Classical electrodynamics in terms of direct interparticle action. Rev. Mod. Phys. 21(3), 425–433 (1949)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  56. Zawadzki, W., Rusin, T.M.: Zitterbewegung (trembling motion) of electrons in semiconductors: a review. J. Phys. Condensed Matt. 23(14), 143201 (2011)

    Google Scholar 

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Acknowledgements

I would like to thank Newshaw Bahreyni, Seth Chaiken, Ariel Caticha, Keith Earle, David Hestenes, Oleg Lunin, John Skilling, and James Lyons Walsh for numerous insightful discussions. I also want to specifically thank James Lyons Walsh for his careful proofreading of this manuscript and his invaluable comments.

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  1. University at Albany, Albany, NY, USA

    Kevin H. Knuth

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  1. Kevin H. Knuth
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Correspondence to Kevin H. Knuth .

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Editors and Affiliations

  1. Physics Department, Saint Anselm College, Manchester, New Hampshire, USA

    Ian T. Durham

  2. Unit for History and Philosophy of Science, University of Sydney, Carslaw, Australia

    Dean Rickles

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Knuth, K.H. (2017). Understanding the Electron. In: Durham, I., Rickles, D. (eds) Information and Interaction. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-43760-6_10

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