Understanding the Electron

  • Kevin H. KnuthEmail author
Part of the The Frontiers Collection book series (FRONTCOLL)


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 .


Dirac Equation Free Particle Directed Distance Particle Behavior Influence Event 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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.


  1. 1.
    Arfken, G.: Mathematical Methods for Physicists. Academic Press, Orlando, FL (1985)zbMATHGoogle Scholar
  2. 2.
    Barut, A.O., Bracken, A.J.: Magnetic-moment operator of the relativistic electron. Phys. Rev. D 24, 3333–3334 (1981)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Barut, A.O., Bracken, A.J.: Zitterbewegung and the internal geometry of the electron. Phys. Rev. D 23, 2454–2463 (1981)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Barut, A.O., Zanghi, N.: Classical model of the Dirac electron. Phys. Rev. Lett. 52, 2009–2012 (1984)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Baym, G.A.: Lectures on Quantum Mechanics. Addison-Wesley (1969)Google Scholar
  6. 6.
    Bjorken, J.D. Drell, S.D.: Relativistic Quantum Mechanics. McGraw-Hill (1964)Google Scholar
  7. 7.
    Bombelli, L., Lee, J.H., Meyer, D., Sorkin, R.: Space-time as a causal set. Phys. Rev. Lett. 59, 521–524 (1987)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Breit, G.: An interpretation of Dirac’s theory of the electron. Proc. Nat. Acad. Sci. 14(7), 553 (1928)Google Scholar
  9. 9.
    Caticha, A.: Consistency, amplitudes, and probabilities in quantum theory. Phys. Rev. A 57(3), 1572–1582 (1998)ADSCrossRefGoogle Scholar
  10. 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)ADSCrossRefGoogle Scholar
  11. 11.
    Cox, R.T.: Probability, frequency, and reasonable expectation. Am. J. Phys. 14, 1–13 (1946)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    De Broglie, L.: Recherches sur la théorie des quanta. Ph.D. thesis, Migration-université en cours d’affectation (1924)Google Scholar
  13. 13.
    Earle, K.A.: A master equation approach to the ‘3 + 1’ Dirac equation. (arXiv:1102.1200 [math-ph]) (2011)
  14. 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. 15.
    Feynman, R.P., Hibbs, A.R.: Quantum mechanics and path integrals. McGraw-Hill, New York (1965)Google Scholar
  16. 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)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. 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)ADSCrossRefGoogle Scholar
  18. 18.
    Gersch, H.A.: Feynman’s relativistic chessboard as an Ising model. Int. J. Theor. Phys. 20(7), 491–501 (1981)CrossRefGoogle Scholar
  19. 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. 20.
    Goyal, P., Knuth, K.H.: Quantum theory and probability theory: their relationship and origin in symmetry. Symmetry 3(2), 171–206 (2011)MathSciNetCrossRefGoogle Scholar
  21. 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. 22.
    Gull, S., Lasenby, A., Doran, C.: Electron paths, tunnelling, and diffraction in the spacetime algebra. Found. Phys. 23(10), 1329–1356 (1993)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Hestenes, D.: The Zitterbewegung interpretation of quantum mechanics. Found. Phys. 20(10), 1213–1232 (1990)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Hestenes, D.: Zitterbewegung modeling. Found. Phys. 23(3), 365–387 (1993)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Hestenes, D.: Electron time, mass and zitter. “The Nature of Time” FQXi 2008 Essay Contest (2008)Google Scholar
  26. 26.
    Hestenes, D.: Zitterbewegung in quantum mechanics. Found. Phys. 40(1), 1–54 (2010)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Huang, K.: On the Zitterbewegung of the Dirac electron. Am. J. Phys. 20, 479 (1952)ADSCrossRefzbMATHGoogle Scholar
  28. 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)CrossRefGoogle Scholar
  29. 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. 30.
    Kauffman, L.H., Noyes, H.P.: Discrete physics and the Dirac equation. Phys. Lett. A 218(3), 139–146 (1996)ADSCrossRefGoogle Scholar
  31. 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 []) (2004)
  32. 32.
    Knuth, K.H.: Information-based physics: an observer-centric foundation. Contemporary Phys. 55(1), 12–32, (arXiv:1310.1667 [quant-ph]) (2014)
  33. 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. 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. 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. 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. 37.
    Knuth, K.H., Skilling, J.: Foundations of inference. Axioms 1(1), 38–73 (2012)CrossRefzbMATHGoogle Scholar
  38. 38.
    Kull, A.: Quantum mechanical motion of relativistic particle in non-continuous spacetime. Phys. Lett. A 303(2), 147–153 (2002)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. 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. 40.
    Merzbacher, E.: Quantum Mechanics (1998)Google Scholar
  41. 41.
    Ord, G.N., Gualtieri, J.A.: The Feynman propagator from a single path. Phys. Rev. Lett. 89(25), 250403–250406 (2002)ADSCrossRefGoogle Scholar
  42. 42.
    Ord, G.N., McKeon, D.G.C.: On the Dirac equation in 3+1 dimensions. Ann. Phys. 222(2), 244–253 (1993)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Pfanzagl, J.: Theory of Measurement. Wiley (1968)Google Scholar
  44. 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. 45.
    Rodrigues, Jr. W.A., Vaz, Jr. J., Recami, E., Salesi, G.: About Zitterbewegung and Electron Structure (1998)Google Scholar
  46. 46.
    Salesi, G., Recami, E.: Field theory of the spinning electron and internal motions. Phys. Rev. A 190(2), 137–143 (1994)MathSciNetzbMATHGoogle Scholar
  47. 47.
    Schrödinger, E.: Über die kräftefreie bewegung in der relativistischen quantenmechanik. Akademie der wissenschaften in kommission bei W. de Gruyter u, Company (1930)zbMATHGoogle Scholar
  48. 48.
    Schumacher, B., Westmoreland, M.: Quantum Processes, Systems, and information. Cambridge University Press (2010)Google Scholar
  49. 49.
    Sidharth, B.G.: Revisiting zitterbewegung. Int. J. Theor. Phys. 48(2), 497–506 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  50. 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. 51.
    Sorkin, R.D.: Geometry from order: causal sets. In: Einstein Online, vol. 2, 1007, (2006)
  52. 52.
    Thomson, J.J.: Cathode rays. The Electrician 39, 104–109 (1897)Google Scholar
  53. 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. 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)ADSCrossRefGoogle Scholar
  55. 55.
    Wheeler, J.A., Feynman, R.P.: Classical electrodynamics in terms of direct interparticle action. Rev. Mod. Phys. 21(3), 425–433 (1949)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. 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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© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.University at AlbanyAlbanyUSA

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