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The Zitterbewegung Interpretation of Quantum Mechanics The Zitterbewegung Interpretation of Quantum Mechanics Jean Louis Van Belle, Drs, MAEc, BAEc, BPhil March 2019 Contents I. Prolegomena ......................................................................................................................................... 1 The nature of space and time ................................................................................................................... 1 The Theory of Everything .......................................................................................................................... 3 Fundamental equations and physical dimensions .................................................................................... 5 What does it mean to understand an equation? .................................................................................... 10 The force law and relativity .................................................................................................................... 13 Easy wave math ...................................................................................................................................... 16 Euler’s function ....................................................................................................................................... 22 What’s the dimension of a pointlike charge? ......................................................................................... 27 II. What’s new in this book? ................................................................................................................... 28 No differential equations—only solutions!............................................................................................. 28 No Copenhagen interpretation: quantum mechanics is a theory—not a procedure ............................ 30 Understanding Einstein’s mass-energy equivalence relation ................................................................. 31 Reintroducing intuition and imagination ................................................................................................ 34 Hidden variables and black boxes: going where Bell tells us not to go .................................................. 35 Radical conceptual renewal: the double-life of −1 ................................................................................. 36 The form factor ....................................................................................................................................... 38 Planck’s constant as a vector .................................................................................................................. 38 Classical clothes and Occam’s Razor ....................................................................................................... 39 Relating amplitudes and probabilities through energy or mass densities ............................................. 39 QED versus QCD: black-and-white versus color vision ........................................................................... 40 The Higgs field: mass as a scalar field. Of course! What else would it be? ............................................ 41 III. History and acknowledgments ........................................................................................................... 41 IV. The two-dimensional oscillator .......................................................................................................... 46 The V-2 metaphor: Ducati versus Harley ................................................................................................ 46 The c = a·ω equation and the wavefunction........................................................................................... 47 Oscillator math ........................................................................................................................................ 48 The relativistic oscillator ......................................................................................................................... 50 Is the speed of light a velocity or a resonant frequency? ....................................................................... 51 The idea of the Zitterbewegung.............................................................................................................. 52 A visualization of the wavefunction ........................................................................................................ 53 Incorporating spin in the wavefunction .................................................................................................. 55 Introducing the wavefunction – and relativity ....................................................................................... 56 i V. The wavefunction and the electron .................................................................................................... 58 The Zitterbewegung model ..................................................................................................................... 58 Introducing relativity – and more! .......................................................................................................... 61 Explaining interference and diffraction .................................................................................................. 65 But what is that oscillation? .................................................................................................................... 66 A geometric interpretation of the de Broglie wavelength ...................................................................... 69 The de Broglie equation as a vector equation? ...................................................................................... 73 Fermionic versus bosonic behavior ........................................................................................................ 74 VI. The wavefunction and the atom......................................................................................................... 76 VII. The wavefunction and the photon ..................................................................................................... 82 VIII. The two-dimensional oscillator model: additional considerations .................................................... 86 IX. The fine-structure constant as a scaling constant .............................................................................. 90 X. The fine-structure constant and the classical electron radius............................................................ 92 XI. The fine-structure constant and the anomalous magnetic moment ................................................. 94 Introduction ............................................................................................................................................ 94 The new quantum physics ...................................................................................................................... 95 Classical electron models ........................................................................................................................ 98 How to test the classical electron models ............................................................................................ 100 Theoretical implications: who ordered this? ........................................................................................ 103 XII. The fine-structure constant and the fine structure .......................................................................... 104 XIII. The meaning of the wavefunction .................................................................................................... 104 Spin-zero particles do not exist! ........................................................................................................... 105 The meaning of the complex conjugate ............................................................................................... 106 Time and well-behaved functions ......................................................................................................... 106 Interpreting state vectors and absolute squares .................................................................................. 107 What’s Hermiticity? .............................................................................................................................. 109 Summary: explaining QED using classical theory .................................................................................. 109 XIV. The interference of a photon with itself ........................................................................................... 113 The interference experiment ................................................................................................................ 113 The idea of a photon ............................................................................................................................. 115 A classical explanation for the one-photon Mach-Zehnder experiment .............................................. 119 XV. The way forward ............................................................................................................................... 124 References ................................................................................................................................................ 125 Permissions: Most illustrations in this book have been created by the author or are open-source (Wikimedia Commons public domain or under the Creative Commons Attribution ShareAlike 3.0 License). The author has
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