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The Zitterbewegung Interpretation of Quantum Mechanics

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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 Cover picture by Jason Hise “Bring forward what is true. Write it so that it is clear. Defend it to your last breath.” ― Ludwig Boltzmann Contents Introduction .................................................................................................................................................. 1 Wild games ................................................................................................................................................ 1 Tame games .............................................................................................................................................. 1 Real games ................................................................................................................................................ 2 So, what is it all about? ............................................................................................................................. 5 For the professional physicist ................................................................................................................... 6 I. Prolegomena ......................................................................................................................................... 9 The nature of space and time ................................................................................................................... 9 The Theory of Everything: U = 0 ............................................................................................................. 11 Fundamental equations .......................................................................................................................... 14 Physical dimensions ................................................................................................................................ 16 What does it mean to understand an equation? .................................................................................... 20 The force law and relativity .................................................................................................................... 24 Easy wave math ...................................................................................................................................... 28 Euler’s function ....................................................................................................................................... 33 What’s the dimension of a pointlike charge? ......................................................................................... 39 II. What’s new in this book? ................................................................................................................... 41 No differential equations—only solutions!............................................................................................. 41 No Copenhagen interpretation: quantum mechanics is a theory—not a procedure ............................ 43 Understanding Einstein’s mass-energy equivalence relation ................................................................. 44 Reintroducing intuition and imagination ................................................................................................ 46 Hidden variables and black boxes: going where Bell tells us not to go .................................................. 48 Radical conceptual renewal: the double-life of −1 ................................................................................. 49 The form factor ....................................................................................................................................... 51 Planck’s constant as a vector .................................................................................................................. 51 Classical clothes and Occam’s Razor ....................................................................................................... 52 Relating amplitudes and probabilities through energy or mass densities ............................................. 52 QED versus QCD: black-and-white versus color vision ........................................................................... 53 The Higgs field: mass as a scalar field—of course! ................................................................................. 54 III. History and acknowledgments ........................................................................................................... 55 IV. The two-dimensional oscillator .......................................................................................................... 61 The V-2 metaphor: Ducati versus Harley ................................................................................................ 61 The c = a·ω equation and the wavefunction........................................................................................... 62 Oscillator math ........................................................................................................................................ 63 The relativistic oscillator ......................................................................................................................... 64 Is the speed of light a velocity or a resonant frequency? ....................................................................... 65 The idea of the Zitterbewegung.............................................................................................................. 67 A visualization of the wavefunction ........................................................................................................ 67 Incorporating spin in the wavefunction .................................................................................................. 69 Introducing the wavefunction – and relativity ....................................................................................... 70 V. The wavefunction and the electron .................................................................................................... 73 The Zitterbewegung model ..................................................................................................................... 73 Introducing relativity – and more! .......................................................................................................... 76 ii Explaining interference and diffraction .................................................................................................. 80 But what is that oscillation? .................................................................................................................... 80 A geometric interpretation of the de Broglie wavelength ...................................................................... 84 The de Broglie equation as a vector equation? ...................................................................................... 88 Fermionic versus bosonic behavior ........................................................................................................ 89 VI. The Zitterbewegung and the Uncertainty Principle ........................................................................... 92 The Zitterbewegung interpretation of an electron: recap ...................................................................... 92 Interpreting the de Broglie wavelength .................................................................................................. 93 Introducing uncertainty .......................................................................................................................... 96 Planck’s quantum of action as a vector .................................................................................................. 97 Modeling uncertainty.............................................................................................................................. 97 Planck’s quantum of action as a vector (2) ............................................................................................. 99 How can we test this? ........................................................................................................................... 100 VII. The wavefunction and the atom....................................................................................................... 102 VIII. The wavefunction and the photon ................................................................................................... 108 IX. The two-dimensional oscillator model: additional considerations .................................................. 112 X. The fine-structure constant as a scaling constant ............................................................................ 116 XI. The fine-structure constant and the classical electron radius.......................................................... 119 XII. The fine-structure constant and the anomalous magnetic moment ............................................... 121 Introduction .......................................................................................................................................... 121 The new quantum physics .................................................................................................................... 122 Classical electron models ...................................................................................................................... 125 How to test the classical electron models ...........................................................................................
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