Diracs Equation in 1+1 D from a Classical Random Walk |
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| Affiliation: | 1. Department of Statistics and Operations Researches, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia;2. Mathematics Department, College of Sciences and Humanities Studies in Al-Kharj, Prince Sattam Bin Abdulaziz University, Saudi Arabia;3. Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt;4. Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt;1. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin 10623, Germany;2. Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Simrol, Indore, Madhya Pradesh 453552 India;1. Department of Economics, Quantitative Methods and Management, University of Milano Bicocca, Piazza Ateneo Nuovo 1, Milano, 20126, Italy;2. Department of Economics and Social Sciences, Catholic University, Via Emilia Parmense 84, Piacenza, 29100, Italy;1. School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China;2. College of Electronics and Information Engineering, South-Central University for Nationalities, Wuhan 430074, China |
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| Abstract: | This paper is an investigation of the class of real classical Markov processes without a birth process that will generate the Dirac equation in 1+1 dimensions. The Markov process is assumed to evolve in an extra (ordinal) time dimension. The derivation requires that occupation by the Dirac particle of a space-time lattice site is encoded in a 4 state classical probability vector. Disregarding the state occupancy, the resulting Markov process is an homogeneous and almost isotropic binary random walk in Dirac space and Dirac time (including Dirac time reversals). It then emerges that the Dirac wavefunction can be identified with a polarization induced by the walk on the Dirac space-time lattice. The model predicts that QM observation must happen in ordinal time and that wavefunction collapse is due not to a dynamical discontinuity, but to selection of a particular ordinal time. Consequently, the model is more relativistically equitable in its treatment of space and time in that the observer is attributed no special ability to specify the Dirac time of observation. |
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