BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chantal Roth (ETH Graduated) DTSTART:20230709T180000Z DTEND:20230709T190000Z DTSTAMP:20260409T220711Z UID:HCS2023/9 DESCRIPTION:Title: Quaternionic foundations of Quantum Mechanics and spin 1/2 visualization\nby Chantal Roth (ETH Graduated) as part of Hypercomplex Seminar 2023\n \n\nAbstract\nThis talk explores the intriguing link between quaternion qu antum mechanics and the\nmodel of the elastic continuum proposed by August in Cauchy\, highlighting the potential of this interdisciplinary connectio n to advance our understanding of quantum physics. We elucidate the deriva tion\nof non- and relativistic wave equations from the Cauchy theory and H amilton quaternion algebra\,\ndemonstrating how the quaternion representat ion of the elastic continuum provides a comprehensive\npicture of quantum mechanics. This innovative interpretation addresses the ontological challe nges often\nassociated with quantum theory\, offering a means to generaliz e and test the theory.\nTransitioning from the theoretical to the practica l\, we delve into a unique visualization of spinors\nusing quaternions. We elucidate how the quaternionic representation enables a comprehension of the\nDirac equation and the concept of spin 1/2\, pivotal to the Planck-Kl einert model and the Pauli Exclusion\nPrinciple. We present an interactive simulation of a periodically twisting 3D grid\, visualizing the spin\n1/2 behavior of fermions in an elastic solid.\n\nBy visualizing Dirac spinors using two orthogonal quaternions\, we illuminate the complex rotation\nbe havior of spin 1/2 particles\, drawing analogies with the famous Dirac bel t trick. We define two quaternion functions that represent rotations as fu nctions of time and distance\, respectively. The visualization of the resu ltant spinor function as a series of concentric shells offers a illuminati ng representation of quantum spin\, enhancing our understanding of its beh avior in both time and space.\n\nKeywords and phrases: quaternion\n LOCATION:https://researchseminars.org/talk/HCS2023/9/ END:VEVENT END:VCALENDAR