2020/12/19 by John Skilling, Kevin H. Knuth, Skilling, John +1
Physics and Astronomy · Arts and Humanities · #Quantum Mechanics and Applications #Philosophy and History of Science
paper · pdf · doi:10.48550/arxiv.2104.05395
The theories of quantum mechanics and relativity dramatically altered our\nunderstanding of the universe ushering in the era of modern physics. Quantum\ntheory deals with objects probabilistically at small scales, whereas relativity\ndeals classically with motion in space and time.\n We show here that the mathematical structures of quantum theory and of\nrelativity follow together from pure thought, defined and uniquely constrained\nby the same elementary "combining and sequencing" symmetries that underlie\nstandard arithmetic and probability. The key is uncertainty, which inevitably\naccompanies observation of quantity and imposes the use of pairs of numbers.\n The symmetries then lead directly to the use of complex " surd mathord-1"\narithmetic, the standard calculus of quantum mechanics, and the Lorentz\ntransformations of relativistic spacetime. One dimension of time and three\ndimensions of space are thus derived as the profound and inevitable framework\nof physics.\n