Quaternion Series as a Semigroup with Inverses
138 views · Published 13 November 2018 · 39:41 · Indexed 18 October 2026
Channel: Doug Sweetser · 2018 · Science & Technology
The video "Quaternion Series as a Division Algebra" has been retracted - it is wrong - and replaced by this one. A semigroup can have multiple inverses as is the case for quaternion series (2^n inverses to be precise). The graph theory for 0, 1, and the real numbers is presented for addition and multiplication. Addition of reals is a hypergraph because two edges have to go to multiple vertices. Quaternions mostly can do what can already be done with other techniques. There are two new views on problems in EM. There is a very natural gauge field that must be eliminated for photons, but might play a role somewhere else. The fundamental forces of physics are invariant under time reversal. The same cannot be said for the Poynting vector. A new appreciation for non-local quantum mechanics happened while creating this video. The conjugate operator necessarily must be applied in applications for quantum mechanics. With quaternions, a conjugate is a mirror reflection. One's mirror reflection is necessarily non-local and space-like separated.
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