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Is there not a model of QM which uses quaternions probabilities? Is there a place where it breaks down?
by tel 12y ago
Is there not a model of QM which uses quaternions probabilities? Is there a place where it breaks down?
- jaekwon 12y agoI remember reading things online where people claim that the natural world (probably including what's known in quantum mechanics) is better explained with quaternions.
- judk 12y agoIt's not broadly true. Quaternions are mainly useful for math on the surface of a sphere.
- deleted 12y ago[deleted]
- lisper 12y agoAaronson actually answers this question directly towards the end of the lecture. The short answer is that quaternions don't work for the same reason that real numbers don't work: the probabilities don't work out right for unitary transformations.
- dnautics 12y agolikely because the probabilities in QM need to be commutative (QM operators are not commutative, but the probabilities themselves are).
- stared 12y agoYou can represent two-state systems (qubits) with quaternions. In general, quantum mechanics is about using complex vectors and unitary operations on them. As it is enough to implement quaternions, they are silently used in quantum mechanics.