Quantum Mechanics Without Maths or Philosophy
articlesbyaphysicist.com
articlesbyaphysicist.com
Skipping from the complex-valued wave function to its real-valued magnitude is a good simplification for an introductory article, but I think the need for complex numbers (the concept of phase) is very important and fundamental. That's what I would really liked explained? Why do cmplx numbers come up, and is there a QM-equivalent model using only real-valued functions?
There is work being done on this sort of thing. If essentially all you care about are the probabilities of certain observations occurring, then you surely can represent any theory with real numbers. The field of "generalised probabilistic/physical theories" attempts to analyse quantum theory without assuming the baggage of Hilbert spaces etc... [0]. Chris Fuchs also has done a lot of work on representing quantum state spaces in terms of outcome distributions over special types of measurements called sic-povms[1,2].
0. https://arxiv.org/abs/quant-ph/0508211
But I wonder why it gets so little attention...
Not sure what you mean by incompatible results. Certainly QBism is incompatible with Many Worlds! The latter states that the quantum state is real and objective, the former states the opposite.
The QBist horsemen have devoted some attention to the question of compatible quantum state assignments. See: https://arxiv.org/abs/quant-ph/0206110
However, Chris Fuchs does not see any problem in someone assigning a probability-1 belief to a measurement outcome and being proven wrong. See section 2.2 of https://arxiv.org/pdf/1705.03483.pdf
This last point in particular should bring home the point that Fuchs does think there is an ontological theory underlying physics, but that we are fooling ourselves about how much of it is objective/observer-independent.
http://www.scottaaronson.com/democritus/lec9.html http://math.ucr.edu/home/baez/rch.pdf
Yes, the Wigner-Weyl transformation produces a completely equivalent way to formulate quantum mechanics without reference to complex numbers. The wavefunction over real space is replaced with a (generically not positive) real-valued pseudo-probability distribution on phase space called the Wigner function.
Some dictators abuse power for material gain. If woke up dictator of Earth I think my tyranny would lean more towards standards bodies. Forcing holdouts to the metric system would actually cost the economy more? Too bad, this is the cruelty of oppression. I at least would promise not to kill or torture anyone.
This might be good as a historical resource because even good stuff disappears off the Internet, and if it made it to the HN front page, it's probably good. (I know, can't do this because copyright. But the Wayback Machine has survived by deleting content on request.)
"Mozart without sound of music notation."
> "Mozart without sound OR music notation."