The Bunkum Mystification of Quantum Mechanics by Non-Physicists

This is not exactly on-topic but I think it may be interesting.

It seems there has been a program going on since a while to determine if the use of complex numbers (which is pretty weird in a physical theory) is essential for quantum mechanics or if they could be dispensed with, using only nice good ol' real numbers instead.

Incredible as it may seems physicist have devised actual real-world experiments to find it out (*) and it seems that, indeed, quantum mechanics does need comples numbers (and then it's fundamentally utterly weird).

Imaginary numbers might seem like unicorns and goblins — interesting but irrelevant to reality.

But for describing matter at its roots, imaginary numbers turn out to be essential. They seem to be woven into the fabric of quantum mechanics, the math describing the realm of molecules, atoms and subatomic particles. A theory obeying the rules of quantum physics needs imaginary numbers to describe the real world, two new experiments suggest.

(*) an article which underpins the theoretical framework for the experiments has been just published by Nature, if you can access the journal it is here, it's also been preprinted on arXiv here) .
it seems that, indeed, quantum mechanics does need comples numbers (and then it's fundamentally utterly weird).
Things get even weirder with the extensions of complex numbers: quaternions, which combine real numbers with three different kinds of "imaginary" numbers, and octonions, which have seven kinds of "imaginary" numbers. Quaternions can be linked to special relativity. In relativity, the three dimensions of space are given one sign, while time is given the other. If you square all of the quantities, you get three negative numbers for space and one positive number for time. In that way, time and space are able to trade off for each other as happens in relativity (travel faster in space according to an observer, and you travel slower in time according to that observer). Meanwhile some physicists are trying to crack the code on matter and energy with octonions, with mixed success. Here's a fascinating article on one of the pioneers in this field, Cohl Furey, and her work with octonions:

I'm just a caveman, but my hunch is that the final theory of physics will employ none of the above kinds of numbers. Instead, it will require a new system of discrete numbers, of which the reals/complex/quaternions/octonions are continuous idealizations — and without which, no one will crack this nut.
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Saw this only now. Pardon for the delay.

Hmm, looks like gravity was a well-chosen example after all:
Newton’s law of gravitation, the linchpin of his new cosmology, broke with explanatory conventions of natural philosophy, first for apparently proposing action at a distance, but more generally for not providing “true”, physical causes. The argument for his System of the World (Principia, Book III) was based on phenomena, not reasoned first principles. This was viewed (mainly on the continent) as insufficient for proper natural philosophy.

Newton's law of universal gravitation was a realist theory intended to explain how the universe actually works whether or not an observer is observing it or interpreting it (bold added):

Newton held a realist reading of scientific theory as based upon inference from facts and observation, and his gravitational-theory (or NGT) as deduced from observed phenomena and Kepler’s laws. Duhem criticises this realist approach to scientific-theory and NGT in particular, claiming empirical evidence cannot force theory-adoption.

According to NGT, every particle in the universe actually attracts every other particle, independent of observers. As the citation above demonstrates (extracted from a 2013 article on instrumentalism/positivism which you and markus appear to subscribe to in terms of your view on science), the discussion on whether science is instrumentalist/positivist or realist is still very much an ongoing debate within the Philosophy of Science. Outside QM (within physics and other natural sciences) and certain social sciences, most scientists, in my subjective experience, tend to be realist in their orientation rather than positivist. They're usually interested in real causes underlying real phenomena. However, I admit not having come across any surveys done on the matter which a credible sampling of a cross-section of the world's scientists of all disciplines would have taken. Such a survey could shed some light into whether my subjective experience corresponds to reality or not (pun intended).

The NGT is not a "true" physical cause in the conventional sense of a cause (as understood during Newton's time) whereby a physical event is explained by a localized cause or a set of localized causes immediately preceding the phenomenon along a chronological causal chain without any strange action-at-a-distance. The law of gravitation proposed by the MGT, which causes attraction between particles, does not operate/occur earlier in time from the actual motion of the particles, or locally. It is simultaneous and universal. Hence, the theory of NGT discusses a non-standard physical cause -- a physical law. But under the PoSR -- in other words, under a realist philosophy of science -- it would still qualify as a physical cause -- a sufficient reason for why the particles of the universe, according to Newton, behave in a certain way. Just not a kind of a cause that occurs along a time dimension. In other words, for Newton the NGT describes a real cause and he did not intend his theory to merely provide a mathematical formula or a calculational device to predict observation outcomes (unlike the QM which is just that), even though that's what it also does with a limited measure of success.
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