The Bunkum Mystification of Quantum Mechanics by Non-Physicists

Mauro

Active Member
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.
https://www.sciencenews.org/article/quantum-physics-imaginary-numbers-math-reality


(*) 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) .
 

Edward Current

Active Member
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: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

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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