Physicists Take the Imaginary Numbers Out of Quantum Mechanics
Postedabout 2 months agoActiveabout 2 months ago
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Quantum Mechanics
Complex Numbers
Mathematical Formulation
Physicists have reformulated quantum mechanics to use only real numbers, sparking debate about whether this truly removes 'imaginary' numbers from the theory or just renames them.
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There is nothing strange about i and claims contrary to that misunderstand what it even is. Partly terminology is to blame. I simply represents a 90° rotation of space. Really quite simple and easily measurable in our 3d world
There is also a construction with matices instead of polynomials.
And perhaps others. Each of them are useful in some cases.
Fascinating. Can you say more about this or point me to where I may learn?
On the other hand, it's very easy to see and measure rational complex numbers with a protractor.
"A 90 turn" is one answer. There are probably others.
Even the roots of a parabola that doesn't hit the z axis are actually the roots of the ninety degree rotated inverse analogue hitting the imaginary plane. Since the apex of such a parabola is always centered at 0i, the imaginary places it hits are symmetric, explaining why if a + bi is one imaginary root, then a - bi is as well.
https://teaching-math.com/unlock-the-secrets-of-complex-root...
Again... There is nothing weird about imaginary numbers. They actually make a lot of sense. It's actually insane to only do math in one dimension when our world has three.
In general there are many algebraic rings with an element that, when multiplied by itself, produces the additive inverse of the multiplicative identity.
https://arxiv.org/pdf/2504.02808
https://physics.stackexchange.com/a/83219/1648
https://www.mdpi.com/2673-9984/3/1/9
"our knowledge of quantities is necessarily accompanied by uncertainty. Consequently, physics requires a calculus of number pairs and not only scalars for quantity alone. Basic symmetries of shuffling and sequencing dictate that pairs obey ordinary component-wise addition, but they can have three different multiplication rules. We call those rules A, B and C. “A” shows that pairs behave as complex numbers, which is why quantum theory is complex."
https://arxiv.org/abs/0907.0909
"the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability of this sequence being a real-valued function of this number pair. By making use of elementary symmetry conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic"