Interesting article, but the headline is misleading. You can rewrite quantum mechanics without imaginary numbers, sure — but only by hiding the same complex phase structure inside a more complicated tensor product. If you still have phase, conjugate quadratures, and 90° rotations, then the physics of i is still there. Removing the symbol doesn’t remove the geometry.
3 weeks ago | 82
This sentence in the article sums it up: "reports of i’s demise may be somewhat exaggerated". You don't *need* complex numbers, but the simplest description of the math involves complex numbers. And what people haven't yet figured out, if I understand correctly, is if there is some deeper reason for why the simplest formulation, involving complex numbers, is the best in some physical sense.
3 weeks ago | 91
This is terrible news for physics undergrads sense of inner smugness
3 weeks ago | 126
I have always believed this was possible. I'm glad these mathematicians proved it.
2 weeks ago | 0
Not a big fan of imaginary stuff. So this is good. Let's stick with reality. I call BS on atoms knowing when you're looking. There's something very wrong with anything that leads to ridiculous conclusions such as that.
3 weeks ago | 1
The next technological singularity is Phase Control. Not power. Not mass. Not computation. Phase Coherence determines Reality Selection.
3 weeks ago | 1
For a lot of math, i makes sense. Rotation for example, start with i, times I is -1, times I is negative I, times I is one. Multiply it again to get back to i. It's rotation, and it can be done very simply. Degrees in radians just make the math harder, especially if you are making a 3D game or visualization. There are of course other ways to do it, and I assume this real number quantum theory is the same thing. It makes sense with imaginary numbers but it can also be done another way. If I had known the question existed, my answer would have been I'm certain there could be a real solution.
3 weeks ago | 14
I wanted to ask them [x,p]=? Looks like in order to eliminate i from QM, they have to eliminate position or momentum from the fundamental concepts of physics.
3 weeks ago | 2
This class of problem including quantized values is that we’re sampling our instruments.
3 weeks ago | 1
The only utility I can think of beyond philosophical is that the extra cludge without i might reveal a new perspective for some future physicist
3 weeks ago | 1
Oh god, why is everybody so puzzled with complex wavefunctions... in classical mechanics, we need both position and momentum to completely characterize how a particle going to behave, if we replace a point particle by a wave distribution, you can't figure out if a wave is going left or right without knowing the speeds of its components. The imaginary part is just that - indication how fast the wave changes while the real component is the current positions. Compex numbers are just a handy way to fit both position and speed into one function - you need both to know how the wave is going to propagate when applying H operator in the time dependent SE. I guess we could replace a complex wavefunction with coupled position/speed distributions, but it's rather messy. The algebra of complex numbers allows to make a beautiful trick of placing them together and treating as a whole
3 weeks ago (edited) | 11
Wasnt it only reformulated as two equations with real numbers only but that doesnt mean the complex numbers were "taken out" of the equation?
3 weeks ago | 1
Complex numbers are just an extension of normal numbers, built out of them in a finite way with some simple additional logic. They're only “necessary” in the way that radians are as opposed to another unit of rotation. This doesn't surprise me at all.
3 weeks ago | 1
I don't get the beef with complex numbers. Negative numbers are just as problematic. There are no negative 5 apples or negative masses, but its an incredibly convenient concept to work with
3 weeks ago | 52
Quanta Magazine
A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth with accurate calculations of hydrogen’s emission and absorption of light. There was, however, a snag. The central equation of quantum mechanics featured the imaginary number 𝑖, the square root of −1.
Physicists knew 𝑖 was a mathematical fiction. Real physical quantities like mass and momentum never yield a negative amount when squared. Yet this unreal number that behaves as 𝑖² = −1 seemed to sit at the heart of the quantum world.
After deriving the i-riddled equation — essentially the law of motion for quantum entities — Erwin Schrödinger expressed the hope that it would be replaced by an entirely real version. (“There is undoubtedly a certain crudeness at the moment” in the equation’s form, he wrote in 1926.) Schrödinger’s distaste notwithstanding, 𝑖 stuck around, and new generations of physicists took up his equation without much concern.
Then, in 2021, the role of imaginary numbers in quantum theory attracted newfound interest. A team of researchers proposed a way to empirically determine whether 𝑖 is essential to quantum theory or a mere mathematical convenience. Two teams quickly followed up to perform the intricate experiments and found supposedly unequivocal evidence that quantum theory needs 𝑖.
This year, however, a series of papers has overturned that conclusion.
In March, a group of theorists based in Germany rebutted the 2021 studies, putting forward a real-valued version of quantum theory that’s exactly equivalent to the standard version. Two theorists in France followed up with their own formulation of a real-valued quantum theory. And in September, another researcher approached the question from the perspective of quantum computing and arrived at the same answer: 𝑖 isn’t necessary for describing quantum reality after all.
🔗 Keep reading:
www.quantamagazine.org/physicists-take-the-imagina…
🎨 Michelle Sclafani for Quanta Magazine
3 weeks ago | [YT] | 1,583