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Complex Numbers

All articles tagged with #complex numbers

Real-Number Quantum Mechanics: Do We Still Need Imaginary Numbers?
science1 month ago

Real-Number Quantum Mechanics: Do We Still Need Imaginary Numbers?

German physicists have demonstrated a fully working quantum-mechanics formulation that uses only real numbers and can predict the same experimental outcomes as the standard complex-number framework, suggesting imaginary numbers aren’t fundamental to quantum mechanics but are still a convenient mathematical language. While the real-number approach matches all predictions, researchers note complex numbers remain useful in describing quantum systems, and this work revisits debates sparked by a 2021 Nature study on the necessity of complex numbers in quantum theory.

Real-number quantum mechanics passes the test, matching all standard predictions
science3 months ago

Real-number quantum mechanics passes the test, matching all standard predictions

Physicists built a working version of quantum mechanics using only real numbers, recreating all predictions of the standard theory by replacing the usual complex-number tensor product with a real-number rule and a bookkeeping flag system. The approach shows complex numbers aren’t fundamental to quantum mechanics, though the work currently covers finite systems and does not alter experimental predictions.

"Supercomputers crack unsolvable number puzzle after 32-year quest"
mathematics3 years ago

"Supercomputers crack unsolvable number puzzle after 32-year quest"

Mathematicians have used supercomputers to calculate the value of the "ninth Dedekind number" or D(9), a complex number that was previously thought to be impossible to calculate. The number represents the number of possible configurations of a certain kind of true-false logical operation in different spatial dimensions. Two separate research groups produced the exact same number for D(9), confirming its accuracy. Dedekind numbers get exponentially larger for each new dimension, making them increasingly difficult to calculate. The newly identified value for D(9) is 286386577668298411128469151667598498812366.