Reality Doesn’t Need Complex Numbers, Physicists Prove

Quick Overview

Physicists demonstrated that quantum theory can be consistently formulated using only real numbers, experimentally falsifying the previous assumption that complex numbers are fundamentally necessary for describing quantum phenomena, as shown by a recent paper that derived a real-valued analogue of quantum mechanics consistent with experimental predictions.

Key Points: A recent Nature paper presented an argument asserting that quantum theory fundamentally requires complex numbers, but later work by other groups showed that a real-number quantum theory can reproduce the outcomes of all multiparticle experiments. The video explains that complex numbers ($i = \sqrt{-1}$) are essential in mathematics but were thought necessary for quantum mechanics to work, especially due to the time evolution described by the Schrödinger Equation, $H|\Psi\rangle = i\hbar \partialt |\Psi\rangle$. Complex numbers ($z = x + iy$) allow for algebraic structures where all polynomial equations have solutions, unlike real numbers ($\mathbb{R}$), which pose problems like $x^2 = -1$ having no real solution. Multiplying by $i$ in the complex plane corresponds to a 90-degree rotation, a key feature that real-only formulations struggle to replicate for quantum states like the entangled state $|0\rangle|1\rangle + |1\rangle|0\rangle$. Recent experimental work confirmed that a real-valued version of quantum theory, which uses only real numbers, can describe the outcomes of quantum experiments, contradicting the previous conclusion that complex numbers were essential. The success of the real-valued formulation means that complex numbers are not fundamentally required for quantum mechanics, although they remain a convenient mathematical tool. The video concludes by promoting the Novium Hoverpen, highlighting its unique magnetic levitation feature and offering a discount code 'SABINE' for 15% off for 48 hours.

Context: The video discusses a significant debate in quantum physics regarding the necessity of complex numbers (involving $i = \sqrt{-1}$) for describing quantum mechanics. Standard quantum theory relies on complex Hilbert spaces and the Schrödinger equation, which explicitly involves $i$. A recent 2021 paper suggested complex numbers were essential, but subsequent experiments and theoretical work, as detailed in the video, provided evidence for a consistent quantum theory based solely on real numbers ($\mathbb{R}$), challenging the long-held belief that complexity was fundamental to physics.