Quantum physics: real numbers are not enough for quantum mechanics

An experiment should provide clarity

Thus it seemed that the complex numbers in quantum mechanics were just a successful tool that simplified lengthy calculations – but could be eliminated if necessary. But in January 2021, physicists working with Marc-Olivier Renau of the Institute for Photonic Science (ICFO) in Barcelona proposed an experiment with multiple particle sources and observers, which should once and for all set the number limit of quantum mechanics. In this case, they found, the predictions of the real and complex formulations differ.

The experiment involves three observers, Alice, Bob and Charlie, who form a line with their measuring instruments. Between Alice and Bob and between Bob and Charlie there is a source that emits entangled particles. Alice and Bob thus receive particles A and B at the same time₁, also meet charlie c and bob b this time₂ One. Alice and Charlie can take a particular measure of their choosing at A and C respectively. On the other hand, Bob B. manipulates₁ and b₂ in such a way that they are then joined with each other. As a result, A and C are also entangled, as they were previously connected to B.₁ or b₂ were confused.

The result of the experiment can be estimated from the complex numbers. Using the actual formalism gives different results. Since the experiment can be implemented with the current technical possibilities, the two working groups seized the opportunity to realize it in 2021. Jian-Wei Pan’s group at the Chinese Academy of Sciences used superconducting qubits, while researchers led by Jingyun Fan of the Southern University of Science and Technology in Shenzhen experimented with entangled photons. Both teams were able to measure a certain parameter that indicates whether the true or complex formulation is correct – and both experiments confirmed the complex version.

However, the purely actual description of quantum mechanics is not entirely clear. There is no suitable version, for example in more dimensions, in which the complex and realistic predictions of the proposed experiment agree. But one could possibly arrive at the same result if one fundamentally changed arithmetic operations, such as the tensor product, and thus the computational laws of quantum physics. However, this would be extremely complex and confusing, which is why this approach is not particularly popular. Also, it would raise further questions in other scenarios. The theory of the microcosm appears to be based on complex numbers – meaning that the number space is more deeply intertwined in nature than previously thought.