Quantum mechanics is known for being complex — not just because of its counter-intuitive concepts, like particles existing in multiple places at once, but also because it fundamentally relies on complex numbers, a mathematical extension of the real numbers we use in everyday life. While real numbers are sufficient to describe classical physics, quantum theory fundamentally depends on complex numbers to capture the behavior of particles. But is this mathematical structure truly sufficient, or could an even more general framework — one based on hyper-complex numbers — be required?
In a recent study, Ece Ipek Saruhan, Joachim von Zanthier, and Marc-Oliver Pleinert from FAU’s Quantum Optics and Quantum Information group have developed a new series of tests to explore this question. Their work builds on an idea from Asher Peres, who proposed using quantum interference to determine whether standard complex numbers fully describe quantum mechanics. By refining and extending this approach, the researchers have made it possible to test the mathematical structure of quantum theory in a broader range of experimental setups, including multipath and multiparticle interference.
Their findings provide a new way to probe the mathematical foundations of quantum mechanics, paving the way for future experiments to determine whether quantum theory is fully captured by complex numbers or if an even deeper structure is at play.
For more details, see the original publication:
Multipath and Multiparticle Tests of Complex versus Hypercomplex Quantum Theory
Ece İpek Saruhan, Joachim von Zanthier, and Marc-Oliver Pleinert
Phys. Rev. Lett. 134, 060201
Quantum mechanics is known for being complex — not just because of its counter-intuitive concepts, like particles existing in multiple places at once, but also because it fundamentally relies on complex numbers, a mathematical extension of the real numbers we use in everyday life. While real numbers are sufficient to describe classical physics, quantum theory fundamentally depends on complex numbers to capture the behavior of particles. But is this mathematical structure truly sufficient, or could an even more general framework — one based on hyper-complex numbers — be required?
In a recent study, Ece Ipek Saruhan, Joachim von Zanthier, and Marc-Oliver Pleinert from FAU’s Quantum Optics and Quantum Information group have developed a new series of tests to explore this question. Their work builds on an idea from Asher Peres, who proposed using quantum interference to determine whether standard complex numbers fully describe quantum mechanics. By refining and extending this approach, the researchers have made it possible to test the mathematical structure of quantum theory in a broader range of experimental setups, including multipath and multiparticle interference.
Their findings provide a new way to probe the mathematical foundations of quantum mechanics, paving the way for future experiments to determine whether quantum theory is fully captured by complex numbers or if an even deeper structure is at play.
For more details, see the original publication:
Multipath and Multiparticle Tests of Complex versus Hypercomplex Quantum Theory
Ece İpek Saruhan, Joachim von Zanthier, and Marc-Oliver Pleinert
Phys. Rev. Lett. 134, 060201