Physicists have proven that imaginary numbers will not be basically required in quantum mechanics.
Physicists at Heinrich Heine College Düsseldorf (HHU), working with the German Aerospace Heart (DLR), have revisited a primary function of quantum mechanics. Their research exhibits that the speculation could be expressed utilizing actual numbers relatively than counting on imaginary numbers.
Quantum mechanics was constructed to explain nature at its smallest scales, the place matter doesn’t behave the best way on a regular basis objects do. On the stage of atoms and subatomic particles, particles can act like waves, go by obstacles they seemingly mustn’t cross, and develop into linked in ways in which defy atypical instinct.
The speculation started taking form within the early 1900s by the work of physicists together with Max Planck, Niels Bohr, Werner Heisenberg, and Erwin Schrödinger. Since then, quantum mechanics has develop into some of the profitable frameworks in physics. It explains results comparable to particle diffraction within the double-slit experiment, which exhibits wave-like habits, and quantum tunneling, during which particles can typically go by a barrier even with out sufficient classical vitality to cross it.
In the present day, phenomena comparable to entanglement and coherence are particularly vital as a result of they underpin rising applied sciences, together with quantum computer systems and quantum communication.
Advanced numbers form quantum principle
Advanced numbers have lengthy been central to the arithmetic of quantum mechanics. Not like atypical actual numbers, advanced numbers embody each an actual half and an imaginary half. In quantum principle, they assist characterize a quantum state’s amplitude and part, two options wanted to calculate how quantum methods evolve and what outcomes experiments might produce.
For a lot of processes, this mathematical construction has appeared indispensable. However physicists have continued to debate whether or not advanced numbers are really constructed into the foundations of quantum mechanics or whether or not they’re primarily a strong calculation instrument. The deeper query is whether or not quantum mechanics could be formulated utilizing solely actual numbers.
A 2021 research argued that advanced numbers are important beneath the usual postulates of quantum mechanics. Experimental work later supported that conclusion.
A brand new postulate adjustments the reply
A brand new evaluation now means that the reply depends upon how the speculation describes mixed methods. A workforce of physicists from HHU and the DLR, led by Professor Dr. Dagmar Bruß and doctoral researcher Pedro Barrios Hita, reexamined the postulates used within the earlier work.
In a paper printed in Physical Review Letters, the team argues that one of those postulates is too restrictive. They propose a physically motivated alternative for formalizing system composition. With that change, they identify a class of theories that can be written entirely with real numbers while remaining experimentally indistinguishable from standard quantum mechanics.
Professor Bruß: “This means that both frameworks yield identical predictions for any conceivable experiment. Within this framework, imaginary numbers are thus not fundamentally necessary in quantum mechanics and can in principle be replaced by alternative formulations using real numbers.”
Reference: “Quantum Mechanics Based on Real Numbers: A Consistent Description” by Pedro Barrios Hita, Anton Trushechkin, Hermann Kampermann, Michael Epping and Dagmar Bruß, 18 June 2026, Physical Review Letters.
DOI: 10.1103/4k13-sdjh
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