#PhysicsJournalClub
"Testing the necessity of complex numbers in traditional quantum theory with quantum computers"
by Jarrett L. Lancaster and Nicholas M. Palladino
Am. J. Phys. 93, 110 (2025)
In classical electrodynamics the use of complex numbers is only due to to its convenience for calculations. Nobody wants to remember all those pesky trigonometric identities, so we use complex numbers to simplify calculations and take the real part at the end. You need to be a bit careful when calculating stuff like the Poynting vector, but this is well addressed ion any half-decent undergrad-level textbook.
But for quantum mechanics the problem is less obvious. On one hand we only ever measure real quantities, but on the other hand the imaginary unit appears explicitly in the Schrödinger equation, and no textbook I am aware of ever even mention the possibility that quantum numbers might be just a calculation convenience like it is in classical electrodynamics.
The question is subtle enough that you are going to find no shortage of well-read Physicists claiming that it is "obvious" that complex numbers are necessary for quantum mechanics, or that it is "obvious" that you could just use real numbers if you wanted.
This paper makes a pretty good job at explaining the problem, going through some of the history and explicit calculations, up to constructing explicitly a real-valued version of QM.
The second part, where they make an "experiment" on a IBM cloud quantum computer is (imho) less interesting, and their conclusion that you need indeed complex numbers not really supported by the evidence, but your mileage might vary 🙂
https://pubs.aip.org/aapt/ajp/article/93/1/110/3327097/Testing-the-necessity-of-complex-numbers-in
#Physics #QuantumMechanics #ITeachPhysics
j_bertolotti /
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2025-01-07 10:17:47
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2025-01-07 10:17:47Event JSON
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"content": "#PhysicsJournalClub\n\"Testing the necessity of complex numbers in traditional quantum theory with quantum computers\"\nby Jarrett L. Lancaster and Nicholas M. Palladino\nAm. J. Phys. 93, 110 (2025)\n\nIn classical electrodynamics the use of complex numbers is only due to to its convenience for calculations. Nobody wants to remember all those pesky trigonometric identities, so we use complex numbers to simplify calculations and take the real part at the end. You need to be a bit careful when calculating stuff like the Poynting vector, but this is well addressed ion any half-decent undergrad-level textbook.\nBut for quantum mechanics the problem is less obvious. On one hand we only ever measure real quantities, but on the other hand the imaginary unit appears explicitly in the Schrödinger equation, and no textbook I am aware of ever even mention the possibility that quantum numbers might be just a calculation convenience like it is in classical electrodynamics.\nThe question is subtle enough that you are going to find no shortage of well-read Physicists claiming that it is \"obvious\" that complex numbers are necessary for quantum mechanics, or that it is \"obvious\" that you could just use real numbers if you wanted.\nThis paper makes a pretty good job at explaining the problem, going through some of the history and explicit calculations, up to constructing explicitly a real-valued version of QM.\nThe second part, where they make an \"experiment\" on a IBM cloud quantum computer is (imho) less interesting, and their conclusion that you need indeed complex numbers not really supported by the evidence, but your mileage might vary 🙂 \nhttps://pubs.aip.org/aapt/ajp/article/93/1/110/3327097/Testing-the-necessity-of-complex-numbers-in\n\n#Physics #QuantumMechanics #ITeachPhysics",
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