It's frequently said by physicists that complex numbers are essential to formulating quantum mechanics. However, this assertion overlooks the possibility of alternative formulations using real numbers.
Mathematically, complex numbers can be re-expressed using real numbers. Hence, no physical theory, including quantum mechanics, is genuinely dependent on the use of complex numbers.
Since the 1960s, formulations of quantum mechanics have existed that operate without complex numbers—demonstrating the flexibility of mathematical formulation in physical theories.
While complex numbers are often viewed as indispensable in quantum mechanics, a thorough examination reveals that they are a convenient choice rather than a necessity.
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