Why Does Quantum Mechanics Require Complex Numbers?

[MichPod]

Is the fact that QM uses complex numbers should be considered as a math artefact (as it is the case when complex numbers are used for alternate current circuit analysis), or, alternatively, it has some deep and important relation to the nature (or at least to the nature of the quantum theory)? If the later is true, could you please clarify or bring some links discussing the topic?

 

[MrRobotoToo]

Complex numbers are needed in order to correctly describe the interference of probabilities. However, the complex phase of the wave function is not merely a mathematical artifact, as is shown by the Aharonov-Bohm effect.

 

[DrClaude]

See http://www.scottaaronson.com/democritus/lec9.html

 

[Denis]

Whatever can be described by one complex number can be described, as well, by two real numbers. Some denotations may look more cumbersome in such a real notation, that's all.

 

[MichPod]

Whatever can be described by one complex number can be described, as well, by two real numbers. Some denotations may look more cumbersome in such a real notation, that's all.

Well, a rational number may be described as a pair of integer numbers as well, but we believe (most of us) that the rational numbers give probably more adequate description of the reality than such a pair.
And... even if we pass to two real numbers instead of one complex number, we still will emulate the complex arithmetic with them. The question is - why? Is the nature in its underneath somehow "complex"?

 

[DrClaude]

The question is - why? Is the nature in its underneath is somehow "complex"?

Physics doesn't answer "why" questions.

I suggest you read the link I gave, and other threads on PF on the subject (look for "Similar Discussions" below).

Thread closed.