Why are amplitudes complex numbers? (2018)
scottaaronson.blog
Why are amplitudes complex numbers? (2018)
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Re: Why are amplitudes complex numbers? (2018)
#2Basically, either you have unsigned numbers (conjugated magnitude), with growth/shrink operations, or you have numbers with a polarity, with displacement operations .
It is incomplete to have the notion of "negative numbers" without also including the imaginary parts.
Re: Why are amplitudes complex numbers? (2018)
#3I would very much enjoy reading the pre-reading for this post.
Re: Why are amplitudes complex numbers? (2018)
#4A simpler preliminary question would be, why are complex numbers present in non quantum wave mechanics, and then how does this compare and contrast to quantum mechanics.
Re: Why are amplitudes complex numbers? (2018)
#5[deleted]
Re: Why are amplitudes complex numbers? (2018)
#6The answer provided essentially requires you to know so much in advance that it would be unsurprising or even obvious to you. I'm not entirely sure who this writing style is for, if not simply Scott Aaronson's note-taking process...
Re: Why are amplitudes complex numbers? (2018)
#7I would very much enjoy reading the pre-reading for this post.
And the pre-pre, and probably pre-pre-pre. Much respect to those who can follow this.
Re: Why are amplitudes complex numbers? (2018)
#8A simpler preliminary question would be, why are complex numbers present in non quantum wave mechanics, and then how does this compare and contrast to quantum mechanics.
Why would this be weird? The classical waves have an amplitude and phase, which is all the QM probability functions really are.
Re: Why are amplitudes complex numbers? (2018)
#9[deleted]
Re: Why are amplitudes complex numbers? (2018)
#10Complex numbers are not a QM feature; they are just more convenient to use in computations. There are equivalent formulations, like Wigner's phase-space with quasi-probabilities and MIC-POVMs that don't have any complex numbers. The weird part is the negative probabilities, not imaginary numbers.