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Dec
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awarded  Popular Question
Nov
3
comment Why are Only Real Things Measurable?
I made further edits to my answers and removed Dirac's quote from two of them.
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revised About the complex nature of the wave function?
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revised Can one do the maths of physics without using $\sqrt{-1}$?
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Nov
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comment QM without complex numbers
I do not disagree with your answer. One can for sure formulate QM in a way that uses pairs of real numbers instead of complex ones. However as Dirac points out, one has to be aware that in QM measurements might not commute. If one would formulate QM with pairs of real numbers, it would be more difficult to distinguish between pairs of real numbers, where measurements commute and between pairs of real numbers, where measurements don't commute.
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comment QM without complex numbers
I'm not sure if that is a good example, but think about the wave function described by Schrödingers equation. One could split Schrödingers equation into two coupled equations, one for the real and one for the imaginary part of the wave function. However one cannot measure the phase and the amplitude of the wave function simultaneously, because both measurements interfere with each other. To make this manifest, one uses a single equation with a complex wave function, and generates the observable real quantity by squaring the complex wave function.
Nov
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comment Why are Only Real Things Measurable?
Dear Qmechanic, I believe otherwise and I'm willing to take the risk and let the crowd decide if my answers are relevant or not for the questions. I don't care about the reputation points. If I get any, I promise I will donate them to Dirac.
Nov
3
comment Quantum version of the Galton Board
Thank you! Your last reference also led me to this article in Wikipedia with a picture of the distribution: en.wikipedia.org/wiki/Quantum_walk . However, is it true that neither for the fermion nor for the boson case the resulting distribution can be expressed in closed form?
Nov
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revised QM without complex numbers
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comment About the complex nature of the wave function?
Dear Qmechanic, isn't is also frown upon to copy-paste identical comments? ;-) However I admit, that my answers were too similar. So I tried to follow your suggestion (iii) and personalized my answers to address the specific question in a better way. However I still believe the quote from Dirac is very relevant and important, so I will refer to it in every answer.
Nov
3
comment Can one do the maths of physics without using $\sqrt{-1}$?
Dear Qmechanic, isn't is also frown upon to copy-paste identical comments? ;-) However I admit, that my answers were too similar. So I tried to follow your suggestion (iii) and personalized my answers to address the specific question in a better way. However I still believe the quote from Dirac is very relevant and important, so I will refer to it in every answer.
Nov
3
comment Why are Only Real Things Measurable?
Dear Qmechanic, isn't is also frown upon to copy-paste identical comments? ;-) However I admit, that my answers were too similar. So I tried to follow your suggestion (iii) and personalized my answers to address the specific question in a better way. However I still believe the quote from Dirac is very relevant and important, so I will refer to it in every answer.
Nov
3
comment QM without complex numbers
Dear Qmechanic, isn't is also frown upon to copy-paste identical comments? ;-) However I admit, that my answers were too similar. So I tried to follow your suggestion (iii) and personalized my answers to address the specific question in a better way. However I still believe the quote from Dirac is very relevant and important, so I will refer to it in every answer.
Nov
3
revised About the complex nature of the wave function?
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revised Why are Only Real Things Measurable?
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Nov
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revised Can one do the maths of physics without using $\sqrt{-1}$?
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Nov
2
answered Can one do the maths of physics without using $\sqrt{-1}$?
Nov
2
answered Why are Only Real Things Measurable?
Nov
2
answered About the complex nature of the wave function?