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asmaier
asmaier
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LetActually you can measure imaginary numbers by measuring separately the old masterreal and the imaginary part. However this is only possible in classical mechanics. In quantum mechanics measuring the two parts simultaneously is not possible, because the first measurement would necessarily change the outcome of the second measurement, as Dirac speakexplains nicely in his book:

"One might think one could measure a complex dynamical variable by measuring separately its real and pure imaginary parts. But this would involve two measurements or two observations, which would be alright in classical mechanics, but would not do in quantum mechanics, where two observations in general interfere with one another - it is not in general permissible to consider that two observations can be made exactly simultaneously, and if they are made in quick succession the first will usually disturb the state of the system and introduce an indeterminancy that will affect the second." (P.A.M Dirac, The principles of quantum mechanics, §10, p.35)

So if I interpret Dirac right, the use of complex numbers helps to distinguish between quantities, that can be measured simultaneously and the one which can't. You would loose that feature, if you would formulate QM purely with real numbers. So to answer your question: One can only measure real numbers, because measuring complex numbers would involve two simultaneous measurements, which would interfere with each other in quantum mechanics.

Let the old master Dirac speak:

"One might think one could measure a complex dynamical variable by measuring separately its real and pure imaginary parts. But this would involve two measurements or two observations, which would be alright in classical mechanics, but would not do in quantum mechanics, where two observations in general interfere with one another - it is not in general permissible to consider that two observations can be made exactly simultaneously, and if they are made in quick succession the first will usually disturb the state of the system and introduce an indeterminancy that will affect the second." (P.A.M Dirac, The principles of quantum mechanics, §10, p.35)

So if I interpret Dirac right, the use of complex numbers helps to distinguish between quantities, that can be measured simultaneously and the one which can't. You would loose that feature, if you would formulate QM purely with real numbers. So to answer your question: One can only measure real numbers, because measuring complex numbers would involve two simultaneous measurements, which would interfere with each other in quantum mechanics.

Actually you can measure imaginary numbers by measuring separately the real and the imaginary part. However this is only possible in classical mechanics. In quantum mechanics measuring the two parts simultaneously is not possible, because the first measurement would necessarily change the outcome of the second measurement, as Dirac explains nicely in his book:

"One might think one could measure a complex dynamical variable by measuring separately its real and pure imaginary parts. But this would involve two measurements or two observations, which would be alright in classical mechanics, but would not do in quantum mechanics, where two observations in general interfere with one another - it is not in general permissible to consider that two observations can be made exactly simultaneously, and if they are made in quick succession the first will usually disturb the state of the system and introduce an indeterminancy that will affect the second." (P.A.M Dirac, The principles of quantum mechanics, §10, p.35)

Source Link
asmaier
asmaier
  • 10.4k
  • 5
  • 67
  • 110

Let the old master Dirac speak:

"One might think one could measure a complex dynamical variable by measuring separately its real and pure imaginary parts. But this would involve two measurements or two observations, which would be alright in classical mechanics, but would not do in quantum mechanics, where two observations in general interfere with one another - it is not in general permissible to consider that two observations can be made exactly simultaneously, and if they are made in quick succession the first will usually disturb the state of the system and introduce an indeterminancy that will affect the second." (P.A.M Dirac, The principles of quantum mechanics, §10, p.35)

So if I interpret Dirac right, the use of complex numbers helps to distinguish between quantities, that can be measured simultaneously and the one which can't. You would loose that feature, if you would formulate QM purely with real numbers. So to answer your question: One can only measure real numbers, because measuring complex numbers would involve two simultaneous measurements, which would interfere with each other in quantum mechanics.