This is an interesting issue raised and thanks for the new reference "Quantum Theory: Concepts and Methods" (Kluwer Academic Publishers, 1998) but the author Asher Peres makes the same problem that underlines science as a whole.
Peres tries to separate math from physics while at the same time acknowledging that the math comes from music yet Peres does not have a proper understanding of the music.
To wit:
"A classical acoustic signal with intensity f(t) also cannot have both precise timing and precise pitch....This is a general property of Fourier transforms, quite independent of the underlying physics. Yet, approximate values for time and frequency are certainly compatible, as every musician knows (see page 214). Likewise, in quantum theory, we can have approximate values for both position and wavelength...."
Peres footnotes the above with:
"Do not attempt to quantize Eq. (10.98) into a time-energy uncertainty relation! Time is not an operator in quantum mechanics -- nor is it a dynamical variable in classical mechanics. It is a c-number, a mere numerical parameter. The measurement of time will be discussed in the last chapter of this book."
So clearly the POV quantum statistics used relies on the above "approximate values" yet the author has made some terribly wrong assumptions -- based on a misunderstanding of the roots of math.
Also since Peres refers this issue to the final chapter of the book I think it's safe to say that it's the most important issue for quantum mechanics.
So we go to the final chapter that Peres refers us to and find:
"Formally, the Poisson bracket (in classical mechanics) or commutator (in quantum theory) of t with any dynamical variable is always zero." (p. 406)
And so reveals Peres error -- the underlying SYMMETRY of the Brahmin phonetic-number ratio system.
I address this issue in chapter 4 of my blogbook --
Mothership Landing and math professor Joe Mazur stated it's "very valuable." Also the "time-frequency uncertainty principle" kicks off my book.
Nonwestern music relies on time as a dynamic of complimentary opposites -- in violation of the commutative principle (i.e. the conversion of uncertainty principle back into logarithmic-based mathematics).