I also have a Masters in physics. You really don't need to explain the FT to me. Or the QFT for that matter. Or any of this stuff. I already know. You understa

I also have a Masters in physics. You really don't need to explain the FT to me. Or the QFT for that matter. Or any of this stuff. I already know. You understand it all yet you somehow overlooked it in my original comment. The first comment that started this all was that if you look at the wave forms on your computer (say, in audacity), it turns out those are discrete, the implication being the computer representation is a discrete approximation of a continuous reality. I originally replied with "If you try to sample continuously and eliminate that discretization error, I have some bad news for you about the nature of reality itself..." The eventual break down into discretely quantized values isn't just an artifact of the digital medium, reality itself is quantized. There is no truly analog tape recorder. Fine you can sample in the fourier basis rather than position basis to keep your "pure sine waves"* in position space, but you're still always going to generate discrete samples and you'll still need the same number of them. You are free to shift representation around, but the same amount of quantized information is present and stored somewhere. The initial observation that the sound wave files on your computer are "1d pixels" is unavoidable. Every quantity, when viewed with sufficient precision, is "pixelized". *really what your doing is measuring in the momentum/energy basis, causing the function to be stepped there, but leaving the superposition intact in the position / time basis...until the listeners ear goes and measures in the position / time basis anyway. In principle if you've measured the sound wave as an ordinary time series down to the accuracy of quantized ear drum positions, it shouldn't matter if you're playing that back directly as "step function time series" or as superposition of sine waves via Fourier trick. In practice of course this never happens.