
Heisenberg's uncertainty principle and the musician's uncertainty principle - montalbano
http://newt.phys.unsw.edu.au/jw/uncertainty.html
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danharaj
The uncertainty principle shouldn't be regarded as the fact that you cannot
exactly and simultaneously know both the position and momentum of a particle.
It should be regarded as the fact that such a concept doesn't even make sense,
the same way that the concept of "instantaneous spectral content" of a signal
doesn't even make sense.

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aswanson
Exactly. I remember asking a prof in undergrad what the spectrum of a single
time sample would be. He didn't give me a straight answer, but I realized
later that question was equivalent to asking what the average age of a single
person was.

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kevinwang
Hm... I think I get what you're saying, but isn't computing the average age of
a person over their lifetime pretty straightforward? integral of their age
divided by their total lifespan, which would be their (total lifespan)/2.

~~~
aswanson
Yeah. It's misworded. It's more like, given a particular person, and a given
instant in time, compute the average of an ensemble of people. It makes no
sense.

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jefftk
If you know the shape of the wave you can do a lot better: for example, for a
sine wave you can measure the distance between (interpolated) zero crossings.
That's what I do for [https://www.jefftk.com/bass-
whistle](https://www.jefftk.com/bass-whistle)

I think you can do even better than that by noticing the shape of the wave,
and then you're only limited by the precision of your hardware.

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sudosysgen
Isn't that basically just doing signal processing on the Fourier transform,
because you know the Fourier series in advance?

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jefftk
Using zero crossings (which only works for pure tones) doesn't involve any
Fourier transform at all. You literally just look at where the signal crosses
zero.

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sudosysgen
Yes, you don't need doing any fourier transform, but it seems to me to be
equivalent to doing signal processing after a fourier transform with the
knowledge that it's a pure tone.

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lidHanteyk
Indeed, the uncertainty principle arises directly from the Shannon-Nyquist
sampling theorem! [0]

[0] [https://arxiv.org/abs/1108.3135](https://arxiv.org/abs/1108.3135)

~~~
blattimwind
You don't need to do a fourier transform to measure a frequency, though. It
doesn't really need anything special to measure the frequency of a 440 Hz tone
to six digits or so given a single cycle. With some trickery you can get right
down to 10-20 ps resolution, which would give you approximately eight digits
from a single 440 Hz cycle. There is no frequency-domain effect here that
would prevent you from measuring the time interval of a single cycle more
accurately, except that it simply gets difficult on an electrical level when
we are talking about resolving sub-ps intervals.

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Misdicorl
Measuring the half wave length of some physical process is literally
performing the Fourier transform and pulling out the dominant coefficient

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stazz1
The Pauli Exclusion principle also fascinating with regards to music, if you
consider that waves must be engaged, but only some intensities and some phases
will do.

Hollow cavities and their acoustics explain the living potential of sound,
much like how electrons become the living potential of the electron cloud.
Does it make sense to consider electron clouds of smooth/continuous
volume/loudness? Or are we certainly limited by the electron states?

~~~
TaupeRanger
Do you have any resources on this? Sounds interesting but I couldn't find any
writing on the links between these ideas.

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mrobot
The line "The momentum of a photon (or anything else) is p = h/λ so,
multiplying the above equation by h gives Δp.Δx > ~1"

Multiplying both sides by h, should this read "Δp.Δx > ~h" or am i missing
something?

