4 ms·
Heisenberg's uncertainty principle and the musician's uncertainty principle
- danharaj 7y agoThe 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.
- aswanson 7y agoExactly. 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.
- aswanson 7y agoSeems like a few folks here know how to project a single sample onto a vector valued function. Brilliant people.
- kevinwang 7y agoHm... 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 7y agoYeah. 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.
- lisper 7y agoThe problem is that the simultaneous position and momentum of a particle does make sense, it just happens not to be how our world works because the world is not actually made of particles, it's made of fields, and those fields obey wave equations. A better analogy IMO is that it's impossible to have a wave whose position and direction are simultaneously well defined. If you throw a stone into a pond you will get a circular wave front with a well-defined position (where the stone landed) and a completely undefined direction. Likewise, you can get a wave that has a well-defined direction (as you do along a seashore, where the waves move perpendicular to the coastline) but to make that happen the wave has to be very wide. It's impossible to make a wave (in open water) that is simultaneously well-localized and moving in a particular direction.
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- lidHanteyk 7y agoIndeed, 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 7y agoYou 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.
- Misdicorl 7y agoMeasuring the half wave length of some physical process is literally performing the Fourier transform and pulling out the dominant coefficient
- vermarish 7y agoI think we're interpreting the link you provided differently. The way I read it, the author is taking the analogy between the Fourier Uncertainty and the Heisenburg Uncertainty and extending it to a similar analogy between the Nyquist Theorem and Brillouin Zones.
- jefftk 7y agoIf 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.
- sudosysgen 7y agoIsn't that basically just doing signal processing on the Fourier transform, because you know the Fourier series in advance?
- jefftk 7y agoUsing 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.
- sudosysgen 7y agoYes, 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.
- stazz1 7y agoThe 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 7y agoDo you have any resources on this? Sounds interesting but I couldn't find any writing on the links between these ideas.
- mrobot 7y agoThe 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?
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