[HN Gopher] The Heisenberg Uncertainty Principle Is Pure Mathema...
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The Heisenberg Uncertainty Principle Is Pure Mathematics
Author : gumby
Score : 32 points
Date : 2021-07-20 14:08 UTC (8 hours ago)
(HTM) web link (www.cantorsparadise.com)
(TXT) w3m dump (www.cantorsparadise.com)
| svat wrote:
| The main paragraph, just before "*This* is Heisenberg's
| uncertainty principle!":
|
| > _The more sure we are that a given particle is inside a small
| interval, the more localized (horizontally squished) the wave
| function of the position is going to be. And since the wave
| function of the momentum is the Fourier transform of the wave
| function of position, the momentum wave function is going to be
| stretched out horizontally meaning that there is going to be a
| greater uncertainty of the momentum. This is due to the above-
| mentioned scaling property of the Fourier transform._
|
| This made me realize I didn't really know the meaning of
| "momentum" (that's physics); I found these helpful:
|
| * https://physics.stackexchange.com/questions/39442/intuitive-...
|
| * https://physics.stackexchange.com/questions/35746/is-there-a...
|
| * https://en.wikipedia.org/w/index.php?title=Position_and_mome...
| sempron64 wrote:
| This is an incredible explanation! I'd love a deeper explanation
| of the uncertainty principle applied to the Doppler effect for
| radar that is mentioned in passing.
| landtuna wrote:
| Here's a decent explanation:
|
| https://www.radartutorial.eu/01.basics/Doppler%20Dilemma.en....
| gballan wrote:
| Cool. I confess I don't have this 100% straight, but it must
| be related to the CRB for range estimation. For time
| (equivalent to range) tau, [2, example 3.13] gives it as
| var(tau) > 1/(Eb/N0 * MSB), where MSB is the mean-square
| bandwidth of the pulse.
|
| [2] Fundamentals of Statistical Signal Processing, Volume 1:
| Estimation Theory.
| gballan wrote:
| You may like Chapter 16, "DURATION-BANDWIDTH RELATIONSHIPS AND
| THE UNCERTAINTY PRINCIPLE", of one of my favorite books [1].
|
| [1] Siebert, William McC.. Circuits, Signals, and Systems. MIT
| Press, 1986.
| PaulHoule wrote:
| That is, it's a property of waves.
| bronzeage wrote:
| Note that interestingly, momentum and position in orthogonal
| directions do commute and don't have uncertainty.
|
| You can know both a particle position in the x direction and it's
| momentum in the y direction with 100% certainty. Some intuitive
| based explanations would give you the wrong impression here.
|
| Another way of looking at it is that momentum operator is
| equivalent to derivation, and derivation and multiplying by x
| don't commute: d/dx x - x d/dx = 1. So, depending on the order in
| which you measured (first momentum then position, or first
| position then momentum) you get a different result.
| onecommentman wrote:
| Isn't this being taught in quantum mechanics and Fourier
| transform courses at the advanced undergraduate level nowadays?
| The basic idea is discussed in Wikipedia pages for both
| Uncertainty Principle and Fourier Analysis. Since Fourier
| Analysis is so fundamental to Information Technology, I assumed
| FA would be covered in the first year or two, so this sort of
| discussion would pop up in a third year or fourth year QM or
| signals processing course.
|
| It's much more insightful than the uncertainty principle
| discussions in the Paleolithic era when I went to school, albeit
| the first FA derivation of the uncertainty principle dates back
| to the 1950s and 1960s.
| alisonkisk wrote:
| Isn't all of theoretical physics pure mathematics? That's the
| point.
|
| Well, maybe not "pure", but HUP isn't particularly "pure" either.
| jfengel wrote:
| What the article means is that the Heisenberg Uncertainty
| Principle isn't just some problem of measurement that could
| possibly be overcome by better tools.
|
| Rather, HUP is a mathematical consequence of the axioms of
| quantum mechanics, and you won't get around it by clever
| technology. Only blowing up QM entirely would get around HUP --
| and the results would almost certainly be less familiar, rather
| than more like classical mechanics. (Indeed, this is already
| the case: it's called Quantum Field Theory.)
| bsaul wrote:
| hey, since you might be familiar with this: so quantum field
| theory is actually a departure from QM instead of its
| continuity ? I'm confused, i thought QM was the best thing we
| had regarding quantum behaviors...
|
| Also, i sometimes saw theoretical physicists talk about
| "quantum gravity" as if it was a solid theory (i tried to
| look at some presentation on the topic, but it was way beyond
| my level)... That made me even more confused, because i was
| under the impression that chord theory was the only thing we
| had to unify quantum mechanic and general relativity, and
| that it was far from accomplished...
|
| Could you (or anyone reading this) help me out of my
| confusion ?
| Koshkin wrote:
| QM alone fails to account for certain facts. QFT does this
| by using somewhat "weird" methods in order to bring Special
| Relativity and QM together. It has been working pretty well
| so far, and it is indeed the best we have. String Theory,
| on the other hand, while being a consistent theory of
| quantum gravity, uses a model (or models) that we may never
| be able to verify experimentally.
| Koshkin wrote:
| The difference between theoretical physics and mathematics is
| 1) the subject and 2) the criterion of truth.
| quantum_state wrote:
| Uncertain about what is being added here ... a straw man seemed
| to be set up and hit ... It is not surprising one cannot take any
| pop science description of science too seriously ... like the so-
| called weird nature of a quantum thing "being at two places at
| the same time" is not accurate and misleading ...
| quantum_state wrote:
| The assertion "Is Pure Mathematics" is wrong and misleading ...
| Koshkin wrote:
| How about "a _logical_ consequence of the wave nature..."?
| (Personally, I make no distinction between "logical" and
| "mathematical.")
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