Re: [Csnd] OT: uncertainty question

Date	2012-09-28 02:18
From	pj@pjb.com.au
Subject	Re: [Csnd] OT: uncertainty question
	Peiman wrote: > Also, does this in anyway relate to the uncertainty principle? Yes, because (until they've been Observed) particles move in Waves (described by Schroedinger's wave-equation); think of them as probability-waves. For example, if you want to know the Momentum of a particle, that's done by measuring the wavelength of its quantum-wave, and to get an accurate answer you need to look at a packet many wavelengths long, so that its fourier-analysis contains only a very narrow band of wavelengths; but that means you don't have a precise measure of the particle's Position, it's spread out over that whole long distance. Conversely, if you want an accurate answer for its position, then you only look at a short snippet of its wave, which means the fourier analysis of that short snippet contains a broad band of wavelengths so your measurement of the momentum will be very uncertain. The maths of fourier-transforms means that there's a very simple equation relating the uncertainty in the momentum to the uncertainty in the position; it's called Heisenberg's Uncertainty Principle. That's between position and momentum; they're called "complimetary variables". There are other pairs of complimetary measurements, like Energy and Time, and they manifest the same uncertainty principle, because of the same simple feature of the maths of fourier-transforms, and the fact that particles move in probability-waves... It's exactly the same maths as when you play a 1-millisec snippet out of a bass-guitar note; the ear hears a click at a precise time, but can't make out what the note was. Regards, Peter Billam (P.S. hope I didn't make too many mistakes :-)) http://www.pjb.com.au pj@pjb.com.au (03) 6278 9410 "Follow the charge, not the particle." -- Richard Feynman from The Theory of Positrons, Physical Review, 1949

Date	2012-09-28 10:17
From	peiman khosravi
Subject	Re: [Csnd] OT: uncertainty question
	Thanks very much for this explanation. Best, Peiman On 28 September 2012 02:18, <pj@pjb.com.au> wrote: Peiman wrote: > Also, does this in anyway relate to the uncertainty principle? Yes, because (until they've been Observed) particles move in Waves (described by Schroedinger's wave-equation); think of them as probability-waves. For example, if you want to know the Momentum of a particle, that's done by measuring the wavelength of its quantum-wave, and to get an accurate answer you need to look at a packet many wavelengths long, so that its fourier-analysis contains only a very narrow band of wavelengths; but that means you don't have a precise measure of the particle's Position, it's spread out over that whole long distance. Conversely, if you want an accurate answer for its position, then you only look at a short snippet of its wave, which means the fourier analysis of that short snippet contains a broad band of wavelengths so your measurement of the momentum will be very uncertain. The maths of fourier-transforms means that there's a very simple equation relating the uncertainty in the momentum to the uncertainty in the position; it's called Heisenberg's Uncertainty Principle. That's between position and momentum; they're called "complimetary variables". There are other pairs of complimetary measurements, like Energy and Time, and they manifest the same uncertainty principle, because of the same simple feature of the maths of fourier-transforms, and the fact that particles move in probability-waves... It's exactly the same maths as when you play a 1-millisec snippet out of a bass-guitar note; the ear hears a click at a precise time, but can't make out what the note was. Regards, Peter Billam (P.S. hope I didn't make too many mistakes :-)) http://www.pjb.com.au pj@pjb.com.au (03) 6278 9410 "Follow the charge, not the particle." -- Richard Feynman from The Theory of Positrons, Physical Review, 1949 Send bugs reports to the Sourceforge bug tracker https://sourceforge.net/tracker/?group_id=81968&atid=564599 Discussions of bugs and features can be posted here To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"