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Proof Mooted For Heisenberg's Uncertainty Principle
ananyo writes "Encapsulating the strangeness of quantum mechanics is a single mathematical expression. According to every undergraduate physics textbook, the uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle — the more precisely one knows the particle's position at a given moment, the less precisely one can know the value of its momentum. But the original version of the principle, put forward by physicist Werner Heisenberg in 1927, couches quantum indeterminism in a different way — as a fundamental limit to how well a detector can measure quantum properties. Heisenberg offered no direct proof for this version of his principle. Now researchers say they have such a proof. (Pre-print available at the arXiv.) If they're right, it would put the measurement aspect of the uncertainty principle on solid ground — something that researchers had started to question — but it would also suggest that quantum-encrypted messages can be transmitted securely."
The uncertainty principle is the same as taking a Fourier transform of a sound pulse. If the time of the wave is short then the uncertainty in the frequency is high, and you get a large width in frequency space. If the wave is on for a long time, you get a nice sine wave and the uncertainty in the frequency is low, but the uncertainty in the time is now high. The maths for momentum/position of electrons comes out the same as time/frequency of sound waves. You get the uncertainty principle with non-quantised waves anyway, its not magic!
Don't fuck with Heisenberg folks.
Yet another proof of the principle.
Now let's see what the cat has to say about it.
If builders built buildings the way programmers wrote programs, then the first woodpecker would destroy civilization.
http://dictionary.reference.com/browse/moot says:
verb (used with object)
4. to present or introduce (any point, subject, project, etc.) for discussion.
5. to reduce or remove the practical significance of; make purely theoretical or academic.
So meaning 4 seems appropriate. Strange that a word simultaneously means to introduce it and to remove it from consideration, but it is a pretty old word I think so it has probably evolved quite a bit.
Origin:
before 900; Middle English mot ( e ) meeting, assembly, Old English gemt; cognate with Old Norse mt, Dutch gemoet meeting. See meet1
Heisenberg was speeding down the highway. Cop pulled him over and says "Son, do you have any idea how fast you were going back there?" Heisenberg said, "No, but I knew where I was". The cop says "You were doing 100 miles an hour" to which Heisenberg replies "Great, now I'm lost".
Here today, gone tomorrow
Robertson proved in 1929 already the general form of the uncertainty relation. It has nothing to do with Fourier transforms, wavefunctions and disturbance by measurements, but only with the operator character of (some) quantum mechanical observables. I got the proof from this textbook by Stephen Gasiorowicz, unfortunately they skipped this important result from the latest edition (that circulates on internet in the usual places). More information can be found in https://en.wikipedia.org/wiki/Uncertainty_principle#Robertson.E2.80.93Schr.C3.B6dinger_uncertainty_relations
From Quantum Physics by Stephen Gasiorowicz, ISBN 0 471 29281-8
It is important to note that the uncertainty relation
(Delta A)^2 (Delta B)^2 >= \langle i[A,B] \rangle^2 / 2
was derived without any use of the wave concepts or the reciprocity between
a wave form and its fourier transform. The results depends entirely on the
operator properties of the observables A and B.
Heisenberg and Schrodinger are driving, and get pulled over.
Heisenberg is in the driver's seat, the officer asks "do you know how fast you were going?"
Heisenberg replies, "No, but I know exactly where I am!"
The officer looks at him confused and says "you were going 108 miles per hour!"
Heisenberg throws his arms up and cries, "Great! Now I'm lost!"
The officer, now more confused and frustrated orders the men outside of the car, and proceeds to inspect the vehicle. He opens the trunk and yells at the two men, "Hey! Did you guys know you have a dead cat back here?"
Schrodinger angrily yells back, "We do now, asshole!"
The more you know about the position of the cat, the less you know about its velocity. Ever try to measure the position of a cat that you just dropped into the bathtub? You know it has a high velocity, but it's hard to tell where it really is.