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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.
I too found the title odd
[moot]
- adjective
1. open to discussion or debate
2. of little practical value
It's not just a practical issue for measurement, so your "fix" is invalid. The correct explanation is in this post: http://science.slashdot.org/comments.pl?sid=3904863&cid=44110125
"Politicians and diapers must be changed often, and for the same reason."
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
Indeed. I don't know what crap "undergraduate textbooks" people use near the north pole, but here down under, the principle of Heisenberg is taught using _math_.
It has always been about measuring (not "knowing", the universe doesn't give a damn about what you know or don't know or it would forbid god from existing. Instead, it just hampers aquiring new knowledge of the full state vector ;p). And it has always been a nice mathematical, strictly quantified trade off between the precision you'll get out of one of the measurements being inversely correlated to the precision you'll get out of the other measurement because the product of the two must be at least half the reduced plank constant.
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
It seems the paper can be understood with undergraduate mathematics. The 3 authors' argumentation seems quite clear, and their proof rather convincing. One wonders, now and at this point, whether a lab experiment could be set up to falsify the whole thing... If not, Heisenberg stands proven true. Of the impact upon quantum cryptography I am not so sure, however, supposing that it takes "some quite advanced mathematics" ( as Wolfram once said about cyclotomic fields ) to tackle that issue.
Religous speak to God. Insane are spoken to by God. When all shut up, one can finally hear Shostakovich in peace
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.
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
Sounds like "theory" to me. What's with the media's reporting of science and ambiguous words? :)
FTFY
No colour or religion ever stopped the bullet from a gun
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!"
My guess would be 'miaow'
Only if it's still alive when you open the box.
Are you sure there's even a cat in the box?
I'm more confused than before
Just look in this box. In it, you'll find either a better summary or a dead cat.
The cow says "Moo." The dog says "Woof." The Timothy says "Thanks, valued customer. We appreciate your input."
It's just pining for the fjords.
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.
Correct fix: The uncertainty principle states that it is impossible for a particle to be in a state in which both the position and momentum (or any pair of observables represented by non-commuting operators) are exactly defined, or even well-defined beyond a certain limit determinable from the commutator of the pair of operators.
It has nothing to do with measurement, and everything to do with the mathematical existence of quantum states with certain properties. TFA is actually dealing with the observer effect, which does have to do with measurement, and which was Heisenberg's original intuitive idea.
SIGSEGV caught, terminating
wait... not that kind of sig.
subatomic particles simply don't have precise position/momentums.
This is exactly correct. Exact position and exact momentum are not properties that a particle may possess simultaneously, no matter how well or poorly you might try to measure them.
SIGSEGV caught, terminating
wait... not that kind of sig.
In the early days, people debated whether uncertainty was just a practical issue of imperfect measuring devices/methods or a fundamental feature of the system.
We now know that it is a fundamental feature. Even if you had a perfect measuring device that did not disturb the system being measured, the act of measuring in any capacity is subject to uncertainty and collapsing of the wave function.
Despite the fact that it seems to violate our common sense (developed at room temperatures with macroscopic physical forces, thus unsuited for quantum reasoning), the world at that tiny level really is probabilistic. It is not a side-effect of our measurement methods or anything else... It simply works that way. Reality as we know it is just a side-effect of all those quantum states interacting and causing wave function collapse... Same reason a quantum computer is harder and harder to make the more bits it has.
Natural != (nontoxic || beneficial)
"So meaning 4 seems appropriate"
4 may be appropriate, but I think it's a thin argument. But even so... so what? Even if 4 is the way it was intended to be used, how is that even remotely headline-worthy?