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 Posted: Sat Sep 08, 2007 6:52 pm
Forgive my simplicity...
But what I gather from this is that...
1) The more "precise" we get, the more powerful/shorter wavelengths are used, and we get a better picture of where a particle is... however, hitting it with that (and forcing it into a state) upsets its momentum (direction as well) terribly.
2) The less 'precise' we are, the less we disturb the momentum, etc., so we know the speed/direction/etc. more.
3) GM more or less says particles are waves and states at once until observed? I think. I tried to find where something like that was said. I'm out of it. Sorry. ;p
4) And of course, by 1+2, those variables cannot be commutative and therefore be exact.. . . . .. something like that. I'm bad at putting words to what I'm 'seeing'/thinking in my head.
Jist of it? ;P
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Posted: Sat Sep 08, 2007 7:31 pm
AirisMagik Forgive my simplicity... But what I gather from this is that... 1) The more "precise" we get, the more powerful/shorter wavelengths are used, and we get a better picture of where a particle is... however, hitting it with that (and forcing it into a state) upsets its momentum (direction as well) terribly. 2) The less 'precise' we are, the less we disturb the momentum, etc., so we know the speed/direction/etc. more. 3) GM more or less says particles are waves and states at once until observed? I think. I tried to find where something like that was said. I'm out of it. Sorry. ;p 4) And of course, by 1+2, those variables cannot be commutative and therefore be exact.. . . . .. something like that. I'm bad at putting words to what I'm 'seeing'/thinking in my head. Jist of it? ;P It's not 'precise' in a general sense of how precise we measure anything, it's how precise we are in terms of position. If we measure the momentum precisely, then we don't disturb the momentum so much, but we lose precision with regard to the position. So it's a matter of either precision in position, or precision in momentum. Also, QM says that the wavefunction of an unobserved particle is the sum of all the wavefunctions of individual states; this is not quite the same as being in all of those states, just as northwest can't be said to be directly north or directly west in the strictest sense, but rather a sum of the two. The non-commutative nature is somewhat difficult to describe intuitively, but that's the general gist of it; non-commutation leads to inexactness.
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Posted: Sat Sep 08, 2007 8:12 pm
The argument seems a little backward: the non-commutative nature of the operators is what "causes" the uncertainty principle's "inexactness" to occur. If two quantum operators do commute — for example, the Hamiltonian [which gives you the energy of the state] and position operators — we can know both observables exactly [tempered by finite resolution effects, but we are not hampered by an additional innate fuzziness which is what happens if we try to get a handle on the position and momentum at the same time].
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Posted: Sat Sep 08, 2007 11:14 pm
Layra-chan AirisMagik Forgive my simplicity... But what I gather from this is that... 1) The more "precise" we get, the more powerful/shorter wavelengths are used, and we get a better picture of where a particle is... however, hitting it with that (and forcing it into a state) upsets its momentum (direction as well) terribly. 2) The less 'precise' we are, the less we disturb the momentum, etc., so we know the speed/direction/etc. more. 3) GM more or less says particles are waves and states at once until observed? I think. I tried to find where something like that was said. I'm out of it. Sorry. ;p 4) And of course, by 1+2, those variables cannot be commutative and therefore be exact.. . . . .. something like that. I'm bad at putting words to what I'm 'seeing'/thinking in my head. Jist of it? ;P It's not 'precise' in a general sense of how precise we measure anything, it's how precise we are in terms of position. If we measure the momentum precisely, then we don't disturb the momentum so much, but we lose precision with regard to the position. So it's a matter of either precision in position, or precision in momentum. Hmm.. You should always be wary of "disturbance" explanations for the uncertainty principle. The uncertainy in QM is much more intrinsic than that. Work with parametric down converters has shown that the uncertainty principle is truly "weird". We can say these strange relationships hold no matter how non-intrusive the method of investigation is. Quote: The argument seems a little backward: the non-commutative nature of the operators is what "causes" the uncertainty principle's "inexactness" to occur. If two quantum operators do commute — for example, the Hamiltonian [which gives you the energy of the state] and position operators — we can know both observables exactly [tempered by finite resolution effects, but we are not hampered by an additional innate fuzziness which is what happens if we try to get a handle on the position and momentum at the same time]. Orthonormal bases! How can a a physical phenomenon simply 'adhere' to a mathematical concept in such an arbitrary/abstract way. It wrecks my head.
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Posted: Sat Sep 08, 2007 11:51 pm
Morberticus Orthonormal bases! How can a a physical phenomenon simply 'adhere' to a mathematical concept in such an arbitrary/abstract way. It wrecks my head. My stock response: it does not; our best means of describing its effects requires this construction. You can hate me for that answer, I expect it.
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Posted: Sun Sep 09, 2007 5:21 am
A Lost Iguana Morberticus Orthonormal bases! How can a a physical phenomenon simply 'adhere' to a mathematical concept in such an arbitrary/abstract way. It wrecks my head. My stock response: it does not; our best means of describing its effects requires this construction. You can hate me for that answer, I expect it. Bah! I'll believe it when I see it.
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Posted: Sun Sep 09, 2007 11:03 am
I UNDERSTANDS MORE!
Huzzah.
I wish I could download information from people's brains. That, or have a photographic memory. Mehh.
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Posted: Sun Sep 09, 2007 2:28 pm
Morberticus,
Math is our best way of describing logical occurrences. The physical reality doesn't care about our mathematical construct, this is correct. But our sole interpretation of nature - the mathematically rigorous formulation of physics - is the only method we have of modelling, describing, or even coming close to understanding what we view as logical cause-effect relationships.
This distinction wasn't nearly as important in classical mechanics. Position and velocity are pretty simple concepts, and the transition from force (physically intuitive) to action (mathematically accurate) was pretty easy. But in quantum mechanics, the mathematical formulation is all we have. We haven't found any other way of accounting for everything we've observed. The mathematically-correct-but-physically-unintuitive (at first) formulation with vector spaces, operators, Hamiltonians, etc. has yet to be equalled in describing the quantum realm.
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Posted: Sun Sep 09, 2007 6:05 pm
Swordmaster Dragon Morberticus, Math is our best way of describing logical occurrences. The physical reality doesn't care about our mathematical construct, this is correct. But our sole interpretation of nature - the mathematically rigorous formulation of physics - is the only method we have of modelling, describing, or even coming close to understanding what we view as logical cause-effect relationships. This distinction wasn't nearly as important in classical mechanics. Position and velocity are pretty simple concepts, and the transition from force (physically intuitive) to action (mathematically accurate) was pretty easy. But in quantum mechanics, the mathematical formulation is all we have. We haven't found any other way of accounting for everything we've observed. The mathematically-correct-but-physically-unintuitive (at first) formulation with vector spaces, operators, Hamiltonians, etc. has yet to be equalled in describing the quantum realm. That's what wrecks my head. The world is 'damn queerer than we suppose'.
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Posted: Sun Sep 09, 2007 11:43 pm
This is why I'm perfectly happy with my non-interpretive, purely mathematical understanding of quantum mechanics. It all makes sense when there's no meaning attached to it.
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Posted: Fri Sep 14, 2007 2:30 pm
I'd have to recommend Layra's approach, at least at first. You have to abandon all preconceptions of the universe, and do your best to understand what quantum mechanics says *mathematically* before you can begin to understand how it should work *physically*. In time, one can - and often does - develop an intuition for what happens at the quantum-mechanical level, however hard that may be to describe.
On a (partial) side note, this is where linguistics comes into effect. The words that we use to describe physical phenomena are entirely intuitive, and clearly derived in the era of classical mechanics. It should come as no surprise that our very language itself defies attempts to describe QM. So, QM requires us to be mathematically accurate and linguistically vague, lest we impart connotations that simply don't exist.
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