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peter
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 Posted: Mon Nov 07, 2011 10:13 am Post subject: Uncertain about uncertainty - and Zeno isn't helping! |
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If I think about it, it seems logical that an object cannot have both a position and a velocity simultaniously. Take a car. Where is it and how fast is it going. Well - it's at point A going at x miles per hour. But if it's moving it can never be stationary at point A or if it's stationary at point A it cannot have a velocity - if you atempt by using ever smaller sub-units of time to get the car to a stationary position you finish up in a sort of 'Zeno's paradox type situation. Is this the reason why a sub atomic particle can never be described in terms both of it's motion and position or have I got it all wrong. Does pure logic lead us to the uncertainty principle on it's own without any need for the math? (not I hasten to add that I could ever describe my twisted form of logic as pure even in my wildest dreams  )
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| Posted: Mon Nov 07, 2011 4:23 pm Post subject: |
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No, you can't get H's Uncertainty Principle merely from common sense reasoning from macro-objects. Quantum objects don't have definite properties prior to measurement, they merely have probabilities of having certain measured properties. They aren't just uncertain, they are indeterminate, due to their wavelike nature and behavior.
It's possible to accurately measure a car' position and velocity, because the wavelike nature and behavior of macro-sized objects is negligible relative to their size.
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| Posted: Mon Nov 07, 2011 4:59 pm Post subject: |
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It isn't that something can't have both a position and velocity simultaneously, it is that we can't know what both are simultaneously...though we can come so close the difference doesn't matter for something like a car that's so big and moving so slow.
A number of interesting things are revealed by examining/analyzing Zeno's paradoxes...but I don't think they're really paradoxical at all.
Much like geometry is hella useful, yet based on things that exist only conceptually [like dimensionless points], most of the paradoxes depend on the same...for instance, the arrow in flight proving motion is illusion depends on something that probably can't be so: an instant with zero duration. In addition, even if there could be an instant with no duration the paradox depends on assuming that the arrow is motionless "during" that instant. It seems counter intuitive perhaps to think something could be moving if there is no time passing...but no more so than imagining the instant without duration in the first place.
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| Posted: Mon Nov 07, 2011 5:55 pm Post subject: |
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I thought that Heisenberg's Uncertainty Principle arose from the fact that, to measure a small particle's position, the act of observation affects it's velocity, and to measure a small particle's velocity, the act of observation affects it's position. This was proposed in 1927, before quantum physics entered scientific discussion.
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| Posted: Mon Nov 07, 2011 7:15 pm Post subject: |
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| wayfriend wrote: | | I thought that Heisenberg's Uncertainty Principle arose from the fact that, to measure a small particle's position, the act of observation affects it's velocity, and to measure a small particle's velocity, the act of observation affects it's position. This was proposed in 1927, before quantum physics entered scientific discussion. |
Well, yes and no. It was part of the beginnings of formal/rigorous quantum theory...before that it was a wild land of maths, spaces, and speculations.
But my understanding [which is a bit loose]: What you say is so because the means for measuring position and velocity exclude each other in a material sense...but that is connected to the also true in the purely conceptual/mathematical. The position and velocity math descriptions share properties, but they are not commutative. The result depends on the order of calculation.
In some strange way those two things are really the same thing.
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| Posted: Tue Nov 08, 2011 3:30 am Post subject: |
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| Vraith wrote: | | It isn't that something can't have both a position and velocity simultaneously, it is that we can't know what both are simultaneously. |
I'm not sure that's exactly right. Heisenberg's original terminology was mistranslated into "uncertainty" when he actually meant "indeterminate." This isn't about what we can know, but what is (which, as a result, determines what we can know). The reason we can't know both properties is because in reality they are indeterminate in themselves, and not because of our relationship with them in the form of measurement acts ... though these acts reveal the indeterminism.
| Wayfriend wrote: | | I thought that Heisenberg's Uncertainty Principle arose from the fact that, to measure a small particle's position, the act of observation affects it's velocity, and to measure a small particle's velocity, the act of observation affects it's position. This was proposed in 1927, before quantum physics entered scientific discussion. |
Well, technically, measuring an object's velocity also affects its velocity. Heck, measuring temperature with a thermometer affects the temperature. So why does the H.U.P. always talk about pairs of properties, and not merely a general sense of uncertainty in any measurement of single properties? Well, because it's not talking about imperfection our measuring devices, or how our measuring devices inevitably affect the system we're trying to measure. Instead, it's talking about conjugate attributes of quantum objects, and how measurements of one affect the possibility of measuring the other. That is strictly within the realm of quantum mechanics, and can't be applied to things like cars.
This is something distinctly different from the issue of measurment interferring with the system, because nothing about Heisenberg's principle limits you from knowing any single attribute to any degree of accuracy ... though uncertainty of its conjugate pair increasese to infinity.
From the book Quantum Reality, page 110:
| Nick Herbert wrote: | | Both Heisenberg and Bohr warned against interpreting the HUP in terms of a measurement disturbance. Rather they claimed that this relation marked the limits beyond which classical notions concerning attributes could not be pushed. One could speak classically about position and momentum only as long as those attributes were not too sharply defined. However, when you imagine conjugate attributes defined with an accuracy greater than that permitted by the HUP, you are thinking about something that cannot exist in nature, like a square circle. |
It is the nature of quantum properties, not measurement itself, which is the issue here. This looks like a measurement problem from our perspective (as macro objects capable of observation). However:
| Nick Herbert wrote: | ... from the quon's [i.e. quantum object] point of view, the spectral area code represents a guarantee from nature itself that its "realm of possibilities" will never be diminshed past a certain point. If you decrease the realm of a quon's position possibilities, you automatically extend the realm of its momentum possibilities. This natural feature of waves--their inability to be spectrally compressed in two conjugate dimensions--is a boon to quons, ensuring each one its own forever irreducible realm of possibilites. I call the HUP, seen from the quon's vantage, the "law of the realm": Thou sholt not decrease a quon's total realm of possibilities below a certain limit. The law of the realm is not arbitrary decreee but a mathematically certain consequence of wave nature itself.
Seen from outside--the human point of view--these obligatory conjugal relations look like "uncertainties." From the inside--the quon's point of view--they feel like "realms of possibility," the basic inalienable estate of every quon in the universe. |
[Don't let the figurative language fool you, this guy is a physicist.]
| Wayfriend wrote: | | This was proposed in 1927, before quantum physics entered scientific discussion. |
| Wikipedia wrote: | | Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of the wave–particle duality of matter and energy. The theory was developed in 1925 by Werner Heisenberg.[1] |
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| Posted: Tue Nov 08, 2011 12:29 pm Post subject: |
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Once again (was it like Socrates) all I can know is that I know nothing, but I think I get (at least) that the reason for the position/velocity problem at the quantum level is not comparable to the type of situation I described with the car above. Thanks for clearing this up for me guys.
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| Posted: Tue Nov 08, 2011 12:50 pm Post subject: |
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I'll read this thread later. Frankly, I have a very difficult time with such things. I've tried more than one book about Relativity, and just can't understand what they're saying. I know nothing about Uncertainty. But the first couple posts mentioned cars. I guess it makes sense that, if you know exactly where a car is in a given instant, you can't know how fast it's going, or in which direction. Like a photo of a car. You can't know even if it's moving, much less velocity.
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| Posted: Tue Nov 08, 2011 5:40 pm Post subject: |
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| Zarathustra wrote: | | Vraith wrote: | | It isn't that something can't have both a position and velocity simultaneously, it is that we can't know what both are simultaneously. |
I'm not sure that's exactly right. Heisenberg's original terminology was mistranslated into "uncertainty" when he actually meant "indeterminate." This isn't about what we can know, but what is (which, as a result, determines what we can know). The reason we can't know both properties is because in reality they are indeterminate in themselves, and not because of our relationship with them in the form of measurement acts ... though these acts reveal the indeterminism.
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That's because quantum stuff is freaking weird. You're right AFAIK that on the quantum scale the measurement problem is caused by the indeterminate nature of what is...[IIRC, there is actually a precise absolute minimum of uncertainty...1/2 the plank length maybe? Somesuch anyway.] But I'm also somewhat confident [I'm reaching back a couple decades here] that even if the "real" situation was NOT indeterminate the uncertainty would still exist both materially because the instruments needed conflict, and conceptually/theoretically in the math...because the results for a single particle [or whatever] change depending on nothing other than the order one performs the calculations.
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| Posted: Wed Nov 09, 2011 7:26 am Post subject: |
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| Avatar wrote: | Everything is uncertain.
--A |
I'm not.
Apologies to Werner, Niels, Max and Erwin, but what every quantum mechanics thread needs is a little Python. 
But while I'm here, good posts Zarathustra and Vraith. |
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| Posted: Wed Nov 09, 2011 11:43 am Post subject: |
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| Avatar wrote: | | Everything is uncertain. |
You sure about that? *rimshot*
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| Posted: Wed Nov 09, 2011 4:16 pm Post subject: |
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I'm definitely getting that it's impossible to know both the velocity and the position of something at the quantum level - but not for the reasons I gave above. But am I also getting that it is also impossible to know both the position and velocity of a car going down a road with absolute accuracy, but for a different set of reasons? eg every time we take a measurement we interfere with the thing being measured (I thought we could 'correct' for that kind of stuff)
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| Posted: Wed Nov 09, 2011 5:05 pm Post subject: |
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We can measure a car's position and velocity no problem, to a degree of accuracy beyond any conceivable need.
We can even do much better: we can shoot tiny probes at distant planets, and actually "hit" our targets, millions of miles away. If there was any meaningful problem with determining position and velocity of macro objects, this would be impossible. Reality trumps Zeno-esque logic.
I'm not sure what you mean by "absolute accuracy." If you're talking about scales smaller than Planck's constant, then no, you're not going to ever be successful in achieving that. But since cars are so many times larger than this scale, you might as well ignore it.
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| Posted: Wed Nov 09, 2011 5:26 pm Post subject: |
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Objects which have a mass sufficient to negate any Heisenberg limitation are subject to being measured or discerned without any noticeable effect. A radar gun does not impede an automobile, nor does it effect the direction or magnitude of its velocity.
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| Posted: Wed Nov 09, 2011 5:49 pm Post subject: |
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| Hashi Lebwohl wrote: | | Objects which have a mass sufficient to negate any Heisenberg limitation are subject to being measured or discerned without any noticeable effect. A radar gun does not impede an automobile, nor does it effect the direction or magnitude of its velocity. |
Yea, that and what Z said: on the macro scale the the difference between the absolutely precise and the achievable precision is so small they can be safely ignored in almost every case.
[though we're rapidly approaching the point where it will affect how common devices are/can be made].
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| Posted: Wed Nov 09, 2011 6:19 pm Post subject: |
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But... Look, I'm not arguing for anything I know anything about here. I'm just saying, if I show you a picture of a car, we can use the landmarks to determine exactly where it is. But you wouldn't be able to tell me how fast and in which direction it's going, or even if it's moving at all. If you try to tell me exactly where a moving car is in any given instant, you won't be able to. Not with absolute precision. Get out your ruler and tell me exactly how many mm it is from the curb, from the corner, etc, and you won't be able to. Because it's moving, and it will not be on that exact piece of pavement by the time you get your reading. Don't tell me where it was within X cm, but you can't be exact because it was moving and you can't tell me to within a thousandth of a millimeter where it was exactly that instant. I want EXACT.
Am I making any sense? 
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| Posted: Wed Nov 09, 2011 6:38 pm Post subject: |
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Thinking about it the wrong way, really.
The properties of subatomic particles are indeterminate because they don't exist in a discrete state like macroscopic objects do - and we can only observe them through their interactions. It should be pretty obvious that any interaction means an exchange of energy in some way, changing the system under observation.
(It's not so much that the subatomic particles behave strangely, but that the macroscopic physics we're used to looking at are an emergent property that comes from viewing what's going on from too far away.)
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