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Old 04-11-2004, 03:58 PM   #1 (permalink)
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Quantum Uncertainty

I'm not entirely sure that this belongs here; it may be a Tilted Philosophy topic. Oh, well. Here goes:

Quantum physics says that certain properties of unobserved subatomic particles are defined, not precisely, but by a probability wave that collapses to a definite answer (within a given range of uncertainty) once it's observed.

For example, an electron has no definite position in space, just the varying probablilty of being in any number of places, until I observe it. Before I've observed it, it can be said that the electron exists in all of these places simultaneously. But once I've observed it, it exists only where I observed it to be.

My question is this: does this apply to the macroscopic level?

Imagine you have a deck of cards. Shuffle them and place one card face down in front of you. Which card is it? Since we've not observed the value (rank and suit) of the card, it has an equal probabilty of being any one of the 52 cards in a deck. Now flip the card over--it's the 9 of diamonds.

Here's the part that I'm trying to figure out--was that card the 9 of diamonds before you flipped it over? Or did it become the 9 of diamonds because (and only because) you observed it? And if it only became the 9 of diamonds because you observed it, what was printed on its face before you flipped it over?
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Old 04-11-2004, 04:17 PM   #2 (permalink)
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Similar to Schroedinger's Cat

From Wikipedia - http://en.wikipedia.org/wiki/Schr%F6dinger's_cat

Quote:
Schrödinger's cat is a thought experiment devised by Erwin Schrödinger that attempts to illustrate the incompleteness of the theory of quantum mechanics when going from subatomic to macroscopic systems.

A cat is placed in a sealed box. Attached to the box is an apparatus containing a radioactive nucleus and a canister of poison gas. When the nucleus decays, it emits a particle that triggers the apparatus, which opens the canister and kills the cat. According to quantum mechanics, the nucleus is described as a superposition (mixture) of "decayed nucleus" and "undecayed nucleus". However, when the box is opened the experimenter sees only a "decayed nucleus/dead cat" or a "undecayed nucleus/living cat." The question is: when does the system stop existing as a mixture of states and become one or the other? The purpose of the experiment is to illustrate that quantum mechanics is incomplete without some rules to describe when the wavefunction collapses and the cat becomes dead or alive instead of a mixture of both.

Contrary to popular belief, Schrödinger did not intend this thought experiment to indicate that he believed that the dead-alive cat would actually exist; rather he considered the quantum mechanical theory to be incomplete and not representative of reality in this case.....
Fun stuff to think about
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Old 04-11-2004, 04:31 PM   #3 (permalink)
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As the card is a known physical object, with a probability based on known parameters (1 of 52), I would suspect it has a set reality, and no fluctuation. As this card is made of billions of subatomic particles, formed into an animate object it has lost the micro-aspect, in favor of its observable macro aspect.
This, to me would change the dynamics of observation and solidify (if you will) the random nature of individual particle interaction, thus making the matter fundamentally stable for observation.

But , I could be talking out my cats ass.
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Old 04-11-2004, 07:02 PM   #4 (permalink)
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That was my instinct, too, but can it be demonstrated that the card has a definite and preset value?
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Old 04-12-2004, 09:44 AM   #5 (permalink)
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I think the problem here, on both the quantum and macro levels, is one of epistemology rather than one of metaphysics. It's not that the electron doesn't have a definite orientation in space; it's just that we can't know it (or, perhaps, that there aren't really electrons, I suppose). Same thing with the card. It's not that it's not definitely the nine of diamonds, it's just that we don't know it.
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Old 04-12-2004, 09:45 AM   #6 (permalink)
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I would think, if the entire deck of cards were spread out, face up. One could then assign a predefined value to any of the individual cards.Once the cards are reshuffled, the value has not changed, but is in fact only now in play, thus the 1 in 52 property.
Physically the card exists in the deck, and has a value defined by the earlier observation. The removal of the card is only the inevitable result of the experiment.
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Old 04-12-2004, 12:26 PM   #7 (permalink)
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Quote:
I think the problem here, on both the quantum and macro levels, is one of epistemology rather than one of metaphysics. It's not that the electron doesn't have a definite orientation in space; it's just that we can't know it (or, perhaps, that there aren't really electrons, I suppose). Same thing with the card. It's not that it's not definitely the nine of diamonds, it's just that we don't know it.
That doesn't work. Fire an electron toward a wall with two slits.

The electron seems to go through _both_ slits and the electron going through the right slit and the electron going through the left slit interfere.

When they hit the photoplate you place beyond the two slits, they form a pretty interferance pattern. Dispite the fact you only fired 1 electron at a time...

I'm a many-universes QMer myself.

It isn't the act of observing that causes QM wave collapse, observing just happens to make the observer and all but one of the observed states rotate to right angles of each other, no longer able to interact.

In any case, when you play with large-scale experiments, usually QM effects get removed by the large number of observer-like actions. So, under almost every interpritation of QM that I know of (all 3 of them, and I only know 'pop-sci' level), that card will be a 9 of hearts, not a "any card of any card"...

Hope at least some of that makes sense. =/
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Old 04-14-2004, 07:43 AM   #8 (permalink)
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fleacircus: i think you're asking, how does not knowing the position of something you don't observe make quantum sized-stuff different from regular-sized stuff? that's a pretty good question.

your analogy is slightly off though. the fact that, at quantum level, you don't know the position of something you don't observe is not a fundamental tenet of quantum physics--it's more of a side effect of another phenomenon--ie, the wave/particle duality (that all objects behave both as a wave and a particle). the fundamental rule is not that the unobserved has no position, but that, when unobserved, it behaves as something that cannot be said to have a position (ie, a wave). the card analogy you used is not the appropriate analog, since you're not talking about something having this duality. if quantum effects happened at our level, it would be as if you were in a vacuumed, very very dark room, and threw two identical cards from one end to the other, and found that, by repeating this experiment over and over again throwing exactly from the same positions and the same way, that the card landing positions were not a nice bell-shaped curve but were instead kind of wavy.

If you don't know what wave/particle duality is, ask me.
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Old 04-17-2004, 01:30 PM   #9 (permalink)
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You silly birds and your electrons...
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Old 04-17-2004, 04:04 PM   #10 (permalink)
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Quote:
Originally posted by rsl12
fleacircus: i think you're asking, how does not knowing the position of something you don't observe make quantum sized-stuff different from regular-sized stuff? that's a pretty good question.

your analogy is slightly off though. the fact that, at quantum level, you don't know the position of something you don't observe is not a fundamental tenet of quantum physics--it's more of a side effect of another phenomenon--ie, the wave/particle duality (that all objects behave both as a wave and a particle). the fundamental rule is not that the unobserved has no position, but that, when unobserved, it behaves as something that cannot be said to have a position (ie, a wave). the card analogy you used is not the appropriate analog, since you're not talking about something having this duality. if quantum effects happened at our level, it would be as if you were in a vacuumed, very very dark room, and threw two identical cards from one end to the other, and found that, by repeating this experiment over and over again throwing exactly from the same positions and the same way, that the card landing positions were not a nice bell-shaped curve but were instead kind of wavy.

If you don't know what wave/particle duality is, ask me.
Rsl, minor problem.

Wave/pariticle duality tells you alot. But, it doesn't deal with funky stuff like entanglement. You can have the states of two "things" entangled, seperate them by a large amount of distance, keeping them in what you call "wave" form, then observe them.

The observations made will correlate.

In fact, you can show using statistics that no "hidden state" in the wave is enough to hold the information needed.

So, now you have to hack in multiple particle entanglement and faster than light quantum communication to your wave/particle model.

Wave/particle duality explains really simple quantum interactions. You need more sophisticated mechanisms or interpritations...

And some of those more sophisticated interpritations do not have a wave/particle duality. (ie, "quantum wave collapse" doesn't "really" occur under some interpritations) In fact, some of those interpritations the card has a wave-like state: just, the wave-like state looks alot like a card to us.

Quote:
Originally posted by SixEdxMia
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I guess you really need a higher post count? =p~
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Old 04-18-2004, 01:24 PM   #11 (permalink)
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All you need to worry about here is:

S = K ln (W) according to the Boltzman equation

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Old 04-27-2004, 06:52 AM   #12 (permalink)
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Re: Quantum Uncertainty

Quote:
Originally posted by FleaCircus
Here's the part that I'm trying to figure out--was that card the 9 of diamonds before you flipped it over? Or did it become the 9 of diamonds because (and only because) you observed it? And if it only became the 9 of diamonds because you observed it, what was printed on its face before you flipped it over?
Yes, it was a nine of dimonds before you flipted it over. It traveled to the top of the deck while you were shuffling. It has observable diffrences other then what's printed on it.
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Old 05-01-2004, 03:15 PM   #13 (permalink)
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FleaCircus, actually the idea of quantum state collapse on measurement is *not* necessarily what Quantum Mechanics says - it is an interpretation of the mathematical formalism, and one that can be argued against. For me, one of the biggest difficulties with this interpretation is specifying how the wave function collapses - is this effect simultaneous everywhere? Given that there is no absolute simultaneity in Relativity etc...

To me, the best explanation of it all is from "Quantum Mechanics: A Modern Development" (Leslie Ballentine, World Scientific, 1998). He is very thorough in trying to dispell misconceptions about the subject, both mathematical and philosophical. For the meaning of quantum state vectors and the difficulties of collapse, see section 9.3 (The Interpretation of a State Vector).

As I understand it, the view presented in this book is that a quantum state does *not* apply to a single system (like your single electron), but to a (large or infinite) ensemble of similarly prepared systems. The implication would seem to be that the individual particle does have definite values of whatever dynamical quantities you're interested in - it's just that you won't know what they are until you measure them, and when you do, and if you repeat the measurement for a sufficiently large ensemble of similarly prepared systems, you will find your probability distribution emerging - which is the only thing you *can* predict. The most obvious example is the double-slit experiment. Trying it with a normal light source is essentially trying it with gazillions of similar systems at once. Try it with single photons, but repeatedly, and you still get the interference pattern building up.

Something else to note is the dubious assertion that if you measure a particle's position accurate to a small amound dx, then its momentum immediately acquires an uncertainty dp, where dx times dp = h / 2Pi (the supposed content of Heisenberg's Uncertainty Principle). Actually, as Ballentine takes great pains to point out in another part of the book, the mathematical derivation of this result is clearly statistical in nature, which points clearly towards the infinite ensemble interpretation. What the Uncertainty Principle actually says is that if you have a system in a state in which the "uncertainty" (actually, standard deviation) in position is dx and the "uncertainty" in momentum is dp for the whole ensemble of all such systems, then dx times dp = h / 2Pi.
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Old 05-01-2004, 04:41 PM   #14 (permalink)
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Quote:
As I understand it, the view presented in this book is that a quantum state does *not* apply to a single system (like your single electron), but to a (large or infinite) ensemble of similarly prepared systems. The implication would seem to be that the individual particle does have definite values of whatever dynamical quantities you're interested in - it's just that you won't know what they are until you measure them, and when you do, and if you repeat the measurement for a sufficiently large ensemble of similarly prepared systems, you will find your probability distribution emerging - which is the only thing you *can* predict. The most obvious example is the double-slit experiment. Trying it with a normal light source is essentially trying it with gazillions of similar systems at once. Try it with single photons, but repeatedly, and you still get the interference pattern building up.
http://en.wikipedia.org/wiki/Quantum_mechanics

Quote:
Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement. He held that quantum mechanics must be incomplete, and produced a series of objections to the theory. The most famous of these was the EPR paradox. John Stewart Bell's theoretical solution to the EPR paradox, and its later experimental verification, disproved a large class of such hidden variable theories and persuaded the majority of physicists that quantum mechanics is not an approximation to a nominally classical hidden-variable theory.
Also see http://en.wikipedia.org/wiki/Interpr...ntum_mechanics

I assume he is ok with faster-than-light communication between particles?

It sounds like the Bohm interpretation.
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Old 05-01-2004, 07:00 PM   #15 (permalink)
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Once you get to something of a readily observable size, the wavelength is so small that the wave/particle duality is negligible. Additionally, the energy put into observing a macroscopic object is not sufficient to change the result of that observation.
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