Uncertainty Question

[foodchain]

No. It is possible to measure both the position and momentum of a particle at the same time with arbitrary precision (but not with exactness). Uncertainty is related to an inherent property of the state itself. A different state will have different values of, say, the uncertainty in position. Uncertainty is determine solely by what state the system is in. It is a statistical quantity. An individual measurement has nothing to do with uncertainty. I.e. you can't reduce the uncertainty in position by using more precise instruments. The only way to reduces uncertainty is to utilize a different quantum state, one for which the position is more localized.

 

Consider a spin-1/2 system which is in a superposition of the spin-up and spin-down states. Even though the spin itself can be measured with exact results (there are only two possible values that can be measured) the uncertainty in the spin is not zero.

 

Pete

 

Right but any single measurement in time regardless of sequence cant ever be free from having to deal with both uncertainty and superposition correct? So say you make a measurement of say some physical observable, making a measurement, ever, currently has to satisfy uncertainty and superposition correct?

 

So basically I just wonder if uncertainty exists in the quantum system because that system experiences superposition, why else does it exist if not for that?

 

I know this boils down to math ultimately but the math in physics has to model reality or pass such a test right? So how much of QM in regards to its physical proof should I view as being nothing more then current mathematical description? Does it not say anything direct about the nature of nature?

[Pete]

Right but any single measurement in time regardless of sequence cant ever be free from having to deal with both uncertainty and superposition correct?

As far as uncertainty goes, no. That is incorrect. Just to be sure we are on the same wavelength please post the definition of the term uncertainty as you understand the term. Thanks.

 

But I don't understand what you mean when you say that that one can't ever be free from having to deal with superposion. Any quantum state for a free particle can be in an eigensate corresponding to one physical observer but be in a superposision of the eigenstates of a complementary observable.

So say you make a measurement of say some physical observable, making a measurement, ever, currently has to satisfy uncertainty and superposition correct?

No. I think that you have the wrong idea what uncertainty is.

So basically I just wonder if uncertainty exists in the quantum system because that system experiences superposition, why else does it exist if not for that?

That's not far from the truth.

 

Pete

[foodchain]

As far as uncertainty goes, no. That is incorrect. Just to be sure we are on the same wavelength please post the definition of the term uncertainty as you understand the term. Thanks.

 

But I don't understand what you mean when you say that that one can't ever be free from having to deal with superposion. Any quantum state for a free particle can be in an eigensate corresponding to one physical observer but be in a superposision of the eigenstates of a complementary observable.

 

No. I think that you have the wrong idea what uncertainty is.

 

That's not far from the truth.

 

Pete

 

 

As I understand uncertainty in relation to QM is limits on how precise a solitary measurement/observation can be in regards to physical observables.

 

Such as if I view a system for instance like an atom, and I use a light or what not, the interaction with the atoms and the light make the observation more uncertain of say the non disturbed or original state before "collapse" on measurement. I also think this deals with entanglement right, rather then the idea of the observer effect, or that its not just a product of human interaction but how stuff on a QM scale actually behaves?

 

I am not sure but does this not deal with the physical observable having to be greater then or at least equal to either the Planck constant or zero point energy thing?

[swansont]

As I understand uncertainty in relation to QM is limits on how precise a solitary measurement/observation can be in regards to physical observables.

 

Such as if I view a system for instance like an atom, and I use a light or what not, the interaction with the atoms and the light make the observation more uncertain of say the non disturbed or original state before "collapse" on measurement. I also think this deals with entanglement right, rather then the idea of the observer effect, or that its not just a product of human interaction but how stuff on a QM scale actually behaves?

 

I am not sure but does this not deal with the physical observable having to be greater then or at least equal to either the Planck constant or zero point energy thing?

 

 

It has to do with complementary variables that don't commute. It is sometimes possible to measure a single variable to great precision, but then the other variable will have an uncertainty such that the inequality is preserved (known as squeezed states)

 

Superposition is two states of the same variable of one system. Entanglement deals with properties of two particles. These are distinct phenomena that you're jumbling together.

[foodchain]

It has to do with complementary variables that don't commute. It is sometimes possible to measure a single variable to great precision, but then the other variable will have an uncertainty such that the inequality is preserved (known as squeezed states)

 

Superposition is two states of the same variable of one system. Entanglement deals with properties of two particles. These are distinct phenomena that you're jumbling together.

 

So the spin or superposition of such for any giving electron for being either up or down cannot be viewed as a product of entanglement?

[swansont]

So the spin or superposition of such for any giving electron for being either up or down cannot be viewed as a product of entanglement?

 

An electron could be in a superposition because of entanglement, but it is not required — they are not the same thing. You could have one without the other.

[foodchain]

An electron could be in a superposition because of entanglement, but it is not required — they are not the same thing. You could have one without the other.

 

That just leaves me confused really. An electron does not have to be an electron does it? A electrons physical observables may not require entanglement to exist in some state, but entanglement is a quantum phenomena that I think can occur with any quantum states right? I still do not understand why uncertainty exists outside of superposition still. In regards to variables such as position or momentum, its all those variables collective behavior then that leads to uncertainty, why is this condition different from superposition? Plus cannot entanglement be discovered from using such variables in the first place to perform an operation in which the states of such can be described in respects to one another?

[swansont]

That just leaves me confused really.

 

Welcome to quantum mechanics

[fredrik]

If this makes no sense forget it, but it's what I think might be a easier way for you to picture this, considering your interests.

 

So basically I just wonder if uncertainty exists in the quantum system because that system experiences superposition, why else does it exist if not for that?

 

I know this boils down to math ultimately but the math in physics has to model reality or pass such a test right? So how much of QM in regards to its physical proof should I view as being nothing more then current mathematical description? Does it not say anything direct about the nature of nature?

 

I think perhaps you are making this more difficult than it is. QM is weird, but perhaps it's the math and the terminology here that makes these points appear weirder than necessary...

 

Swansont wrote

It has to do with complementary variables that don't commute. It is sometimes possible to measure a single variable to great precision' date=' but then the other variable will have an uncertainty such that the inequality is preserved (known as squeezed states)

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To try to conceptualize this with a minimum of math, I'd propose to think in terms of questions and answers, since they loosely correspond to the notions of measurements and their abstraction "operators". This is something that is easy to relate to.

 

The two measurements operators doesn't commute, conceptually means that you have two questions(Q1 and Q2) that doesn't commute. That in turns means that if you ask these two questions in a sequence, the answer of the second question may be different than if it was asked first and the order of asking them may leave you with different final states of information.

 

So [math]Q1 Q2 \neq Q2 Q1[/math]

 

This can be seen logically possible because how do you a priori know that you questions, that you can constructed so to speak are "independent"?

 

QM suggests that asking for position and asking for momentum, are two questions that doesn't commute, which is consistent with experiment. This in itself can be understood without reference to the notion of superposition.

 

If you want to probe something, to learn about it's properties, we start by constructing questions, right? To get answers one first has to ask questions, and to ask questions one first has to formulate/construct questions. Then from the point of view of survival, there shouldn't be far fetched to associate here that there might be more or less efficient ways to construct and fire questions, right? Clearly an observer who keeps asking redundant questions only will not learn as much. Ever played the games of figuring out what the other person are thinking of, asking the smallest number of yes/no questions? The one who solves the problem with a minimum number of questions wins.

 

But how do you know that your questions are compatible with each other? You might admitt that it's logically possible that asking one question "interferes" with other questions. That's what is going on in QM.

 

The classical intuition that position and momentum are not interfering is not something we know, it's something we thought, but which now in the quantum world has proven to be incorrect.

 

--------

Superposition (wether classical or quantum) could be thought of as a state where we do not know the answer to the question, but we know that the answer is one of a set of possible answers.

 

This view holds both classically and quantum mechanically. The difference lies in the logic of interference between "the possibilities".

 

If we ask a question Q, and know that it has two possible answers: U or D.

 

Then we might say that the system subject to questioning, as per our information, are in the state: (U or D). This means that we will treat it like a superposition. And it seems plausible that an environment which has the same information, will also treat it as a superposition. So in effect, the system IS in superposition. To think that - once it's measured and found to be at say U, then it was in U all the time - isn't right, because there is really no physical basis for claiming that something is this or that until it's measured.

 

This is some of the conceptual basis of QM. It's weird relative to classical realism, but once you start to appreciate it, i think it really makes more sense than the classical logic - it's a more sophisticated logic in a sense, and therefore I think more efficient. I figure nature made the same conclusion

 

Edit: I tried to communicate earlier. I am not trying to be abstract, I personally think this is a very simple way of thinking of this. QM is best thought of IMO, as the mechanics of information exchange, and the only states of relevance are states of information. If you try to switch perspective everything is easier. This is not to appear abstract or fancy, I really think this is the easy perspective.

 

/Fredrik

 

Does it not say anything direct about the nature of nature?

 

I think what it should say is that asking about the nature of nature, is a process, and more specifically a process composed of information exchange and self-organisation between it's parts. Where the parts can sort of be seen as abstract observers, observing it's environment.

 

So instead of looking for the nature of nature as some small absolute blocks, it could be (but presumably noone knows for sure yet!) that nature is nothing but relational processes.

 

So if you are to survive and grow in that environment, it does seem reasonable that you can not fire random questions, it seems more plausible that patterns will self-organized and the logic of this may follow a self-constructing logic.

 

Maybe the nature of nature is "questions" and information exchange. And perhaps certain questions construct and stabilise, and this is what we see as matter? I figure an atom, must be cleverly constructed to be stable. And the logic of it's stability may be the clue to understand QM and its' logic.

 

/Fredrik

Edited July 7, 2008 by fredrik
corrected formualtion

[foodchain]

Its not that I am trying to visualize just as much as I don’t understand the point of separation for concepts like superposition and relativity, or entanglement. The only interpretation I like is decoherence really. With that decoherence uses entanglement in regards to superposition and uncertainty correct, so in that formalism how do the variables come into play in a way that gives segregation to superposition and uncertainty.

[Pete]

As I understand uncertainty in relation to QM is limits on how precise a solitary measurement/observation can be in regards to physical observables.

Not at all. The very definition of uncertainty is statistical by nature. Is this what you think the definition of uncertainty is? If so then its wrong. There is a very precise mathematical formula for the uncertainty of a physical observable. It is dependant on the particular initial state that the system is in. A different initial state thus gives a different uncertainty for the observable.

Such as if I view a system for instance like an atom, and I use a light or what not, the interaction with the atoms and the light make the observation more uncertain of say the non disturbed or original state before "collapse" on measurement. I also think this deals with entanglement right, rather then the idea of the observer effect, or that its not just a product of human interaction but how stuff on a QM scale actually behaves?

No. This is all wrong. Even throwing a die has a non-zero undertainty associated with the outcome.

I am not sure but does this not deal with the physical observable having to be greater then or at least equal to either the Planck constant or zero point energy thing?

I'm not sure what you're asking in this question but let me say this - If you were to consider a state whose position wave function which has a width of delta x and and whose momentum wave function has a width of delta p then its the product of those widths that satisfies the uncertainty principle.

 

Pete

Edited July 8, 2008 by Pete
multiple post merged

[pioneer]

I think the confusion is the math predicts the uncertainty but the explanation of "why", does not exist without the math. I wonder if uncertainty is an artifact of the math since that is how we explain it.

 

Let me give an example. Say we replaced the newtonian equations of gravity with a statistical model. We would build in uncertainty. If we were asked to explain why there is uncertainty in our predictions and observations we would use this math to show that it does indeed exist.

 

Now if we developed the Newtonian second, since it does not display the uncertainty would that make it wrong since everyone expects its and has used this assumption so wide and far?

[Pete]

I think the confusion is the math predicts the uncertainty but the explanation of "why", does not exist without the math. I wonder if uncertainty is an artifact of the math since that is how we explain it.

 

Let me give an example. Say we replaced the newtonian equations of gravity with a statistical model. We would build in uncertainty. If we were asked to explain why there is uncertainty in our predictions and observations we would use this math to show that it does indeed exist.

Your analogy is quite flawed. There is no uncertainty intrinsic to Newtonian mechanics whereas in quantum mechanics there most definitely is. The very meaning of the wave function as the square being a probability density demands uncertainty. It can't be taken out no matter how its formulated unless the meaning of the wave function is changed, i.e. if the postulates of quantum mechanics were different.

 

Pete