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Thread: The Heisenberg Uncertainty Principle

  1. #1 The Heisenberg Uncertainty Principle 
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    My older brother told me that you can never know the position and momentum of a particle at the same time. So I looked it up on Wiki and it's called the Heisenberg Uncertainty Principle. But I don't see how this can be true, because it doesn't make any sense. Can somebody explain why you can't know them both at the same time?

    Thanks


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    Quote Originally Posted by MarkS1 View Post
    My older brother told me that you can never know the position and momentum of a particle at the same time. So I looked it up on Wiki and it's called the Heisenberg Uncertainty Principle. But I don't see how this can be true, because it doesn't make any sense. Can somebody explain why you can't know them both at the same time?

    Thanks
    You need to learn the basics of quantum theory. Why doesn't it make sense to you?


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    Quote Originally Posted by MarkS1 View Post
    My older brother told me that you can never know the position and momentum of a particle at the same time. So I looked it up on Wiki and it's called the Heisenberg Uncertainty Principle. But I don't see how this can be true, because it doesn't make any sense. Can somebody explain why you can't know them both at the same time?

    Thanks
    That's not exactly what the Heisenberg Uncertainty Principle (HUP) states. The HUP states that the position and momentum of a particle is not simultaneously determined. For example: suppose to have a quantum mechanical system which you have prepared in a certain state . Now measure the position exactly and record it. Then return the system back to its original state and repeat the measurement over again, once again measuring the position exactly and recording it. Keep doing this a number of time (perhaps a 10 thousand times). Each time you do it you will get a different result, all of which are about a particular value. After this is done calculate the standard deviation of the position measurements. Label the result . Then go back and do the same thing all over again but this time measure the momentum. This time calculate the standard deviation of the measured results and label it . The two values and are a function of the initial quantum state that the system is in. The results will satisfy the Heisnberg uncertainty reltionship



    If you then started from scratch but this time changed the initial state of the system and repeated the wehol process described above you'd get different values of and , however the uncertainty relationship would stil hold. As one value increased the other value would decrease while at the same time satisfying the uncertainty relation above.

    This is what your older brother was refering to. Although he may not have fully understood it.
    Last edited by pmb; July 9th, 2012 at 06:28 PM. Reason: mistake in latex symbols
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    Quote Originally Posted by mathman View Post
    You need to learn the basics of quantum theory. Why doesn't it make sense to you?
    The HUP refers to the results of lab experiments and that can be described rather easily in a single post. See post #3 above. You might like it. If not then let me know and we can work towards a common understanding.
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    Quote Originally Posted by pmb View Post


    The "greater than" sign is supposed to be a "greater than or equal to" sign. I just don't know how to write the later.
    Its \geq
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    Quote Originally Posted by mathman View Post
    Quote Originally Posted by MarkS1 View Post
    My older brother told me that you can never know the position and momentum of a particle at the same time. So I looked it up on Wiki and it's called the Heisenberg Uncertainty Principle. But I don't see how this can be true, because it doesn't make any sense. Can somebody explain why you can't know them both at the same time?

    Thanks
    You need to learn the basics of quantum theory. Why doesn't it make sense to you?
    mathman, it doesn't make any sense because in order to know the momentum, I have to know the position. If I measure the particle's position at point "A" and then I measure it again at point "B" then I just need to do a little math to figure out its momentum. So I can know both its position and its momentum at point "B". The more precisely that I know the particle's position, the more precisely I know its momentum.
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    [QUOTE=MarkS1;336393][QUOTE=mathman;336385]
    Quote Originally Posted by MarkS1 View Post
    My older brother told me that you can never know the position and momentum of a particle at the same time. So I looked it up on Wiki and it's called the Heisenberg Uncertainty Principle. But I don't see how this can be true, because it doesn't make any sense. Can somebody explain why you can't know them both at the same time?

    Thanks
    I think that you're confusing single measurements with an ensemble of measurements. Its the ensemble of measurements that hte Heisenberg uncertainty relation is all about.
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    Quote Originally Posted by pmb View Post
    Quote Originally Posted by MarkS1 View Post
    My older brother told me that you can never know the position and momentum of a particle at the same time. So I looked it up on Wiki and it's called the Heisenberg Uncertainty Principle. But I don't see how this can be true, because it doesn't make any sense. Can somebody explain why you can't know them both at the same time?

    Thanks
    That's not exactly what the Heisenberg Uncertainty Principle (HUP) states. The HUP states that the position and momentum of a particle is not simultaneously determined.

    So are you saying that I can know both the position and momentum at the same time, if I measure its position and determine its momentum, but what I can't do is predict what they will be at some point in the future? The more precisely that I can predict one, the less precisely I will be able to predict the other?
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    Quote Originally Posted by pmb View Post
    I think that you're confusing single measurements with an ensemble of measurements. Its the ensemble of measurements that hte Heisenberg uncertainty relation is all about.
    Is there any way to determine momentum other than by making two measurements, and calculating the momentum?

    EDIT: That's what's confusing me I guess. In order to know the momentum I have to make two measurements and then calculate the momentum. Thus the second measurement will tell me both position and momentum.
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    To determine the momentum of a particle requires a measurement of position at two points. On way to intuitively think about the problem is to note that the measurement of a particle requires us to bounce light off of it to see it, or at least something to that effect. But when we hit the particle with a photon of light, this inherently changes the momentum of the particle. There is no way to make measurements without altering the state of the particle. The more accurately we want to know the particles position, the shorter wavelength and in turn higher energy of light we must use. As a result, very accurate measurements require very energetic light, the higher the energy the bigger the effect on the momentum.

    Heisenburgs uncertainty principle goes even deeper than that though, and an understanding of the phenomena requires a bit of knowledge about Fourier transformations and conjugate variables.
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    Quote Originally Posted by MarkS1 View Post
    So are you saying that I can know both the position and momentum at the same time, if I measure its position and determine its momentum, but what I can't do is predict what they will be at some point in the future?
    At the same time is not something I know how to work with since a measurement of one variable causes the system to collapse into an eigenstate of the observable. If you measure the position of a particle then the system collapses into an eigenstate of position. If you measure the momentum of a particle then the system collapses into an eigenstate of pmomentum. Quantum mechanics can't tell you what happens when you measure two incompatiable observerables simultaneously.

    All you can do is to speak of the likelyhood of measuring a particular value. Once the position of a particle is measured the state of the system collapses into a eigenstate of position. If you were to measure the position imediately after that then you'd measure the same exact value of position. If you were to measure the momentum right after that then you could theoretically measure any value. The same holds the other way, i.e. if the system is in a general state and you measured the momentum with then the state of the system would collapse to an eigenstate of momentum. If you were to then measure the momentum right after that then you'd measure the same value. If right afrer that you tried to measure the momentum then you could could theoretically measure any value.
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    Quote Originally Posted by TheObserver View Post
    To determine the momentum of a particle requires a measurement of position at two points. On way to intuitively think about the problem is to note that the measurement of a particle requires us to bounce light off of it to see it, or at least something to that effect. But when we hit the particle with a photon of light, this inherently changes the momentum of the particle. There is no way to make measurements without altering the state of the particle. The more accurately we want to know the particles position, the shorter wavelength and in turn higher energy of light we must use. As a result, very accurate measurements require very energetic light, the higher the energy the bigger the effect on the momentum.

    Heisenburgs uncertainty principle goes even deeper than that though, and an understanding of the phenomena requires a bit of knowledge about Fourier transformations and conjugate variables.
    Suppose a photon was absorbed by an atom in the ground state. If we then measured the position of the atom and measured the energy state of the atom then we'd know the position and momentum of that photon. The momentum of the photon can be determined by the energy level the atom is in after its absorbed. The energy will then tell you the energy of the photon and its momentum.

    Of course this just means that you've changed it to a measurement of the location and energy of an atom.
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    Quote Originally Posted by TheObserver View Post
    To determine the momentum of a particle requires a measurement of position at two points. On way to intuitively think about the problem is to note that the measurement of a particle requires us to bounce light off of it to see it, or at least something to that effect. But when we hit the particle with a photon of light, this inherently changes the momentum of the particle. There is no way to make measurements without altering the state of the particle.
    TheObserver, but I'm not concerned about what the momentum will be after I make the measurement. I'm concerned about what it is at the moment that I make the measurement. And while it's true that the measurement changes the momentum, doesn't it also change the position? So after the measurement I don't know either the position or the momentum. But at the actual point of measurement I should know them both.

    At least it seems to me that I should.
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    Quote Originally Posted by pmb View Post
    Once the position of a particle is measured the state of the system collapses into a eigenstate of position. If you were to measure the position imediately after that then you'd measure the same exact value of position. If you were to measure the momentum right after that then you could theoretically measure any value.
    Okay, this part is confusing me. What do you mean by "measure the momentum" How do you measure the momentum? The only way that I can think of is to measure the position and calculate the momentum. Maybe that's where I'm confused, how do you measure momentum without measuring position, and then calculating momentum? Or is it that HUP is defining the wave function of the observables, but measuring the particle collapses the wave function and thus HUP no longer applies? It applies immediately before the measurement, and immediately after, but not at the point of measurement.

    I'm not sure, but that's obvious.
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    Quote Originally Posted by MarkS1 View Post
    Okay, this part is confusing me.
    You and me both Mark.

    Quote Originally Posted by MarkS1 View Post
    What do you mean by "measure the momentum" How do you measure the momentum?
    Now thar is an excellant question. I don't know.

    Let me ask some of the experts that I know. I'll get back to you on this.
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    Quote Originally Posted by pmb View Post
    That's not exactly what the Heisenberg Uncertainty Principle (HUP) states. The HUP states that the position and momentum of a particle is not simultaneously determined. For example: suppose to have a quantum mechanical system which you have prepared in a certain state . Now measure the position exactly and record it. Then return the system back to its original state and repeat the measurement over again, once again measuring the position exactly and recording it. Keep doing this a number of time (perhaps a 10 thousand times). Each time you do it you will get a different result, all of which are about a particular value. After this is done calculate the standard deviation of the position measurements. Label the result . Then go back and do the same thing all over again but this time measure the momentum. This time calculate the standard deviation of the measured results and label it . The two values and are a function of the initial quantum state that the system is in. The results will satisfy the Heisnberg uncertainty reltionship



    If you then started from scratch but this time changed the initial state of the system and repeated the wehol process described above you'd get different values of and , however the uncertainty relationship would stil hold. As one value increased the other value would decrease while at the same time satisfying the uncertainty relation above.

    [/QUOTE]

    I know that I am way out of my depth here, but I have started reading a book written by Chad Orzel. The book is called " How To Teach Quantum Physics To Your Dog " In the book he defines the Heisenberg relationship as " Deltax Deltap = h/4pi " which is different from your formula. He then goes on to say that the formula is usually written with a greater than or equal to sign, I am lost.
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    Quote Originally Posted by Dave Wilson View Post
    I know that I am way out of my depth here, but I have started reading a book written by Chad Orzel. The book is called " How To Teach Quantum Physics To Your Dog " In the book he defines the Heisenberg relationship as " Deltax Deltap = h/4pi " which is different from your formula. He then goes on to say that the formula is usually written with a greater than or equal to sign, I am lost.
    Thanks for your response. See Uncertainty principle - Wikipedia, the free encyclopedia

    Of couse the link and I could both be right. I'm not at home right now so I don't have my texts on quantum theory to look it up in. However I can do that when I get home this afternoon.
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    Heisenberg's Uncertainty Principle states that, 'It is impossible to measure simultaneously both the position and velocity [or momentum] of a microscopic particle with absolute accuracy or certainty'.
    Delta x . Delta p > or = h/4pi
    Delta x- Uncertainty in position of the particle.
    Delta p- Uncertainty in momentum of the particle.
    This principle has a direct consequence of Dual nature of Matter and Radiation.
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    Quote Originally Posted by kvskvt View Post
    Heisenberg's Uncertainty Principle states that, 'It is impossible to measure simultaneously both the position and velocity [or momentum] of a microscopic particle with absolute accuracy or certainty'.
    kvskvt, that's what I'm wondering. I don't know how someone can measure momentum, without measuring the position of the particle at two points and then calculating the momentum. But that would mean that it's not only possible to measure them both simultaneously, it's absolutely necessary. The only way to know the momentum, is to measure the position, which then tells you both position and momentum.

    But there must be something that I'm missing here. I just don't know what it is.
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    My take on that is that the uncertainty principle is not a very useful notion. The simplest explanation for me is the one of TheObserver.
    It had always bug'ed me that it is impossible to know the position alone of something. That is also true for a car.
    Where it is ?
    "but there look !", ok I see it, But give me something more precise...
    "see ? now I touch it", ok, when do you touch it ?
    If you are gona make any kind of measurement, you are going to have to deal with so call measurement-errors. Even relative to yourself, if it make sense for a body constituted of Gillions of moving particles.
    Then try to get this information along to another entity (a friend), and get ready for a headache.

    I read a book once on fractal mathematics, and since then It dawn on me that the uncertainty principle is just fake (but usefull).
    You never notice it in real-life because macroscopic objects are measured at their level, let say meter * 10^-3 . You did not even bother that the precision of your tool is much better let's say 10^-6. You round up anyway.
    But hey !, your are a scientist, so you didn't want to round anything, you want to be precise/exact ! So you keep the 6 digit, but notice that the last is changing randomly. After some more improving of your measurement you have to make do with the fact that this behaviors still hold, no matter the increased precision.
    So you build statistic based laws, because they are great tools for handling this randomness feature (and they are good tough mathematics)
    But then you begin to think that the world itself is random, because whatever you do, it feels like it.
    You certainly do not think that it is your your way of doing science that implies those randomness. The people most drawn into this self delusion even believe that all these decimals from -6 to -infinity and beyond are some kind of probability wave that need to collapse (into the welcoming arms of the experimentor). That's very romantic science.

    Quantum mechanics does not even bother to specify where begin microscopic. And no, not at micro. Because a micron of a galaxy is something quite huge.
    They specialize over particles because when searching for more and more precision, they begin working with smaller and smaller entities. Not strangely enough, the more they experiment on smaller "thing", the more this randomness where creeping up the decimals abyss.
    You can measure a car position with one photon (feed back time), and measuring the momentum of a faraway galaxy with one photon (red shift).
    If you do that on a electron, chances are the electron is going to go Berserk.

    I relate this to fractal mathematics, because Quantification requires to invent some boxes of finite quantities. Numbers are just that: boxes of tens inside boxes of tens add infinitum (change your base at will). But then you are able to stop somewhere and pass it to your friend Joe.
    It would be difficult for PI, which point on the boxing line never fall on box borders. But then even the number 2 is grossly inaccurate, because it should be written 2.0000000 ... add infinitum. Who got a paper sheet big enough ? The implied missing precision is a pretty good saving cost invention.

    I really thing that the next big thing will need totally different mathematics, which will come from non-linear/chaotic/fractal ones.
    Numbers are too rough.
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    Quote Originally Posted by pmb View Post
    Quote Originally Posted by Dave Wilson View Post
    I know that I am way out of my depth here, but I have started reading a book written by Chad Orzel. The book is called " How To Teach Quantum Physics To Your Dog " In the book he defines the Heisenberg relationship as " Deltax Deltap = h/4pi " which is different from your formula. He then goes on to say that the formula is usually written with a greater than or equal to sign, I am lost.
    Thanks for your response. See Uncertainty principle - Wikipedia, the free encyclopedia

    Of couse the link and I could both be right. I'm not at home right now so I don't have my texts on quantum theory to look it up in. However I can do that when I get home this afternoon.
    Thank you for your reply. I am just home from work. I will have a read of your link, then it is off to bed with a book.
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    Quote Originally Posted by kvskvt View Post
    Heisenberg's Uncertainty Principle states that, 'It is impossible to measure simultaneously both the position and velocity [or momentum] of a microscopic particle with absolute accuracy or certainty'.
    Delta x . Delta p > or = h/4pi
    Delta x- Uncertainty in position of the particle.
    Delta p- Uncertainty in momentum of the particle.
    This principle has a direct consequence of Dual nature of Matter and Radiation.
    The uncertainty principle is a statistical statement and therefore does not pertain to individual measurements. The uncertainty statement also doesn't pertain to just position and momentum. It applies to all conjugate observables. Take as an example the components of spin. The z-component of the spin of an electron can have only one of two values, i.e. or . So when a component is measured the value is always exact. However that doesn't mean that .
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    Quote Originally Posted by Kerling View Post
    This is the same as it is with heisenberg, the more accurate we know the location, the more uncertain we are about its energy. And the more certain we are about its energy the less we know about its position.
    That is true in a statistical sense, not for sinlge measurements.
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    Quote Originally Posted by Kerling View Post
    No that isn't true.
    Yes. It is true. I explained this above in post #22

    Quote Originally Posted by Kerling View Post
    The Heisenberg uncertainty principle is valid even for single particles.
    That is incorrect. The uncertainty in a quantum observabe is defined as the standard deviation of the measured eigenvalues in actual experimental observations. For the position operator that would be represented by . Each measurement of the opbservable is recorded and the experiment repeated with the system being reset to the exact state it was in before. After a large enough sample for the standard deviation to be accurate (e.g. 1000, 10,000 etc.) the standard deviation is then calculated. If the state was not in an eigenstate of position and the observable is, for example, an eigenvalue of the position operator, then the standard deviation will not be zero, i.e. . Yet each measurement could have an accuracy far less that the . Many people confuse accuracy with , The experiment is then startged all over again, this time we meaure a conjugate observable such as momentum and get . The idea here is not to confuse accuracy of a measurement, which pertains to single measurements, with the standard deviaton, i.e. uncertainty.

    Consider once again the example I gave in post #22. We considered the observable of spin in that post, i.e. the z-component of spin. Each measurement can yield only one of two values, i.e. or -. So each measurment will be exact and the resulting measured observable can only be exsact as well. But for an arbitrary but well-defined state the spin measurement will not be the same. In this case the accuracy will be exact, no error. Once again we measure the spin and record it. After 10,000 repetitions of the same measurement, with the system being reset in the same exact state, the standard devuation of the spin will not be zero and thus the uncertainty inthe z-component of spind will not be zero.

    Its been decade since I've studied the original thought experiment by Heisenberg so I'd have to review that to see how it was done. I'm sure that it pertains to many measurements. After all, the derivation of the uncertaintly principle is derived in the sense I just explained. i.e. in the statistical sense. That's well-known in the quantum mechanics community.
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    al right, I made a rather elaborate post concerning your reply.
    Basically it boils down to this, look up for instance in Bransden en Joachain and find yourself an general derivation of uncertainty principles for observables. It will show that any set of complementary observables obey a uncertainty principle.
    In your above argument you merely express a repetitive measurements. That is a statistical experiment. But the uncertainty principle, and the adjoined limit for for instance optics, tells us how far we can define our accuracy. It doesn't say that you cannot infinitely accurately measure position or momentum. But that when you measure these simultaneously then there are limits of what can be discovered. The uncertainty principle isn't about how inaccurate separate measurements can be. In fact, for a separate measurement one can easily show that two observables are (in most practical cases) independent.

    In short the uncertainty principle is a way of saying how a quantum state, after measurement has lost information. Since the unmeasured state contains the 'true' information of position and momentum. Putting the state back into its original state is (of course) not going to show a Heisenberg uncertainty. Since they are different quantum states, and so the observables are commutative.

    I hope this does clear things up for you.
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    I ran into something quite interesting this noon. A friend of mine is an expert in many fields, quantum mechanics being one of them. I discussed this subject with him over lunch and I mentioned this topic. It turns out that I wasn't wrong regarding the meaning of uncertainty, how its determined (i.e. standard deviation etc). What he added was that was a second, equivalent, interpretation which applies to single measurments and in that sense you can't measure conjugate observables simultenously. The thing is that I wasn't wrong either. Its all quite new and strange to me. He told me that this is not very well known and that's why I haven't come across it before. He told me that Feynman explains all of this very nicely. I'm more than willing to admit the error of my ways (otherwise I'd neverf admit all this) and will eat my share of crow. But that might only come after I study Feynman on this point.

    I recommend that anybody who is interested in this subject also read Feynam on this point too.
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    Quote Originally Posted by pmb View Post
    I recommend that anybody who is interested in this subject also read Feynam on this point too.
    I recommend that everybody reads as much Feynman as possible on any subject.
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    Quote Originally Posted by Kerling View Post
    al right, I made a rather elaborate post concerning your reply.
    Basically it boils down to this, look up for instance in Bransden en Joachain and find yourself an general derivation of uncertainty principles for observables.
    I already did as an undergraduate and in my graduate series. Its basic stuff. I know the derivation quite well. I use Cohen-Tannoudji et al, a great QM text. They define uncertainty just as I did it has the same meaning as I stated.

    Quote Originally Posted by Kerling View Post
    It will show that any set of complementary observables obey a uncertainty principle.
    And you somehow got it into your head that I disagree with that? If that's the case then you didn't pay attention to what I've been saying. I clearly outlined its meaning in post #3. Please read it carefully. The proper lingo is not "simultaneously measured" but "simulteneously determined".

    Quote Originally Posted by Kerling View Post
    In your above argument you merely express a repetitive measurements. That is a statistical experiment. But the uncertainty principle, and the adjoined limit for for instance optics, tells us how far we can define our accuracy.
    There are two compatible ways of intepreting the uncertainty priniple. The one I just explained to you is found in nearly all QM texts. The other is found in Feynman, which I was unaware of until this noon. I won't say anything about that until I read it as my friend recommended. You don't seem to understand that, by definition, the uncertainty of an observable is the [standard deviation[/] of measurements from systems in identical states.

    Quote Originally Posted by Kerling View Post
    It doesn't say that you cannot infinitely accurately measure position or momentum. But that when you measure these simultaneously then there are limits of what can be discovered.
    I don't disagree with that. Never did.

    Quote Originally Posted by Kerling View Post
    In short the uncertainty principle is a way of saying how a quantum state, after measurement has lost information.
    That is correct. After an observable is measured the quantum state collapes into the eigenstate corresponding to the measured eigenvalue.

    Quote Originally Posted by Kerling View Post
    I hope this does clear things up for you.
    You say that as if I'm ignorant on this subject. I'm not. I took the full course of the graduate series of quantum mechanics in graduate school so I know the subject very well. Just because someone disagrees with you it doesn't mean that they are unclear of something. Regarding the definition of the term uncertainty as it's used in quantum mechanics. From Principles of Quantum Mechanics - Second Edition, R. Shankar, page 128
    The Uncertainty

    In any situation descibed probalistically, another useful quantity to specify besides the mean is the standard deviation. which measures the average fluctation around the mean. It is defined as



    and often called the root-mean-squared deviation. In quantum mechanics, it is reffered to as the uncertainty in . ...
    All the advanced QM texts that I have say the same thing so I won't get into it any further. Consider yourself educated on the precise mathematical definition of the the term uncertainty in this interpretation of the Heisenberg Uncertainty Principle.

    It's clear to me is that you're not aware of the two different interpretations and that we're merely discussing different versions of it. I suggest that you learn more about the statistical nature of uncertainty. All QM texts define it as the standard deviation, a statistical quantity. The other version of the HUP refers to uncertainty as being synomymous with accuracy. That's the version you seem to know and the one that pertains to the X-ray telescope.
    Last edited by pmb; July 14th, 2012 at 05:10 PM.
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    pmb, you seem to be of the impression that I know little about the matter. And in many parts I agree with you, I just wish to state that it is a very important realisation that the uncertainty principle is also very important in single measurements.

    Luckily I am part of the quantum mechanical community myself, and I have a few beautiful books about a meter away from me, so I decided to look it up, and with the help of some articles aswell. Do know that I quite enjoy the discussion because it heightens the way I can express and communicate the knowledge of QM I have.

    After browsing through several books of I see that the discussion we had above is a common one in science. The interpretation of the matter is often blurred by the different interpretations of quantum mechanics and the formalism that are derived of such interpretations are often difficult. I will (for everyone not for you) present a arguments how the uncertainty principle generally takes place in practice, and how in theory it is found, and what happens at a single measurement.

    How does it happen in practice?
    In practice we must look at HOW we make a measurement of a state. Since most theoretical reasonings are with free particles, lets stick with those. For instance how do we 'see' where a 'particle' is. This is rather difficult. We could make a nano grating in such a way that the particle causes light through dispersion in the medium and pinpoint the location, then however the uncertainty in the location is quite apparent and correlates with the scintillation boxes size, in the meantime though it also helps us to discover how high the momentum was by the intensity of light production.
    Or we could use Heisenberg's example of a gamma ray microscope that could pinpoint the location. This however is difficult because if we want to accurately pinpoint the location we need short wavelengths. And then the compton effect cannot be excluded anymore. This means the photon's hit the particle (for observation at least once) and then the recoil give the particle an undetermined momentum in a random direction. We however know something about the momentum, as we know the wavelength of the light, we do not however know how this collision took place and thus it renders us with an uncertainty about both momentum and impuls even though knowing quite accurately the position, and have some information about the momentum. To paraphrase Heisenberg ( Ueber den anschaulichen Inhalt det quantentheoretischen Kinematik und Dynamik (1927) page 174, translated): "At the moment of location determination, or the moment the light qauntum is scattered by the electron, the electron will suddenly change momentum. (...) At the moment where the location of the electron is know, the momentum can only be known to an order of size that corresponds to this sudden change; so the more accurate the location is determined, the less well we know the momentum and vice versa. "

    The above expresses the quantum uncertainty principle for a measurement, and it is rather important to see a distinction here. As is also pinpointed by Micheal Redhead which I will use later. This is an example how a system inherits the uncertainty principle or distortion from a measuring device/method. Even if the system has two observables that are not complementary (Noting that any system always has at least on set of observables that is complementary to one another), hell even a classical system will inherit the 'quantal' nature of a method of observation. Where Heisenberg's microscope is just an example. A more thorough proof will follow.

    Let us look at the definition of the uncertainty and what it actually means: DELTA_phi A = (<Phi|Opp[a]^2|Phi> - <Phi|Opp[a]|Phi>^2)^(1/2)
    In words it is important to know that the uncertainty is defined in conjuction with the state of the system. As Chris J. Isham mentions on page 141 of his book 'Quantum Theory - Mathematical and Structural Foundations'. This in conjuction with knowledge of the Hilbert space formalism (will follow) is, and I quote: "Thus the uncertainty DELTA_phi A is a good measure of the extent to which a value A is NOT 'possessed' by by an individual system. "

    The Uncertainty principle can be seen as the same as the Schwarz inequality for Hilbert space. This results into a much stronger statement of inequality (eq. 7,55 Isham) As this is applicalble regardsless of mechanics used. (Heisenberg or Schrödinger) Eventually a nice expression is given of the uncertain relations dependants on state using angular momentum. :

    7.58 DELTA_phi J_x*DELTA_phi J_y >= hbar*0.5 <J_z>_phi

    In other words, for states for which <J_z>_phi there is no lower bound on the size of the product DELTA_phi J_x*DELTA_phi J_y
    However this doesn't tell us much about single measurements, in fact Isham himself brings forward this matter as debatable, what does the uncertainty tell us about measurements applied to a single event? Isham refers to various interpretational problems about the matter, the meaning of probability, the of measurement, the reduction of the state vector. And this is where hard science descends into more metaphysical physics. ( matter which I hope to excel in the coming year)
    And the answering of the question what does it tell us about a single event, descends into the hard and time consuming world of metaphysical physics. A field, which I would like to remind everyone to, few physicist tend to venture in as it is 'beyond' that concern.

    But how about single measurements?
    Because we now know that the answer to our question lies within the metaphysical fog of quantum physics, we ask a philosopher to answer the question. At page 63 of Michael Redhead's "Incompleteness, Nonlocality and realism - A Prolegomenon to the Philosophy of Quantum Mechanics" we see the first example of this question:
    What if we start with a quantum state, that isn't an eigenket of either two complementary observables? Is there any sense in which we can claim to be able to measure these observables (let's call them Q & Q') simultaneoulsy in such a state?
    There are several schemes thought of to answer this question is a positive manor. (And I'd advice everyone to read Redhead himself, as I cannot paraphrase it more comprehensively)
    The general proof of these scheme is to show that there is another observable U, which does commute to Q but has an equal probability distribution as Q'. And would therefore constitute as a simultaneous measurement without the problem of uncertainty. However, in the proofs U is made up by (linear) calculation from Q (hence it always commutes). Does this prove that we are allowed to state that Q and Q' can be measured simultaneously? Well, it of course doesn't. It is only of that counter-factual could be sustained that a genuine claim to joint measurement of Q and Q' could be made.

    In short what is the most important conclusion from Redhead is rather simple, yes many people have tried to prove that the uncertainty principle isn't valid for simultaneous measurements (and the reason is in general with the dissatisfaction of the Copenhagen interpretation). However these proofs have all failed. And therefore there is no interpretation of quantum mechanics that can exclude the Uncertainty principle for single events. Naturally the uncertainty principle is also a statistical thing, as pmb explained quite well above.

    If you want to dive in to the philosophical implications of science I rather not discuss this on the forum, as I've been busy with it for almost a decade now (personal preference) And, I have a Holiday and I don't want to work too much in my Holiday.
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    Quote Originally Posted by Kerling View Post
    pmb, you seem to be of the impression that I know little about the matter.
    I apologize if I gave you that impression. I too was under the impression that you thought I knew little about the matter. Since we've gotten the wrong impressions I think its best if I drop out of this discussion. Please don't take that personally. Latley I've decided to drop out of discssions whenever I see personalities start to get involved in the sense that people start forming impressions about the competency of others I loose all interest in the discussion. I also don't like to read long posts but that
    s only secondary to my desire toback out when personal impressions become part of the discussion.

    Last comment: As I said earlier, a friend of mine recently made me aware of the second interpretation that I was unaware of and have decided not to continue or discuss this subject matter until I become well educated in how Feynman discusses all this.
    Last edited by pmb; July 15th, 2012 at 10:04 AM.
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    Quote Originally Posted by pmb View Post

    Last comment: As I said earlier, a friend of mine recently made me aware of the second interpretation that I was unaware of and have decided not to continue or discuss this subject matter until I become well educated in how Feynman discusses all this.
    Actually since I am really deepening myself in the matter could you let me know when you figure out what it is? I am very interested what a rolemodel like Feynman had to say about it. As he is often left out on the heavier philosophical debates, so please let me know
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    Quote Originally Posted by Kerling View Post
    Quote Originally Posted by pmb View Post

    Last comment: As I said earlier, a friend of mine recently made me aware of the second interpretation that I was unaware of and have decided not to continue or discuss this subject matter until I become well educated in how Feynman discusses all this.
    Actually since I am really deepening myself in the matter could you let me know when you figure out what it is? I am very interested what a rolemodel like Feynman had to say about it. As he is often left out on the heavier philosophical debates, so please let me know
    I'm in no hurry to read Feynman. At the momentum I'm repeating my graduate studies in QM and that will take a very long time to review. Plus as I said, I don't like to post in discussions where personal assumptions are floating around.

    May I ask you a personal question? What is the nature of your education in quantum mechanics? I have a BA in Physics and did some graduate work in physics at Northeaster University where I took the graduate series in quatum mechanics, classical mechanics and electrodynamis. Due to the nature of the employment environment back in the early 90's I ended up working in computational physics and digital signal processing. I never had a chance to work in quantum mechanics but I kept myself fresh in it to a certain point. Our text in gradschool was Quantum Mechanics by Cohen-Tannoudji, Diu and Laloe. I have other texts by Shankar, Sakurai, Liboff, French & Taylor as well as several texts in modern physics.

    I try never to say that someone is wrong since for all I know I could be wrong or we could bothe be wrong or both be right or simply have a misunderstanding. I think you misinterpreted disagreement with me thinking that you're uneducated. I have no idea what your education is and I would never presume to make an assmption. The only thing I expressed here was that my understaning of the uncertaintly principle was not something that you seemed aware lof. i..e that you didn't seem to recognize the relationship between the standard deviation and uncertainty. As I learned yesterday there are two interpretations. one where the uncertainty is the standard devition and one where it was a synonym with accuracy. So in sense we were both right.

    Please, in the future, never assume that I have an impression or an assumption of you that I don't exlicitly state. Okay? Right now you seem educated in QM and come across as a pleasant person. My impression that I got somewhere of you was that I was ignorant of some point that you were trying to make. Perhaps I was wrong but I don't like to continue discussions when that happens. That in no way should be interpretated as meaning that this applies to other threads. Each thread starts anew.
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    I have done my BSc in Theoretical Physics, and hope to Finnish my Masters in Theoretical solid state physics before October, since then I will (and I am really excited of it) work in Copenhagen at the Niels Bohr institute . And I am really looking forward to that. Though I will have to restrict my personal philosophical research to spare time, as my research will be about an quantum optical approach to solid state quantum computing. I have however always had a great interest in the quantum philosophy, that is why I have read all the books about it. Some, more cumbersome then the other. But nothing is quite as hard to get through as Bohr :P

    I greatly appreciate your post! I must admit though I quite like the critical voice. Especially because most physicist I know. (and admittingly most of them are experimentalists) Couldn't give a flying fuck about the interpretation of the theory they use. Where that in my personal experience is the one great way to understand this world we are living in. And sometimes make difficult problems rather simple indeed. I have been into QM philosophy from the age of 15, and was my main goal to even study physics. Naturally I see moving to Copenhagen as a 'mission succes' when I actually get to work there

    If you'd like, you should look up the delayed choice experiment by wheeler. Read his comments on the matter (just the original article is very simple indeed) and image to yourself just what the Copenhagen interpretation is telling you about the world. :P

    I appreciate your ways of communicating. And yes, sometimes I am a bit too short in my argumentation, I 'jump' to fast from one thing to the other, as also my professors say :P
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    Quote Originally Posted by Kerling View Post
    I have done my BSc in Theoretical Physics, and hope to Finnish my Masters in Theoretical solid state physics before October, ..
    So we have equivalent educations. Nice to know.

    Quote Originally Posted by Kerling View Post
    since then I will (and I am really excited of it) work in Copenhagen at the Niels Bohr institute . And I am really looking forward to that.
    What a coincidence. That friend I mentioned? He just came back from Europe. I think he stopped there too. His name is Dr. John Stachel. Do you know him?

    Quote Originally Posted by Kerling View Post
    Though I will have to restrict my personal philosophical research to spare time, as my research will be about an quantum optical approach to solid state quantum computing. I have however always had a great interest in the quantum philosophy, that is why I have read all the books about it. Some, more cumbersome then the other. But nothing is quite as hard to get through as Bohr :P
    Nice!! I'm glad to hear that. After I finish my review of QM I'll be turning to studies in quantum computing. It's nice to know that someone who is knowledgable in the subject frequents here.

    Quote Originally Posted by Kerling View Post
    I greatly appreciate your post! I must admit though I quite like the critical voice. Especially because most physicist I know. (and admittingly most of them are experimentalists) Couldn't give a flying fuck about the interpretation of the theory they use. Where that in my personal experience is the one great way to understand this world we are living in. And sometimes make difficult problems rather simple indeed. I have been into QM philosophy from the age of 15, and was my main goal to even study physics. Naturally I see moving to Copenhagen as a 'mission succes' when I actually get to work there
    Thanks. I have a deep interest in the philosophy of science. It was Fritz Rohrlcih who once said ...ignoring philosophy in physics means not understanding physics. That's from his text Classical Charged Particles in the first chapter which is entitled Philosophy and Logic of Physical Theory. It's a wondeful text. Are you famliar with the book The Logic of Scientific Discovery by Karl Popper? Also a great book.

    Quote Originally Posted by Kerling View Post
    If you'd like, you should look up the delayed choice experiment by wheeler. Read his comments on the matter (just the original article is very simple indeed) and image to yourself just what the Copenhagen interpretation is telling you about the world. :P
    Is that a text? I looked it up on Amazon and couldn't find a book by that titled. Where I can I find it?

    Quote Originally Posted by Kerling View Post
    I appreciate your ways of communicating. And yes, sometimes I am a bit too short in my argumentation, I 'jump' to fast from one thing to the other, as also my professors say :P
    Thanks Kerling. I appreciate that very much.
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    Quote Originally Posted by pmb View Post
    What a coincidence. That friend I mentioned? He just came back from Europe. I think he stopped there too. His name is Dr. John Stachel. Do you know him?
    Europe is a big place :P I am currently in the Netherlands.

    Quote Originally Posted by pmb View Post
    Thanks. I have a deep interest in the philosophy of science. It was Fritz Rohrlcih who once said ...ignoring philosophy in physics means not understanding physics. That's from his text Classical Charged Particles in the first chapter which is entitled Philosophy and Logic of Physical Theory. It's a wondeful text. Are you famliar with the book The Logic of Scientific Discovery by Karl Popper? Also a great book.
    I agree with Fritz on that, And yes I know Popper.

    Quote Originally Posted by pmb View Post
    Is that a text? I looked it up on Amazon and couldn't find a book by that titled. Where I can I find it?
    Let me look it up; It is from 'Mathematical Foundations of Quantum Theory' Page 9, ISBN 0-12-473250
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    Quote Originally Posted by Kerling View Post
    Let me look it up; It is from 'Mathematical Foundations of Quantum Theory' Page 9, ISBN 0-12-473250
    Thanks. I'd love to read it.
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