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    (Original post by grumballcake)
    Actually, the "vast majority" of scientists don't, including such notaries as Einstein. It's been noted that the uncertainty principle helps the maths work, but that doesn't mean that it's right.
    Many physicists accept the uncertainty principle as one possible explanation, but only if they also accept Schroedinger and the Copenhagen interpretation.
    Einstein is famous for having hated quantum mechanics - the general consensus is that he was wrong. You're confusing the Copenhagen interpetation and the uncertainty principle - they are independent. Quantum mechanics itself is built around the uncertainty principle - the copenhagen interpretation is one of several (and the most widely accepted) intepretation of the consequences - it says the universe is fundamentally indeterministic, with measurement causing the collapse of the wave function, whereas the many-worlds intepretation, for example, rejects the indeterminism by having all possibilities - in effect, we access part of the wave function when we measure. Find me a quantum physicist who rejects the uncertainty principle and I'll be very impressed.

    (Original post by grumballcake)
    No, I'm not. I know there's only one photon in transit (it's a light-proof box), so I know where it came from and when. Since I also know the distance it's travelled and the time it took, I know its velocity and direction. Those are 'now' quantities. How are you proposing that you measure velocity? What means of measuring velocity does not include two discrete observations in time? What evidence do you offer for this bald assertion? You can't invoke the uncertainty principle in order to justify itself.
    You can't know its the same photon because they pop in and out of existence as part of quantum randomness - although I think you can get round this depending on how you detect it. You know neither the distance its travelled nor the time it has taken. I can invoke the uncertainty principle because of the way you're trying to refute it - by counterexample. Well, if the uncertainty principle holds, your counterexample is impossible. The particle doesn't have to have travelled in a straight line - as I said, uncertainty affects your measurement of time so there is more than one possible path it could have taken.


    (Original post by grumballcake)
    We know where it was and where it is. We also know its velocity (it must be exactly the speed of light, if it's a photon), so we can check that it took the correct time to travel from source to destination (since we know how far apart they are). That rules out the chance that it's not the same photon, or that it took a path other than a straight line from source to detector. You're left to argue that it QM tunnelled to some other location at some point and thus arrived on a different vector. However, you can repeat the experiment many times and QM tunnelling becomes exceptionally unlikely as a possibility (it's blooming unlikely to start with over a distance as large as 1m).
    You can't know the exact distance between the source and the destination because you can't know exactly where they are. You can't know the exact time either. Your argument rests on refuting uncertainty by making exact measurements, which is exactly what uncertainty says you can't do.
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    (Original post by wanderer)
    You can't know its the same photon because they pop in and out of existence as part of quantum randomness
    This is special pleading. You can repeat the experiment a million times and show that the same results occur. You might have the occasional random event, but I doubt very much that a new photon would continue on the same path, so it would never get detected. Remember, our detector only needs to be a single photon in diameter (or to have a granularity at that level), so it ignores any strays.
    You know neither the distance its travelled nor the time it has taken.
    There's the problem, you are using a circular definition. You say we can't know anything for certain, including physical dimensions. But you're ignoring what the principle says. it says that I can't know both the momentum and the position of a photon at the same time. It doesn't say that I can't measure a distance exactly, rather the contrary, I can measure a static distance exactly, because it isn't moving (i.e. has no momentum). Oh, I grant that the atoms in the slit and detector are oscillating slightly but we can average those out over a few million experiments.
    uncertainty affects your measurement of time
    Not in any version of the principle I've seen. Could you give me a reference, please?
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    (Original post by grumballcake)
    This is special pleading. You can repeat the experiment a million times and show that the same results occur. You might have the occasional random event, but I doubt very much that a new photon would continue on the same path, so it would never get detected. Remember, our detector only needs to be a single photon in diameter (or to have a granularity at that level), so it ignores any strays.
    There's the problem, you are using a circular definition. You say we can't know anything for certain, including physical dimensions. But you're ignoring what the principle says. it says that I can't know both the momentum and the position of a photon at the same time. It doesn't say that I can't measure a distance exactly, rather the contrary, I can measure a static distance exactly, because it isn't moving (i.e. has no momentum). Oh, I grant that the atoms in the slit and detector are oscillating slightly but we can average those out over a few million experiments. Not in any version of the principle I've seen. Could you give me a reference, please?
    The uncertainty principle doesn't just apply to position and momentum - where did you get that idea? It relates to several pairs of observable variables - position and momentum, time and energy, something to do with angular momentum ... I think there are others that are more technical. http://en.wikipedia.org/wiki/Uncertainty_principle

    How exactly do you plan to measure a distance exactly? I'm not using a circular definition - I'm using what the conditions would be under the uncertainty principle. The uncertainty principle isn't just a random idea used to interpret things - its a mathematical result that follows from the equations of quantum theory. If quantum theory is correct, so is the uncertainty principle - and I'm sure you realise that there is a huge amount of evidence for the truth of quantum theory. Again, do you seriously think the majority of 20th century physics is disproved by this thought experiment?

    And whenever you're talking about averaging out possibilities over lots of experiments so they are improbable - the uncertainties following from the principle are very, very small. You have to get rid of all doubt, not just get a very high probability.
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    I've just been informed by some physicsy people that both our arguments are fairly unrelated to reality. There's some complicated reason to do with the wave/particle duality and the photon diffracting through the slit that I couldn't quite follow, and apparently we've been using momentum and speed interchangeably, which is wrong. The momentum that is uncertain is not c, but is given by p = E/c, where E is the energy of the photon - which has an uncertainty relationship with time.
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    (Original post by wanderer)
    It relates to several pairs of observable variables - position and momentum, time and energy, something to do with angular momentum
    I know, but time & distance are not related variables in this case.
    How exactly do you plan to measure a distance exactly?
    It's a thought experiment, just like the Einstein/Bohr box. You might as well ask how you emit one photon at a time and detect it. Anyway, the exact distance isn't material to the argument as long as it's greater than any reasonable quantum tunnelling.
    uncertainty principle isn't just a random idea used to interpret things - its a mathematical result that follows from the equations of quantum theory.
    Even quantum physicists can't agree on the central tenets of QM. If you want to attack the experiment properly, you need to do so by using physics, not just an appeal to authority.

    The thought experiment has been presented to some top physicists by Dr Bell, as he told us (with great glee). I guess I could ask him whether anyone has taken it seriously. I know that no-one had an answer when he presented it at a conference. That doesn't mean it's right, of course, just that I haven't heard a refutation.

    Personally, I think it may be like the EB Box and that the emission of a photon causes the apparatus to move, so that you don't have a consistent time basis.
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    (Original post by grumballcake)
    It's a thought experiment, just like the Einstein/Bohr box. You might as well ask how you emit one photon at a time and detect it. Anyway, the exact distance isn't material to the argument as long as it's greater than any reasonable quantum tunnelling.
    It is material becaue for the experiment to work you need to know the exact position of your detector - again you're assuming you already have accurate knowledge of uncertain variables. And apparently the photon diffracts after it goes through the slit - it acts as a wave until you make your measurement, after which it behaves as a particle, although I don't really follow that part, I'm quite shaky on wave/particle duality.

    (Original post by grumballcake)
    Even quantum physicists can't agree on the central tenets of QM. If you want to attack the experiment properly, you need to do so by using physics, not just an appeal to authority.
    Sorry, but thats simply not true. There's certainly a lot of disagreement on the interpretation ofQM, but the theory has been complete and agreed upon for nearly eight decades. There is absolutely no controversy whatsoever over the central tenets of quantum mechanics, which are supported by a body of experimental evidence more accurate than any of its proponents could have hoped for.

    EDIT - oh, and you haven't yet said how you would determine the momentum, given that (as I said) its not the same thing as the speed.
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    (Original post by wanderer)
    It is material becaue for the experiment to work you need to know the exact position of your detector
    Why? Firstly, it's a thought experiment. All I need is a detector. For its position to be uncertain, you have to say why it's uncertain. You can't invoke the uncertainty principle here - that's simply self-referential. You need a reason why I can't determine the distance which doesn't involve the uncertainty principle. Let's assume I have a number of fixed observation points and determine the position of the detector by triangulation.

    Anyway, you're missing the point. The distance is only used in order to confirm that the photon which arrived had travelled at the speed of light and must have travelled in a straight line.
    And apparently the photon diffracts after it goes through the slit
    I know that. What was your point? The detector is simply at the location where the photon lands. It could be a very large detector with a fine granularity to identify the location of the impact.
    it acts as a wave until you make your measurement, after which it behaves as a particle
    Nonsense. You're using your pre-determined conclusions before you've performed the experiment. That is, you're assuming the Copenhagen interpretation. Let's be clear, I do not believe the Copenhagen interpretation. I think it's logical nonsense which happens to fit the maths.
    the theory has been complete and agreed upon for nearly eight decades.
    . So were phlogiston theory and Newtonian mechanics.
    you haven't yet said how you would determine the momentum, given that (as I said) its not the same thing as the speed.
    Why do I need to? I have established the position of the photon and its vector at the same time. If you prefer, my detector can also measure the energy of the photon at impact.
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    (Original post by grumballcake)
    Why? Firstly, it's a thought experiment. All I need is a detector. For its position to be uncertain, you have to say why it's uncertain. You can't invoke the uncertainty principle here - that's simply self-referential. You need a reason why I can't determine the distance which doesn't involve the uncertainty principle. Let's assume I have a number of fixed observation points and determine the position of the detector by triangulation.
    What are you trying to argue? Of course I can reference the uncertainty principle. Otherwise you're arguing that you can disprove it using a theoretical apparatus to which uncertainty does not apply - you're begging the question, not me. Clearly, if you have determined the exact position of your detector (at least without having to atrribute infinite momentum to it), then uncertainty has already been disproved and your experiment is pointless.

    (Original post by grumballcake)
    Nonsense. You're using your pre-determined conclusions before you've performed the experiment. That is, you're assuming the Copenhagen interpretation. Let's be clear, I do not believe the Copenhagen interpretation. I think it's logical nonsense which happens to fit the maths.
    Then how do you explain the double slit experiment? If you use a hidden variable explanation (that there is always a definite state of the system, one that we are simply unable to fully determine - this is what Einstein thought) how do you explain Bell inequalities?

    (Original post by grumballcake)
    So were phlogiston theory and Newtonian mechanics.
    And it is certainly possible that at some point, QM will contradict experiments and a new theory will be needed. That hasn't happened yet, despite a lot of experiments being done, but its always a possibility in science. I was rejecting your claim that the theory itself is in any way controversial or disagreed upon. To clarify - are you arguing against QM itself now? Or do you still claim you can have QM without the uncertainty principle?

    (Original post by grumballcake)
    Why do I need to? I have established the position of the photon and its vector at the same time. If you prefer, my detector can also measure the energy of the photon at impact.
    Because the uncetainty principle in this case links position and momentum, not position and velocity. And, as I've said, you cannot measure energy exactly at a given time, without explaining how you've already got over the uncertainty principle.
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    (Original post by wanderer)
    What are you trying to argue? Of course I can reference the uncertainty principle.
    Bohr didn't in his conversation with Einstein. He argued using principles with which Einstein agreed. You're making this pointless by saying (wrongly) that everything is uncertain.

    So it's a waste of time, really. You've already decided that you can appeal to authority (everyone believes it) and to a circular argument (everything's uncertain, so you can never measure anything, ergo everything's uncertain).

    Your argument hinges on some notion that we can't know the position of a single body relative to another. Except that that's not something which the uncertainty principle claims. (Wel,, not in anything I've read, but feel free to give me a reference).

    QM is a flawed model, it's merely better than the previous ones (which had just as many authorities defending them in the past). It will be overturned and future schoolboys will proudly mock anyone who ever believed in it.

    To make this worthwhile, you need to argue in terms that don't involve your invoking the uncertainty principle as some Cartesian denial of all knowledge (and I've already given an example of such an argument). If not, I'm dropping out.
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    (Original post by grumballcake)
    Bohr didn't in his conversation with Einstein. He argued using principles with which Einstein agreed. You're making this pointless by saying (wrongly) that everything is uncertain.
    This is simply false. The arguments Bohr used against Einstein went along exactly the same lines as I've just used - "it is decisive that, contrary to genuine instruments of measurement, these bodies along with the particles would constitute, in the case under examination, the system to which the quantum-mechanical formalism must apply. With respect to the precision of the conditions under which one can correctly apply the formalism, it is essential to include the entire experimental apparatus." Both of Einstein's famous thought experiments were defeated on the basis of indeterminacy applying to the measurement apparatus.

    (Original post by grumballcake)
    So it's a waste of time, really. You've already decided that you can appeal to authority (everyone believes it) and to a circular argument (everything's uncertain, so you can never measure anything, ergo everything's uncertain).

    Your argument hinges on some notion that we can't know the position of a single body relative to another. Except that that's not something which the uncertainty principle claims. (Wel,, not in anything I've read, but feel free to give me a reference).
    The appeal to authority is, of course, undecisive - its just worth considering why, exactly, Einstein's arguments along these lines have been completely rejected (Einstein actually gave up on them - he moved on to hidden variable arguments and the EPR paradox). But what is key here is that I have not made a circular argument. The uncertainty principle applies if and only if everything in the universe is made up of particles obeying the laws of quantum mechanics. You can either show that this is not true (which you can't do by a thought experiment, and I think you're highkly unlikely to do it by an actual one), or you can show that the theory is internally inconsistent - that is, show that even if everything is governed by QM, you can get around the uncertainty principle. You haven't done this - you just keep claiming that saying uncertainty applies to your apparatus is a 'circular argument'. Why? In fact, I'll set it out properly

    P1 - If QM is true, uncertainty applies to all objects in the universe.
    P2 - If uncertainty applies to your apparatus, your experiment cannot be performed.

    Assumption -
    QM is true.

    C1 - Uncertainty applies to all objects. (From P1 and Assumption)
    C2 - Uncertainty applies to your apparatus. (From C1)
    C3 - Your experiment cannot be performed if QM is true (From C2 and P2, Assumption removed).

    Show me the circularity.

    (Original post by grumballcake)
    QM is a flawed model, it's merely better than the previous ones (which had just as many authorities defending them in the past). It will be overturned and future schoolboys will proudly mock anyone who ever believed in it.
    Quite possibly. As I said, thats true of all science. But QM is flawed because it requires input data and is incompatible with general relativity - it is not inconsistent.

    (Original post by grumballcake)
    To make this worthwhile, you need to argue in terms that don't involve your invoking the uncertainty principle as some Cartesian denial of all knowledge (and I've already given an example of such an argument). If not, I'm dropping out.
    Pity. As I've explained above, its perfectly admissible for me to do that on the assumption that QM is true, because the denial of all knowledge (in a sense) follows from QM. As I said - your logic is circular, not mine.
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    (Original post by wanderer)
    Both of Einstein's famous thought experiments were defeated on the basis of indeterminacy applying to the measurement apparatus.
    Only because Bohr showed that the loss of energy would result in movement, which would affect the time measurement under special relativity. He didn't say "You can't measure the mass because it's uncertain".
    P1 - If QM is true, uncertainty applies to all objects in the universe.
    P2 - If uncertainty applies to your apparatus, your experiment cannot be performed.

    Assumption -
    QM is true.
    I can only comment that you were possibly wise to give up philosophy in favour of maths. You postulate a global premise and then produce a conclusion which is completely predicated on that assumption. Yet you think that's somehow convincing. Let me simplify your argument:

    P1 - I am a woman.
    P2 - If I am a woman, I have a womb.

    C1 - I have a womb.

    The only problem is that I'm not a woman. Oh, and not all women have wombs.

    You've made a false premise that QM necessarily involves the uncertainty principle for all measurements in all dimensions. What about the case where some QM priciples are true, but uncertainty is not? That's what Einstein and others have debated. That's why the Copenhagen interpretation is not universally agreed - there's still room for exploration. Ultimately, I think it will be that most of QM is shown to be a limited subset of a wider theory. Just like Newtonian physics is true only to a limited extent.
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    (Original post by grumballcake)
    Only because Bohr showed that the loss of energy would result in movement, which would affect the time measurement under special relativity. He didn't say "You can't measure the mass because it's uncertain".
    I can only comment that you were possibly wise to give up philosophy in favour of maths. You postulate a global premise and then produce a conclusion which is completely predicated on that assumption. Yet you think that's somehow convincing. Let me simplify your argument:

    P1 - I am a woman.
    P2 - If I am a woman, I have a womb.

    C1 - I have a womb.

    The only problem is that I'm not a woman. Oh, and not all women have wombs.

    You've made a false premise that QM necessarily involves the uncertainty principle for all measurements in all dimensions. What about the case where some QM priciples are true, but uncertainty is not? That's what Einstein and others have debated. That's why the Copenhagen interpretation is not universally agreed - there's still room for exploration. Ultimately, I think it will be that most of QM is shown to be a limited subset of a wider theory. Just like Newtonian physics is true only to a limited extent.
    I'll pass over your insult. I've already pointed out that QM does, in fact, necessarily involve uncertainty - its a consequence of the equations. There is no such thing as QM without uncertainty - if you have a reference, show me it. The Copenhagen interpretation is not the same thing as uncertainty - the other interpretations also involve it. In your argument, both premises are false - you've yet to show that mine are.

    Your last statement I agree with - I have high hopes for string theory. However, its highly unlikely that any further theory will do away with uncertainty, because of the Bell inequalities.

    Oh, and Bohr's argument with the box does rely on uncertainty - relativity comes in when translating one kind of uncertainty into another.
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    (Original post by wanderer)
    I've already pointed out that QM does, in fact, necessarily involve uncertainty
    Well of course, that's not what I said, is it? QM does not necessarily involve uncertainty in every measurement. It merely says that there will be uncertainty between pairs of non-commuting values. So you can know the position of a particle or its momentum, but not both at the same time.
    In your argument, both premises are false - you've yet to show that mine are.
    <sigh> You haven't proved that there is guaranteed uncertainty in individual measurements either, so I'm not bound to accept it as a premiss. In fact, the thought experiment is entirely consistent with the basic premisses of QM. It only relies on measurements in a single time frame and where none of the objects are moving relative to each other (except the photon, obviously). I've also pointed out a possible weakness in the experiment (derived from Bohr's objection) which you've studiously ignored.

    Anyway, I'm going to email Dr Bell with my ideas and see what he says.
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    (Original post by grumballcake)
    Well of course, that's not what I said, is it? QM does not necessarily involve uncertainty in every measurement. It merely says that there will be uncertainty between pairs of non-commuting values. So you can know the position of a particle or its momentum, but not both at the same time.
    <sigh> You haven't proved that there is guaranteed uncertainty in individual measurements either, so I'm not bound to accept it as a premiss. In fact, the thought experiment is entirely consistent with the basic premisses of QM. It only relies on measurements in a single time frame and where none of the objects are moving relative to each other (except the photon, obviously).
    Exactly. You have to know that the detector is not moving relative to the emitter and the slit. You are right that QM allows you to determine either value to an arbitrary level of accuracy - however, doing so makes any experiment totally unfeasible. How exactly is your experiment immune to Bohr's answer to Einstein's first thought experiment (the screens and the slits, not the box)?
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    (Original post by wanderer)
    You have to know that the detector is not moving relative to the emitter and the slit.
    There's nothing in QM that says I can't know that. Anyway, as I keep repeating, the distance is irrelevant. All I have to know is that neither is moving relative to each other.
    How exactly is your experiment immune to Bohr's answer to Einstein's first thought experiment (the screens and the slits, not the box)?
    Bohr's objection (as I understand it) was that the loss of mass would cause the box to move on the scale, so the two would not have a consistent time base. I've already said that the loss (and detector's later gain) of the photon ought to cause the apparatus to move apart which would distort the time base under relativity. However, we can figure out exactly how much it will move and therefore, the exact time dilation. After all, we're emitting photons of a single frequency, so they all have the same energy (and thus, relativistic mass). We know the vector, (because we know where the photon landed), so we can exactly allow for the relative movement of the two.

    As far as I can see, the only possible objection is to claim that each photon QM tunnels to somewhere else before setting off on its journey. However, if we make our slit material very thick, then the probability of any QM tunnelling vanishes. That only leaves QM tunnelling en route, which makes re-establishing the original vector interesting.
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    (Original post by grumballcake)
    Bohr's objection (as I understand it) was that the loss of mass would cause the box to move on the scale, so the two would not have a consistent time base. I've already said that the loss (and detector's later gain) of the photon ought to cause the apparatus to move apart which would distort the time base under relativity. However, we can figure out exactly how much it will move and therefore, the exact time dilation. After all, we're emitting photons of a single frequency, so they all have the same energy (and thus, relativistic mass). We know the vector, (because we know where the photon landed), so we can exactly allow for the relative movement of the two.
    Wrong thought experiment. As I said, I'm talking about Einstein's first idea, the one with the slits and a screen, not the EB box (although Bohr's objection involves more than you've detailed - becuse of the necessity of weighing the box, it must be moved back to its original position, and its here that the time dilation becomes a problem, as the uncertainty in determining the position of the box when you move it translates into a time uncertainty due to relativity).

    (Original post by grumballcake)
    There's nothing in QM that says I can't know that. Anyway, as I keep repeating, the distance is irrelevant. All I have to know is that neither is moving relative to each other.
    What? Of course there is something in QM that says you can't know that. Bohr's objection to Einstein's first thought experiment was that you need to know the position of your detector exactly. Which means its momentum is completely uncertain. Or, vice versa, you need to know with total accuracy that your detector is not moving relative to your emitter - which means its position is completely uncertain.

    Again - "With respect to the precision of the conditions under which one can correctly apply the [quantum mechanical] formalism, it is essential to include the entire experimental apparatus." My argument is Bohr's argument.
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    In the experiment, we have a system where the slit and the detector are not moving relative to each other, so they have no relative momentum. If they have no relative momentum, then their relative positions cannot change. So we can establish, with arbitrary accuracy the vector between the source and the strike in terms of their relative positions. What I mean by this is that any point on the source has a fixed correspondence with any point on the detector. Thus, there is a vector f(x,y) which linearly translates one coordinate on the surface to the other. Since the surface of each is not moving relative to the object itself, we can obtain x and y to arbitrary precision on each.

    Therefore, we can establish their relative positions with arbitrary accuracy. There's no violation of uncertainty so far, agreed? Then we fire the photon and observe where it lands on the detector. After launch, the source will recoil slightly, but that doesn't affect the point of launch. After impact, the detector will also start to move, but that doesn't affect the fact that we already know where it hit on the detector. We can calculate how much each part of the apparatus moves by using photons of a fixed frequency, but we don't need to.

    So, we now know (x,y) on the source and (x', y') on the detector. We can thus compute the vector f(x,y) in relative terms. Since nothing effectively moved during the transit of the photon, we now have a vector and a position.
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    You've just stated the exact same thing in more technical terms, rather than answering my argument.

    Therefore, we can establish their relative positions with arbitrary accuracy. There's no violation of uncertainty so far, agreed?
    No, I don't agree. To set up your experiment, you must first ensure that they are not moving relative to each other - fine. And their relative position does not change as long as they are not moving relative to each other. However, as soon as you measure the relative position - as soon as you establish the correspondence between them - you introduce uncertainty as to their relative motion, and you can no longer be certain that they are not moving relative to each other. This is exactly what the uncertainty principle is about - you can't just first measure the momentum accurately and then measure the position accurately.

    I think you might be working under the misconception that you can perform experiments in a state where things are effectively motionless, in which you can then measure positions without uncertainty interfering. This is false - the uncertainty principle works the same whether the momentum is equal to zero or not. You still have to measure it and establish that it is zero, and this still gives uncertainty of position. Uncertainty applies to determining a lack of motion in your system as much as it does to motion.
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    (Original post by wanderer)
    To set up your experiment, you must first ensure that they are not moving relative to each other - fine. And their relative position does not change as long as they are not moving relative to each other.
    Well, I'm actually going to join them together, so that they form one big structure. I'm not having them moving freely in space. So, it's not hard to establish the distance between them and to be sure that it doesn't change (i.e. they are at constant temperature throughout, so there's no expansion or contraction).
    I think you might be working under the misconception that you can perform experiments in a state where things are effectively motionless
    I don't think that's quite as hard to achieve as you're making out. Well, as a thought experiment anyway.
    the uncertainty principle works the same whether the momentum is equal to zero or not.
    I'm not convinced. The only reason that the momentum would stop being zero is if you have a source of energy. You'll have to give an explanation for that change, without resorting to a deus ex machina like vacuum fluctuations.

    Remember I only have to reduce uncertainty below the theoretical limit for there to be a problem.
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    (Original post by grumballcake)
    Well, I'm actually going to join them together, so that they form one big structure. I'm not having them moving freely in space. So, it's not hard to establish the distance between them and to be sure that it doesn't change (i.e. they are at constant temperature throughout, so there's no expansion or contraction).
    Now thats certainly more interesting. However, you still have to know their motion relative to the photon in transit, which introduces an equivalent problem.

    (Original post by grumballcake)
    I don't think that's quite as hard to achieve as you're making out. Well, as a thought experiment anyway.

    I'm not convinced. The only reason that the momentum would stop being zero is if you have a source of energy. You'll have to give an explanation for that change, without resorting to a deus ex machina like vacuum fluctuations.

    Remember I only have to reduce uncertainty below the theoretical limit for there to be a problem.
    Well, reasons for a change do spring to mind, under the kind of reasoning you've already mentioned - emitting and colliding with a photon. Joining together your apparatus removes your justification in a previous post, as the recoil of the source will now affect the detector. The 'photons of a fixed frequency' solution doesn't work, as you can only work like that when dealing with light as a wave - 'A photon of a definite frequency is not a localized particle.' (This comes out of the time/energy uncertainty relationship, as energy is proportional to both wavelength and momentum).

    However, I'm not sure this challenge is valid in the first place, as it follows classical reasoning. I think quantum fluctuations might be relevant, despite you ruling them out (give me a better reason - they're a consequence of the QM formalism, which as I've said has to apply to the whole experiment) although I don't know enough about them to be sure. I think they can have a small effect and set off a small amount of motion. Also, as we are dealing with your apparatus on a quantum mechanical level, the motion of the individual particles making up the apparatus will still be taking place, unless the apparatus is at absolute zero, a situation in which it is impossible to make any kind of measurement. While the (uncertain) motion of these particles averages out to zero in macroscopic terms, there are going to be microscopic fluctuations in the momentum of the entire system. It is even possible under QM (although the probability is incredibly small, enough to be totally ingnored most of the time) for these fluctuations to be macroscopic. Brian Greene has used the example of a dropped cup shattering and then flying back together again - this is possible in QM, although so unlikely we wouldn't expect anything like it to happen in the lifetime of the universe.

    You may point out that I'm talking about tiny fluctuations and small probabilities - but the point is, the amount of uncertainty predicted by Heisenberg is incredibly small. You're right that if you showed an amount of uncertainty less than that you would beat the principle, but the only way to do that is through the maths, or by showing the possibility of perfect accuracy.
 
 
 
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Updated: September 14, 2010
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