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Understanding the Uncertainty Principle

  1. Mar 3, 2008 #1
    Hi.

    This semester I am taking a Philosophy class (introductory) and a Modern Physics class (introductory) and we just recently (in the latter) began officially learning about Heisenberg's Uncertainty Principle.

    From the lecture (and other reading I've done), I am seeing that the math for determining the momentum and position of a particle are directly linked and, together, have a "lower bound". This is my understanding of the premise for the Uncertainty Principle.

    Given that, I wanted to ask something to make sure I understand it properly. The principle is saying that it is impossible for us to know, fully, the momentum and position of a particle. However, and here is my question, the particle has a specific momentum and position, it is simply unknowable. Is this correct, or am I misunderstanding? Does the fact that we cannot know both its position and momentum imply it has no specific position and momentum?

    Thanks, I hope you understand my inquiry.
     
  2. jcsd
  3. Mar 3, 2008 #2
    The problem starts with imagining the electron as a "billiard ball' with a definite position and a definite momentum, i.e., the classical picture. In quantum mechanics, the electron cannot be strictly imaged this way. For example, if you throw a rock into a lake, what is the position and the momentum of the waves generated?
     
  4. Mar 3, 2008 #3
    I don't follow nor think that is an applicable analogy (though I could be missing your point).

    The electron (like all, complex or simple, objects) falls under the "wave-particle duality" concept, but that does not mean they are strictly waves--it also has the particle aspect. This includes position and mass/momentum, no?

    It seems our equations lead us to the fact that we cannot know these two values together, but does that imply they do not exist?

    This questioning was alluded to by a discussion (in my Philosophy class) on metaphysics and the question of whether anything exists outside of our minds. Does the fact that we cannot know anything outside of our minds imply it does not exist? No, of course not, maybe it does, maybe it doesn't--it is impossible to prove from within our minds. Well, extending that to this principle, does the fact that we cannot know the (precise) position and momentum of an electron imply it does not have a position and momentum?
     
    Last edited: Mar 3, 2008
  5. Mar 3, 2008 #4
    Here's a nice website with additional info:
    http://www.colorado.edu/physics/2000/quantumzone/debroglie.html

    Depending on the circumstances, electrons exhibit either wave-like or particle-like behavior. These "like" behaviors in no way force electrons to strictly conform to the corresponding classical concepts, though.

    Why would momentum and position, understood in their classical incarnations, be applicable "as is" in a quantum sense? If the electron is a quantum beast why would you think it should behave in such a way as to offer both classical position and momentum to observers? Note that in the realm of quantum mechanics, position and momentum are complementary observables. This property doesn't exist in classical mechanics.

    Physics has nothing to say about that question, except that objective reality is assumed to exist. Otherwise, it wouldn't make much sense to do Science.
     
  6. Mar 3, 2008 #5
    Your question could be interpreted in two different ways; one would be if you are asking whether the outcome of a measurement is decided "in advance", i.e. is there something "hidden" in the wave function which causes a measurement to come out the way it does, or is the outcome inherently unknowable? The other would be if you're asking whether the particle in question is actually "there" and behaving as a classical particle before we measure it.

    The answer to the latter, as nanobug said, is definitely no, and we know this because quanta show properties that make no sense in a classical frame, such as interference and non-locality. As for the former, you would probably be better served by asking in your philosophy class. There are many interpretations of QM which give different answers to this question, and though some may be more popular than others, anyone who tells you that one has more evidence behind it than another is misinformed.
     
  7. Mar 3, 2008 #6
    It is very important to realise that a particle can not be described by a position and momentum that is given in advance, but which we do not know.

    This is the crux of the argument given by Bell about local hidden variable theories. It has been experimentally proven that reality does not work that way. Specifically - one can not always describe a local (or independent) state for a particle which has "hidden" (predetermined, but unknown) values for position and momentum.

    This argument relies on entanglement, which hopefully you will cover shortly in your course... but in it does lie the answer to your question - the position and momentum can not simultaneously "really" exist. Kyuzo mentioned that there are many interpretations of Q.M. but they all must agree on this point.

    Whether anything exists outside our minds is a question I can not answer... :)
     
  8. Mar 3, 2008 #7
    While I appreciate your responses, I am not fully satisfied so please bear with me. ;)

    As the reading you suggested mentions, we shouldn't look at the electron's orbit around an atom as a circular orbit but rather as a standing wave. But if we do this, as you seemed to suggest, what does the Uncertainty Principle mean? Does it not specifically refer to the electron's momentum and position? What does that mean if the electron is a wave? The principle does not seem to apply to the wave-like nature of the electron; only to the particle-like nature of the electron, no?

    I think I have isolated my concern:

    The Heisenberg Uncertainty Principle states:
    "Locating a particle in a small region of space makes the momentum of the particle uncertain; and conversely, that measuring the momentum of a particle precisely makes the position uncertain."

    The question was:
    "Does the fact that we cannot know both the specific position and specific momentum of a particle imply it has no specific position and specific momentum?"

    If I am not mistaken, you answered this by saying:
    "It is not a particle, it is a particle-wave, so it need not be confined to position and momentum."

    But how can that be so, and if that is so, what does the Uncertainty Principle mean?
     
  9. Mar 4, 2008 #8
    Well my response was different... when one looks a bit deeper (at entire systems that are made up of more than one particle) then your question is answered:
    "Yes, that is right, even if you think of it as a sort of particle (not a wave), it is incorrect to say that it has some specific position and momentum that we simply can not know (but might exist)"

    I should explain my qualifications to that statement, just to be precise. Bohmian mechanics (thought up by David Bohm) is an interpretation of Q.M. where we envisage just what you say - particles are flying around with specific positions and velocities but with some probability distribution. These particles don't behave like normal particles (i.e. follow Newton's laws), but move in ways to create interference and other quantum effects.

    So, to throw some extra confusion, if you have one particle in your universe, then it can be possible to interpret it as a particle flying about with some unknown, but none-the-less defined, momentum and position. As everyone begins to learn Q.M. by starting with just one particle, this can be confusing and contradicts what you get taught!

    But the universe isn't made up of one particle - it's made of lots which are interacting and getting entangled with each other all the time. Bell, and the experimenters, have shown that such an interpretation is inconsistent with reality - you can not always describe particles in that way (specifically, if it is entangled). Thus, we have to conclude that the position and momentum of a particle do not exist.

    Well, it means exactly what it says. It simply says how well we can approximately know positions and momenta of particles. It says that big objects can have relatively well defined momenta and positions, and that the everyday world appears to behave in the way our intuition works, but that our intuition is actually fundamentally wrong, especially when we look at small things. I believe you should interpret it as saying that the particle does not have a specific position and momentum.
     
  10. Mar 4, 2008 #9
    Hmm, okay, thanks for your clarification andyferris. I understand your point a lot more now, though haven't quite made up my mind as to what I think is true (need to think about it more, and get a bunch more information--especially on that entanglement stuff!).

    That said, could you provide any (ideally popularized) experiments which show the particle's non-existence of specific position and momentum? That isn't to say the inability to measure their specific position/momentum, but the actual non-existence of them as you explained.

    The type of experiments I am thinking of is the interaction between two particles (like in a particle collider). From what I know, we shoot a particle at another and they can interact in a particle-like manner. Whether or not we can measure the precise momentum and position of those particles isn't important (to this discussion), but rather the fact that they do or do not collide at a specific position with a specific momentum.

    That is to say: if we took that event, that specific instant in time when the two particles collide, and considered it again given the same preconditions of the entire system (be that the room, planet, or universe), that the two constituent particles would interact in precisely the same way.
     
  11. Mar 4, 2008 #10
    In the double slit experiment, when an electron goes trough both slits at the same time, what is the position of the electron?

     
    Last edited by a moderator: Sep 25, 2014
  12. Mar 4, 2008 #11
    But in that experiment the entire interaction becomes rather wave-like. Isn't the interaction in a particle collider rather particle-like? How do we explain the interaction between two particles in a particle collider? If they are hitting, doesn't that mean they have a specific position and momentum?
     
  13. Mar 4, 2008 #12
    Sure, but given that we are talking about electrons, what is the position? Or why is it that we cannot easily talk about position in this case?

    They are not "hitting". They are interacting (exchanging energy/momentum) via photons.
     
  14. Mar 4, 2008 #13
    the way we got taught it is that the electron has a wavefunction which can give the position and a K space interpretation that gives the momentum using the de brogile idea of wave particle duality. These two properties the wavefunction and the K(wave number) function are interlinked by the fourier transformations. We usually think of an electron as a wave packet a series of waves superimposed. If we take the modulus of the wave function and square it then we will get an area in whcih we should expect to find the position of the electron(This is a postulate as far as I am aware) this is linked by fourier transform to the K function which gives us an expected value for the momentum.

    If we have an infinite wavefunction ie we know the precise momentum of the particle/electron but know nothing of the position.

    All these ideas as to how the world works eg physics are just that ideas. They are there to explain what we see. Whether they are real in an external/physical world is up to your belief. I am an idealist so I would say that they can't be shown to be real therefore they can't be real but at the same time you have to concede the possibility of them been real.
    Either way it would seem that the idea of probability is built into quantum mechanics no matter wether you believe in the physical world or not.

    This post would be very much nicer with some nice diagrams and stuff but im sure you can find them about the net.

    Alex
     
  15. Mar 4, 2008 #14
    The question is not whether (A & B) exists but what can be known about (A & B).
     
  16. Mar 5, 2008 #15

    Fra

    User Avatar

    This is an interesting position.

    I'm all with you on that physics, like Bohr said, is about what we can say about nature, not what nature us is.

    IMO, this does not imply an objective absolute reality. In fact I can't figure out how we can DEFINE an objective reality? The best definition is the collective one, ie, the agreement among a local set of subjective reality views, as communicated between them.

    In the everyday sense of science, it is supposedly objective - ie results must be repeatable by others etc. However this has more do to with the science in the sociologicla context. I personally think taking some kind of objectivity idea to it's extreme is misleading.

    All I can speak of is MY subjective view of reality. I communicate with others and we compare our views, and most of the time it makses sense. But I can not make the conclusion that there is some absolute objective reality out there because of that. The locally objective reality lies in our communicated, partial, agreements. But this is subject to ongoing change IMO.

    This seems to be somewhat "loosely" (all analogies are flawed) analogous to Einsteins search for absolute reference frames where his conclusion was that it doesn't exists, and instead the only reference we have is the local gravitational field.

    What the correspondence to the local gravitational field of the analogy in this case? :)

    /Fredrik
     
    Last edited: Mar 5, 2008
  17. Mar 5, 2008 #16
    Ah, sorry for the delay, I was getting emailed every time there was a response and as soon as I observed this phenomenon (of being emailed when there is a response) it seemed to change and I stopped getting the emails. How appropriate, eh? Anyway...
    Could you explain this a bit more? I don't have much knowledge in the area so I can't say that I understand that phenomenon of exchanging energy through photons when there were no photons present...?

    What do you mean? I understand that there could be limitations on what can be known about A & B, but I don't understand how that implies A & B don't exist.
     
    Last edited: Mar 5, 2008
  18. Mar 5, 2008 #17

    Fra

    User Avatar

    I think the point is that when we are posing questions, care should be taken so that the question is a proper question from a scientific and physical viewpoint. Sometimes the difficulty in finding consistent answers to a question, is because the question is invalid in the first place. Any sequence of words that grammatically looks like a question is not necessarily a scientifically or physically well defined question.

    Now that may be an interesting point. What does it mean for a question to be invalid? IMO, it means that this question can not be constructed from the premises. The formulation of the question itself, requires some additional structure, and this missing structure is also why it's not possible to find intrinsic answers. That's how I see it.

    In this sense, the question "what is A & B" is simply much more poorly defined than is "what do we know about A & B".

    From the philosophical view, QM puts large emphasis on this. The idea of measurable things, is the idea that proper questions are those that have measurable answers. In QM the idea at least, is that the process of answering is the measuring process. And the physically possible measurements does constraint the possible proper questions.

    /Fredrik
     
  19. Mar 5, 2008 #18
    I see what you are saying but can't help but disagree. That isn't to say I take the converse stance, which would be that something can exist without being measurable, but rather that I am skeptical about either conclusion.

    You stated that:
    And while I know it is your opinion, I see no reasoning for that deduction. Why should a 'proper question' be confined to physically measurable answers? Or conversely, why shouldn't it? Do you see my point? It is a matter of being certain and being skeptical; while indeed it is useful to make a decision, I don't feel it is scientific to neglect the other side of the argument should you be forced to make a decision (be it for experimental or theoretical reasons). Maintaining awareness of the initial argument seems imperative to scientific thought, and this seems to be something many of us are forgetting as we delve deeper into attempting to understand Q.M.

    This seems to be the root of my issue with the Uncertainty Principle, and more specifically with the responses I've received. I feel as if many of you feel/know there is some reason to deduce what you said (that which I quoted), yet have not shown any. Of course, I will gladly consider my position given any reasonable explanation for that dedution. ;)
     
    Last edited: Mar 5, 2008
  20. Mar 5, 2008 #19

    Fra

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    Of course what you quoted of me, is not a "deduction", so you are free to it my opinon if you like. And even if it was a deduction, it would be a subjective one.

    I can not prove anything of what I said as in "formal proof". Internally my own reasoning is justified by subjective plausabilities. I don't think formal deductions are applicable to nature, except as idealisations.

    There is another complexity here. From the human point of view, the question does make sense, because you obviously posed it. So it's real. But then the human brain is supposedly more complex than a particle. So the question is what the particle level constraints shaves off the set of posable questions.

    I think we can agree that alot is subjective here. And that's part of the problem as I see it, but this is also what IMHO at least makes the subjectivity plausible. The subjectivity acknowledges the subjective view - ie what I KNOW about something. And from the subjective viewpoint, what's beyond what I know is very foggy.

    Maybe you'd ask: so which subjective view is "right"? Then I think that's the whole point. All views are equally right. There is no contradiction in this. Because the contradiction would appear only when you actually compare the views. And IMO, the comparasion is a physical process. And I think the supposed contradictions (which really arent' contradictions) is partyl what gives rise to non-trivial interactions. The fact that we don't see random interactions could be because there are in a sense local objectivity, as defined by the consensus of the local neighbourhood of interacting observers.

    Again, this is no deduction... I'm just adding some subjective reflections. The plausability of this may be subjective too.

    That said, some of what I said suggest that QM as it stands still has problems. So I didn't mean to say I have all answers. I sure don't :)

    /Fredrik
     
  21. Mar 5, 2008 #20
    Very wise words fra and I think I share a simmilar belief as you that we cannot objectively know something without introducing some kind of belief/probability.

    What is an objective reproduceable experiment?

    One in which the observers on average agree on the outcome of the experiment. With probability in QM doesn't this make an objective result harder to achieve. Obviously in this case we must look at the probability diustrubution in order to test our theories. But QM treads sticky philosophical ground IMO.

    Alex
     
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