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Just finished reading "In Search of Schrödinger's Cat". I am currently trying to explain the Uncertainty principle to myself as if I was 5. Concretely, why it is not possible to measure both position and momentum with 0 error. Is it because it is not possible to be in two places at the same time? The way I understand is that trying to predict where a particle is going to be in the future is same as trying to predict where a life boat is going to be in an ocean in the future - if you zoom in enough to confidently know where the boat is, you will loose the track of the waves, and vise versa.

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  • $\begingroup$ There is nothing to explain. The existence of non-commuting properties is one of the defining features of wave-like objects. That is what makes a quantum object a quantum object. $\endgroup$
    – CuriousOne
    Jun 6, 2016 at 14:11
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    $\begingroup$ You can leave this thread with one of three things: (i) an inaccurate analogy that makes you feel like you sort of get it (but don't), (ii) an abstract mathematical justification that gives you no physical insight, or (iii) abandon your notion of what a particle is and accept that you'll never really understand the nature of the world. Take your pick. $\endgroup$
    – lemon
    Jun 6, 2016 at 14:12
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    $\begingroup$ @lemon: What a particle is is well defined in physics. It's the approximation of the movements of an extended object by the trajectory of its center of mass in classical mechanics. What a particle track is, is also well defined in particle physics: it's the result of the weak interaction of a high momentum state with matter in a detector. Having said that, it's well known that most books that attempt to explain QM to layman (and to physics students) fail to mention both definitions and they end up hopelessly confusing readers between particles and quanta. $\endgroup$
    – CuriousOne
    Jun 6, 2016 at 14:18
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    $\begingroup$ @CuriousOne When I say "abandon your notion of what a particle is", I'm not referring to our models of particles but rather the essence of particles themselves. $\endgroup$
    – lemon
    Jun 6, 2016 at 14:28
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    $\begingroup$ Related: physics.stackexchange.com/q/132111, physics.stackexchange.com/q/200326, physics.stackexchange.com/q/169730, and many more. $\endgroup$
    – Martin
    Jun 6, 2016 at 14:32

2 Answers 2

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In qm a particle is described by a wave packet. A wave packet has both position and velocity spread. For a large wave packet the velocity spread is small so the velocity and hence momentum can be fairly accurately determined but the position is very uncertain. On the other hand for a small wave packet the position of the particle is more or less fixed but velocity spread of such packet is very large so momentum of the particle becomes indeterminate.

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You cannot know the exact position and momentum of a particle at the same time because to measure the position of a particle with accuracy you have to use gamma rays (because they have the shortest wavelength of the electromagnetic spectrum) but because they have high energy you will not know the energy of the particle very well. If you want to know the energy of a particle with accuracy you need to use radio waves (because they have the lowest energy the electromagnetic spectrum) but then you won't know the position with accuracy. So either you know the position of a particle with accuracy or it's momentum.

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  • $\begingroup$ Don't know why this reply was down-voted. It attempts to explain uncertainty in simple, experimental terms. It will be helpful to get a reason for a down-vote than a down-vote alone. @Chess_Player21, can you explain the 'energy measurement' a little more? $\endgroup$
    – Amey Joshi
    Aug 9, 2017 at 16:52
  • $\begingroup$ The downvotes will be because it's perpetuating the idea that the uncertainty principle comes solely from a limitation of our experimental apparatus $\endgroup$
    – CDCM
    Aug 10, 2017 at 8:07

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