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Heisenberg has said that the position and velocity of a small object cannot be known 100% accurate. Now, suppose I take a big metal box within which there is only one electron (somehow). I don't know the position of the electron in space nor do I know its velocity. Now suppose I'm compressing the box from all sides uniformly, keeping all physical quantities constant. The vertices of the cube were already noted before compressing it. Now as the cube is compressed from all sides equally the vertices are also noted down in such a manner that one of the vertices remains as the origin $(0,0,0)$. Now as the cube is compressed on and on, the specific region of space within which the electron is located is known with certainty. The cube is compressed until the electron just fits the cube. Correct me if I'm wrong. Is this against Heisenberg's Principle?

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    $\begingroup$ have you ever heard of quantum tunneling? oh boy you gonna have fun! $\endgroup$ – AccidentalFourierTransform Jan 13 '16 at 18:55
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    $\begingroup$ No, actually im a class 12 student and im finding this quantum theory very interesting and researching as much as i can knowat this level.So i will be very happy if you guys help me out :) $\endgroup$ – user10379 Jan 13 '16 at 18:58
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    $\begingroup$ Oh, you can put an electron in a cube, alright, and then you can squeeze. And if you squeeze real hard then you will find that suddenly there is not just an electron in there but tons of photons and other electrons and positrons and neutrinos will be emitted by the cube and then suddenly quarks and gluons and Ws and Zs and Higgs will be showing up. They call that cube a particle accelerator, by the way. :-) $\endgroup$ – CuriousOne Jan 13 '16 at 19:05
  • $\begingroup$ Also, it seems that you've assumed the electron has a definite size in the second to last sentence. ;) $\endgroup$ – Arturo don Juan Jan 13 '16 at 19:05
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    $\begingroup$ Keep in mind that Heisenberg said that the velocity and the position can not be measured with infinite accuracy at the same time! It is possible to measure position or velocity with infinite precision separately. Moreover, squeezing the box and thus more accurately determining the position of the electron will result in something called quantum confinement where the electron energy becomes larger as the box becomes smaller. So it's harder to keep squeezing as the electron will resist. $\endgroup$ – David VdH Jan 13 '16 at 21:08
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The wikipedia article for Particle in a Box neatly explains how it obeys the uncertainty principle. Basically, a smaller box gives the particle a wider distribution of momentum, or more uncertainty in momentum.

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