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Location and speed of the electron

  1. Aug 2, 2010 #1
    Hello, people
    Why is it impossible to determine accurately the place and the speed of an electron??
     
  2. jcsd
  3. Aug 3, 2010 #2
  4. Aug 4, 2010 #3
    You need to interact with the electron to get any information out of it. But the interaction changes its state.
     
  5. Aug 4, 2010 #4
    electron is not really a "ball" moving around, at small scales its more of a wave which we can sort-of calculate the probability density for its location
     
  6. Aug 4, 2010 #5

    Born2bwire

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    You can measure the position and momentum of an electron and the results will be valid. The problem is that in quantum mechanics we are interested in an ensemble of measurements. That is we are interested in the results of a large number of measurements on identical systems. The position and momentum properties of a system are described by two different sets of bases or states. The consequence is that if we find the system in some position state A_x, then for the momentum the state could be A_p, B_p, C_p, etc. This causes an ensemble of measurements to have a certain degree of spread in their results. So if we only look at position measurements that yielded A_x, we may get 10% of them to have momentum A_p, 25% B_p, and so on. Likewise, if we only look at measurements that yielded a momentum A_p, we would get some A_x, D_x, F_x results for the position.

    The spread in the results, the variance, is described by the Heisenberg Uncertainty Principle. This principle makes no assumptions about the accuracy or precision of a measurement but is simply a consequence of the mathematics of quantum mechanics. So even if we can perfectly measure the position and momentum of an electron, we say that we cannot simultaneously know the two because over a large set of measurements we will end up with a variance in our results.

    Another way to think about it is that we cannot gleam the entire information about a system in terms of position and momentum at the same time. Because a position state can correspond to multiple valid momentum states (and vice-versa), then the momentum of our position state is a superposition of momentum states.
     
    Last edited: Aug 4, 2010
  7. Aug 4, 2010 #6

    Mentallic

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    Are there any theoretically viable methods to observing the electron without transferring a change in momentum to it?
     
  8. Aug 4, 2010 #7
    It's like you're in Chicago and you have a cousin in LA. You could have a pretty good idea of where he is, and you may even have an address for him, but he's always in motion. Since you only find out where he currently is when you talk to his mom by phone, and by the time you get the message, he's moved, he's gone to the next room, or gotten in his car and taken off. You are too far away, and the time lag is too great.
     
  9. Aug 8, 2010 #8
    Why is it impossible to determine accurately the place and the speed of an electron?

    Just some nitpicking: you can.
    Measuring accurately its "place" and "speed" simultaneously, however, is impossible.
    It's fantastic how many times this crucial word is omitted.
     
  10. Aug 10, 2010 #9
    Heisenberg uncertainty principle :D
     
  11. Aug 10, 2010 #10

    sophiecentaur

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    I was given a 'practical' explanation for this.
    If you want to observe something then you can 'look at it' using em radiation. The wavelength of the em used limits the accuracy of position measurement so you use as short a wavelength as possible. The photon will have high momentum so it will affect the speed (momentum) of the object in a way you can't be sure of. So the more accurately you can measure its position, the more uncertain is its momentum. etc. etc..
     
    Last edited: Aug 10, 2010
  12. Aug 10, 2010 #11
    Yes. You can observe that it's not somewhere else. You can have quantum interactions like the Elitzur-Vaidman bomb-tester. You can make a measurement of a quantum observable that is not "demolished" by making the measurement (used in gravitational wave experiments).
     
  13. Aug 13, 2010 #12
    I don't understand what do u mean by "interact with the electron"
     
  14. Aug 14, 2010 #13

    Mentallic

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    In total darkness how do you see anything? You need a flashlight to see the reflection it creates. The same thing with the electron, you need to bounce a photon off of it to see it, this is the interaction that causes the uncertainty principle.
     
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