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Simple questions on uncertainty principle

  1. Aug 10, 2011 #1
    Hi all, I am sure this is a quite simple question but I just cant figure it out, any helps would be greatly appreciated.

    If a particle stay in a state in a very short time, then by energy time uncertainty relation, it's energy must has a great uncertainty. Also because of energy is propotion to momentum, then does it mean the momentum is uncertained aswell?So one measure it's momentum percisely just became impossible?
  2. jcsd
  3. Aug 10, 2011 #2
    I can't answer with 100% certainty, but I can tell you something that could clarify something.
    when we did this, our professor said that the energy-time indetermination principle has to be interpreted in a different way than the position-momentum one: while the latter refers to dynamic variable, so it can be interpreted as "we can't measure both position and momentum with infinite precision", the former takes into account time, which, at least in non-relativistic quantum mechanic, is not a dynamic variable, or at least is treated differently from momentum and space - just think that in Schroedinger's equation (non relativistic) time appears in a first partial derivative while space in a second partial derivative, so they are not treated equally.
    So, the energy-time indetermination principle has to be interpreted as "a state that has a certain indetermination on the energy can exist for a certain amount of time"; some examples of application can be the following:
    a state with fixed energy ([itex]\Delta E=0[/itex]) is a stationary state ([itex]\Delta t=\infty[/itex]);
    a particle that has a greater mass than another lives less.

    I know that I haven't answer directly to your question, but I actually don't know the correct answer, so I was just putting down few ideas :D :D
  4. Aug 10, 2011 #3
    Not a simple question!!

    In essence, if you want an accurate/precise series of measurements of momentum (at various points in time) you can get them to arbitrary precision. You don't have that ability with time/energy and momentum/position pairs.

    In simple terms, Heisenberg uncertainty applies to certain characteristics whose values do not commute: energy and time are one pair; position and momentum another. One way to view the implication of this is that if you measure one before the other, then reverse the order of measurement you'll get a different measurement. But that is not the whole story.

    Here is an essential component of a very long discussion on (almost) your question (I think that discussion is still being argued):

    This is from Zapper:



    Somebody in the recent past posted this....my boldface.. (I did not record the poster, maybe even Zapper??..was a trusted source here.) I'm posting this to confirm that it is an equivalent description, that it matches Zappers blog...

    Here are two more complementary explanations from that discussion:


    Originally Posted by fuesiker:

  5. Aug 10, 2011 #4
    ok, here is the very long discussion from which I made the excerpts in my previous post:

    what is it about position and momentum that forbids knowing both quantities at once?


    Reading the first dozen or two dozen posts there might be worthwhile.....
  6. Aug 10, 2011 #5

    Thank you for your replay, and it's indeed a great help. Now I am just waiting for more people to come and bring more ideas:) thanks again.
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