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Law of noncontradiction

  1. Sep 11, 2012 #1
    Hello,

    when i first heard about quantum physics and the superposition of particles, i immediately questioned myself about the law of non contradiction ( either A or ~A can be true, but not both at the same time and under the same interpretation).

    From what i've read, quantum physics does not violates it because superposition means that the particle has the "potential" to be in either one state or another when observed, but once observed it gets exactly one, and hence it respects the LNC in both states.

    Am i correct? I fear that the LNC may not hold someday, is it safe to use it daily? Can we be wrong? I know i am alive and not dead, i know i'm writing here and not somewhere else, but can i be sure that i will never find a situation where the LNC will fail? This is terrifying me, i'm starting to be unable to think correctly because i always consider the chance of A and ~A
     
  2. jcsd
  3. Sep 11, 2012 #2
    Different interpretations of Quantum Mechanics will yield different answers to this question. (All of them, note, are ways to describe the mathematics in intuitive terms.)
     
  4. Sep 11, 2012 #3
    But do you believe in the LNC in your everyday?
     
  5. Sep 11, 2012 #4
    Well, yea, it's quite unlikely for any quantum effects to have significant impact on everyday life.
     
  6. Sep 11, 2012 #5
    But do you believe that, even without quantum effects, its impossible to find something that is P and not P at the same time?
     
  7. Sep 11, 2012 #6
    Aristotle's concept was ""one cannot say of something that it is and that it is not in the same respect and at the same time".

    The stipulation "at the same time" is not always meaningful or relevant when using math that does not address time. There may be a better example, but for example:

    If we let N=1-1+1-1+1-1...

    We can group the terms like this:

    N=(1-1)+(1-1)+(1-1)... which becomes N=(0)+(0)+(0)... suggesting N might be 0

    or like this:

    N=1+(-1+1)+(-1+1)+(-1+1)... which becomes N=1+(0)+(0)=(0)... suggesting N might be 1

    Does N=1 and N=0 "at the same time", or do neither of these ways of looking at N have any relation to time in the usual sense?
     
  8. Sep 12, 2012 #7
    No. The LNC applies only in logically consistent systems, which the real world is not. The dividing of the world into categories is useful but breaks down under close (too close?) examination. So for something to be both P and not P at the same time is the norm. It may be biased greatly one way or the other, but both qualities are usually present to at least a very faint degree.

    Artificial intelligence systems built upon logic fail to deal with real life.
     
  9. Sep 12, 2012 #8
    If you have a superposition of state [itex]A[/itex] and state [itex]B[/itex] in the form [itex]\frac{1}{\sqrt{2}}(A+B)[/itex] it is in the state [itex]\frac{1}{\sqrt{2}}(A+B)[/itex] which is not [itex]A[/itex]. What makes this weird is the fact that a measurement will find it in [itex]A[/itex] or [itex]B[/itex]. The superposition itself is not that weird.

    If I'm not being clear, I'm trying to say that [itex]\frac{1}{\sqrt{2}}(A+B)[/itex] is not [itex]A[/itex]. That is not a contradiction. If you measure it and it becomes [itex]A[/itex] it is no longer [itex]\frac{1}{\sqrt{2}}(A+B)[/itex].

    (In this I am assuming the standard formalism of QM)
     
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