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Acts of random uncertainty

  1. May 6, 2004 #1
    I am confused as to the significance of the uncertainty principle. As I understand it, the uncertainty principle states that either the position of a sub atomic particle can be measured or the velocity of the sub atomic particle but not both. This uncertainty principle as I have come to understand it propagates the potential for activity that can be described as "random". This randomness than allowed Stephen Hawkins in a paper to declare that "God does indeed play dice." My confusion is, however, how could it be that simply our inability to measure both position and velocity means true randomness exists. Is it so that just because we are uncertain as to what will happen, what will happen is not a matter of cause and effect
     
    Last edited: May 6, 2004
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  3. May 6, 2004 #2

    chroot

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    It is a common novice mistake to assume that the uncertainty principle has something to do with our technical sophistication. It might seem reasonable that, given "infinite technology," we should be able to build a machine to determine the position and momentum of a particle precisely. However, that is not true. The uncertainty principle has nothing to do with how we measure, it has to do with what can possibly be measured. As it turns out, Nature is fundamentally random at its deepest known level, and no advance in technology will ever let us see "past" the uncertainty principle.

    It's not that we're just not able to measure the position and momentum simultaneously; it's that the particle does not actually have a precise position and momentum at the same time.

    Quantum particles are not like little billiard balls that you can watch rolling past a detector -- they are smeared out in space, and have a wavelike character. They exhibit diffraction, for example, just like all waves do.

    If quantum mechanics is the correct description of Nature (and it so far seems to be), then yes, the world is fundamentally, truly, random.

    - Warren
     
  4. May 6, 2004 #3
    "they are smeared out in space, and have a wavelike character. They exhibit diffraction, for example, just like all waves do."- Warren[/QUOTE] Can you please help me understand what this means and why people believe it to be so?
     
  5. May 6, 2004 #4
    because it gives results that fit with experiment VERY well, e.g. using quantum theory you can predict the energy levels of most simple atoms/molecules. Its easy to test they are correct by looking at the wavelengths of light these atoms/molecules give off. I know of no other theory that can predict all this.
     
  6. May 6, 2004 #5
    When you first encounter quantum mechanics, it appears counterintuitive and hard to accept. Even after you are convinced that the experiments prove that quantum mechanics provides a good description of many aspects of the physical world, it may be hard to comprehend on an intuitive level.
    Some people are not bothered by this and continue studying the math, which allows them to move forward. Others prefer to have some kind of "interpretation" of the math which makes sense to them. You may be the kind of person (like me) in the second category.
    Quantum mechanics is very powerfull in its predictive powers (uncertainty and all) but I think the most exciting part is its paradoxes. There are things that apparently don't make sense. But as we know that at least the math is correct, we are left as an only option to assume that our interpretation, (the mental "picture" that the theory evokes) may need to be changed if we want to make sense of the theory.
    I would advice that you look at these issues with an open mind. You won't be able to understand it the first time or from reading just one (or two) books.
    There are many popularizations (those non-mathematical books you find at your local book store) and I think they are very useful. I actually think it would be good for students to read some of those books before getting into the math of quantum mechanics. Not only do they introduce the concepts but they give you some of the stories behind the discoverires.
    Some books:
    "In Search of Schrodinger's cat" by John Gribbin
    "The Strange Story of the Quantum" by Banesh Hoffman
    "Thirty years that changed physics" Nick Herbert??
    But if you wand to have a really deep understanding, you'll have to learn some of the math. You'll also need some knowledge of classical physics (newtonian physics and electricity and magnetism might be sufficient to start)
    I don't know what level of math you have, but to understand quantum mechanics you'll need at least a knowledge of complex numbers, some calculus and linear algebra.
    But before you get into the math I'll give you a list of interesting topics that you may research through Google or look them up in books:
    1) Double slit experiment
    2) Wave packets
    2) Wave-particle duality
    3) Copenhagen interpretation
    4) Debates between Bohr and Einstein
    5) The measurement problem
    6) Schrodinger's cat
    7) EPR experiment
    8) Many-worlds interpretation

    Once you have some mathematical background you may want to look into the following:
    1) Hilbert space
    2) Dirac notation
    3) 1/2h spin systems
    The older books start with the wave function and a lot of tedious integrals. I you are looking for intuitive understanding, it is better to start with the above.
    Good luck,
    --Alex--
     
    Last edited: May 6, 2004
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