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Homework Help: The Heisenberg Uncertainty Principle

  1. Apr 11, 2012 #1
    The general definition is that we cannot determine the location and velocity of a particle at any given moment. However, my intuition is to assume this is due to shortcomings in technology and measurement, but apparently that's false. This is a rule of nature.

    Can you explain what exactly the HUP is in more detail? And why is it a threat to Determinism?

    Also note that I'm in 10th grade and haven't taken Physics yet so I only know the rawest basics of quantum mechanics. If you're using any terms I wouldn't know, please explain :smile: .

    I only care about this principle in how it relates to determinism vs. randomness of the Universe.

  2. jcsd
  3. Apr 11, 2012 #2
    The way Heisenberg originally postulated it was in the form [tex]ΔxΔp≈h[/tex]
    where x= position, p= momentum, h= planck's constant (a very small number) and Δ= 'uncertainty in'.
    Heisenberg based this off of the idea that a particle's location was really determined by a wave function, therefore you could never be sure of its position, and therefore the uncertainty principle.

    More mathematically (and note: I can't actually do some of the math I'm about to talk about, so I apologize if I make a math mistake), the location of the particle is not a specific place, but rather one of many possible places, where the likelihood of the particle being at a specific place is given by the value of the wave function at that point (specifically, the square of the value of the wave-function at a point is the probability of the particle being at that point).

    In math there is an operation you can do to a function called a Fourier transformation. When you do a Fourier transform on the position wave-function, you get a function describing the momentum of the particle.
    It turns out, simply because of the way Fourier transformations work, that there is a certain uncertainty always present between a function and its Fourier transformation, meaning the more precise a function is the 'more spread out' its Fourier transformation is. This is the basis of the uncertainty principle.

    This relates to determinism in the following way:

    In classical mechanics, given an object (or set of objects) and full knowledge of their initial state, someone could predict the entire future of those objects based solely on the repeated use of the same laws, without actually waiting to see what happened.

    This is because (initial state)-->(physics equations)=(specific end state). The idea that the entire future can be predicted like this is determinism.

    The problem with quantum mechanics is, because of the uncertainty principle, you never know the exact state of an object, you only know a range of possible states and have to approximate which one is the true state, meaning: in quantum mechanics (initial range of possible states)-->(physics equations)=(several possible end states)

    Because you have a range of initial values due to the uncertainty principle, you have a range of possible end values, and therefore can't be sure what will happen next. If you are not sure the outcome of a state, you can't predict its future, and determinism fails,
  4. Apr 11, 2012 #3
    thank you for the response and the time you put in. That helped somewhat.

    So are you saying that a particle doesn't have a specific position and velocity simultaneously? Or are you saying that it is impossible to know the particle's position and velocity simultaneously?

    This doesn't prove that particles move randomly right? There are still antecedent factors that determine what position and velocity a particle will have at any given moment right?
  5. Apr 11, 2012 #4
    First and foremost, you are right in saying particles don't move randomly. Whoever told you that quantum particles move randomly is mistaken, obviously particle's paths can be predicted or you couldn't throw a basketball and expect it to land in the net.

    Rather, what the uncertainty principle says that that when you factor in all the details (position, speed, acceleration etc...), instead of getting a specific position (or path) like you would in classic physics, you get several different (albeit similar) positions.

    If you have a particle and you want to measure its velocity (for example, position works too), imagine you throw another particle at it and measure its velocity by recording the way the other particle is left after the collision. If you perform this test, you are going to get a specific answer- the specific velocity of the particle of interest at the time. However, if you perform this exact test on the same particles in the same initial state many times, you aren't going to get the same value for velocity every time, but rather you are going to get a range of different velocities.

    This seems strange because the initial condition was exactly the same every time, but this is the consequence of the uncertainty principle.
  6. Apr 11, 2012 #5
    Are we completely sure that the initial condition is exactly the same? If so, do we know what causes the velocity to change, or does it change at random? If it doesn't change at random, then how does that invalidate determinism?
  7. Apr 12, 2012 #6
    Yes, positive. Its not that the velocity changes. Its like this:
    The apple (just to be nice on the ears) doesn't have a momentum of 5 in the quantum world, it has a momentum velocity of 3-7. Check it once it will be 4, another time it will be 7, another time it will be 5.

    This is because the function describing momentum doesn't say it has a momentum value of 3, it says theres a 40% chance of a 3, 20% chance for a 6 and so on (all for example of course). Meaning if you measure the position of the apple 100 times, statistically, 40 of the times you will measure a momentum of 3, 20 times you will measure a momentum of 6, and so on.

    The value doesn't change, its just a range of possible values not a single value.
  8. Apr 12, 2012 #7
    Thank you that was very clear, I get it now
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