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Dec2-10, 05:04 PM
P: 356
A big fuzzy thing is probably the closest analogy, but it isn't always a ball. It could have a lot of different shapes--some common ones that you find when dealing with electrons around an atom are dumbbell shapes, rings, and other kinds of lobed structures (read up on atomic orbital shapes if you're interested.)

The equations of quantum mechanics tell you what kinds of shapes are possible for a given situation, and how they change through time. For instance, if an electron is by a proton, the equations will tell you the way in which the proton attracts the electron, and pulls its fuzziness into different shapes. But if you put an electron in empty space, where there's nothing around to attract it, its fuzzy shape will just keep spreading out forever, getting bigger and bigger. After enough time, there really isn't even a well-defined center to the fuzzy cloud anymore, it's nearly the same density everywhere. The electron is still just as real as it ever was, but it doesn't have a well-defined position--like a ripple on a pond after it's expanded out.

Then, when you observe the electron, you "collapse the wavefunction", which means all of a sudden the fuzzy cloud shrinks down to a tiny point. The location of that point is random, but the probability of it being at a certain place is proportional to the density of the fuzzy cloud at that point. So if the fuzzy cloud was very very small, you have a pretty good idea where the measurement will be. But in the case above, where the cloud spread out a great deal, you have very little idea where that point will be--in the most extreme case, every location in the universe could be equally probable.

Finally, once the observation is made, the tiny collapsed fuzzy point starts to spread out again, and after enough time it will once again be very large in size. So if you observe the electron again after only a very short time, the cloud didn't have much time to grow, so you can be fairly sure of where it is. But the longer you wait, the more the uncertainty grows.