Monday, April 07, 2008

Physics and Philosophy - Thoughts on the Implications of Quantum Mechanics, and Other Matters #10iv

10. On Quantum Mechanics:
iv. Position and momentum are complimentary dynamical observables. If we wish to determine a particles position, then we will no longer have any idea as to its momentum. In other words, after observing its position, the act of observing sends it off in an unknown (and unknowable) direction. Likewise, if we know its momentum, then its position is unknown (and unknowable). Therefore, an exact time and place cannot be calculated (even in theory). Another pair of complimentary variables are time and energy. An important point to understand (without actually resorting to equations) is that if we wish to know one observable with some, but not a precise degree of accuracy, we may also know the complimentary observable with a proportionate degree of accuracy. The famous Heisenberg’s Uncertainty Principle is the mathematical statement of this phenomenon. (Sometimes equations are simpler.) We may never know the precise trajectory of a subatomic particle.

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