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Old 27-June-2008, 08:03 PM
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Let me second what Ken said. We can see the "uncertainty principle" all the time in macroscopic wave phenomena.

A classic example I remember having to do as an exercise back in school was the frequency-time thing using the Fourier transform. You can show something like

delta-w*delta-t = constant (which I can't remember but it involves pi )

Delta-t is roughly the duration of a signal that you receive and delta-w is the frequency bandwidth. The shorter the bandwidth, the more time it takes to transmit a given amount of information.

For example, delta-w = 0 would be a single frequency, which would be a sine wave that went from -infinity < t < +infinity. Delta-t is infinite (and a pure, eternal sine wave can transmit no information at all, at least in finite time). Delta-t = 0 would be a delta function thing which would consist of all frequencies from 0 to infinity (negative would be involved in the complex form, but that translates into sines and cosines -- I forget all those details :sigh.

IOW, delta-t = 0 requires infinite bandwidth.

That's the Uncertainty Principle in action right there as well. The faster we want to transmit information, the more bandwidth we need.

-Richard
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