What’s the underlying principle on why you can’t know the position and momentum of a particle at the same time? Is there an explanation? I don’t have any knowledge of calculus or the math behind anything so I’m asking here, thanks!
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The energy of a particle is related to the frequency of its corresponding wave. Suppose you wanted to measure the frequency of a sound wave. You could do it by counting the number of peaks and troughs that hit your microphone in a given time. Say you measure for a second, and count 1000 peaks, so you report that the frequency is 1000 Hz. But there could have been an almost-peak at the end if the second that you didn’t count, so there’s a 1/1000 uncertainty in the measured frequency. If you count for 5 seconds instead, you can reduce that uncertainty by a factor of 5, but now there’s a cost — you can’t say exactly **when** that measurement represents, since it’s smeared over that 5 seconds.
Similarly, you can measure the energy of a particle, but the more precisely you try to measure it, the more you have to give up on knowing its exact position.
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