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Chemomechanics t1_j3y7rbt wrote

An analogy I've found useful: where is a 1 Hz sinusoidal wave? Well, it's everywhere. Having a precise frequency goes hand in hand with extending from -∞ to ∞. It has no single location.

What's the frequency of a point? Well, it doesn't have one; there's no physical extent for us to examine its periodicity.

In between these two extremes, you could have a localized wave whose position can't be well defined because it's not pointlike. Its frequency also can't be well defined because it's not perfectly periodic. You could estimate these two values, but they'll always contain ambiguity; in fact, as one becomes more certain, the other becomes less certain. This has nothing to do with a measurement limitation. It's a fundamental constraint.

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luckyluke193 t1_j3yl3cm wrote

I wouldn't call this an analogy, it is actually the same thing. Planck's relations tell us that the energy of a particle is the frequency of its wave function time Planck's constant, and momentum is the wavevector times Planck's constant.

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Chemomechanics t1_j3yobpe wrote

> I wouldn't call this an analogy, it is actually the same thing.

Ah, good. It's outside my research field, so I hedged my language in case the correspondence wasn't exact.

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