For those who don't get this comment, the Heisenberg uncertainty principle applies to any two quantities that are connected in QM via a Fourier transform. Such as position and momentum, or time and energy. It is really a mathematical theorem that there is a lower bound on the variance of a function times the variance of its Fourier transform.

That lower bound is the uncertainty principle, and that lower bound is hit by normal distributions.

thank you for that reminder/clarification. I forget sometimes how much we think we have clear pictures of how things like that work when really we're just listening to someone trying to explain what the math is doing and we're adding in detail.

Thats. I always assumed it was more a quirk of the universe than something driven by pure mathematics. Amazing.