This always confuses me and I’m not sure how it works. Please explain…
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My, admittedly limited, understanding is that we CAN know both of a particular something. It’s just one or the other will have very spread out distributions on repeated experiments. Put another way, if you have an experiment that sends out an electron you can’t precisely predict both the position and momentum of said electron (more precisely, the product of your standard deviation of both has a lower bound). However when you actually do the experiment and an electron does come out, the principle doesn’t stop you from measuring it.
I think explanations are best left to people who actually understand better; I recommend [this video by Sabine Hossenfelder](https://www.youtube.com/watch?v=qC0UWxgyDD0). However I’ll try to do my best below, if only to get some feedback and corrections on my own understanding.
The spread out distribution bit is a property of waves in general. For the extremes think about how a single frequency is just a sin wave that keeps waving across all time while say a unit pulse in frequency domain contains every frequency. For the middle, I think it’s easiest to bust out your favorite graphing calculator/software and plot the sum of sin(nx)/(nx) with n from 1 to increasingly large numbers. You should see that with more and more frequency you can constrain your signal tighter and tighter in time.
After that, we need to relate certain pairs of property to time and frequency distribution. For example, energy of photons is plancks constant * frequency. So now all of a sudden a wide distribution in frequency results in a wide distribution in energy of, say, photons shooting out of something. However the energy of a particular photon can still be known.
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