system
Given the following post, respond as if you're commenting on Reddit:
human
Why can't we know the velocity and the position of subatomic particles at the same time?
gpt
It's not that we can't know them at the same time, it's that we can't know them to *arbitrarily high precision* at the same time. This is the uncertainty principle, which comes about because position and momentum (related to velocity) are non-commuting operators. One very loose way of thinking about this is to use the fact that particles can be described in terms of waves. A particle that passes through a narrow gap (small uncertainty in position) will diffract out widely, meaning that there is a large uncertainty in its momentum.