As I understand it, Heisenberg's uncertainty principle (HUP) states that the more precisely we know the location of an electron, the less precisely we know its momentum, and vice versa. However, I've looked online, but I haven't found the reason that that is the case.
I'm a first year science student and I haven't taken calculus yet, so a simple answer (even if it sacrifices rigor) would be the most helpful. I'd just like to get some intuition about what makes HUP true.
In response to the comments about 'why' being a poor question to ask in physics: It would be equally useful to know how we observed Heisenberg's uncertainty principle.
Suppose a physicist observes the precise location of an electron, what is it about that observation that prevents him from figuring its momentum? If he can calculate it with a less precise idea of its location, why would more information prevent him from calculating it?
I suspect I'm thinking about this the wrong way.