What’s the underlying principle on why you can’t know the position and momentum of a particle at the same time? Is there an explanation? I don’t have any knowledge of calculus or the math behind anything so I’m asking here, thanks!
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The Heisenberg Uncertainty Principle doesn’t say you can’t know the position and momentum of a particle at the same time; that kind of holds in normal, non-quantum mechanics.
How do you measure how fast something is going?
You take two points, you measure the distance between them, and measure how long it takes the thing to get from one to the other.
So in order to measure how fast something is going it needs to be moving. Which means it has to be at two different points. So how can you measure both how fast something is going *and* where it is?
Now it turns out we can get around that problem using limits, and get a kind of instantaneous speed, to the extent that makes sense.
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So what does the Uncertainty Principle say? To [quote Wikipedia](https://en.wikipedia.org/wiki/Uncertainty_principle):
> the uncertainty principle states that the more precisely the position of some particle is determined, the less precisely its momentum can be predicted from initial conditions, and vice versa.
In quantum mechanics things don’t take exact, predictable values. Instead, when you measure something about a system, the answer you get will be based on a probability distribution, with an average value and an uncertainty (or standard deviation). You might find it has one value, but it might have a different value, and there is no way to predict that (beyond using probability tools).
The Uncertainty Principle puts a hard limit on how small these uncertainties can get; specifically, if you multiply two of them together you get a minimum value. This means that you can never get either of them down to 0, but also the lower you get one the higher you get the other – the more you can lock down where something is, the harder it is to lock down how fast it is going.
If you want to visualise this, imagine a bubble of air trapped under a thin sheet of plastic; it has a certain fixed volume that you can’t squeeze it below. So if you try to squeeze it one way you can make it narrower, but it will spread out in another direction. You try to squeeze it that way and it will spread out in the first direction. No matter what you do, you will get some spread-out-ness in all directions.
As for “why”, why questions are always tricky in physics, because the answer ultimately boils down to “because that’s the way the universe appears to work.”
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