system
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human
What is the Heisenberg Uncertainty Principle?

I am an aspiring physicist but currently have little to no professional education in the subject (high school freshman). I have been trying to learn whatever I can outside of school, and I feel I know a bit about quantum mechanics from lectures by Lawrence Krauss, videos online, etc. Can someone explain what the Heisenberg Uncertainty Principle is? What does it govern on the quantum scale?
gpt
Particles are not discrete balls of "stuff". Rather, they are like waves of "stuff" that cannot be broken down and behave according to some very specific equations. It moves in a way most analogous to how temperature spreads out in an object. This means that it doesn't mean anything to talk about "where" a particle is or "how fast" it is moving. Just imagine small wave of water, can you  tell me where it is? No, because it's spread out. Can you tell me how fast the heat in a room is spreading? No, because it moves at different speeds at different places.

We can imagine that this "wave" is distributed somehow in space, and then look at the standard deviation of this distribution, Sx. The bigger the standard deviation, the more spread out the particle is. The smaller the standard deviation, the less spread out it is and more it looks like a ball of "stuff". But the particle will be moving at different speeds, some speeds will be more preferred than others, so we can imagine that all these speeds have their own distribution. We can then look at the standard deviation of this distribution too, Sp. The larger the standard deviation, the more it is moving like a wave. The smaller the standard deviation, the more it is moving in a uniform way, like a ball does. If Sx is small then it "looks" like a discrete particle. If Sp is small then it "moves like" a discrete particle.

The Uncertainty Principle says that the product (Sx)(Sp) cannot get too small. This means that we can't have Sx and Sy be small simultaneously. In other words, it can either *look* like a discrete particle or *move* like a discrete particle, never both. This is just a consequence of the fact that particles are these weird wave-things and are not discrete particles. 

The Uncertainty Principle is not restricted to Quantum Mechanics, it's actually just an idea from probability and statistics that is used in quantum mechanics.