Heisenberg’s Uncertainty Principle. Why, exactly, can you not know both the velocity and position of a particle?
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Remember that velocity is a vector, and has a directional component.
Imagine a big pool. Someone jumps in and makes a big splash. You can easily look at the splash and say “that’s the location of the splash, that’s where the position is”. But what’s the velocity of the splash? Well, its speed is equal in all directions, so it must cancel out to zero, right? Can you meaningfully assign a velocity to the wave produced by the splash?
Now imagine the splash dissipates and the wind picks up, pushing waves across the surface of the pool. It’s much more obvious what the velocity of the waves are: they have both a speed and a direction. But where are the waves? Well, they’re everywhere.
Quantum objects typically inhabit some point on a spectrum between these two states. It’s not a matter of lacking the precision necessary to measure both qualities, the fact is that both qualities just cannot be well defined at the same time.
This isn’t a uniquely quantum property, either. This uncertainty comes directly out of the wave-like nature of quantum objects. The wave function that describes the position and momentum of particles is characterized by the sum of a series of sine waves of various frequencies and amplitudes. Critically, these waves go on forever in all four dimentions: space and time. In order tohave a well-defined position you have to add lots of high-frequency sine waves, which forces the momentum to be spread out across a large range of frequencies.
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