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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>What’s the underlying principle on why you can’t know the position and momentum of a particle at the same time?
I think you are approaching this as though this is a problem of knowledge about the particle. In other words, you are thinking that a quantum particle *has* both a position and momentum, we are just somehow limited in how to measure those two things simultaneously.
Think of looking down at a pool table and you see a cue stick hit the cue ball, and a sheet is pulled between you and the pool table the moment after it’s hit. After it bounces around long enough underneath this sheet on this ideal, frictionless table, your ability to predict where it is gets foggier and foggier until it could be anywhere under there. But this is a problem of knowledge; the cue ball itself “knows” where it is, it’s just that you don’t.
This is **not** a correct picture of the quantum model of a particle. The quantum model says that a particle *literally does not have* both of these properties to infinite resolution. It’s not that we can’t measure them, it’s that they are not simultaneously there.
So now picture that you’re looking down at the pool table and the cue stick hits the cue ball. At that moment, there is no sheet pulled. You can see everything at every moment. But, now the cue ball starts to spread out into a blob and dim. At any moment, you can stick a million pool cues down and have them all take a stroke, and when you do that, all of that energy will coalesce again into a solid cue ball in front of one of the cue sticks and go heading off in a new direction.
But which cue will be the one that hits the ball? Where on the table will that happen? We can only say with probability based on the last interaction. Again, this is not because we just lost track of it, but rather because the cue ball itself does not have a particular position and momentum. These properties of the ball’s relationship to the table literally disperse as things proceed from the last collapse of its wave function.
Now, keep in mind that I am talking about the quantum model here. This is *our model* of the universe. Is it what is literally happening in the real physical world? We think so *but it is a guess* and we also know that it is not a complete picture of what is actually happening, and we don’t know where the mismatches are. It is also possible that there’s something completely different going on that we haven’t fully grasped.
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