Heisenberg Uncertainty Principle?
When physicists say there is a so-and-so chance that a particle is in a particular place, do they mean…
1) that the particle has an exact location, but the best they can do with their crude measurements is to calculate the chance that it is in any place in particular
2) that the particle’s position is literally a fuzzy zone of chance with no absolute position
3) something else?
This also (of course) applies for speed, but I don’t want to confuse things…
Answer ( 1 )
The HUP is about limitations in measuring capability. The wave function is about the particle itself.
The so-and-so chance that a particle is somewhere in space is about the probability density function of that particle. (ANS 2.) And that’s called its wave function.
EX: Suppose there is a particle whose wave function is the normal curve probability density function. That means there is a 99% chance of finding it within plus/minus 3 standard deviations, 95% of finding it inside plus/minus two SDs, and about a 2/3 probability of locating it inside plus/minus 1 standard deviation.
That was a two dimensional illustration for simplicity. Of course in reality the probability density functions are three dimensional or even four if we fold time into the model.
Note we have the wave function even though no measuring has been attempted. Now when we try to find that little guy, we’d naturally look where the probability density function says is the most likely spot.
And when we do detect it, there is no more uncertainty as to where it’s located. And that’s when they say the wave function collapses. I’d say that it’s more like when the wave function becomes spike whose sum is exactly 1.00. Certainty.
And this is where the HUP comes to the fore. Because when we find the particle with certainty, we find that we cannot find the particle’s momentum (velocity). And that results because of limitations in our detection devices. And this is ANS 1.