Comments by "Harry Mills" (@harrymills2770) on "What is the Heisenberg Uncertainty Principle? - Chad Orzel" video.
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You make no clear connection between wavelength and momentum. You just make the claim and treat it as fact from that point forward. It makes for a nice, slick presentation, but it is not very informative, and possibly misleading. Allow me to mislead you some more, with my simplistic take.
Here's how I understand Heisenberg:
Imagine you could locate a single water molecule in an ocean wave. You have to get small to locate it. By the time you're that small, you have no awareness of the larger wave in which it resides, no very good measure of the wavelength of the particle.
Now, to measure the WAVELENGTH with high accuracy, it's a simple matter to step back a mile, count the wave crests over a fixed - preferably LONG - distance. Then divide by that distance. The average you obtain is a very precise measure of the wavelength. But from your great distance, you have very little idea of where exactly that one water molecule we were just talking about actually IS.
This simple idea leads to all kinds of nonsensical and unsupported statements.
In quantum mechanics, we can't get down to the subatomic particles, so, like a statistician, we look at the behavior of millions or billions of particles, and observe their behavior as a group, attempting to reason our way to what the individual particles are actually doing. That's why you hear people talk about a particle being "smeared" probabilistically across many locations, simultaneously.
Your inability to locate that one electron or one quark or whatever doesn't mean it doesn't have an actual position. It's just that you're unable to do more than locate a general area in which that particle must reside at a specific point in time.
I think this is why Einstein said "God does not play dice," in his disputes with Niels Bohr.
An analogy I use comes from a statistical device called "the bell curve." It is described by an exponential function ( exp(-x^2) )that decreases symmetrically as you move farther and farther from the average (in this case, x = 0). Like quantum mechanics, inasmuch as populations tend to congregate near the average and super-small or super-tall individuals, farther from the average, are fewer in number. This sort of fits nature pretty well, because most of the action takes place within 2 or 3 standard deviations (In this case, sigma = 1) from the average.
Nevertheless, there is a positive probability of a person standing over 500 feet tall, because that decaying exponential is a positive function for all real values of (in this case) height. There are zero 500-foot-tall people, but according to the standard normal distribution, if you get enough people together, you're eventually going to encounter a 500-footer!
Writers, entertainers, and grifters all love this quantum mechanics stuff because it makes it SEEM like the world is magical and not deterministic. I'm OK with quantum mechanics as long as it makes useful predictions, much the same way I'm OK with a traditional Chinese herbalist who knows a particular plant will cure your upset stomach, even though his explanation involving dragons in your stomach are defeated by the magic herb which makes them cross-eyed and paranoid is total poppycock.
I'm still more on Einstein's side than Bohr's. I don't consult a statistician to predict where that rock flying towards my head is going to hit. I might ask one for the best hiding place when the mob comes for me, though.
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