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905 clicks; posted to Geek » on 22 Feb 2012 at 4:31 PM (5 years ago)   |   Favorite    |   share:    more»

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My understanding of quantum uncertainty can be explained with a little story.

Imagine that you are in an old-timey fort in the Wild, Wild West and that it is a moonless night. There are Indians wandering around in the dark, which is so complete that the only way to determine the position of an indian is to fire a cannon ball out of one of the fort's cannons (let's say they are five-pounder balls).

Thus, if you fire a cannon ball, you can determine the position of an indian from the yelp when he is hit. However, being hit by a five pound cannon ball, you can't be sure he is a live indian (bad) or a dead indian (good) and you certainly can't determine his momentum. However, if you miss the indian, you may be able to determine the rough direction and momentum of his departure from the doppler effect of his scream, but you won't be able to precisely say where he is now, especially if he is smart enough to keep his mouth shut and move on quietly.

Thus you can not determine the position of an indian if you miss him, and his position doesn't matter much if you hit him, while you can determine the momentum of the indian from the noise he makes running away, but not his precise location.

The quantum indeterminancy is the result of the size of your cannon balls. Smaller balls would allow you to determine the location and momentum of an indian more precisely, but you only have five-pounders so you can never be sure beyond a certain statistic probability, where an indian is, and where he is going, if anywhere, unless it is the Happy Hunting Ground. And you can't be sure of that, even. You might hit a lot of indians who don't make a sound, and a few of them will whoop in terror even if you miss them by a mile. Most of them will silently move on.

In short, you have only the crudest sense of where the indians are at any time, and so statistically speaking, they are smeared thinly over the country side, with greater or lesser probabilities of being in certain places and avoiding others.

In fact, your observations actually change the location and momentum of most of the indians in the vicinity of wherever they are currently landing.

All in all, it is not the world that is uncertain, but the observers. If we had something better than cannon balls to shoot out of our cannons, we could locate indians with some precision. Golf balls, for example, would be handy, and ping pong balls would actually allow you to tell a fat indian from a skinny indian. But your tools limit your observations and even alter them. Use too much calibre and you may send indians flying in all directions, without being able to determine how many you hit, where they are, or where they'll come down coontil you hear the thud).

Moral: A smart indian keeps his mouth shut under fire.

If I understand the article correctly, it isn't just the size of your balls that matter. The crafty indians are holding buffalo hides stretched on frames, which act as trampolines when hit by the cannon balls, thus protecting the indians from discovery. There's no telling where the indian is. He could be behind the trampoline, or to one side. There could be more than one indian holding the trampoline between them. And the angle of the trampoline is difficult to determine a posteriori, let alone a priori. Instead of vivid cursing, much of the time all you hear is a "Sproing!" sound as the ball bounces harmlessly off the buffalo hide or maybe the odd tent here and there.

"I haf no idea, officer, but I know exactly vere I am!"

when I was taught about the Heisenberg Uncertainty Principle we were taught both about measurement uncertainty, which they discuss in the article. That is, by bouncing light off the system you've altered the system. But we also learned about inherent uncertainty, and the explanation of that wasn't so hard to understand, either.

At the quantum level, everything is wave-like (or at least can be thought of as such), when dealing with a wave, you inherently have trouble discerning "position" and "momentum" at the same time. Imagine a string, infinitely long, vibrating at a given frequency. If I were to ask what its momentum is, you'd have no trouble at all (it's a function of frequency, and you know that precisely), but if I asked what is the position of the wave, you'd have a problem, because it's location is, broadly, along the string.

Now imagine a string with just one pulse on it (one crest of a wave, say) and I asked you the location of the wave. Now that answer is easy, but what's the momentum? You need the frequency for that, but the frequency is uncertain with just one crest. Since everything is a wave at the quantum level, everything is afflicted by this inherent uncertainty.

/sorry for the rant

The string example was super!

Therefore ...aliens?

I've always been of the opinion that the uncertainty principle doesn't jive with the rest of the observable universe. Everything we know about the macroscopic world says that, given X and Y of something, Z is the only possible answer. In practice, we must still rely on probability because the level of precision needed for anything outside of extremely small, extremely controlled environments would require too much of an investment in terms of time and energy, and any remainder or shortfall can be planned around (presuming it is even an appreciable amount).

Initially, my understanding of the uncertainty principle was also that it was only a function of our ability to observe the quantum world; however, I'm told by smarter and more knowledgeable people than myself that the uncertainty principle is innate to quantum mechanics, not merely a limitation of how we observe details at that scale. In short, any observation (e.g. interaction) affects the energy of the system you're observing (because you either have to impart energy and observe the reaction, or absorb energy that's being passively emitted).

But that's just, like, my ignorance, man. I'm sure we'll have a few physicists in the thread to set everyone straight.

Niveras:
Initially, my understanding of the uncertainty principle was also that it was only a function of our ability to observe the quantum world; however, I'm told by smarter and more knowledgeable people than myself that the uncertainty principle is innate to quantum mechanics, not merely a limitation of how we observe details at that scale. In short, any observation (e.g. interaction) affects the energy of the system you're observing (because you either have to impart energy and observe the reaction, or absorb energy that's being passively emitted).

No, the point of the article is that is not the correct. Measurement can change the state of a system, but that's not the whole story. The uncertainty principle describes a fundamental property of every quantum particle, due to the probabilistic nature of nature, regardless of measurement errors.

'...of that we can be, quite sure..." (God bless you Rowan Atkinson)

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