Heisenberg Uncertainty PrincipleDate: 01/01/2002 at 11:01:19 From: D. J. Jacquard Subject: Heisenberg uncertainty principle I read in New Scientist about a team at Harvard that stopped a photon. This was done in their search for quantum computing. What I want to know is, when you look at the Heisenberg uncertainty principle, Plank's constant necomes zero, so is Plank's constant wrong, or the uncertainty principle? As best I can recall, the article was in New Scientist in late 1999. The article said that they were able to get information from this photon with better than 100% accuracy, which suggests enough time for more than one reading. As I understand, the Uncertainty Principle reads(delta)p(delta)v is approximately equal to or greater than h (Plank's constant). The same applies to time and energy. Make any of these values zero, and Plank's constant must become zero. The Uncertainty Principle is wrong, Plank's constant is wrong, or my question (and an ill-formed one it is) is wrong... or perhaps all are wrong. I am trying to find out which. Looking forward to finding out how I am wrong - don`t want the universe flying off its axis, you know. Sincerely, Darren Jacquard Date: 01/16/2002 at 13:44:31 From: Doctor Mitteldorf Subject: Re: Heisenberg uncertainty principle Dear Darren, The Uncertainty Principle is confusing for even for trained physicists, so you're in good company. But a lot of the confusion comes when you try to think about particles; for waves it's comparatively clear (and, of course, one message of QM is that all particles are also waves). Think about trying to tune an orchestra. The oboe offers a long 440-A, and people listen for several seconds to make sure they have the pitch accurately in mind. The longer you listen, the better you can define the pitch. You might even imagine using a sensitive air pressure meter to count the individual pulses; if you count 1320 of them in 3 seconds, you can divide to get the frequency to about 1 part in 1320; but if you just had a blast of sound, say 1/100 of a second, you'd have only 4 or 5 pulses to count, so you'd have ~20% uncertainty in the pitch. This is the essence of the Uncertainty Principle: If you have a long sample of a wave, it's spread out over time but its frequency (energy) is defined well. If you have a short burst of a wave, you can define its occurrence well in time, but then the frequency is very uncertain. Similarly in space: if you can observe a water wave that is smooth and even, spread out over a large surface with many evenly-spaced ripples, then you can define its wavelength very accurately. (In QM, inverse wavelength corresponds to momentum.) But a wave that is localized at one place doesn't contain enough ripples to accurately define its wavelength. When you think in these terms, the fact of slowing light's speed through a medium doesn't have much to do with the Uncertainty Principle. Whether the wave is slow or fast, it is still possible to send a short pulse of light (well-defined in space, but with uncertain momentum) or an extended stretch of evenly-spaced light waves (well-defined wavelength (momentum) but spread out over space). - Doctor Mitteldorf, The Math Forum http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/