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Heisenberg Uncertainty Principle


Date: 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/   
    
Associated Topics:
College Physics
High School Physics/Chemistry

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