Re: IS this for real?!
From: Bill Unruh (unruh_at_string.physics.ubc.ca)
Date: 08/18/04
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Date: 17 Aug 2004 22:45:56 GMT
Mok-Kong Shen <mok-kong.shen@t-online.de> writes:
]Douglas A. Gwyn wrote:
]> Mok-Kong Shen wrote:
]>
]>> Douglas A. Gwyn wrote:
]>>
]>>> the Heisenberg uncertainty principle, which is a
]>>> direct consequence of a standard fact about Fourier
]>>> transforms.
]>>
]>> Could you kindly elaborate this a little bit in a way
]>> that a layman can understand? Thanks.
]>
]>
]> The product of the widths of conjugate distributions
]> is bounded below by a constant.
]> I'm not sure a "layman" understands Fourier analysis
]> at all!
]I do have some knowledge of Fourier transform but, having
]no advanced knowledge in physics, a connection between
]the uncertainty principle and Fourier transform is unknown
]to me till now. Is there a good reference where the uncertainty
]priciple is derived in some details from the theory of
]Fourier transform? Thanks in advance.
The fourier transform is of use for showing the standard x,p uncertainly
relation but is irrelevant in general. Heisenberg's uncertainly is of far
far greater applicability.
If two observables do not commute, then the uncertainties ( the difference
between the average of the square of the observable and the square of the
average-- its standard deviation squared)multiplied is greater than the
square of the average of the commutator. This follows directly from the
fact that expectation values of squares are always positive. It applies
also to fourier transforms but to many other things as well.
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