Subject: Re: Uncertainty principle debate
From: Ramin Pichevar <Ramin.Pichevar(at)USHERBROOKE.CA>
Date: Fri, 30 Jan 2004 16:11:19 -0500
http://www.usherbrooke.ca/vers/virus-courriel
Fred,
If I understand well your email, you mention that the uncertainty bound is
not equal to 1/2 as derived by Gabor but much less than that (let say
0.004). But does this mean that there is no uncertainty? First of all, one
should imagine an experiment in which he/she can find the difference between
the two points you are talking about. In my opinion, the computation of this
distance requires a threshold detecting device. Note that if we even imagine
that an infinite precision threshold detectors exists, I am not sure that
there won't be any time-frequency uncertainty in this device. In fact, a
threshold detector is a device that compares values at times (t-n), (t-n+1),
(t-n+2), ..., t in addition to comparing the current value at time t to a
predefined threshold value (note that the slope is important to detect
in-phase points and not out-of-phase (a lag equal to pi) points). If we
accept this fact, then a very slow varying tone (with a very low frequency)
will need a very long window (n) (the window used in the threshold
detector). In my opinion, this implicitly implies the uncertainty somewhere.
On the other hand, in quantum physics the bound is much smaller than 0.004
(in fact it is in the order of the Plank constant). In my opinion again,
this means that theoritically we can develop other approaches (not in the
framework of the Fourier transform but in another framework) that can give
us much less uncertainty, but there will still be an uncertainty in our
processings.
Regards,
Ramin
-----Message d'origine-----
De : AUDITORY Research in Auditory Perception
[mailto:AUDITORY(at)LISTS.MCGILL.CA]De la part de herzfeld
Envoye : 30 janvier, 2004 14:37
A : AUDITORY(at)LISTS.MCGILL.CA
Objet : Uncertainty principle debate
Hello List,
The current controversy about the application of the uncertainty
principl;e is to me at least interesting and somewhat perplexing in that
it is still, seems to me, misunderstood.
There are two two methods of defining frequency. One of these is the
inverse of the time difference between two points of equal phase in a
recurring signal. This definition is NOT limited by the uncertainty
principle.[Kneser, H.O. Bermerkungen ueber Definition and Messung der
Frequenz. Arch. Elekt. Uebertr. 1948 2 167-169}
Bekesy in many of his works (based on experimental data) has stated :
Frequency is already determined in 2 cycles of a sinusoidal signal. At a
frequency of 500 Hz the estimate that I have is that the aproximate DL =
1 Hz. Now two cycles of 500 Hz is 4 mS. The product of delta t and
delta f is 0.004. Very obviously less than 1/2 which (the 1/2) as I
recall was first derived by Gabor [ Gabor, D. Theory of communication.
J. Instn. Elect. Engrs. 1946 93(3) 429-457] See also [Licklider J.C.R.
"Basic correlates of the auditory sto,i;is" in S.S. Stevens (ed)
Handbook of experimental psychology pp 985-1013 1951 Wiley, New York]
Licklider (one of my teachers) compares this to Heisenberg's uncertainty
principle.
Based on this type of data the determination of frequency by at least
humans and perhaps other vertebrates must be based on time differences.
Fred
--
Fred Herzfeld, MIT'54
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