Subject: Re: Uncertainty principle debate From: "John G. Beerends" <J.G.Beerends(at)TELECOM.TNO.NL> Date: Mon, 2 Feb 2004 11:15:15 +0100I think the answer lies in the a priori knowlegde, if one knows the cycle comes from a long sinusoid one can violate the uncertainty relation. The uncertainty relation on the cycle itself is maintained. John Beerends -----Original Message----- From: herzfeld [mailto:herzfeld(at)ALUM.MIT.EDU] Sent: Friday, January 30, 2004 8:37 PM To: AUDITORY(at)LISTS.MCGILL.CA Subject: 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 78 Glynn Marsh Drive #59 Brunswick, Ga. 31525-0504 USA Tel: (912) 262-1276 Fax: (912) 262-1276 by request