I had a typo and was confusing about the 50/50 likelihood below. Corrections in CAPS.
The interference pattern is of the form: Interference field = [cos(ax)+i*0.8sin(ax)]exp(ibZ-iwt) If Beam A and Beam B had EQUAL amplitudes, you would maximize the uncertainty of the photon origin since you have to say 50/50 likelihood for a photon coming from either A or B. -----Original Message----- From: Russell Standish [mailto:[EMAIL PROTECTED] Sent: Saturday, August 14, 2004 2:51 AM To: Fred Chen Cc: 'Everything List' Subject: Re: Quantum Rebel On Fri, Aug 13, 2004 at 11:43:10PM -0700, Fred Chen wrote: ... > > A better (and far simpler) way to challenge complementarity would be > to use a low-intensity interferogram in a photographic film or CCD. At > first the photons being detected are few so the shot (particle-like) > aspect is more obvious. As more photons are integrated, the classical > interference pattern is observed. Can there be a transition region > where both aspects are observable? > This does not challenge complementarity. Consider a double slit apparatus with the photon source's intensity down so low that each individual photon can be observed hitting the screen one at a time. But when one plots the distribution of positions where the photons strike the screen after observing many of them, the interference pattern results. This is simple and uncomplicated, but is not what the complementarity principle is about. Now consider that you have information about which slit the photon passed through before hitting the screen - ie each photon is labelled 1, 2, 1, 1, etc, according to whuch slit it passed through. Therefore, you can separate the observed photons into two sets, according to which slit the phtons passed through. The distribution of each subset corresponds to a single slit experiment, and the final distribution must be the sum of the two single slit experiements. But single slit experiments do not have interference patterns - hence the sum cannot have an interference pattern either. Consequently, if you have any way of knowing which slit the photon went through (the "which way" information), then you cannot have an interference pattern. This is what the complementarity principle means. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ------------------------------------------------------------------------ ---- A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (") Australia [EMAIL PROTECTED] Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ------------------------------------------------------------------------ ----
