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:R.Standish.domain.name.hidden]
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
--
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Received on Sat Aug 14 2004 - 20:33:39 PDT