I do not know how complementarity is applied to this scenario - anyone
else have a suggestion?
On Sat, Aug 14, 2004 at 04:56:12PM -0700, Fred Chen wrote:
> Russell, I agree with what you state below. But consider the following
> experiment.
>
> Instead of two beams of equal intensity interfering, as in classical
> inteferometry, one has unequal amplitude beams. Specifically,
>
> Beam A: 0.9*exp(iax+ibz-iwt)
> Beam B: 0.1*exp(-iax+ibz-iwt)
>
> The interference pattern is of the form:
>
> Interference field = [cos(ax)+i*0.8sin(ax)]exp(ibx-iwt)
>
> So the resulting photon distribution follows the intensity, or the field
> amplitude squared:
>
> Interference intensity = 0.64+ 0.36*cos^2(ax)
>
> This wave pattern will begin to appear after sufficient number of
> photons, but each photon is always ~99% (81/82) likely to have
> originated from Beam A, based on conservation.
>
> If Beam A and Beam B had different 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.
>
> The complementarity principle's strongest statement is 100% certainty,
> and that cannot be attained. But we can still get an idea of the wave
> interference pattern and 'which way' information with high (but not
> 100%) certainty in gray-transition cases such as above.
>
> Fred
>
> -----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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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 R.Standish.domain.name.hidden
Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
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Received on Sat Aug 14 2004 - 20:19:22 PDT