RE: Quantum Rebel
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
--
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is of type "application/pgp-signature". Don't worry, it is not a virus.
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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
(")
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Re: Quantum Rebel
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:[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 StandishDirector
> 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
>
>
>
--
*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 Centrehttp://parallel.
Re: Quantum Rebel - complementarity
As I had mentioned in a previous post, complementarity doesn't even
crack a mention in the textbook I learnt QM from (Shankar's book). I
found it in another textbook I had (Schiff's book), which describes it
as being a another way of expressing Heisenberg's uncertainty
princple. I'm not even sure that's true, and in any case I believe
Shankar's book to be superior of the two.
When I thought about it, I realised what complementarity refers in the
double slit experiment - this is what I've been discussing. I'm not at
all certain how it applies in other contexts, however.
Cheers
On Sat, Aug 14, 2004 at 09:58:10AM -0400, John M wrote:
> Dear Russell,
>
> I really would like to read (if ever) about that darn complementarity -
> based on/around a different example from the stale double-slit experiment
> (which it was really constructed for).
>
> IMO the 'double' nature of particle-wave is not (well?) understood and this
> resulted in sweating out the 'complementarity' syndrome to explain some
> hard-to-follow experimental results within the ongoing formalism. (I mean to
> match the quantized items within the system).
>
> Since 2x10^m million experiments - calculations and 3x10^n papers (not to
> speak about hundreds of prizes, tenthousands of tenure) have been devoted to
> the concept - taught to 3 consecutive generations of
> young receptive brains, it would be a BIG job to reformulate it.
>
> Yet it would be refreshing to approach the concept from another side
> (another framework), - maybe a new one??
>
> John Mikes
>
> - Original Message -
> From: "Russell Standish" <[EMAIL PROTECTED]>
> To: "Fred Chen" <[EMAIL PROTECTED]>
> Cc: "'Everything List'" <[EMAIL PROTECTED]>
> Sent: Saturday, August 14, 2004 5:50 AM
> Subject: Re: Quantum Rebel
>
>
--
*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 Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
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Description: PGP signature
RE: Quantum Rebel
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:[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
Re: Quantum Rebel - complementarity
Unfortunately, it seems that there are very few people seriously working on radical ideas like the models proposed by 't Hooft. My favorite idea is that particles are not real. You could imagine that QM is an effective statistical theory (similar to what 't Hooft says) in which particles appear in a similar way as virtual particles appear in quantum field theory. If the Feynman rules had been discovered by experimentalists, you would have discussions about photons and electrons violating causality except when we observe them... - Oorspronkelijk bericht - Van: "John M" <[EMAIL PROTECTED]> Aan: "Saibal Mitra" <[EMAIL PROTECTED]> CC: <[EMAIL PROTECTED]> Verzonden: Saturday, August 14, 2004 04:51 PM Onderwerp: Re: Quantum Rebel - complementarity > Thanks! Maybe even further? > John M > - Original Message - > From: "Saibal Mitra" <[EMAIL PROTECTED]> > To: "Russell Standish" <[EMAIL PROTECTED]>; "John M" > <[EMAIL PROTECTED]> > Cc: <[EMAIL PROTECTED]> > Sent: Saturday, August 14, 2004 10:35 AM > Subject: Re: Quantum Rebel - complementarity > > > > Maybe we should look at deterministic theories, such as: > > > > > > http://arxiv.org/abs/hep-th/0104219 > > > > John M wrote: > > > > > Yet it would be refreshing to approach the concept from another side > > > (another framework), - maybe a new one?? > > > > > >
Re: Quantum Rebel - complementarity
It is not clear that the theory proposed by 't Hooft is incompatible with EPR. As 't Hooft explains there are several loopholes in Bell's theorem. E.g. in a completely deterministic world you cannot claim that you could have chosen to measure a different component of the spin than the one you actually measured... - Oorspronkelijk bericht - Van: "Brent Meeker" <[EMAIL PROTECTED]> Aan: <[EMAIL PROTECTED]> Verzonden: Saturday, August 14, 2004 10:19 AM Onderwerp: RE: Quantum Rebel - complementarity > If it can't deal with EPR, what good is it? > > Brent Meeker > > >-Original Message- > >From: Saibal Mitra [mailto:[EMAIL PROTECTED] > >Sent: Saturday, August 14, 2004 2:35 PM > >To: Russell Standish; John M > >Cc: [EMAIL PROTECTED] > >Subject: Re: Quantum Rebel - complementarity > > > > > >Maybe we should look at deterministic theories, such as: > > > > > >http://arxiv.org/abs/hep-th/0104219 > > > >John M wrote: > > > >> Yet it would be refreshing to approach the concept > >from another side > >> (another framework), - maybe a new one?? > > > > > > >
RE: Quantum Rebel - complementarity
If it can't deal with EPR, what good is it? Brent Meeker >-Original Message- >From: Saibal Mitra [mailto:[EMAIL PROTECTED] >Sent: Saturday, August 14, 2004 2:35 PM >To: Russell Standish; John M >Cc: [EMAIL PROTECTED] >Subject: Re: Quantum Rebel - complementarity > > >Maybe we should look at deterministic theories, such as: > > >http://arxiv.org/abs/hep-th/0104219 > >John M wrote: > >> Yet it would be refreshing to approach the concept >from another side >> (another framework), - maybe a new one?? > > >
Re: Quantum Rebel - complementarity
Thanks! Maybe even further? John M - Original Message - From: "Saibal Mitra" <[EMAIL PROTECTED]> To: "Russell Standish" <[EMAIL PROTECTED]>; "John M" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Saturday, August 14, 2004 10:35 AM Subject: Re: Quantum Rebel - complementarity > Maybe we should look at deterministic theories, such as: > > > http://arxiv.org/abs/hep-th/0104219 > > John M wrote: > > > Yet it would be refreshing to approach the concept from another side > > (another framework), - maybe a new one?? > >
Re: Quantum Rebel
Russell Standish wrote:
Let |i> refer to the state where the photon travels on path i. Then
one can write down a few relations, such as:
|1> = 1/sqrt{2}|3> + 1/sqrt{2}|4> = |5>
|2> = 1/sqrt{2}|3> - 1/sqrt{2}|4> = |6>
If a photon is detected on path 5, then the probability it travelled
along path i is <5|i>. Since <5|1>=1 and <5|2>=0, we have "which way"
information.
Now inserting an absorber on path 4 is mathematically equivalent to
inserting a projection operator |3><3| in the middle of the
propagator. The the probability of a photon detected at path 5 taking
path i becomes <5|3><3|i>. Computing these values by the above
formulae gives:
<5|3><3|1>=1/2 and <5|3><3|2>=1/2
Thanks for the elaboration, it's been a while since I studied QM. A
question: I had thought the notion of "probability" only makes sense when
talking about actual measured outcomes, and that paths in a path integral
can only be assigned a probability amplitude, not a probability, since if
you tried to talk about the "probability" of each path (just by squaring the
path's amplitude, I guess) the probabilities would not necessarily add
together classically. Is my memory wrong, or when you talk about the
"probability" that a photon took a path i do you really mean the probability
amplitude?
Jesse Mazer
Re: Quantum Rebel - complementarity
Maybe we should look at deterministic theories, such as: http://arxiv.org/abs/hep-th/0104219 John M wrote: > Yet it would be refreshing to approach the concept from another side > (another framework), - maybe a new one??
Re: Quantum Rebel - complementarity
Dear Russell, I really would like to read (if ever) about that darn complementarity - based on/around a different example from the stale double-slit experiment (which it was really constructed for). IMO the 'double' nature of particle-wave is not (well?) understood and this resulted in sweating out the 'complementarity' syndrome to explain some hard-to-follow experimental results within the ongoing formalism. (I mean to match the quantized items within the system). Since 2x10^m million experiments - calculations and 3x10^n papers (not to speak about hundreds of prizes, tenthousands of tenure) have been devoted to the concept - taught to 3 consecutive generations of young receptive brains, it would be a BIG job to reformulate it. Yet it would be refreshing to approach the concept from another side (another framework), - maybe a new one?? John Mikes - Original Message - From: "Russell Standish" <[EMAIL PROTECTED]> To: "Fred Chen" <[EMAIL PROTECTED]> Cc: "'Everything List'" <[EMAIL PROTECTED]> Sent: Saturday, August 14, 2004 5:50 AM Subject: Re: Quantum Rebel
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 Centrehttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
pgpyItfmsIInq.pgp
Description: PGP signature
Re: Quantum Rebel
From: "Fred Chen" > Can there be a transition region where > both aspects are observable? It is difficult to observe a one-particle pattern http://www.optica.tn.tudelft.nl/education/photons.asp But if you are interested in things like whether there is an experimental smooth, Yin-Yang type :-), transition between the particle-like and the wave-like behaviour, try the links below. Greenberger and Yasin wrote P^2 + V^2 = 1, where P is the *probability* for the particle taking one of the two possible paths, and V the visibility of the fringes. http://arxiv.org/abs/quant-ph/9908072 http://arxiv.org/abs/quant-ph/0311179 http://arxiv.org/abs/quant-ph/0201026 http://arxiv.org/abs/quant-ph/0404013 In other words, the Greenberger and Yasin relation states that the "entity" has a double nature (wave-like,particle-like) and that there is a "smooth" transition between one and the other nature. Following Greenberger and Yasin, we must restate the complementarity principle as *coexistence* between particle-like and wave-like properties, and not as reciprocal *exclusion*. (Btw, it is well known that Heisenberg was against the complementarity principle, since in matrix mechanics there are no waves at all ... It is also well known that the Bohr-Heisenberg debate, on this point, was very hard indeed).
