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From: scerir <scerir.domain.name.hidden>

Date: Mon, 26 Apr 2004 23:00:49 +0200

From: "Jesse Mazer"

*> Would this experimental result actually be predicted by the quantum
*

*> formalism, though? It sounds like they had a setup similar to the
*

*> double-slit experiment and found a small amount of interference even when
*

*> they measured which hole the particle traveled through, but I thought the
*

*> quantum formalism predicts that interference would be completely destroyed
*

*> by such a measurement.
*

There is a lot of confusion about all that.

I hope I do not make more damages here!

There are also many different versions of Bohr's complementarity

principle. Complementarity of what? Waves (there are no waves in

matrix mechanics!) and particles? Interference pattern and "which

way"? Continuous and discontinuous? Localization and superposition?

Separability and unitarity? Reversibility and irreversibility?

The modern view says that ...

"The superposition of amplitudes is only valid if there

is no way to know, even in principle, which path the particle

took. It is important to realize that this does not imply

that an observer actually takes note of what happens.

It is sufficient to destroy the interference pattern,

if the path information is accessible in principle from

the experiment or even if it is dispersed in the environment

and beyond any technical possibility to be recovered, but

in principle 'still out there'".

Anton Zeilinger, Rev. Mod. Phys., 1999, page S-288

"In an experiment the state reflects not what is actually

known about the system, but rather what is knowable, in principle,

with the help of auxiliary measurements that do not disturb

the original experiment. By focusing on what is knowable in

principle, and treating what is known as largely irrelevant,

one completely avoids the anthropomorphism and any reference

to consciousness that some physicists have tried to inject

into quantum mechanics"

Leonard Mandel, Rev. Mod. Phys., 1999, p. S-274.

So, the key word now is "indistinguishability". Must this

"indistinguishability" be absolute? What does it happen in case of

partial "indistinguishability"? (Anticipated answer: there is a smooth

transition between particle-like and wave-like behaviour).

In 1979, Wootters and Zurek (Complementarity in the double-slit

experiment: Quantum nonseparability and a quantitative statement of

Bohr's principle, PR, D-19, 1979, p. 473-484) presented a famous

gedanken experiment, showing that photons still have a wave-like

behaviour even if their paths are predicted almost (say: 99%)

certainly. The set-up, in the gedanken, was essentially a single-slit

plus a double-slit; and also a double-slit plus a specific

'textured' screen capable of detect and record both the interference

pattern and the 'which way'. Yes this is possible.

Coupling Wheeler's 'delayed choice' and the above gedanken experiment,

Wim Rietdijk wrote (circa 1982) an interesting paper. Very shortly,

QM explains the two-slit interference via Heisenberg principle.

Hence the slits measure the position of the 'object'; because of this

measurement there is a scattering; |<p(y)|psi|^2 gives the probability

function for the 'object' emerging from the slits with momentum

p(y); this probability function causes the interference pattern.

Thus - that is important - after the 'object' has passed through

the two-slit, the probability function |<p(y)|psi|^2 is fixed.

And - second important point - there is a principle of conservation

of momentum. Thus, nothing can change that fixed momentum (rectius:

that fixed probability function). Now comes the weirdness. After

the 'object' has passed the two-slit, we have *still* some time to

choose if we wish to detect the 'welcher weg' (wich way, which path)

the 'object' took, or if we wish to record just the 'impact' of the

'object' on the screen or, in general, if we wish to get both,

the 'welcher weg' and the 'interference pattern' at the same time

(this is technically possible, provided we use a screen with a special

'texture'). Here is the weirdness: does QM say that any knowledge

of the 'welcher weg' causes the loss of the interference pattern? Yes?

Does Feynman say this in his Lectures? Ok. Thus QM says that the

the probability function |<p(y)|psi|^2, already fixed at the two-slit

level, is a function of our later, delayed, free choice of a specific

detector (of the interference pattern only; of the interference pattern

and the 'wich path' at the same time).

Coming back to the point of that "absolute" indistinuishability.

Greenberger and Yasin wrote down the relation, P^2 + V^2 = 1,

where P is the probability for the electron (or photon)

taking one of the two possible paths, and V the visibility

of the fringes (interference pattern).

http://arxiv.org/abs/quant-ph/9908072

http://arxiv.org/abs/quant-ph/0311179

http://arxiv.org/abs/quant-ph/0201026

In other words, the Greenberger and Yasin relation states that

the "entity" (electron, photon, etc.) has a double nature (wave-like,

particle-like) and there is a "smooth" transition between one and the

other nature.

So, the "indistinuishability" is not an absolute, by experiment.

See this specific new test http://www.arxiv.org/abs/quant-ph?0404013

Of course there are interesting perspectives using "weak"

measurements http://www.arxiv.org/abs/quant-ph?0310081

and photons of different energy (wave-lenght)

http://www.arxiv.org/abs/quant-ph/0304086 and so on

(non-local two-slit interferometers, interference

between two correlated sources, interference between

two uncorrelated sources, interference in time of any kind,

quantum beats, etc.).

In summa. There is no new at all.

After all Bohr even incorporated Chinese traditional Yin-Yang Symbol, and

related smooth transition, into his Coat of Arms.

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Complementarity/Comp

Copen.html

Received on Mon Apr 26 2004 - 18:10:49 PDT

Date: Mon, 26 Apr 2004 23:00:49 +0200

From: "Jesse Mazer"

There is a lot of confusion about all that.

I hope I do not make more damages here!

There are also many different versions of Bohr's complementarity

principle. Complementarity of what? Waves (there are no waves in

matrix mechanics!) and particles? Interference pattern and "which

way"? Continuous and discontinuous? Localization and superposition?

Separability and unitarity? Reversibility and irreversibility?

The modern view says that ...

"The superposition of amplitudes is only valid if there

is no way to know, even in principle, which path the particle

took. It is important to realize that this does not imply

that an observer actually takes note of what happens.

It is sufficient to destroy the interference pattern,

if the path information is accessible in principle from

the experiment or even if it is dispersed in the environment

and beyond any technical possibility to be recovered, but

in principle 'still out there'".

Anton Zeilinger, Rev. Mod. Phys., 1999, page S-288

"In an experiment the state reflects not what is actually

known about the system, but rather what is knowable, in principle,

with the help of auxiliary measurements that do not disturb

the original experiment. By focusing on what is knowable in

principle, and treating what is known as largely irrelevant,

one completely avoids the anthropomorphism and any reference

to consciousness that some physicists have tried to inject

into quantum mechanics"

Leonard Mandel, Rev. Mod. Phys., 1999, p. S-274.

So, the key word now is "indistinguishability". Must this

"indistinguishability" be absolute? What does it happen in case of

partial "indistinguishability"? (Anticipated answer: there is a smooth

transition between particle-like and wave-like behaviour).

In 1979, Wootters and Zurek (Complementarity in the double-slit

experiment: Quantum nonseparability and a quantitative statement of

Bohr's principle, PR, D-19, 1979, p. 473-484) presented a famous

gedanken experiment, showing that photons still have a wave-like

behaviour even if their paths are predicted almost (say: 99%)

certainly. The set-up, in the gedanken, was essentially a single-slit

plus a double-slit; and also a double-slit plus a specific

'textured' screen capable of detect and record both the interference

pattern and the 'which way'. Yes this is possible.

Coupling Wheeler's 'delayed choice' and the above gedanken experiment,

Wim Rietdijk wrote (circa 1982) an interesting paper. Very shortly,

QM explains the two-slit interference via Heisenberg principle.

Hence the slits measure the position of the 'object'; because of this

measurement there is a scattering; |<p(y)|psi|^2 gives the probability

function for the 'object' emerging from the slits with momentum

p(y); this probability function causes the interference pattern.

Thus - that is important - after the 'object' has passed through

the two-slit, the probability function |<p(y)|psi|^2 is fixed.

And - second important point - there is a principle of conservation

of momentum. Thus, nothing can change that fixed momentum (rectius:

that fixed probability function). Now comes the weirdness. After

the 'object' has passed the two-slit, we have *still* some time to

choose if we wish to detect the 'welcher weg' (wich way, which path)

the 'object' took, or if we wish to record just the 'impact' of the

'object' on the screen or, in general, if we wish to get both,

the 'welcher weg' and the 'interference pattern' at the same time

(this is technically possible, provided we use a screen with a special

'texture'). Here is the weirdness: does QM say that any knowledge

of the 'welcher weg' causes the loss of the interference pattern? Yes?

Does Feynman say this in his Lectures? Ok. Thus QM says that the

the probability function |<p(y)|psi|^2, already fixed at the two-slit

level, is a function of our later, delayed, free choice of a specific

detector (of the interference pattern only; of the interference pattern

and the 'wich path' at the same time).

Coming back to the point of that "absolute" indistinuishability.

Greenberger and Yasin wrote down the relation, P^2 + V^2 = 1,

where P is the probability for the electron (or photon)

taking one of the two possible paths, and V the visibility

of the fringes (interference pattern).

http://arxiv.org/abs/quant-ph/9908072

http://arxiv.org/abs/quant-ph/0311179

http://arxiv.org/abs/quant-ph/0201026

In other words, the Greenberger and Yasin relation states that

the "entity" (electron, photon, etc.) has a double nature (wave-like,

particle-like) and there is a "smooth" transition between one and the

other nature.

So, the "indistinuishability" is not an absolute, by experiment.

See this specific new test http://www.arxiv.org/abs/quant-ph?0404013

Of course there are interesting perspectives using "weak"

measurements http://www.arxiv.org/abs/quant-ph?0310081

and photons of different energy (wave-lenght)

http://www.arxiv.org/abs/quant-ph/0304086 and so on

(non-local two-slit interferometers, interference

between two correlated sources, interference between

two uncorrelated sources, interference in time of any kind,

quantum beats, etc.).

In summa. There is no new at all.

After all Bohr even incorporated Chinese traditional Yin-Yang Symbol, and

related smooth transition, into his Coat of Arms.

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Complementarity/Comp

Copen.html

Received on Mon Apr 26 2004 - 18:10:49 PDT

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