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