An alternative to quantum complementarity
Ghenadie~N.~Mardari
The natural state of an unmeasured quantum system can be described by two competing types of hypotheses. One is the lottery model, according to which the system is constantly fluctuating, as if being in many states at once, until the measurement collapses it. The other stems from a roulette analogy, where the measurement alone induces a chaotic shift from one defined state to another. Both the Copenhagen interpretation and the de-Broigle-Bohm realism are based on the lottery model. Yet, the latest experimental data contradict its implications beyond reasonable doubt. A likely solution is to interpret the probabilistic nature of quantum mechanics with a roulette model.
quant-ph0409197.tex

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\begin{document}

\title{An alternative to quantum complementarity}

\author{Ghenadie~N.~Mardari}
email[]{g.mardari@rutgers.edu}
%\homepage[]{Your web page}
%\thanks{}
%\altaffiliation{}
\affiliation{Rutgers~University, 89 George St., New~Brunswick, NJ
08901}

\date{\today}

\begin{abstract}
The natural state of an unmeasured quantum system can be described
by two competing types of hypotheses. One is the lottery model,
according to which the system is constantly fluctuating, as if
being in many states at once, until the measurement collapses it.
The other stems from a roulette analogy, where the measurement
alone induces a chaotic shift from one defined state to another.
Both the Copenhagen interpretation and the de-Broigle-Bohm realism
are based on the lottery model. Yet, the latest experimental data
contradict its implications beyond reasonable doubt. A likely
solution is to interpret the probabilistic nature of quantum
mechanics with a roulette model.
\end{abstract}

\pacs{03.65.Ta, 03.65.Ud, 11.27.+d, 42.50.Xa}

%\keywords{}


\maketitle

The formalism of quantum mechanics is one of the greatest
achievements of modern science. Yet, its interpretation is still a
matter of debate. For example, it is well-known that some pairs of
observables must be described by non-commuting operators. By
implication, only one of the two can have an exact solution with
real numbers at the same time. So, according to the Copenhagen
interpretation, one observable must have no identifiable real
qualities, when the other is fully detected. Despite the
far-reaching success of this approach, it is becoming increasingly
difficult to defend, given the results of several recent
experiments. Hence, Santori {\it et al.} have proven the reality
of interference between single photons emitted by independent
deterministic sources \cite{str}. This should have been
impossible, according to the energy-time complementarity. In this
case, {\it time} is described by the phase and {\it energy} by the
number of photons. Deterministic sources of photons produce
squeezed states of light, in which the number of quanta is
certain, and phase coherence should be impossible to achieve.
Therefore, interference should have been undetectable, but it was
clearly demonstrated.

Similar proofs exist against the postulated complementarity
between path knowledge and fringe visibility in interferometric
settings. Several recent experiments have demonstrated
interference between non-intersecting coherent beams of single
photons \cite{fon,zou,kwi}. These experiments have produced
interference that evidently could not be explained in terms of
local particle collisions. Nevertheless, which-path information
was well-defined, because the two beams did not overlap. Thus,
path knowledge did not destroy interference. In fact, even the
famous wave-particle complementarity is under fire. The latest
experiments of Afshar have proven conclusively the reality of wave
effects, when particle properties alone should have been detected
\cite{afs}. In this context, it is remarkable that the
Michelson-Morley experiment was specifically designed to detect a
wave property of light, but failed. This shows that wave
properties do not simply become manifest when they can be
detected. Looking in the right place is just as important as how
to look. Consequently, waves and particles --- like many other
complementary observables --- are very likely to have a real
co-existence that is not anticipated by the Copenhagen
interpretation.

It is very important to emphasize that these inconsistencies do
not stem from the formalism of quantum mechanics. The quantitative
concepts are abstract by definition. It is the role of
interpretations to decide what should apply to what. The
Copenhagen interpretation insists that quantum properties are
meaningless prior to measurement, and often ignores their causal
potential. This peculiarity is most likely a consequence of its
interpretation of the probabilistic nature of quantum-mechanical
observables. This non-classical approach is based on a {\it
lottery} model of underdetermination, which implies that
unmeasured states have multiple values at the same time, the
function of measurement being to choose one at random. Yet, there
is at least one other way to explain uncertainty. This is the {\it
roulette} model, according to which the system has only well
defined states, one at a time, but the act of measurement induces
random shifts, due to the chaotic nature of its unavoidable impact
on the observable.

Note that the de-Broigle-Bohm realism \cite{bom}, which is the
most successful alternative to the Copenhagen interpretation, is
also based on the lottery model. Hence, the hypothesis of hidden
local variables leads to Bell's inequality \cite{bel}, because
they are presumed to require separable factors for their
correlations. One has to assume that prior common factors are not
real, and that local variables cannot stop fluctuating without
non-local collapse, for this to be necessary. Given this
limitation, the pilot-wave theory could not simplify our
understanding, despite its intuitive appeal. On the other hand, if
alternative assumptions are allowed for consideration, the
hypothesis of hidden local variables does not lead necessarily to
Bell's theorem \cite{sgo}.

According to the roulette model, quantum properties must be
assumed to be always well-defined in reality, despite their
selective manifestation through measurement. For example, the
wave-particle dualism can be solved by assuming that quanta are
particles, surrounded by waves in some sort of medium. In this
context, the detectable speed of light must be determined by
particle motion. Therefore, its invariance cannot be used for
generalizations about the wave properties of fields. When
Michelson and Morley performed their influential experiments,
there were no reasons yet to consider the possibility of photons.
With the emergence of quantum mechanics, their conclusions have
acquired a limited validity. In other words, mediation is still a
valid scientific hypothesis. In order to falsify it, the speed of
electrostatic and magnetostatic pulses must be proven to be
invariant as well.

Furthermore, when statistical phenomena are tackled with a
roulette model, quantum mechanics must be treated as a classical
theory. This makes it possible for us to appeal to macroscopic
analogies for the explanation of fundamental processes. Consider,
for example, the motion of a boat, which creates waves with
predictable wavelength on a given aquatic surface. If the boat
were to pass through a gate that is narrower than the wavelength,
it would have to be perfectly equidistant from the two edges, in
order to maintain a straight trajectory. The slightest deviation
from the central point would result in uneven instant recoil from
each side, causing a change in velocity. The narrower the gate ---
the wider the dispersion of likely trajectories after this
"measurement". It is quite plausible that a similar process
governs the probabilistic distribution of detected photons during
diffraction experiments. The analogy can even be extended to the
analysis of interference. Hence, when many boats move in the same
direction on a common surface, they must experience lateral
trajectory deviations, as if surfing on each other's waves. Yet,
the opposite slopes of two adjacent waves must cancel out their
effects near the points of constructive interference.
Consequently, all boats should behave as if guided towards
equilibrium lines crossing the peaks of constructive interference.
When many boats are launched out of the same gate, diffraction
alone should be detectable, because all waves are concentric. When
two or more gates are used, the boats must create interfering
waves, and end up clustering in predictable ways. Similarly,
particles can build up interference fringes during interferometric
experiments, without colliding directly with each other. And,
given the necessary reaction of the medium to the presence of any
particle, interference patterns should be sensitive to any attempt
to observe the process directly.

If quanta are treated as real particles, self-interference must be
ruled out. A particle cannot be in two places at once, nor can it
exhibit interference due to its own waves. This process requires
at least two particles with independent pathways, which must also
be close enough for interaction. Consequently, there must be a
limit, beyond which interference should vanish in the single
photon regime. This prediction has been confirmed by a recent
experiment of Kim {\it et al.} with a Young-type interferometric
setting \cite{kim}. Using the signal beam of a parametric down
converter (and discarding the idler), the authors controlled the
distance between pairs of photons, iterated at $90MHz$, and
checked for fringe visibility. Similarity with the double-slit
experiment was ensured by the relatively large area of emission,
which implied that photons were emerging from various points, as
if from different slits. This also meant that fringes from
different source-points would overlap, washing out visibility.
Therefore, narrow-band interference filters were required. The
reported result is that fringe visibility dropped very quickly, as
the delay between photons approached the picosecond range. We
believe that this finding does not contradict previous
experiments, but only their interpretation. Earlier tests, which
produced interference beyond nanosecond intervals \cite{pku,pkd},
relied on attenuated light sources, without being able to control
the length of single photons. Still, even such settings were shown
to produce no interference, when light attenuation was much
stronger \cite{baz}. The same conclusion holds for experiments
with electrons as well. In their famous demonstration of
single-electron interference in a two-slit setting, Tonomura {\it
et al.} \cite{ton} reported a loss of fringe contrast at lower
emission intensities. They attributed this feature to the
possibility of a systemic measurement error. Nevertheless, this
still means that the evidence in favor of self-interference is
inconclusive.

The lottery model was not able provide a single explanation for
all types of interference. For the simple double-slit experiment,
reference was made to self-interference. For interference between
photons from isolated sources, the explanation was given in terms
of entanglement. The problem was that some settings were
ambiguous. Hence, in a Young interferometer, in which the slits
are switched on alternatively very fast \cite{sil}, only one path
is open at a time and the process resembles the situations with
two independent sources of photons. Yet, entanglement does not
apply, and explanation is given in terms of self-interference. The
switching mechanism works faster than the uncertainty in times of
detection, facilitating the assumption that the two paths are
indistinguishable in the interference volume. Remarkably, path
distinguishability depends here on the average interval between
single photons. As shown above, the roulette approach can explain
all types of interference by reference to the latter.

Where the lottery model required a complementary relationship
between self-interference and entanglement, the roulette approach
makes a distinction between electric and magnetic photon
interactions. For example, when two photons are temporally
distinguishable, their magnetic waves must propagate in parallel
planes. Thus, the role of polarization should become
insignificant. In contrast, the interaction via electric waves
should acquire primary importance, as revealed by the dependency
of fringe visibility on phase-coherence. This prediction is
confirmed to the letter by a recent experiment of Kim and Grice
\cite{kgc}, which analyzed the details of photon bunching with
identical photons, well separated in time. First of all, they
found that interference vanishes altogether, when separation is
increased towards the picosecond range. Secondly, they found that
fringe visibility at smaller delays between photons depends on
subwavelength tweaking, {\it i.e.} on phase coherence. Finally,
they came to the firm conclusion that polarization was irrelevant
for the outcome of the experiment, after many iterations with
varied adjustments. Such photonic behavior is in stark contrast
with the settings that involve simultaneous pulses, when phase
coherence is not an issue, but polarization is the crucial factor
for fringe visibility. Parametric down-conversion is a good source
of polarization-determined interactions. Though, few experiments
are so revealing as the tests of the hypothetical quantum erasure.

A very interesting test of quantum erasure was performed by
Walborn {\it et al.} \cite{wal}. The authors directed
polarization-entangled pairs of simultaneous identical photons
along different paths. One photon (called $p$) went straight to
its detector (a photon counter), while the other ($s$) was sent
through a double-slit interferometer. The two slits were covered
by orthogonal polarizers, designated as path markers, and
therefore no interference was expected. The authors claim that
interference was recovered when the polarization of $p$ particles
was measured. Moreover, this had to work even when the $p$
particles were detected after the $s$ particles, and the fringes
were already recorded. Quantum erasure follows logically from the
principles of the Copenhagen interpretation, but it is difficult
to accept in terms of the experiment itself. First of all, the
recovered fringes did not correspond to the whole pool of photons
that passed the interferometer. The technique of coincidence
counts merely separated the detection events into a set with
fringes, and another with antifringes, which could create back the
non-interference distribution when added. It is quite plausible
that the two interference subsets were there even when the $p$
photons were counted without polarization measurements. Secondly,
it is not clear why the process only worked one way. If quantum
erasure is real, the $s$ photons could have acted on the $p$
photons too, washing out fringe visibility, particularly during
the so-called delayed erasure. Thirdly, it was not proven that the
fringes were indeed produced by the self-interference of $s$
photons. This could have been done by demonstrating the build-up
of fringes with the beam of $p$ photons discarded at emission, and
without polarization markers. The existing data rules out
self-interference, because the fringe patterns correlate strongly
with the presence of $p$ photons. Hence, all fringes are
strikingly asymmetric in the case of early detection of $p$
photons, with or without polarization markers, and less so during
delayed measurement. There is no reason for such asymmetry under
the assumption of self-interference. Yet, the assumption of direct
interaction requires them. When $p$ photons were detected too
early, their interaction with $s$ photons had to be imperfect,
producing a poorer dispersion of their intensity. Finally, there
is sufficient evidence from other sources for the possibility of
direct $s-p$ interaction, leading to fringe build-up. Such
interference appears to be a normal property of simultaneous
identical photons following adjacent paths \cite{fon,zou,kwi}.
Moreover, in a similar test of quantum erasure, Schwindt {\it et
al.} demonstrated recovery ``even when no which-way information
was available to erase'' \cite{swi}. That is to say, they showed
that polarization markers produced separate sets of fringes at
various mutual angles, regardless of their potential to affect the
level of which-path information. The crucial element for
interaction was the presence of simultaneous
polarization-entangled photons. In terms of the details of the
experiment, the $s$ photons were well-positioned to interfere
directly with the $p$ photons. This means that the $p$ photons
were not forced to change alignment at measurement. They arrived
already at the right angle to be detectable in coincidence counts
with the $s$ particles that they interfered with. This also means
that the fringes were produced by $s$ photons taking one path, and
the antifringes corresponded to those that went along the
orthogonal path.

In light of the above, the interpretation of quantum processes in
terms of lottery models is no longer satisfactory. They lead to
complicated generalizations, which have a limited predictive range
and violate the experimental record. In contrast, the roulette
approach produces verifiable explanations in classical terms that
are uniquely able to fit the formalism and might even eliminate
some inconsistencies between related branches of physics.
Nevertheless, the hypothesis of real magnetic and electric waves
necessarily brings up an old question: what are they waves of? The
answer, we believe, has already been produced by recent
astrophysical investigations. As it is known, quantum field
theories could not provide a satisfactory answer to the problem of
accelerated expansion of the Universe \cite{swn,sah}, but the gap
was filled in part by the brane-world cosmologies. Notably, some
theories from the latter group are focused on the hypothesis that
matter could be localized on a 3D domain wall, embedded in a
higher-dimensional bulk \cite{ran,lan,bro}. So, particles can be
described as moving inside a real brane and causing vibrations
that propagate as magnetic and electric waves in superposition.

Brane scenarios are easily adaptable to the properties of optical
processes. Hence, a domain wall can be defined as a
three-dimensional architecture of interwoven elastic strings,
governed by some sort of local symmetry. Whenever a photon has an
impact on a string, it must produce a set of longitudinal brane
waves along the direction of action, which obey the inverse square
law, like the electric force. The same action must also generate
an orthogonal transverse wave, which corresponds to the profile of
the magnetic force. This fundamental unit of action must determine
the value of Planck's constant, while the distance between any two
strings must become the absolute unit of distance. Given the
elasticity of the brane, this unit must be fundamentally flexible.
Whenever photons travel through excited regions of the brane, they
must behave as if embedded in a curved space, exhibiting
well-known relativistic and electromagnetic properties.

This model has another unexpected advantage. Current theories
explain many particle properties in terms of finite harmonic
oscillators. Yet, harmonic oscillators must allow for continuous
distributions of energy values, despite the assumption of integer
number of wave-lengths. When overtones are considered, the number
of standing waves can increase infinitely, producing arbitrarily
small values for energy units. Moreover, it is well known that
such a mechanism cannot explain the probability of detecting a
quantum in a given volume either. An oscillating body will have
the smallest probability of detection in the middle, whereas the
probability of quantum positions diminishes with distance from an
identifiable center. In contrast, the brane can be treated as an
infinite oscillating medium, which excludes the possibility of
actual standing waves. Instead, the harmonic patterns must be
produced by the sustained agency of a source --- the particle,
which plucks the strings of the brane. If so, the probability of
finding the quantum agent must be the highest at the source (when
time-evolution is ignored), and the energy of the waves can only
be quantized. Hence, the brane scenario is uniquely suitable for
the interpretation of the fundamental properties of matter. Note
that it is mathematically convenient to treat the source points of
waves as infinitesimals. Though, every unit of action must have an
irreducible volume, defined by the product of wavelength and
amplitude. There is no such thing as a fraction of a pluck. So,
the real propagation of waves must begin at a well-defined
distance from the conventional source-point, and the inverse
(exponent) law must break down for energy estimates at
subwavelength intervals from it. If this phenomenon is ignored,
the fortuitous conclusion must be that finite action produces
infinite energy very close to the source. Thus, non-classical
interpretations in terms of probability waves often lead to
unexplained singularities and infinities, predicting enormous
forces among adjacent quanta. The hypothesis of moving particles,
as uniform sources of real waves, is the only one known to us that
can explain the quantized nature of field energy without
inconsistencies.

As a corollary, the ontological gap between classical mechanics
and quantum mechanics is merely a consequence of widespread
adherence to lottery models of uncertainty. These models are
non-local by definition and therefore offer no chance for
consistency between macro and micro processes. On the other hand,
classical interpretations of quantum phenomena are the only ones
which appear to fit the data, being only consistent with the
so-called roulette approach to uncertainty.



%\bibliography{toprl}
\begin{thebibliography}{22}
\expandafter\ifx\csname
natexlab\endcsname\relax\def\natexlab#1{#1}\fi
\expandafter\ifx\csname bibnamefont\endcsname\relax
  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname citenamefont\endcsname\relax
  \def\citenamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname
urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

\bibitem[{\citenamefont{Santori et~al.}(2002)\citenamefont{Santori, Fattal,
  Vu\v{c}kovi\'c, Solomon, and Yamamoto}}]{str}
\bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Santori}},
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Fattal}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Vu\v{c}kovi\'c}},
  \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Solomon}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Yamamoto}},
  \bibinfo{journal}{Nature} \textbf{\bibinfo{volume}{419}},
  \bibinfo{pages}{594} (\bibinfo{year}{2002}).

\bibitem[{\citenamefont{Fonseca et~al.}(1999)\citenamefont{Fonseca, Ribeiro,
  P\'adua, and Monken}}]{fon}
\bibinfo{author}{\bibfnamefont{E.}~\bibnamefont{Fonseca}},
  \bibinfo{author}{\bibfnamefont{P.} \bibnamefont{Suoto~Ribeiro}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{P\'adua}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Monken}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{60(2)}},
  \bibinfo{pages}{1530} (\bibinfo{year}{1999}).


\bibitem[{\citenamefont{Ou et~al.}(1990)\citenamefont{Ou, Zou, Wang, and
  Mandel}}]{zou}
\bibinfo{author}{\bibfnamefont{Z.}~\bibnamefont{Ou}},
  \bibinfo{author}{\bibfnamefont{X.}~\bibnamefont{Zou}},
  \bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Wang}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Mandel}},
  \bibinfo{journal}{Phys. Rev. Lett.} \textbf{\bibinfo{volume}{65(3)}},
  \bibinfo{pages}{321} (\bibinfo{year}{1990}).

\bibitem[{\citenamefont{Kwiat et~al.}(1990)\citenamefont{Kwiat, Vareka, Hong,
  Nathel, and Chiao}}]{kwi}
\bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Kwiat}},
  \bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Vareka}},
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Hong}},
  \bibinfo{author}{\bibfnamefont{H.}~\bibnamefont{Nathel}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Chiao}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{41(5)}},
  \bibinfo{pages}{2910} (\bibinfo{year}{1990}).

\bibitem[{\citenamefont{Afshar}(2004)}]{afs}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Afshar}},
  \eprint{http://www.irims.org/quant-ph/030503/}.

\bibitem[{\citenamefont{Bohm and Hiley}(1993)}]{bom}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Bohm}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{B.}~\bibnamefont{Hiley}},
  \emph{\bibinfo{title}{The undivided universe}}
  (\bibinfo{publisher}{Routledge}, \bibinfo{year}{1993}).

\bibitem[{\citenamefont{Bell}(1987)}]{bel}
\bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Bell}},
  \emph{\bibinfo{title}{Speakable and unspeakable in quantum mechanics}}
  (\bibinfo{publisher}{Cambridge}, \bibinfo{year}{1987}).

\bibitem[{\citenamefont{Shafiee and Golshani}(2005)}]{sgo}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Shafiee}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Golshani}},
  \bibinfo{journal}{Fortschr. Phys.} \textbf{\bibinfo{volume}{53(1)}},
  \bibinfo{pages}{105} (\bibinfo{year}{2005}).

\bibitem[{\citenamefont{Kim et~al.}(2000)\citenamefont{Kim, Chekhova, Kulik,
  Shih, and Rubin}}]{kim}
\bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Kim}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Chekhova}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Kulik}},
  \bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Shih}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Rubin}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{61(5)}},
  \bibinfo{pages}{051803} (\bibinfo{year}{2000}).

\bibitem[{\citenamefont{Parker}(1971)}]{pku}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Parker}}, \bibinfo{journal}{Am.
  J. Phys.} \textbf{\bibinfo{volume}{39}}, \bibinfo{pages}{420}
  (\bibinfo{year}{1971}).

\bibitem[{\citenamefont{Parker}(1972)}]{pkd}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Parker}}, \bibinfo{journal}{Am.
  J. Phys.} \textbf{\bibinfo{volume}{40}}, \bibinfo{pages}{1003}
  (\bibinfo{year}{1972}).

\bibitem[{\citenamefont{Dontsov and Baz}(1967)}]{baz}
\bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Dontsov}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Baz}}, \bibinfo{journal}{Sov.
  Phys. - JETP} \textbf{\bibinfo{volume}{25(1)}}, \bibinfo{pages}{1}
  (\bibinfo{year}{1967}).

\bibitem[{\citenamefont{Tonomura et~al.}(1989)\citenamefont{Tonomura, Endo,
    Matsuda, Kawasaki and Ezava}}]{ton}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Tonomura}}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Endo}},
  \bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Matsuda}},
  \bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Kawasaki}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{H.}~\bibnamefont{Ezawa}},
  \bibinfo{journal}{Am. J. Phys.}
  \textbf{\bibinfo{volume}{57(2)}}, \bibinfo{pages}{117}
  (\bibinfo{year}{1989}).

\bibitem[{\citenamefont{Sillitto and Wykes}(1972)}]{sil}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Sillitto}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Wykes}},
  \bibinfo{journal}{Phys. Lett. A} \textbf{\bibinfo{volume}{39(4)}},
  \bibinfo{pages}{333} (\bibinfo{year}{1972}).

\bibitem[{\citenamefont{Kim and Grice}(2003)}]{kgc}
\bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Kim}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Grice}},
  \eprint{quant-ph/0304086}.

\bibitem[{\citenamefont{Walborn et~al.}(2002)\citenamefont{Walborn, Cunha,
  P�dua, and Monken}}]{wal}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Walborn}},
  \bibinfo{author}{\bibfnamefont{M.} \bibnamefont{Terra~Cunha}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{P\'{a}dua}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Monken}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{65(3)}},
  \bibinfo{pages}{033818} (\bibinfo{year}{2002}).


\bibitem[{\citenamefont{Schwindt et~al.}(1999)\citenamefont{Schwindt, Kwiat,
  and Englert}}]{swi}
\bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Schwindt}},
  \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Kwiat}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{B.}~\bibnamefont{Englert}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{60(6)}},
  \bibinfo{pages}{4285} (\bibinfo{year}{1999}).

\bibitem[{\citenamefont{Weinberg}(1989)}]{swn}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Weinberg}},
  \bibinfo{journal}{Rev. Mod. Phys.} \textbf{\bibinfo{volume}{61(1)}},
  \bibinfo{pages}{1} (\bibinfo{year}{1989}).

\bibitem[{\citenamefont{Sahni and Starobinski}(2000)}]{sah}
\bibinfo{author}{\bibfnamefont{V.}~\bibnamefont{Sahni}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Starobinski}},
  \bibinfo{journal}{J. Mod. Phys. D} \textbf{\bibinfo{volume}{9}},
  \bibinfo{pages}{373} (\bibinfo{year}{2000}).

\bibitem[{\citenamefont{Randall and Sundrum}(1999)}]{ran}
\bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Randall}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Sundrum}},
  \bibinfo{journal}{Phys. Rev. Lett.} \textbf{\bibinfo{volume}{83(23)}},
  \bibinfo{pages}{4690} (\bibinfo{year}{1999}).

\bibitem[{\citenamefont{Langlois}(2003)}]{lan}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Langlois}},
  \bibinfo{journal}{Prog. Theor. Phys. Suppl.} \textbf{\bibinfo{volume}{148}},
  \bibinfo{pages}{181} (\bibinfo{year}{2003}).

\bibitem[{\citenamefont{Brax and van~de~Bruck}(2003)}]{bro}
\bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Brax}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{van~de~Bruck}},
  \bibinfo{journal}{Class. Quant. Grav.} \textbf{\bibinfo{volume}{20}},
  \bibinfo{pages}{R201} (\bibinfo{year}{2003}).

\end{thebibliography}

\end{document}

quant-ph0409197.extracted_bib
\begin{thebibliography}{22}
\expandafter\ifx\csname
natexlab\endcsname\relax\def\natexlab#1{#1}\fi
\expandafter\ifx\csname bibnamefont\endcsname\relax
  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname citenamefont\endcsname\relax
  \def\citenamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname
urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

\bibitem[{\citenamefont{Santori et~al.}(2002)\citenamefont{Santori, Fattal,
  Vu\v{c}kovi\'c, Solomon, and Yamamoto}}]{str}
\bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Santori}},
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Fattal}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Vu\v{c}kovi\'c}},
  \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Solomon}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Yamamoto}},
  \bibinfo{journal}{Nature} \textbf{\bibinfo{volume}{419}},
  \bibinfo{pages}{594} (\bibinfo{year}{2002}).

\bibitem[{\citenamefont{Fonseca et~al.}(1999)\citenamefont{Fonseca, Ribeiro,
  P\'adua, and Monken}}]{fon}
\bibinfo{author}{\bibfnamefont{E.}~\bibnamefont{Fonseca}},
  \bibinfo{author}{\bibfnamefont{P.} \bibnamefont{Suoto~Ribeiro}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{P\'adua}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Monken}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{60(2)}},
  \bibinfo{pages}{1530} (\bibinfo{year}{1999}).


\bibitem[{\citenamefont{Ou et~al.}(1990)\citenamefont{Ou, Zou, Wang, and
  Mandel}}]{zou}
\bibinfo{author}{\bibfnamefont{Z.}~\bibnamefont{Ou}},
  \bibinfo{author}{\bibfnamefont{X.}~\bibnamefont{Zou}},
  \bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Wang}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Mandel}},
  \bibinfo{journal}{Phys. Rev. Lett.} \textbf{\bibinfo{volume}{65(3)}},
  \bibinfo{pages}{321} (\bibinfo{year}{1990}).

\bibitem[{\citenamefont{Kwiat et~al.}(1990)\citenamefont{Kwiat, Vareka, Hong,
  Nathel, and Chiao}}]{kwi}
\bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Kwiat}},
  \bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Vareka}},
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Hong}},
  \bibinfo{author}{\bibfnamefont{H.}~\bibnamefont{Nathel}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Chiao}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{41(5)}},
  \bibinfo{pages}{2910} (\bibinfo{year}{1990}).

\bibitem[{\citenamefont{Afshar}(2004)}]{afs}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Afshar}},
  \eprint{http://www.irims.org/quant-ph/030503/}.

\bibitem[{\citenamefont{Bohm and Hiley}(1993)}]{bom}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Bohm}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{B.}~\bibnamefont{Hiley}},
  \emph{\bibinfo{title}{The undivided universe}}
  (\bibinfo{publisher}{Routledge}, \bibinfo{year}{1993}).

\bibitem[{\citenamefont{Bell}(1987)}]{bel}
\bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Bell}},
  \emph{\bibinfo{title}{Speakable and unspeakable in quantum mechanics}}
  (\bibinfo{publisher}{Cambridge}, \bibinfo{year}{1987}).

\bibitem[{\citenamefont{Shafiee and Golshani}(2005)}]{sgo}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Shafiee}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Golshani}},
  \bibinfo{journal}{Fortschr. Phys.} \textbf{\bibinfo{volume}{53(1)}},
  \bibinfo{pages}{105} (\bibinfo{year}{2005}).

\bibitem[{\citenamefont{Kim et~al.}(2000)\citenamefont{Kim, Chekhova, Kulik,
  Shih, and Rubin}}]{kim}
\bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Kim}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Chekhova}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Kulik}},
  \bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Shih}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Rubin}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{61(5)}},
  \bibinfo{pages}{051803} (\bibinfo{year}{2000}).

\bibitem[{\citenamefont{Parker}(1971)}]{pku}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Parker}}, \bibinfo{journal}{Am.
  J. Phys.} \textbf{\bibinfo{volume}{39}}, \bibinfo{pages}{420}
  (\bibinfo{year}{1971}).

\bibitem[{\citenamefont{Parker}(1972)}]{pkd}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Parker}}, \bibinfo{journal}{Am.
  J. Phys.} \textbf{\bibinfo{volume}{40}}, \bibinfo{pages}{1003}
  (\bibinfo{year}{1972}).

\bibitem[{\citenamefont{Dontsov and Baz}(1967)}]{baz}
\bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Dontsov}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Baz}}, \bibinfo{journal}{Sov.
  Phys. - JETP} \textbf{\bibinfo{volume}{25(1)}}, \bibinfo{pages}{1}
  (\bibinfo{year}{1967}).

\bibitem[{\citenamefont{Tonomura et~al.}(1989)\citenamefont{Tonomura, Endo,
    Matsuda, Kawasaki and Ezava}}]{ton}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Tonomura}}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Endo}},
  \bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Matsuda}},
  \bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Kawasaki}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{H.}~\bibnamefont{Ezawa}},
  \bibinfo{journal}{Am. J. Phys.}
  \textbf{\bibinfo{volume}{57(2)}}, \bibinfo{pages}{117}
  (\bibinfo{year}{1989}).

\bibitem[{\citenamefont{Sillitto and Wykes}(1972)}]{sil}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Sillitto}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Wykes}},
  \bibinfo{journal}{Phys. Lett. A} \textbf{\bibinfo{volume}{39(4)}},
  \bibinfo{pages}{333} (\bibinfo{year}{1972}).

\bibitem[{\citenamefont{Kim and Grice}(2003)}]{kgc}
\bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Kim}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Grice}},
  \eprint{quant-ph/0304086}.

\bibitem[{\citenamefont{Walborn et~al.}(2002)\citenamefont{Walborn, Cunha,
  P�dua, and Monken}}]{wal}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Walborn}},
  \bibinfo{author}{\bibfnamefont{M.} \bibnamefont{Terra~Cunha}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{P\'{a}dua}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Monken}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{65(3)}},
  \bibinfo{pages}{033818} (\bibinfo{year}{2002}).


\bibitem[{\citenamefont{Schwindt et~al.}(1999)\citenamefont{Schwindt, Kwiat,
  and Englert}}]{swi}
\bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Schwindt}},
  \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Kwiat}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{B.}~\bibnamefont{Englert}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{60(6)}},
  \bibinfo{pages}{4285} (\bibinfo{year}{1999}).

\bibitem[{\citenamefont{Weinberg}(1989)}]{swn}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Weinberg}},
  \bibinfo{journal}{Rev. Mod. Phys.} \textbf{\bibinfo{volume}{61(1)}},
  \bibinfo{pages}{1} (\bibinfo{year}{1989}).

\bibitem[{\citenamefont{Sahni and Starobinski}(2000)}]{sah}
\bibinfo{author}{\bibfnamefont{V.}~\bibnamefont{Sahni}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Starobinski}},
  \bibinfo{journal}{J. Mod. Phys. D} \textbf{\bibinfo{volume}{9}},
  \bibinfo{pages}{373} (\bibinfo{year}{2000}).

\bibitem[{\citenamefont{Randall and Sundrum}(1999)}]{ran}
\bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Randall}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Sundrum}},
  \bibinfo{journal}{Phys. Rev. Lett.} \textbf{\bibinfo{volume}{83(23)}},
  \bibinfo{pages}{4690} (\bibinfo{year}{1999}).

\bibitem[{\citenamefont{Langlois}(2003)}]{lan}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Langlois}},
  \bibinfo{journal}{Prog. Theor. Phys. Suppl.} \textbf{\bibinfo{volume}{148}},
  \bibinfo{pages}{181} (\bibinfo{year}{2003}).

\bibitem[{\citenamefont{Brax and van~de~Bruck}(2003)}]{bro}
\bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Brax}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{van~de~Bruck}},
  \bibinfo{journal}{Class. Quant. Grav.} \textbf{\bibinfo{volume}{20}},
  \bibinfo{pages}{R201} (\bibinfo{year}{2003}).

\end{thebibliography}