AAWSAP DIRD The Space Communication Implications of Quantum Entanglement and Nonlocality March 30 2010
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30 March 2010
ICOD : 1 December 2009
DIA-08- 1003-016
The Space-Communication
Implications of Quantum
Entanglement and Nonlocality
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The Space-Communication Implications of Quantum
Entanglement and Nonlocality
Prepared by:
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Directorate for Analysis
Defense Intelligence Agency
Author:
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Contents
Foreword and Introduction ....................................................................................iv
I. Quantum Entanglement, Nonlocality, and EPR Experiments ............................... 1
II. The Quantum No-Signal Theorems .................................................................... 4
III. Nonlocality Versus Special Relativity? ............................................................. 5
IV. Momentum Domain Entanglement and EPR Experiments .................................. 5
V. Coherence-Entanglement Complementarity ..................................................... 10
VI. Nonlocal Communication Versus Signaling ..................................................... 11
VII. A Transactional Analysis of the Nonlocal Communication Test ...................... 13
VIII. Superluminal and Retrocausal Nonlocal Communication ............................. 17
IX. Paradoxes and Nonlocal Communication ........................................................ 18
X. Superluminal Communication without Paradoxes ............................................ 19
XI. Example: Real-Time Earth Control of Mars Rover............................................ 20
XII. Another Superluminal Possibility: Nonlinear Quantum Mechanics................. 22
XIII. Conclusion ................................................................................................... 23
Appendix: Glossary .............................................................................................. 24
Figures
Figure 1. Schematic of the 1972 Freedman-Clauser Experiment ............................ 2
Figure 2. Schematic of the 1995 Ghost Interference Experiment of the Shih
Group ...................................................................................................... 6
Figure 3. Ghost Interference Position Distributions at X2 ....................................... 7
Figure 4. "Unfolding" the Ghost Interference Experiment ...................................... 8
Figure 5. Schematic of the 1998 Dopfer Experiment .............................................. 9
Figure 6. Thick-Source Effect ............................................................................... 10
Figure 7. Slit-Imaging Coincidence-Free Version of the Ghost Interference
Experiment to Demonstrate Nonlocal Communication ........................... 12
Figure 8. Transactional Interpretation Diagrams for Case 1 ................................. 15
Figure 9. Transactional Interpretation Diagrams for Case 2 ................................. 16
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Figure 10. Slit-Imaging Coincidence-Free Version of the Ghost Interference
Experiment Demonstrating Superluminal and Retrocausal Signaling .. 17
Figure 11. A Superluminal Nonlocal Communication System in Which the
Communication Spans a Spacelike Interval ........................................ 20
Figure 12. Schematic of Earth-to-Mars Real-Time Control of a Rover ................... 21
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The Space-Communication Implications of Quantum
Entanglement and Nonlocality
Foreword and Introduction
This paper reviews quantum entanglement and nonlocality and considers the
possibility that this phenomenon could be used for sending observer-to
observer signals. Such a demonstration would break several quantum "no
signal theorems" in the physics literature. Nonlocal quantum signaling would
have far-reaching implications as an enabling technology for superluminal and
retrocausal signaling. Scenarios that might lead to nonlocal quantum
communication are described, and applications to retrocausal signaling and
real-time space communication are considered. Also considered briefly is the
nonlocal communication implications of nonlinear quantum mechanics.
Communication in space at the scale of the solar system is severely limited by
the space-time scale set by the speed of light. Light signals, whether in the
form of radio waves, microwaves, visible light, X-rays, or gamma rays, require
about 3.3 microseconds to travel a distance of 1 kilometer. A light signal sent
from Earth requires about 1.3 seconds to reach the Moon, between 4.4 and 20
minutes to reach Mars, and between 4 and 4.3 hours to reach Neptune,
depending on their orbital positions. This time delay makes real-time control
of remote space-based devices impossible and leads to the need for pre
programmed robotic devices with enough "intelligence" to perform limited
operations with a minimum of remote control.
The burden of these limitations raises the question of whether there is some
way to speed up the space communications link. The conventional answer is
"No!," because the well-established special theory of relativity is viewed as
limiting signal transmission speed to the speed of light, with superluminal
communications strictly forbidden. However, as will be discussed in Section
III, relativity prohibits only certain forms of superluminal communication,
while other forms are not in conflict with relativity. One phenomenon that
appears, at least superficially, to exhibit superluminal aspects while
preserving compatibility with special relativity is quantum nonlocality, the
ability of quantum phenomena to enforce correlations between quantum
states over large separations in space-time.
When two photons emerge from a single quantum event, the state of one
photon may be subtly connected to that of the other. The classical view is that,
once separated, such photon states must be fixed according to mechanics and
conservation relations that act at the point of their origin, so that modifying
one later will not affect the other. In quantum physics, however, as borne out
by experiment (Reference 1, 2), the outcome of a measurement of the state of
one of the photons, even well after their point of joint creation, can affect the
state of the other photon. This connection is referred to as quantum
entanglement, a phrase first coined by Erwin Schrodinger (Reference 3).
Questions raised by the phenomenon of quantum entanglement are: (1) what
is the causal connection between entangled states, and (2) can the
phenomenon possibly be used for sending observer-to-observer signals? This
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paper attempts to address these questions by taking a close look at quantum
entanglement, quantum nonlocality, the experiments that have explored them,
and proposed experiments to test the causal and faster-than-light
communication issues evoked by such physics.
Quantum entanglement describes the condition of separated parts of the same
quantum system in which each of the parts can be described only by
referencing the state of other parts. This is one of the most counterintuitive
aspects of quantum mechanics, because classically one would expect system
parts out of "local" contact to be completely independent. Thus, entanglement
represents a kind of quantum "connectedness" in which measurements on one
isolated part of an entangled quantum system have nonclassical consequences
for the outcome of measurements performed on the other (possibly very
distant) part of the same system. This quantum connectedness acting in
entangled quantum systems is called quantum nonlocality.
Nonlocality was first highlighted by Albert ~instein and his coworkers Boris
_fodolsky and Nathan ,Rosen in their famous EPR paper (Reference 4). They
argued that the nonlocal connectedness of quantum systems was unphysical
in that it implied a faster-than-light connection in apparent conflict with
special relativity. Despite their objection, quantum nonlocality has now been
demonstrated (see Section I) in many quantum systems (Reference 1, 2). In
the physics community, it is now generally acknowledged to be implicit in the
quantum formalism as applied to entangled systems, although there remain a
few Copenhagen "holdouts" who would require an explicit demonstration of
nonlocal signaling before admitting that nonlocality can be considered a real
quantum phenomenon.
The question investigated in this paper is whether quantum nonlocality is the
private domain of nature or whether it can be used in experimental situations
to send signals from one observer to another. As we will see, there is at
present no compelling answer to this question. However, it is clear that if such
nonlocal observer-to-observer communication were possible, it would have
far-reaching implications. In particular, it would represent an enabling
technology for superluminal (and retrocausal) signaling and communications,
and perhaps make possible the real-time exploration of the universe.
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I. Quantum Entanglement, Nonlocality, and EPR
Experiments
In the quantum mechanical description of elementary entities like photons, there is a
duality between the description as a particle and as a wave. Photons can be thought of
as traveling through space as waves but delivering energy (and other conserved
quantities) at detection as particles. By choosing the kinds of measurements made on
such objects, one can force wave-like or particle-like behavior to be exhibited in the
measurements results. Between the entangled parts of a quantum system (for
example, the emission of a pair of entangled photons), this wave-like or particle-like
behavior in a measurement on one part of the system may force similar behavior in the
other part. This is considered further in Section IV below.
The quantum entanglement condition is usually a consequence of some conservation
law acting within the system, so that the subsystems are connected by the conserved
quantities. For example, if two photons are emitted back to back in a joint state that
has zero angular momentum and positive parity, then whatever linear or circular
polarization state one photon is measured to have, the other photon must have an
identical polarization if measured in the same basis (linear or circular). This condition
must exist to ensure that the net angular momentum of the two photon states is zero.
In this situation, if the photons are measured for circular polarization, they must both
be in states of right circular polarization or in states of left circular polarization. Because
linear polarization is a coherent superposition of circular polarization states, if measured
in the vertical/horizontal linear polarization basis, they must be in the same vertical or
horizontal polarization state, and in the 45° left or right linear polarization basis, they
must be in the same 45° left/rig ht polarization state.
Classically, such a polarization correlation condition could in principle exist in some
particular polarization basis but not in all of the many possible polarization bases
simultaneously. This is the underlying physics of the Bell Inequalities (Reference 8),
which deal with the falloff rate of the correlations as the polarization basis of one of the
measurements is rotated in angle. The Bell Inequalities demonstrate mathematically
that the predictions of sem i-classical local hidden-variable theories are inconsistent with
those of standard quantum mechanics. Tests of such polarization correlations have
been the basis for a number of Bell-Inequality tests (or so-called EPR experiments), in
which the validity of the predictions of quantum mechanics and the inadequacies of
semi-classical local hidden-variable theories have been demonstrated to high statistical
precision (Reference 1, 2) .
It was later demonstrated (Reference 5, 6) that the issues surrounding a violation of
the Bell Inequalities could be separated into violations of either parameter
independence (the outcome probability of a measurement on one of a pair of entangled
particles is independent of the choice of parameters of a measurement performed on
the other member of the entangled pair) and violations of outcome independence (the
outcome probability of a measurement on one of a pair of entangled particles is
independent of the outcome of a measurement performed on the other member of the
entangled pair). The observation of a violation of the Bell Inequalities indicates a
violation of either parameter independence or outcome independence (or both).
Outcome independence is fairly evident in the quantum formalism, while parameter
independence is more elusive and depends on specific assumptions. Below, the
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implications of this dichotomy are considered in the context of the "no-signal"
theorems .
It is noted that there is some misinformation in the literature concerning the chronology
of successful EPR polarization correlation experiments, and here we wish to set the
record at least somewhat straighter. The experimental measurement that first
demonstrated a polarization correlation related to EPR nonlocality was performed by C.
S. Wu and I. Shanknov in 1949 (Reference 7), well before Bell's work and the
subsequent interest in testing Bell's Inequality. Wu and Shanknov showed that the
linear polarizations of back-to-back entangled gamma rays from electron-positron
annihilation (an L=O negative parity state) were anticorrelated, for example, if one
photon was polarized vertically, then the other was polarized horizontally. They did not,
however, investigate the falloff of the correlation with polarimeter angle, which is the
basis of Bell Inequality tests, nor did they depict their results as a consequence of
quantum nonlocality.
Almost two decades passed before the publication of John Bell's pivotal work (Reference
8) in 1964 and 1966. In 1972, Freedman and Clauser (Reference 1) performed the first
definitive Bell inequality test by measuring the polarization correlation of entangled
photons from a positive parity L=O atomic cascade in calcium. Their results were in
agreement with the predictions of quantum mechanics and were inconsistent with local
hidden-variable theories by 6. 7 standard deviations. A decade later, in 1982, EPR
measurements of the Aspect group (Reference 2) eliminated several "loophole"
scenarios that might constitute unlikely ways of preserving classical locality and again
demonstrated agreement with quantum mechanics and inconsistency with local hidden
variable theories, this time by 46 standard deviations. In a more recent example of an
EPR experiment, the Gisin group (Reference 9) used the fiber-optic cables owned by the
Swiss Telephone System to demonstrate the nonlocal connection between EPR
measurements made at locations in Geneva and Bern, Swiss cities with a line -of-sight
separation of 156 km-a direct demonstration, if one was required, that quantum
nonlocality can operate over quite large distances.
Ca-OVEN
LENS LENS
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Figure 1. Schematic of the 1972 Freedman-Clauser Experiment (Reference 1)
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Do these EPR experiments constitute a demonstration of the existence of quantum
nonlocality? There is more than one way of interpreting the implications of the
experimental results (Reference 1, 2), and one can find much discussion in the
literature as to whether it is locality or "realism" (the objective observer- independent
reality of external events) that has been refuted by these EPR measurements.
Noble Laureate Anthony Leggett of the University of Illinois recently pushed this issue
somewhat further (Reference 10). He demonstrated that by focusing on the falloff of
correlations with elliptical polarization rather than the linear polarization used in the Bell
Inequality EPR experiments, one can compare the predictions of quantum mechanics
with a class of nonlocal realistic theories that he constructed. The resulting Leggett
Inequalities can be used in the same way as the Bell Inequalities, but to test theories
incorporating nonlocal realism instead of local realism. Anton Zeilinger's group at the
Institute for Quantum Optics and Quantum Information (IQOQI) in Vienna performed a
definitive test of the Leggett Inequalities (Reference 11). The results show that using
elliptically polarized entangled photons, the Leggett Inequalities in two observables are
violated by 3.6 and by 9 standard deviations. This is interpreted as a statistically
significant falsification of the whole class of nonlocal realistic theories constructed by
Leggett. The IQOQI group summarizes its results with the statement "We believe that
our results lend strong support to the view that any future extension of quantum theory
that is in agreement with experiments must abandon certain features of realistic
descriptions."
It is our view, however, that this is mainly an exercise in demolishing a "strawman."
Leggett's nonlocal realistic theories assume that when entangled photons emerge from
their emission source, they are in a definite state of polarization. It is well known that
when that assumption (and no others) is made, one does not observe the quantum
mechanical prediction of Malus's Law for the correlations of the photon pair.
However, Leggett solves that problem by assuming an unspecified nonlocal connection
mechanism between the detection systems that fixes the discrepancy. In effect, the two
measurements talk to each other nonlocally in such a way that the detected linea rly
polarized photons obey Malus's Law and produce the same linear polarization
correlations predicted by quantum mechanics calculations. Leggett then shows that this
nonlocal "fix" cannot be extended into the realm of elliptical polarization, and that
quantum mechanics and this type of nonlocal realistic theories give differing predictions
for the elliptic polarization correlations. In other words, the "reality" that is being tested
is whether the photon source is initially emitting the entangled photons in a definite
state of polarization. It is this version of "reality" that has been falsified by the IQOQI
measurements.
It is our view that this assumption, clearly inconsistent with the formalism of quantum
mechanics, is invalid, and that nature is both nonlocal and unrealistic, if by realism one
means that when entangled photons emerge from their emission source, they are in a
definite state of polarization. This very restricted definition of realism is not required,
and it is assumed that the intrinsic nonlocality of standard quantum mechanics is a
physical fact.
It is noted that the several polarization bases used in t hese ki nds of polarization EPR
experiments make demonstrating the quantum nonlocal connections straightforward
but also make it effectively impossible to use those connections for observer-to-
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observer signaling (Reference 12), because one would need to deduce from the arriving
photons the polarization basis that was being used in the distant measurements. This is
an aspect of the parameter independence mentioned above. While each observer is free
to choose a parameter that specifies the polarization basis (for example, circular
right/left, linear at any angle) for the measurement, he is not free to force the photon
into a particular state of that basis, as would be required for nonlocal communication.
However, measuring polarization correlations in a system with angular momentum
constraints is not the only way to demonstrate the nonlocal connection between the
entangled separated parts of a quantum system. Below, EPR experiments that use
momentum entanglement are discussed, and the question of whether such quantum
systems might provide a better vehicle for observer-to-observer nonlocal
communication is explored, because by using momentum entanglement, an observer is
able to force the photon into particle-like or wave-like behavior.
II. The Quantum No-Signal Theorems
As Einstein implied with his well-known "spooky actions at a distance" comment,
enforcement of quantum correlations across spacelike and negative timelike intervals
by nonlocality is very counterintuitive. It appears to imply the twin possibilities of
superluminal commun ication and of reverse causation through back-in-time
communication between observers. However, a number of authors (Reference 13) have
presented "proofs" that such nonlocal observer-to-observer communication is
impossible within the formalism of standard quantum mechanics. These theorems
assert that in separated measurements involving entangled quantum systems, the
quantum correlations will be preserved, but there will be no effect apparent to an
observer in one sub-system if the character of the measurement is changed in the
other sub-system . Thus, it is asserted, nonlocal signaling is impossible.
As mentioned above, EPR experiments can be viewed (Reference 5, 6) as
demonstrating violations of outcome independence or parameter independence or both.
Outcome independence cannot be used for nonlocal signaling, while parameter
independence can. Thus, any test of nonlocal signaling is, in effect, a test of the
parameter independence of quantum phenomena, and the no-signal theorems are
"proofs" of parameter independence.
Do these no-signal "proofs" really have the status of mathematical theorems? Perhaps
not. Recently it has been pointed out (Reference 14) that at least some of these
"proofs" ruling out nonlocal signaling are tautological, assuming that the measurement
process and its associated Hamiltonian are local, thereby building the final conclusion of
no signaling into their starting assumptions. Standard quantum mechanical Bose
Einstein symmetrization in systems of bosons has been raised as a counter-example,
shown to be inconsistent with the initial assumptions of some of these "proofs."
Therefore, at least from some perspectives, the possibility of nonlocal communication in
the context of standard quantum mechanics remains open and appropriate for
experimental testing.
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III. Nonlocality Versus Special Relativity?
If nonlocal communication is possible, would it be in conflict with special relativity, with
its well-known prohibition against faster-than-light signals? The answer is no.
The prohibition of signals with superluminal speeds by Einstein's theory of special
relativity is related to the fact that the definite simultaneity of two separated space
time points is not Lorentz invariant. Since some hypothetical superluminal signal could
be used to establish a fixed simultaneity relation between two such points-for
example, by clock synchronization-this would imply a preferred inertial frame and
would be inconsistent with Lorentz invariance and special relativity. In other words, it
would be inconsistent with the even-handed treatment of all inertial reference frames in
special relativity.
However, if a nonlocal signal could be transmitted through measurements at separated
locations performed on two entangled photons, the signal would be "sent" at the time
of the arrival of the photon in one location and "received" at the time of arrival of the
other photon. By varying path lengths to the two locations, these events could be made
to occur in any order and time separation in any reference frame. Therefore, nonlocal
signals (even superluminal and retrocausal ones) could not be used to establish a fixed
simultaneity relation between two separated space-time points, because the sending
and receiving of such signals do not have fixed time relations. The transmission and
arrival instants of a nonlocal signal cannot be used for synchronization because the
transmission and reception instants are path- and delay-dependent variables.
To put it another way, the nonlocal connections of entangled photons lie along
segmented lightlike world lines that transform properly under Lorentz transformations.
Therefore, there is no conflict between nonlocal signaling and the Lorentz invariance of
special re lativity. On the other hand, the principle of causality (cause must precede
effect in all reference frames) appears very likely to be violated (or at least violate
able) if nonlocal signaling is possible.
Is it possible that the universe does have some preferred reference frame, perhaps that
laid down by the cosmic microwave background or implied by Mach's Principle?
Perhaps, but if such a preferred frame existed, its existence could not be established by
nonlocal communication.
IV. Momentum Domain Entanglement and EPR
Experiments
Einstein's original objection (Reference 4) that quantum mechanics appeared to be
nonlocal was made with arguments based on a gedankenexperiment in the momentum
domain. However, almost all of the modern EPR experiments testing the Bell Inequality
and demonstrating quantum nonlocality have been performed in the polarization (that
is, angular momentum) domain, usually with linearly polarized photons. Interestingly, it
appears that if nonlocal quantum communication is possible at all, it may be more
easily achieved in the momentum domain of Einstein's original focus.
The optical process of spontaneous parametric down-conversion (Reference 15) turns
out to be a very useful way of generating photon pairs entangled in either the
polarization or the momentum domains. In this process, a photon from a "pump laser"
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interacts with a nonlinear crystal and is transformed into two photons with energies and
vector momenta that add up to those of the original pump photon. Depending on the
type of down-conversion process, there are well-defined polarization correlations
between the entangled photons. The down-converted photons may also be easily
prepared in momentum -entangled states, because within the nonlinear medium, the
vector momenta of the down-converted pair of photons must add to give that of the
pump photon.
The first measurement using
momentum-entangled down-conversion
photons that might be related to 35 1 nm
nonlocal communication is the Ghost
Interference experiment reported in
1995 by the Shih group (Reference 16), Ar Laser
shown schematically in Figure 2. The
experimenters used degenerate
collinear Type-II down-conversion of
351-nm UV pump radiation from an BS
argon-ion laser passed through a 3-
mm-long BBO (f3-BaB2Q4) crystal that
f1
had been cut with the optic axis at a
0 Slits
phase-matching angle of 42.2° to the
pump beam to produce a pair of
collinear momentum-entangled 702-nm
photons with opposite polarizations. The
entangled photons emerge from the
crystal very nearly parallel with the fiber Gating
pump beam. The pump beam is then
split off from the pair using refraction in
a quartz prism (UV Prism), and the
entangled photons are separated with a Gated
polarization-selecting beam splitter (BS)
that reflects the "extraordinary"
vertically polarized photon (e) and Figure 2. Schematic of the 1995 Ghost Interference
transmits the "ordinary" horizontally Experiment (Reference 16) of the Shih group
polarized photon (o) . Both photons are
passed through 702 ± 10-nm wavelength-selective filters (f1,2) and then detected
(D1,2).
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The experimenters demonstrated that 300
passing the vertically polarized photon (a) Two slits
(e) through a double- or single-slit 250
system before detection at D1 produced "'
C:
::, 200
0
a "comb" interference distribut ion or a 0
Ql
150
"bump" diffraction distribution, (.)
C:
Ql
respectively, in the position X2 of the 'C
·.:; 100
C:
horizontally po larized photon (o) ·5
0 so
detected at D2 when the pair of photons
is examined in coincidence. I n other 0 L _ _ , = . . J . - - - - ' - - ~ _ _ J _ ~ - - - - - ' - - - ~ - ' - - ~ . . . , _ _ ~~ '---'
·8 ·6 ·4 ·2 0 2 4
words, the position distribution of the
De tec tor 2 position (mm)
straight-through photon shows patterns
characteristic of the single- or double
slit system through which its tw in
500
(b) One slit
entangled photon passed. Figure 3 "' 400
C:
shows the observed position ::,
0
0
distributions for the two cases . a,
0
300
C:
Ql
From the viewpoint of nonlocal ~ 200
C:
commun ication, we note that modifying ·o
0
the slit system before D1 through which 100
the reflected photon passes, wh ich can
be thought of as the action of a ·8 ·4 ·2 0 2 4
"sending" observer, nonlocally causes Detector 2 position (mm)
an observable change in the Xrposition
distribution of the undeflected photon, Figure 3. Ghost Interference Position Distributions
at x,
as detected by a " receiving" observer at
D2. This is a nonclassical effect t hat demonstrates the nonlocal connection between the
entangled pa ir and that might form the basis for transmission of a nonlocal signal
between the two observers. However, the Ghost I nterference experiment does not, in
the form reported, demonstrate nonlocal commun ication, because of its use of a
classical communication link in imposing the coincidence requirement between the
detected photons.
In t heir paper, the authors comment that with the two-slit system in place, in t he
absence of coi ncidences there is no observable two-slit interference pattern
distributions at either D1 or D2. They attribute this lack of an interference "signal" to the
horizontal variation in the creation position of the down-converted photons . The
variation is enough to cause the "e" photons to arrive at the two slits with relative path
lengths that may differ by more than a wavelength, t hereby randomly shifting and
wash ing out any interference pattern. Furthermore, their source of entangled photons
was very inefficient and noisy. Only about 1 in 10 10 pump photons produced an
entangled pa ir, while many unentang led "noise" photons of the same wavelength were
created by fluorescence in the crystal. Therefore, even if the coincidence requirement
had been in principle removable (see below), it is not surprising that coincidences were
required to observe the reported effects .
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a)
Pump
Figure 4. "Unfolding" the Ghost Interference Experiment
The authors point out that there is a simple way of thinking about momentum
entanglement measurements involving entangled photons. It can be shown from Snell's
Law and conservation of momentum in the crystal that if one photon has a small
momentum that causes it to be slightly deflected to the right of the pump beam by an
angle 0, then the twin entangled photon will be deflected to the left by the same angle
0, a situation reminiscent of reflection from a mirror. This allows the experiment to be
"unfolded" by replacing the effective reflection by a straight-through path, as shown in
Figure 4. The point of the unfolding is that the entangled photons behave exactly as
would be the case if the direction of the deflected photon was reversed, so that it
originated at the detection point D1, passed through one or two slits at C and D, and
produced a one or two slit interference pattern at X2 detected by D2.
Why is the coincidence needed? First, it should be clear from Figure 2 that detector D2
detects not only the entangled twins of the photons that pass through the slit openings,
but also the entangled twins of the much larger number of photons that are stopped by
the opaque parts of the slits. Therefore, without coincidences, no interference pattern
could possibly be observed at X2, Moreover, one can see from Figure 4b that detector D1
behind the slits receives light in a very localized region, and if it were moved vertically
in the diagram, the interference pattern at D2 would be shifted, with maxima becoming
minima and vice versa. Without coincidences requiring a particular location for the
detection at D1, the D2 distribution would have to average over all possible D1 positions,
washing out the two-slit interference pattern. Therefore, because of the geometry used,
the Ghost Interference experiment required a coincidence to observe a two-slit
interference pattern like the one shown in Figure 3a.
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Another momentum-entangled EPR experiment was the 1998 Ph.D. thesis of Birgit
Dopfer (Reference 17) performed at the University of Innsbruck and shown
schematically in Figure 5. In the Dopfer experiment, moving a detector in one arm
non locally changes the observed interference pattern in the other arm. Dopfer used
351 - nm UV pump radiation from an argon -ion laser with Type I down-conversion in a
nonlinear Lil03 crystal cut with the optic axis at 90° to the pump beam to produce a
pair of 702-nm momentum-entangled photons that emerged from the crystal at angles
of 28.2° to the right and left of the pump axis, as shown in Figure 5.
.. . . . . . . . . .. .. . . . . . . . . . .2f
. . . .. . . .. . . .. . . . ~ . . .. .. . .2f
.. . . . .. . . . . . .... .. ~ ........ . .
♦ - .. . ... . ........ .
702.2 nm
f
Coincidence
Figure 5. Schematic of the 1998 Dopfer Experiment (Reference 17)
The lower entangled photon passed through a pair of slits and into a detector, while the
upper photon passed through a lens that could image the two slits to perform a "which
way" measurement if detector D2 was placed two focal lengths behind the lens (2f).
However, if detector D2 was placed in a position one focal length behind the lens (f), the
sl its were not imaged, and light on the reflected line passing through either slit could
reach the detector at the same points, producing a result similar to that of the Ghost
Interference experiment. A structured two-sl it interference pattern could be switched on
and off by moving a detector in the other arm of the experiment between the f and 2f
positions.
Again, from the viewpoint of nonlocal communication, it is noted that moving detector
D2, which can be thought of as the action of a "sending" observer, nonlocally causes an
observable change in the position distribution of the second photon, as detected at
"receiver" position D1. However, the Dopfer experiment does not demonstrate nonlocal
communication because, like the Ghost Interference experiment, it requires a classical
communication link to impose the coincidence requirement between the detected
photons because of the geometry of the experiment.
Exam ination of these two experiments raises a very interesting question: Can the
coincidence requirement be removed? The answer is not clear. In principle, the two
entangled photons are connected by nonlocality whether they are detected in
coincidence or not. The coincidence should therefore be removable. However, in both
experiments the authors report that no two- slit interference distribution is observed
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when the coincidence requirement is relaxed. This may be explain ed by the action of
coherence-entanglement complementarity, as discussed in the next section.
V. Coherence-Entanglement Complementarity
As discussed above, the finite extent of the source is expected to limit the possibility of
observing a two-slit interference pattern, which would be the "signal" if nonlocal
commun ication were possible. Figure 6 shows schematically (not to scale) this "thick
source" effect. The source volume on the left is the region of the nonlinear crystal that
is illuminated by the UV pump-laser beam directed along the u axis. The source volume
is a cylinder a few mm thick and a mm or so in radius with a center point C. The source
cylinder is assumed to be tilted at an angle 0 with respect to the horizontal z axis on
which the slit system and detector plane are symmetrically centered. We note that 0 =
0° in the Ghost Interference experiment and 0 = 28.2° in the Dopfer experiment. A
horizontal distance Lxs away from the source is a two-slit system, a pair of apertures a
with center-to-center separation d. Light passing through the slit system travels a
horizontal distance Lsd and is detected at detector plane at position x,.
Slit Detector
B Source System Plane
Volume
Figure 6. Thick-Source Effect (not to scale): Waves arriving at the two slits from points A and B at the
extrema of the source volume may have sig nificant path length and phase differences, while waves from the
central point C are in phase at the slits.
If the point of photon production is off the z axis, there will be a path length difference
between waves relative to C as they arrive at the two slits . In Figure 6, waves from
points A and B could have path length differences greater that half a wavelength and
phase differences greater than 180°. Roughly speaking, this shifts the interference
pattern relative to waves created at central point C so that maxima become minima
and vice versa. The net effect of averaging over all points in the source volume would
therefore be to wash out the two-slit interference pattern. That two-slit interference
pattern must be observed unambiguously, because it is the "signal" that would be used
in any nonlocal communication. This operability is quantified by an observable called
"visibility," which is related to the peak-to-valley ratio of the interference pattern.
The constancy of the relative phase at the two slits for photons arriving from various
parts of the source is called "coherence" and ensures a high visibility. It should be clear
that a point-like source has perfect coherence, wh ile a source with a large solid angle as
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viewed from the slits will have reduced coherence. The path length difference at the
slits is, to a good approximation, inversely proportional to Lxs, Therefore, making Lxs
large-that is, placing the slits some distance from the source volume-can reduce the
path length differences to a value that increases coherence and allows observation of a
sharp two-slit interference pattern signal at detector D1. Alternatively, placing a thin,
double-concave diverging lens at point P of Figure 6 can have the same effect by
causing the shorter path lengths to pass through a greater thickness of lens glass. Such
a lens would also demagnify the source, producing the equivalent of a longer path
length and smaller source solid angle.
However, increasing source coherence has another consequence. The momentum
entanglement of photons from the source arises from momentum conservation.
Restricting the solid angle of the source, as viewed from the slits, means fewer photon
pairs can be entangled and still satisfy the geometrical constraints of the experimental
configuration. The Saleh group at Boston University has shown that there is a
complementary relation between source coherence and two-photon entanglement
(Reference 18). As the source-slit distance Lxs is increased, there are smooth transitions
from one-slit to two-slit interference patterns and from a highly entangled source to a
highly coherent source. We note, as mentioned above, that the parametric down
conversion technology used in the Ghost Interference and Dopfer experiments was
fairly inefficient and noisy, with fairly improbable production of entangled pairs
competing with much more probable production of unentangled "noise" photons of the
same wavelength from pumped fluorescence in the crystal. This would tend to limit the
entanglement of the source.
Nonlocal communication using momentum entanglement requires source coherence.
Source coherence is needed in order to observe the "signal" of a two-slit interference
pattern and two-photon entanglement so that a measurement of one of the photons
"connects" with the interference pattern produced by the other photon. Where there is
coherence without entanglement or entanglement without coherence, nonlocal
communication with momentum-entangled photons is not possible. An unresolved issue
that requires further theoretical consideration and experimental testing is whether there
is a "sweet spot" in the experimental design that embraces both partial coherence and
partial entanglement and that permits the transmission of nonlocal signals.
VI. Nonlocal Communication Versus Signaling
The possibility of nonlocal communication is an unresolved issue. It is perhaps likely
that the coherence-versus-entanglement tradeoff is nature's way of preventing nonlocal
signaling, but that has not been demonstrated. In this section, we assume that nonlocal
signaling is possible and will examine its implications. As will be seen, they are so far
reaching that they could be taken as a strong indication that nature would not allow
such things and therefore nonlocal signaling must be impossible.
Figure 7 shows a variation of the Ghost Interference experiment (Reference 16) in
which the slit-imaging technique of the Dopfer experiment (Reference 17) is used to
ensure that entangled photon pairs passing through slits reach both detectors, and that
those intercepted by the opaque regions of the slits reach neither detector. In
particular, a lens of focal length f is placed in the path alter the BBO crystal and before
the polarization splitter so that both entangled photons pass through this lens. A pair of
slits S1 is placed at a path distance f beyond the lens in the path of the "o" photons,
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which are linearly polarized horizontally (HLP) and are transmitted by the splitter. As
Dopfer has shown, because of momentum entanglement, an image of slit system S1 will
be formed by the "e" photons linearly polarized vertically (VLP) at a path length f
beyond the lens on the deflected path at position S2 1 where a pair of "cleanup" slits are
located that pass only those photons whose entangled twins passed through S1. We
note that because of the optical geometry, this imaging occurs even for waves that
pass through both of the image points and ultimately interfere.
BBO
VLP
Double Convex Lens - 351 nm
Focal Length = f c::::= :t:::=::::>--.---
IR Pass
Filter )>
VLP -,
702nm (0
D
0
::J
Image Slits 0
IR Pass f ::J
Path to Lens= f Filter
r
Q)
Cl)
HLP (1)
702nm -,
Object Slits
Path to Lens = f s1
Camera
"O" u 1 11
Figure 7. Slit-Imaging Coincidence-Free Version of the Ghost Interference Experiment to Demonstrate
Nonlocal Communication
At the image position of each slit at S2, we place an optical fiber, as shown. The fibers
conduct the light to an optical switch, at which the light either is sent directly to two
avalanche photodiode detectors D (providing which-way information about which of the
S1 slits the photon entered) or alternatively is routed to an optical combiner C, with the
in-phase output of the combiner then detected, so that waves passing through both
slits can contribute constructively to the detection event. We note that this fiber
switching system is the fiber-optic equivalent of a Mach-Zehnder interferometer
(Reference 20), in which one can activate and deactivate the last half-silvered mirror by
switching, so that which-way information can be switched on and off. (We also note
that similar fiber-combiner-detector technology could be employed after the S1 slits to
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determine the presence or absence of coherent interference, but this will not be
considered further here.)
A quantum sensitive cooled CCD camera is substituted for detector D1 of the Ghost
Interference experiment (Reference 11) and is set to measure distributions like those
shown in Figure 3. In the arrangement in Figure 7, switching the optical fiber routing
can be considered an act of transmitting a binary O or 1 signal. If the switch is in the
position leading to the outer detectors, then which-way information is available, and the
pattern detected by the camera should be a single-slit diffraction pattern labeled "l" in
Figure 7. If the switch is in the position leading to the combiner and middle detector,
waves from both slits contribute to the detection, no which-way information is
available, and the pattern detected by the camera should be the two-slit interference
pattern labeled "0" in Figure 7.
If the pattern observed by the camera can indeed be changed by switching the optical
fiber routing, then this would constitute a direct demonstration on nonlocal
communication. Such an observation would falsify the no-signal theorems mentioned
above, which require that in a noncoincidence scenario, no action on one entangled
photon can produce a "signal-capable" observable result at the detection of the other
entangled photon of the pair.
It should be emphasized that demonstrating nonlocal communication with momentum
entangled photons, as described above, is not the same as actually sending a signal. It
should be clear that no rea l signal can be communicated with a single photon pair. Only
when multiple photons are detected can the underlying distribution function become
apparent. One can estimate that if the distribution functions to be distinguished are a
"pure" two-slit interference pattern modulated by a diffraction envelope and a "pure"
two-slit diffraction pattern, then about 10 photon detections would be required for a 3cr
decision between these two possibilities.
However, as mentioned in the previous section, it is likely that if nonlocal
communication is possible at all, it would have to be accomplished in a situation where
some compromise between entanglement and coherence has been achieved, and such
a compromise would inevitably cause the two patterns to be distinguished to be more
similar and more difficult to separate. Therefore, the 10 photon detections cited above
must be taken as a rather optimistic lower limit, and it is likely that a significantly larger
number of detections (perhaps ~100 or more) would be required. The time required to
send a single bit of information would then be the product of the photon detection rate
in the two arms of the experiment times the number of photons that must be detected
to receive the signal. In principle, such a transmission rate might be improved (and
fluorescence noise suppressed) by pulsing the pump laser, so that "clusters" of
entangled photons would be received with each such pulse.
VII. A Transactional Analysis of the Nonlocal
Communication Test
Now the transactional interpretation of quantum mechanics (Reference 19) to analyze
the system described above is used. The transactional interpretation describes the
formation of a quantum event as a three-stage process: (1) sending retarded "offer"
waves ('!') from emission location(s), (2) back-in-time responses from the reception
location(s) of advanced "confirmation" waves('!'*), and (3) the formation of a space-
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time standing wave (w•) between the locations (for example, a photon source and a
photon detector). After an initial exchange of offer and confirmation waves, a particular
transaction is selected probabilistically from all that are possible, based on the \Jf\/1*
values of the alternatives. The offer/confirmation exchange continues until all the
conserved quantities (energy, momentum, angular momentum, and so forth) have
been transferred.
For the nonlocal communication test system described above, we will consider two
cases:
• Case 1: The switch is positioned so that each fiber from the slits is routed to one
detector, producing a "which-way" measurement of the slit through which the VLP
photon passed. In this case, the HLP photon as detected by the camera should have
a recorded position that falls on a broad single-slit-diffraction-pattern distribution,
(not a two-slit interference pattern).
• Case 2: The switch is positioned so that light from the two fibers is combined before
detection. Therefore, the detection produces no information on the path of VLP
photon, which could have passed through either slit. In this case, the HLP photon
detected by the camera should be in a position that falls on a two-slit interference
pattern distribution.
Figure 8 shows the transaction that forms for the nonlocal communication test system
in the Case 1 configuration. Here, as in the Ghost Interference experiment, we have
treated the nonlinear crystal source of entangled pairs as an effective "reflector" and
have represented the rays with straight-through paths to "unfold" the system,
duplicating the lens for each photon and representing the system as two-lens optical
imaging, with nearly parallel rays between the two lenses. Slit systems S1 and S2 are
located one focal length f away from the lenses. The left-going photon is assumed to
arrive at the upper slit of S2 and to be detected by the upper detector (circled). The
momentum-entangled right-going photon must then go to S1, which is the optical
image of S2, and be diffracted by the slit and detected by the camera. If Figure 8 were
vertically inverted, it would provide a similar diagram for the equally probable arrival of
the left-going photon at the lower slit of S2 and detection by the lower detector. The
three stages of transaction formation are shown.
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-
RI
G)
E
RI
u
Offer Waves
-
RI
G)
E
RI
u
G;impleted Transaction
Figure 8. Transactional Interpretation Diagrams for Case 1. The left-going offer waves pass through the
upper slit of 52 and reach the upper detector (circled) . The momentum-entangled right-going offer waves pass only
through the lower slit of 51, which is the optical image of upper 52 , and are diffracted to the camera. Confirmation
waves return , and the one-slit transaction forms .
Figure 9 shows t he transaction that forms for the nonlocal communication test system
in the Case 2 configuration. The left-going photon passes through bot h the upper and
lower slits of S2 . The two paths connect to a combiner and are detected by the central
detector (circled). The momentum-entangled right-go ing photon must then also pass
through both slits of S1, which are t he optical images of S2, to form a two-slit
interference pattern detected by the camera . The three stages of transaction formation
are shown.
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...ca
G)
E
ca
u
Offer Waves
Non&r-r
ei,naI
Confirmah.on Waves
Comple12d Transaction
Figure 9. Transactional Interpretation Diagrams for Case 2, The left-going offer waves pass through both
slits of S2, where the waves are combined and detected by the center detector (circled) . The momentum-entangled
right-going offer waves pass through the both slits of S1 , which are the optical images of S2, and interfere at th e
camera. Confirmation waves return, and the two -slit transaction forms .
Therefore, from the point of view of the transactional interpretation of quantum
mechanics (Reference 19), the nonlocal connection between detection events at the two
ends of the experiment arises because the detection transactions for the two entangled
photons must share a "two- way handshake" at the nonlinear crystal, a condition that
can be realized only when the summed vector momenta of the two photons equals that
of the pump-laser photon that created them. This view explains Dopfer's observations
(Reference 19) and indicates that, in the absence of overwhelming noise or restrictions
imposed by coherence/entanglement complementarity, no coincidence should be
required between the two detectors in the experiment to observe that change in the
pattern observed at D1 when detector D2 is moved. This remains true in the
configurations discussed below, when slit S2 is lengthened with many kilometers of
fiber-optic light transmission cable to enable superluminal and retrocausa l signal
transmission. In other words, analysis of the nonlocal communication test system with
the transactional interpretation reveals no "show-stopper" aspects that would prevent
superluminal and retro-causa l signal transmission. The transactional interpretation is
neutral on whether such signals are possible.
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VIII. Superluminal and Retrocausal Nonlocal
Communication
As mentioned in the previous section, we will assume for the sake of discussion that
nonlocal signaling is possible and will consider its implications for the speed of
transmission of signals. For definiteness, schemes for doing this are based on the slit
imaging coincidence-free version of the Ghost Interference experiment described above
and shown in Figure 7. In that system, the instant at which a nonlocal signal is sent is
the arrival of the VLP photon at the fiber-optic system on the left, and the instant at
which the signal is received is the arrival of the HLP photon at the camera at the
bottom of the diagram. Assuming the workability of this scheme, both the instants of
sending and of receiving can be delayed, in principle, by the introduction of delay
paths-for example, runs of fiber-optic cables-in the system.
In particular, the "send" instant could be made to occur well after the "receive" instant
in the system, constituting a direct demonstration of retrocausal signaling. This is
shown in Figure 10. Here the cleanup two-slit system S2 becomes the entrance for two
10-km-long runs of fiber-optics that are carefully matched to have identical exit phases
at SJ, the end of the fiber runs where the light enters the optical switching arrangement
described above. If the index of refraction of the fiber is 1.5, light transiting the 10-km
path requires about 50 µs. In the presence of detection noise or the degradation of
pattern visibility because of compromises between entanglement and coherence,
considerably more photon detection events-say 100-might be required.
BBO
VLP
JSI nm
10km
Image Slits IR Pass
Apertures Path lo Lens = f Filler
10km
HIJ>
702 nm
0!¥ctSlits
Path to Lens= f S1
Camera
u1 n
[/SJ
Figure 10. Slit-Imaging Coincidence-Free Version of the Ghost Interference Experiment Demonstrating
Superluminal and Retrocausal Signaling
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Assume then that the fiber coils of Figure 10 remain rolled up and stored in a corner of
the laboratory and that the source can be made strong enough so that the average rate
at wh ich the entangled photon pairs are detected is 10 MHz (which would correspond to
the efficient detection of about 3 nW of 702-nm photons) . This would require a source
of entangled photons considerably stronger than is achievable with the "bulk" BBO or
Lil03 crystals used in the Ghost Interference and Dopfer experiments, which produce a
usable entangled photon pair from only about 1 in 10 10 pump photons.
Fortunately, a recently emerging technology makes the production of entangled photon
pairs much more efficient through the use of "periodically poled" nonlinear crystals. In
"bulk" nonlinear crystal there is a "walk-out" phenomenon that limits the distance
within the crystal over which phase matching holds, permitting entangled pairs to be
produced efficiently by down-conversion. However, nonlinear crystals like potassium
titanyl phosphate (KTiOPQ4 or KTP) have very large nonlinear coefficients and are also
ferroelectric, with a large electric dipole moment. By using a large pulsed electric field
during crystal production, one can "write" on KTP crystals to change the orientation of
their local dipole moment over small distances (a few tens of wavelengths) periodically
along the pump direction through the crystal, so that the phase drift regularly reverses
and cancels out as the pump rad iation progresses through the crystal. This is called
"periodic poling." With this kind of crystal, the walk-out is suppressed, and one can use
very long crystals that efficiently produce entangled pairs of photons over their entire
length. The IQOQI group of Anton Zeilinger in Vienna, using a periodically polled KTP
crystal 25-mm long, has measured the entangled pair production rate at 2. 73 x 10 5
pairs per second per mW of pump radiation per nm of wavelength 20 . Such a source
should be easily able to produce the 10-MHz detection rate assumed above.
Now consider that the "sending" detector system and the "receiving" camera are in the
same room and separated by a distance of 1 meter or less. If the switch is set on the 0
or 1 position, the " message" that it is in that position begins to arrive at the camera 50
µs before the switch position is moved. If 100 photon counts constitute a signal, then,
even allowing for the latency in signal reception, the message could be received 40 µs
before it was sent. This would be a direct demonstration of retrocausal signaling using
nonlocal communication and would constitute a direct violation of the principle of
causality.
IX. Paradoxes and Nonlocal Communication
The setup described above, with its retrocausal communication link, raises some time
communication paradoxes. First, let us consider the issue of "bilking." Suppose we
construct a million linked systems of the type shown in Figure 10 (or use 10 7 km of
nonattenuating fiber). Then the transmitted message would be received 40 seconds
before it was sent. Now suppose a tricky observer receives a message from himself 40
seconds in the future and then decides not to send it. This produces an inconsistent
timelike loop, which has come to be known as a "bilking paradox." Could this happen?
If not, what would prevent it?
There are discussions of such bilking paradoxes in the physics literature by Wheeler and
Feynman (Reference 22), who were considering the retrocausal aspects of the advanced
waves of absorber theory, and by Kip Thorne and colleagues (Reference 23), who were
considering the paradoxes that might arise from timelike wormholes. The general
consensus of both groups is that nature will forbid it and will require a consistent set of
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conditions. Thorne and coworkers showed that "nearby" to any inconsistent paradoxical
situation involving timelike wormholes there is always a self-consistent situation that
does not involve a paradox. As Sherlock Holmes sa id, "When the impossible is
elim inated, whatever remains, however improbable, must be the truth." These
speculations assert that equipment failure producing a consistent sequence of events is
more likely than producing an inconsistency between the send and receive events. The
implications of this are that bilking itself is impossible, but very improbable events
could perhaps be produced in avoiding it.
The other issue raised by retrocausal signaling might be called the "immaculate
conception" paradox. Suppose you are using the setup described above, and you
receive from yourself in the future the manuscript of a best-selling novel with your
name listed as the author. You sell it to a publisher and become rich and famous. And
when the time subsequently comes for transmission, you duly send the manuscript
back to yourself, thereby closing the timelike loop and producing a completely
consistent set of events. But the question is, Just who wrote the novel? Clearly, you did
not; you merely passed it along to yourself. Yet highly structured information (the
novel) has been created out of nothing. And in this case, nature should not object,
because there was no bilking, and you produced no inconsistent t imelike loops.
It is not known how to resolve either of these paradoxes. Here are a few possibilities:
• If nonlocal signaling is impossible, then the paradoxes need no resolution, but better,
more "air-tight" proofs of the impossibility of nonlocal signaling would be needed.
• If nonlocal signaling is possible and can be used to form timelike loops, then
paradoxes become important subjects for further experimental testing, study, and
theoretical treatment.
• As suggested by Stephen Hawking (Reference 24 ), perhaps nature "abhors" timelike
loops, so that if one is about to be created, quantum vacuum fluctuations will grow
without limit and destroy the apparatus that is attempting to produce the loop. Even
in this case, use of nonlocal signaling might still be possible, provided timelike loops
were carefully avoided in such systems. (See below.)
X. Superluminal Communication Without Paradoxes
One path to avoid the retrocausal paradoxes outlined above would be to make sure
there were no timelike loops in the communication system. This can be achieved by
careful arrangement of the propagation delays in the sending and receiving ends of the
hypothetical nonlocal commun ication.
Consider the space-time interval 5, as defined by the equation: 5 2 = x 2 - (ct)2, where
x is the spatial distance separating two events (for example, send and receive), t is
their separation in time, and c is the speed of light. A positive value of 5 2 means the
interval is spacelike and s=O is a lightlike interval, and a negative value of s2 means
the interval is timelike. The interval s is a Lorentz-invariant quantity that, in particular,
retains its sign independent of the choice of inertial reference frame from which the two
events are viewed.
As long as the nonlocal communication system is arranged so that the space-time
interval between the sender and the receiver is always separated by a spacelike or
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lightlike interval, and in particular is never separated by a timelike interval that can go
backwards down the t ime stream, then t imelike loops are avoided, along with the
paradoxes they imply.
Figure 11 shows such a system. Entangled photons in the two arms of the system are
propagated through fiber-optic cables of equal length. Therefore, in the reference frame
of the system, the send and receive events are simultaneous, and, aside from the
latency associated with the reception of enough photons to establish the reception of a
signal bit, the communication is instantaneous but does not create a timelike loop.
BBO
VLP
351 n>tt
IR Pass
Filur
I
I
litt.age Slits IR Pass
Path to Le..,. - f 1km
Filter
1km
Object Slits
Pa:th to Le:ns - f
Camera
Figure 11. A Superluminal Nonlocal Communication System in Which the Communication Spans a
Spacelike Interval
XI. Example: Real-Time Earth Control of Mars Rover
Now consider the application of a " rover" operated at interplanetary distances, with
nonlocal communications used to provide rea l-time "virtual reality" control of the mobile
device . Figure 12 shows a schematic of the Earth-based operation of a Mars rover. A
base station on Mars wou ld contain a high-intensity source of entang led photon pairs.
One stream of photons from the entangled pairs, after passing through image slits,
would be transmitted from the probe to an Earth control station, allowing a nonlocal
signal to be "sent" from the control station by a time sequence of choices of whether to
detect the stream of arriving photons as waves or particles . The other stream of
photons from the entangled pairs, after passing through object slits, would be detected
locally at the Mars base station near the source and analyzed for the presence or
absence of an interference pattern, thereby "receiving" the nonlocal signal as a logical
"0" or "1," respectively.
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Figure 12. Schematic of Earth-to-Mars Real-Time Control of a Rover
In order to avoid having to transmit two streams of entangled photons, the equivalent
of the two fiber-optic links in Figure 10, at the base station the photons from one image
slit would be polarized horizontally and those the other slit would be polarized vertically
before transmission. Then, at the Earth control station, detection of the polarization of
photons in the stream would constitute "particle" measurements, while separating,
rotating to the same polarization state, and recombining the waves so that they could
interfere before detection would constitute a "wave" measurement.
In parallel with this nonlocal link, a conventional microwave or optical link would be
used to communicate video images and other data to the Earth station. The video
images and data would experience a propagation delay equal to the transmission
distance divided by the speed of light, and would arrive at the Earth station seconds,
minutes, or hours aher they were transmitted. The entangled photons would experience
the same delay, but the nonlocal control signal would be sent backwards up the time
stream, arriving at the probe at the instant the video signals and data were being
transmitted, so that the nonlocal signal could steer and control the probe in real time,
and an Earth - based operator could "drive" the rover on Mars using virtual-reality
techniques. One can imagine driving the Mars Rover around the planet, actively
steering around obstacles, activating analysis instruments in real time as interesting
objects were found, and actively controlling repair equipment to deal with problems
that arise.
Such a communication loop (conventional + nonlocal) would be a light-like loop, with
the two-way send and receive points located on the light cone. As such, it would not
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lead to any causality problems or paradoxes but would bring the remote parts of the
solar system and perhaps the universe to the here and now.
XII . Another Superluminal Possibility: Nonlinear Quantum
Mechanics
Thus far, the focus has been on the possibility of nonlocal communication within the
framework of standard quantum mechanics. However, even if nonlocal communication
proves impossible in standard quantum mechanics, there could be another path to
nonlocal communication.
The no-signal theorems described in Part III above are based on the formalism of
standard quantum mechanics. Such "proofs" become invalid if quantum mechanics is
allowed to be slightly "nonlinear," a technical term meaning that when quantum waves
are superimposed, they may generate a small cross-term not present in the standard
formalism. Steven Weinberg, Nobel laureate for his theoretical work in unifying the
electromagnetic and weak interactions, investigated a theory that introduces small,
nonlinear terms to standard quantum mechanics (Reference 25). The onset of nonlinear
behavior is seen in other areas of physics-for example, laser light in certain media
and, he suggested, might also be present but unnoticed in quantum mechanics itself.
Weinberg's nonlinear quantum mechanics subtly alters certain properties of the
standard theory, producing new physical effects that can be detected through precise
measurements.
Two years after Weinberg's nonlinear quantum mechanics theory was published, Joseph
Polchinski published a paper demonstrating that Weinberg's nonlinear corrections upset
the balance in quantum mechanics that prevents superluminal communication using
EPR experiments (Reference 26). Through the new nonlinear effects, separated
measurements on the same quantum system begin to "talk" to each other, and faster
than-light and/or backward-in-time signaling becomes possible. Polchinski describes
such an arrangement as an "EPR telephone."
The Weinberg/Polchinski work had implications that are devastating for the Copenhagen
Interpretation's representation of the wave function as "observer knowledge."
Polchinski has shown that a tiny nonlinear modification transforms the "hidden"
nonlocality of the standard QM formalism into a manifest property that can be used for
nonlocal observer-to-observer communication. This is completely inconsistent with the
Copenhagen Interpretation's "knowledge" interpretation.
Weinberg's experimental predictions have led to a large number of experimental tests
that have searched for the predicted effects. Regrettably, all such experimental
attempts to observe the nonlinear effects have failed, producing only very low upper
limits. Apparently, if there are nonlinear effects that modify the quantum formalism,
they are extremely small in Earth-based laboratories. These negative results are not
surprising, however, because the atomic transitions used involve only a few electron
volts of energy. If quantum mechanics does have nonlinear properties, they would be
expected to depend on mass-energy and to appear only at a very high energy scale,
particularly at the highest energy densities or in very high gravitational fields. In the
everyday world of weak gravity and fairly flat space, this path to nonlocal
communication appears to be blocked, because the "vehicle" for sending the signal is
not observable.
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However, emerging from work on quantum gravity offers the possibility of an explicitly
nonlinear form of quantum mechanics that reduces to linear quantum mechanics in the
limiting case of weak or no gravity. Using the wave picture, it is possible to formulate a
Laplace-Beltrami wave equation for gravitationally curved space. The Laplace-Beltrami
operator on the left-hand side contains information about the space-time geometry (the
metric te nsor) and operates on the wave function. On the right-hand side is the same
term found in the flat space Klein-Gordon wave equation. In flat space (no gravity), this
"curved-space" wave equation reduces to the Klein-Gordon wave equation, but in
curved space it is nonlinear in a way that could facilitate nonlocal communication. Thus,
in an environment where strong space curvature is expected-for example, the vicinity
of a neutron star or black hole-sufficient quantum nonlinearity may exist to facilitate
nonlocal communication .
XIII. Conclusion
Ultimately, the question of whether nonlocal communication is possible is an
experimental one. The issue should be resolvable by testing for nonlocal communication
and observing what experimental lim its appear. In particular, are the limits of
coherence/entanglement complementarity so severe as to preclude signaling? Currently
at least one experiment in progress aims to produce a coincidence-free version of the
Ghost Interference experiment. We await the outcome of such tests.
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Appendix: Glossary
Basis: In quantum mechanics, a choice of an observable quantity that may be
complementary to another variable, so that both cannot be measured at the same time.
An example is the choice of measuring position, which prevents the simultaneous
measurement of momentum. In EPR experiments, one must choose a polarization basis
(for example, linear polarization that may be either vertical or horizontal). Since both
circular polarization and 45° left/right polarization are linear superpositions of
vertical/horizontal polarization, they may not be measured simultaneously. In quantum
mechanics, the measurement causes the wave function to collapse to a particular basis
value, excluding other possible values .
Bell's Theorem: A mathematical proof by John S. Bell (Reference 8) demonstrating
that in a polarization-based EPR experiment, the fal loff of correlations as the basis
angle of a polarization measurement is changed is qualitatively different, as predicted
by local hidden-variable theories and by standard quantum mechanics. In particular,
local hidden-variable theories predict a linear falloff, while quantum mechanics predicts
a quadratic falloff. This difference in predictions is represented as an inequality in
measurement intensity ratios that all local hidden variable theories must satisfy, while
quantum mechanics does not. Tests of these predictions have been found to agree with
quantum mechanics and to falsify local hidden-variable theories.
Bilking Paradox: A type of back-in-time communication paradox in which an
inconsistent causal loop is created. A well-known example is the Grandmother Paradox,
a time-travel scenario from science fiction in which a time traveler travels to the past
and kills his grandmother before she had children. The question then arises, How could
he have been born if his grandmother had no children? Several works in the physics
literature (Reference 17, 18) have concluded that such trans -temporal bilking is
impossible, that nature will not permit inconsistent timelike loops, and that it is more
likely that some apparatus will fa il than that a "bilk" of nature could be achieved .
Causality: The observation, which is regarded as a law of physics, that a cause must
precede its effects as viewed in any and all reference frames. Sometimes referred to as
"Cause and Effect" or "the Law of Cause and Effect."
Correlations: The mathematical connection between two variables or two measured
quantities. As an example, in an EPR measurement, the basis polarization of one
photon is selected, the basis polarization of the twin entangled photon is varied, and
the coincidence counting rate versus varied angle is measured to establish the
correlation between the two polarizations.
Coherence: Describes whether two waves (for example, t hose arriving at a pair of slits
or at a detector) have a definite phase relation (in which case they are completely
coherent), have a random phase relation (in which case they are completely
incoherent), or have someth ing in between.
Coherence-Entanglement Complementarity: The theoretical expectation and
experimental observation (Reference 15) that perfect coherence and perfect
entanglement cannot be achieved for an entangled pair of photons at the same time.
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Coherent Superposition: The formation of a quantum mechanical state (for example,
right circular polarization) by add in g components of other states (for example, le~ and
right polarization) with a definite complex phase between the added states.
Collapse: A quantum mechanical wave function is said to collapse to a particular basis
value when a measurement is made in that basis. For example, if a photon is emitted
isotropically (with equa l probability in all directions), its wave function is distributed
uniformly over a sphere with a radius that grows at the speed of light until it is
detected . Upon detection, the photon's wave function is localized at the detection point
and disappears everywhere else .
Entangled: The separated parts of the same quantum system are said to be entangled
when each of the parts can be described only by referencing the state of other parts .
This is one of the most counterintuitive aspects of quantum mechanics, because,
classica lly, system parts out of "local" contact should be completely independent. Thus,
entanglement represents a kind of quantum " connectedness" in which measurements
on one isolated part of an entang led quantum system have nonclassical consequences
for the outcome of measurements performed on other (possibly very distant) parts of
the same system.
EPR Experiment: A class of experiments with entang led particles, usually photons,
that demonstrate quantum nonlocality. A gedankenexperiment of this kind was first
suggested in the famous 1936 paper by Einstein, Podolsky, and Rosen (Reference 4) in
which a set of criticisms of quantum mechanics were presented.
Hidden Variable Theories: A set of alternatives to quantum mechanics intended to
satisfy the objections of the EPR paper in which the uncertainty principle does not apply
and a quantum system can simultaneously have definite values of complementary
variables like positi on and momentum, provided one of these values is somehow
"hidden." Hidden variable theories are usually also "local" (see below) to deal with
Einstein's objection to the nonlocality of quantum mechanics.
Immaculate Conception Paradox: A type of back-i n-time commun ication paradox in
which a completely consistent causal loop produces information with no known origin.
An example is the Book Paradox, in wh ich an author receives a book in a message from
the future. He publishes it, and when the t ime comes, he transmits the manuscript to
himself in the past. The question then arises, Who wrote the book? In this case, no
inconsistent timelike loops are involved, and the arguments against bilking (see above)
do not apply in this case .
Locality: The assumption that the correlations between parts of a system can be
established only while the subsystems are in contact (or speed-of-light communication),
and that once out of such contact, no changes in such correlations are possible.
Nonlocality: The situation, apparently present in quantum mechanics, in wh ich
correlations between parts of a system can be established independent of the
separation of the parts in time and space.
Retro-Causal: Situations in theory or in the real world where t he effect precedes the
cause, in violation of the principle of causality .
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1 S. J. Freedman and J. F. Clauser, Phys. Rev. Letters, 28, 938-942 (1972) .
2 A. Aspect, J. Dalibard, and G. Roger, Phys . Rev. Letters, 49, 91-95 (1982); A. Aspect, J. Dalibard, and G. Roger,
Phys. Rev. Letters, 49, 1804 (1982).
3 Erwin Schrodinger, Proc. of Cam bridge Philosophical Society, 31, 555- 563 (1935); 32, 446-451 (1936).
4 A. Einstei n, B. Podolsky, and N. Rosen, Physical Review. 47, 777-785 (1935) .
5 Jon P. Jarrett, Nous, 18, 569 (1984) .
6 Abner Shimony, Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds., Chapter 12, pp.
182-203, Clarendon Press, Oxford (1986).
7 C. S. Wu and I. Sha nknov, Phys. Rev ., 77, 136 ( 1950).
8 J.
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