mechanics tells us that pairs of particles may be entangled,
a term coined by Schrödinger, with their wave functions inextricably linked so
that a measurement on either can influence measurement outcomes for the other.
This link persists even if the particles are separated by light-years of
spatial distance. Further, if one of
the entangled particles is made to interact with another particle in a process
called "entanglement swapping", the entanglement may be passed down the line
to particle after particle. Chains
of "quantum repeaters" operating on this principle are now being constructed
Einstein with colleagues Podolsky and Rosen (EPR) first pointed out the
existence and implications of quantum entanglement in 1935.
They regarded this as demonstrating that quantum mechanics was wrong.
In the year that followed, Schrödinger elaborated on the presence of
entanglement in the quantum formalism in great detail.
However, entanglement was largely ignored by the physics community until
the 1970s. Since then, hundreds of
EPR experiments demonstrating many aspects of entanglement have been preformed
in quantum optics laboratories around the world, and entanglement is now
reluctantly accepted by the physics community as a necessary but peculiar
feature of many-body quantum systems.
is perhaps more difficult for many physicists and others to accept, however, is
that the entanglement link may span time
rather than space. As discussed
below, a particle may be entangled with a second particle that did not even exist when the first particle was created, detected,
and disappeared. Here we'll
consider this quantum peculiarity in more detail, starting with a brief review
of quantum entanglement.
are quantum particles entangled at all? Entanglement
comes from two seemingly contradictory elements of the quantum formalism:
conservation laws and uncertainty. Energy,
momentum, and angular momentum, important properties of light and matter, are
conserved in all quantum systems, in the sense that, in the absence of external
forces and torques, their net values must remain constant and unchanged as the
system changes and evolves. On the
other hand, some of these conserved quantities (including energy, momentum, and
angular momentum) may be indefinite and unspecified in the wave functions
describing a system and typically can span a large range of possible values,
as required by Heisenberg's uncertainty
non-specificity of the conserved variables persists until a measurement is made
that "collapses" the wave function and fixes the measured quantities with
specific values. Rather miraculously, when this wave-function collapse does
occur, the conservation laws are satisfied everywhere.
seemingly inconsistent requirements of conservation and uncertainty raise an
important question: how can the wave functions describing the separated members
of a system of particles have arbitrary and unspecified values for the conserved
quantities and yet respect the conservation laws when the wave functions are
conundrum is called the EPR paradox. It
is what Einstein famously labeled as "spooky actions-at-a-distance".
It is present in the multi-particle quantum formalism because the quantum
wave functions of entangled particles, even when describing system parts that
are spatially separated and well out of light-speed contact, continue to depend
on each other and cannot be separately specified as independent mathematical
functions. In particular, the
conserved quantities in the system's parts (even though individually
indefinite) must always add up to the values possessed by the overall quantum
system before it separated into parts. It
is a part of the multi-body quantum formalism, but the mechanism behind it is
not well understood, except by practitioners of the transactional interpretation
the details of entanglement in quantum wave mechanics formalism were spelled out
in great detail by Schrödinger in
1935-36, it took three or four decades, with the 1964-66 theoretical work of
John Stewart Bell and the 1972 experimental work of Stuart Freedman and John
Clauser, before theoretical understanding and experimental physics had
progressed enough for quantum entanglement to make predictions that could be
tested and demonstrated in the laboratory. Freedman
and Clauser's EPR experiment was discussed in some detail in my
AV column "Einstein's Spooks and Bell's Theorem", which appeared in the
Briefly, they demonstrated that when two polarization-entangled
back-to-back photons are detected by linear polarimeters that are misaligned by
an angle θ, the falloff in
photon-coincidence counting rate depends on θ2 rather than θ, a result that, as
significance of the Freedman-Clauser experiment is that, as quantum mechanics
requires, their photons were emitted in indefinite but entangled states, so that
if they were both measured to be in any
selected state of polarization (circular or linear along any transverse axis) ,
their polarization states must always match.
In some sense, the experimental determination in some location that one
photon is in some particular state of polarization somehow reaches across
space-time and forces the other photon at another location to be in the same polarization state. Otherwise,
angular momentum would not be conserved.
photons of the Freedman-Clauser experiment traveled equal distances in opposite
directions to their polarimeters and were detected "in coincidence", i.e.,
simultaneously. But alternatively,
it would have been possible to place a mirror at the end of the right-going
photon's long flight path that would bounce it back in the other direction, so
that it arrived back at the the left-going photon's polarimeter, but arrived
some time later. As we understand Bell's mathematics, this modification would not change the polarization-match
result. Entanglement would still act
between the first and second detections to enforce that both photons were
measured to be in matching polarization states, no matter what was the
polarization-state setting of the detector.
The moral of this thought experiment is that entanglement can span time
as well as space.
Recently, a more elaborate demonstration of trans-time entanglement was
done by Eli Megidish and his colleagues at the Hebrew University of Jerusalem.
They pumped a nonlinear β-BaB2O4
crystal with a pulsed laser having a pulse period of 13.2 nanoseconds to produce
pairs of polarization-entangled photons. They
created an EPR situation in which photon 1 of an entangled pair was detected
with a linear polarimeter and stopped immediately, while photon 2 was sent on a
long 31.6 m flight path, travelling for 105.6 nanoseconds before meeting
entangled photon 3, which had been produced eight pulses later by the nonlinear
crystal. Photons 2 and 3 were mixed
with a beam splitter and detected by linear polarimeters.
Photon 4 of the second entangled pair was then sent on the same flight
path for 105.6 nanoseconds before being detected by a linear polarimeter.
All polarimeters registered whether arriving photons were polarized
horizontally or vertically.
the polarization correlations of all photon pairs, the experimenters
demonstrated that photons 1 and 4 were entangled, even though photon 1 had been
detected and stopped some 105.6 nanoseconds before photon 4 was created and
211.2 nanoseconds before photon 4 was detected and stopped.
The correlated detection events of entangled photons 1 and 4 were well
separated in time but very close in space.
is a demonstration, if one was needed, that photon entanglement can connect
entangled pairs separated in time alone and does not depend on the entangled
particles existing at the same time. If
it was possible to send observer-to-observer messages via entanglement (we
can't, but Nature can), we could manipulate the detection of photon 4 to send
a message back in time by 211.2 nanoseconds to an observer detecting photon 1.
Quantum entanglement across time is an essential part of quantum
could such trans-time entanglement and the preservation of conservation laws
across both space and time in the presence of the uncertainty principle possibly
be arranged by Nature? The
mathematics of quantum mechanics gives us no answers to this central question;
it only insists that the wave functions of parts of an entangled quantum system
do depend on each other, even when separated by large space-time intervals and
out of speed of light contact.
most of the interpretations of quantum mechanics that are widely embraced by the physics
community, in particular the Heisenberg-Bohr Copenhagen interpretation, the
deBroglie-Bohm guide-wave interpretation, and the Everett-Wheeler many-worlds
interpretation, utterly fail to provide any explanation of any underlying
mechanism. In fact, only one of the
many interpretations of quantum mechanics easily explains what is going on in
trans-time entanglement in general and the Megidish
experiment in particular.
is my transactional interpretation of quantum mechanics, first presented
to the physics community in Reviews
of Modern Physics in 1986 and recently spelled out in much greater
detail in my 2016 Springer book, The
- Entanglement, Nonlocality, and Transactions.
The transactional interpretation views the ψ*
wave function complex-conjugates that are present everywhere in the wave
mechanics formalism as time-reverse waves that travel from the future to the
past, providing verifying "handshakes" with the forward going wave functions
and forming "transactions" that implement quantum events, convert waves to
particles, and enforce the conservation laws of physics.
the Megidish experiment described
above, the advance waves that implement the detection of photon 4 travel back in
space and time to the second two-photon emission event from the nonlinear
crystal, where it was created along with photon 3.
The V-shaped transaction representing this two-photon emission with
subsequent detections cannot form unless photons 3 and 4 have correlated
polarizations, so photon 3 is only allowed to form and to be detected with a
polarization properly correlated with that measured for photon 4.
photon 3 is mixed with photon 2 and they are detected together, these photons
become entangled and the polarization restrictions are passed from 3 to 2, which
must be polarization-correlated. The
advanced waves that implement the detection of photon 2 then travel back to the
first two-photon emission event from the nonlinear crystal, where photons 1 and
2 created together. The V-shaped
transaction representing the first two-photon emission with subsequent
detections cannot form unless photons 1 and 2 have correlated polarizations, so
photon 1 is only allowed to form and be detected with a polarization properly
correlated with that of photon 2.
is how the trans-time entanglement connection between photons 1 and 4 is
implemented by Nature. The action of
the back-in-time advanced waves ψ*
and the forward-in-time retarded waves ψ
involved in transaction formation handshake act to enforce angular momentum
conservation and insure that the polarization correlations indicating
entanglement are present.
emphasize that for this case and for many others, as spelled out in my book, the
transactional interpretation is the only game in town.
It is uniquely able to explain all of the many paradoxes and problems of
quantum physics, problems demonstrated by several decades of peculiar and
optics experiments and thousands of pages of debate by physicists and
philosophers of science.
"Experimental Test of Local Hidden-Variable Theories", Stuart J. Freedman and John F. Clauser, Phys. Rev. Letters 28, 938 (1972).
Between Photons that have Never Coexisted",
John Cramer's book on Quantum Mechanics: a non-fiction work describing his Transactional Interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available for purchase online as a printed or eBook at: http://www.springer.com/gp/book/9783319246406 or https://www.amazon.com/dp/3319246402.
SF Novels by John Cramer: my two hard SF novels, Twistor and Einstein's Bridge, are available as eBooks by Book View Cafe and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .
Columns Online: Electronic
reprints of 205 "The Alternate View" columns by John G. Cramer,
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