Quantum 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 in China and the USA to facilitate un-tappable quantum communication links.

Albert 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.

What 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.

Why 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 principle.

This 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.

The 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 collapsed?

This 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 (see below.)

Although 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 January-1990 Analog.  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 Bell proved mathematically, requires quantum entanglement.

The 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.

The 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.

Recording 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.

This 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 mechanics.

How 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.

Moreover, 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.

That 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 Quantum Handshake - 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 ψ and forming "transactions" that implement quantum events, convert waves to particles, and enforce the conservation laws of physics.

In 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.

Since 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.

This 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.

I 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 puzzling quantum optics experiments and thousands of pages of debate by physicists and philosophers of science.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: http://www.springer.com/gp/book/9783319246406 or https://www.amazon.com/dp/3319246402.

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at https://www.amazon.com/Twistor-John-Cramer/dp/048680450X and https://www.amazon.com/EINSTEINS-BRIDGE-H-John-Cramer/dp/0380975106. His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: http://www.npl.washington.edu/av .

References:

EPR Experiments:

"Experimental Test of Local Hidden-Variable Theories", Stuart J. Freedman and John F. Clauser, Phys. Rev. Letters 28, 938 (1972).

"Entanglement Between Photons that have Never Coexisted", E. Megidish , A. Halevy, T. Shacham, T. Dvir, L. Dovrat, and H. S. Eisenberg, Phys. Rev. Letters 110, 210403 (2013); ArXiv: 1209.4191v1

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