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Quantum Entanglement Disentangled

by John G. Cramer

Alternate View Column AV-223

Keywords: quantum, entanglement, conservation laws, uncertainty principle, EPR
Published in the March-April-2023 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 11/07/2022 and is copyrighted ©2022 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

The 2022 Nobel Prize in Physics was awarded to John Clauser, Alain Aspect, and Anton Zeilinger for their work on the experimental aspects of quantum entanglement.  Clauser and Zeilinger are friends of mine.  In the Fall of 2013, my wife and I spent a week at Zeilinger's lab in Vienna, trying (and fortunately failing) to convince him to undertake an entanglement-based quantum-communication experiment that would not have worked.  What I learned during that visit cleared my last conceptual roadblocks and enabled me to write my 2016 book, The Quantum Handshake.

This wonderful set of Nobel Prize awards motivates me to write this AV Column, in which I want to explain what quantum entanglement is, why it exists, how its existence was demonstrated by John Clauser and his graduate student Stuart Freedman, and how the underlying mechanism behind entanglement can be understood.  Basically, entanglement comes from two requirements of quantum mechanics that seem to be on a direct collision course:

(1)   Conservation Laws:  As in the rest of physics, in all quantum systems energy, momentum, and angular momentum are conserved.  In the absence of external forces or torques, their values must remain unchanged as the system evolves.

(2)   Heisenberg Uncertainty:  energy, momentum, and angular momentum are all subject to Heisenberg's uncertainty principle.  Whenever their complementary variables (time, position, and angle, respectively) are tightly determined, energy, momentum, and angular momentum may be indefinite and unspecified and typically can span large ranges of possible values.  This non-specificity persists until measurements are made that fixes them with measured values.

The seemingly incompatible requirements of (1) and (2) raise an important question: How can the wave functions describing separated components of a system of particles, perhaps light-years apart, have uncertain values for the conserved quantities and yet respect the conservation laws when measurements are made, wave functions are collapsed, and values of the conserved quantities determined?  This question was first raised by Einstein, Podolsky, and Rosen in a 1935 paper, and it is called the EPR paradox.

The EPR paradox fits within the formalism of quantum mechanics because the quantum wave functions of particles are entangled, the term coined by Schrödinger to mean that even when the wave functions describe system parts that are spatially separated and out of light-speed contact, the separate wave functions continue to depend on each other and cannot be separately specified.  If a measurement is made on one component of an entangled system, its outcome influences the future outcomes of subsequent measurements made on all the other system components.  In particular, the conserved quantities of the system's parts (even though individually uncertain) must always add up to the values possessed by the overall quantum system before it was separated into parts.

The mechanism that implements this cross-space-time dependence and enforces conservation laws is not apparent in the quantum formalism.  Therefore, entanglement joins the unresolved quantum mysteries of wave-particle duality and wave function collapse.  Einstein called entanglement "spooky actions at a distance" and felt that it had no place among the rational theories of physics.


Here is a specific example of quantum entanglement, one that is used in most EPR experiments demonstrating the actions of entanglement.  Photons of light carry one h-bar unit of angular momentum, and so are said to be "spin-1 particles".  If the photon is circularly polarized, then its 1-unit angular momentum spin vector points either along its direction of motion (left circular polarization or LCP) or against its direction of motion (right circular polarization or RCP).  Linear polarization is made by superimposing half-amplitudes of LCP and RCP, with the relative phase of these amplitudes determining the plane of the linear polarization (horizontal, vertical, diagonal, anti-diagonal, etc.)

The 1972 Freedman-Clauser experiment (FC) used a zero-angular-momentum two-photon cascade de-excitation in an excited calcium atom to produce entangled photon pairs.  The back-to-back photons FC studied were entangled because the atomic system's zero angular momentum was conserved in the atomic cascade, requiring that the photons, using any polarization basis, would measure identical polarizations.  This was independent of whether the basis of the polarization measurements was right/left circular, horizontal/vertical linear, diagonal/anti-diagonal linear, or any other basis.  (We note that there are now far more efficient ways of producing entangled photon pairs than the one used by FC, including laser-pumped parametric down-conversion in nonlinear crystals and Toshiba's new quantum-dot-based entangled- light emitting diodes.)

The F-C experiment was motivated by previous theoretical work of John S. Bell (see my Alternate View column in the January-1990 issue of Analog), who in 1964 and 1966 published a pair of theoretical papers demonstrating (in a rather arcane way) that experimental tests involving photon-polarization measurements were possible in which one could distinguish between standard quantum mechanics and alternative entanglement-free "local hidden-variable theories" (LHVT).  These LHVT had been introduced by David Bohm and other Einstein-defenders in the 1960s and promoted as classical alternatives to standard quantum mechanics.

Bell's test measured how fast the coincidence rate between linear polarimeters detecting entangled photon pairs falls off as the transmission axes of the two polarimeters are misaligned.  He defined "Bell inequalities" that are violated by QM, but not by LHVT.  If the two polarimeters are misaligned by a small angle A, Bell showed that all LHVT predict a coincidence-rate falloff proportional to A, while quantum mechanics predicts a falloff proportional to A2.

The F-C measurement, published in 1972, verified the quantum-mechanics-based prediction to a statistical accuracy of 6.7 standard deviations.  A decade later in 1982, Alain Aspect and his group in France repeated the F-C work with better equipment and a stronger source, closed some so-called "loopholes", and demonstrated the effect to a statistical accuracy of 46 standard deviations.  More recently, Anton Zeilinger and his groups in Innsbruck and Vienna have investigated many aspects of quantum entanglement, including entanglement in systems with more than two photons.  This body of experiments can be taken as convincing experimental demonstrations that quantum entanglement is a real physical phenomenon, an important aspect of quantum mechanics, and, spooky or not, is the way the world works.  None of these experiments, however, reveal how the separated-but-entangled systems are connected or suggest any underlying mechanism by which Nature enforces Her conservation laws across space-time.


What is the mechanism behind quantum entanglement?  At present, this question takes us into the domain of quantum interpretations, where no experimental tests can separate a correct idea from wrong ones.  QM interpretations began in the 1920s, when the founders of quantum mechanics realized that their new formalism for describing Nature at the atomic level lacked any physical picture that could guide them in understanding what was going on.  The quantum formalism was requiring particles to sometimes become waves and for these waves to sometimes collapse into particles in very mysterious ways.

In response, Bohr, Heisenberg, and others constructed the Copenhagen interpretation to deal with wave-particle duality and collapse.  They decreed that the quantum wave function, even though it is a solution of a differential equation relating mass, energy, and momentum, is not a physical wave travelling through space.  Rather, it must be a mathematical representation of the knowledge of some observer who is studying the system.  When the observer makes a measurement, its outcome changes his knowledge, and so the wave function must collapse to reflect that change.

Unfortunately, when it comes to entanglement, the Copenhagen interpretation draws a blank and provides no insights as to mechanism.   Bohr's 1935 response to the EPR paper does not even mention entanglement, and instead focuses exclusively on wave-particle duality and complementarity.  Most alternative interpretations of quantum mechanics (see Wikipedia) that address wave-particle duality and collapse have not done any better in explaining (or ignoring) entanglement.

The exception is my own transactional interpretation of quantum mechanics (TI), described in detail in my book The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016).  The basic idea behind the TI comes from the formalism of quantum mechanics itself, which typically makes predictions of quantum events by combining a quantum wave function with its complex conjugate (i.e., making negative the complex function's imaginary part).  It is well known that if a wave function describes a wave moving forward in time, its complex conjugate describes that wave moving backwards in time.  Thus, the quantum formalism itself suggests that actually, each quantum interaction is a forward-going wave and a backward-going wave connecting as a handshake across space-time.

This is the key to understanding the mechanism behind quantum entanglement.  In the case of the F-C experiment, the source atom emits two waves of indeterminant polarizations.  When these waves arrive at the two polarimeters and are detected, only the part of the wave with polarization that matches the polarimeter's setting is detected, and that detection creates a back-in-time wave that returns to the source, arriving at the instant of emission.  The final source-plus-two-polarimeter event can occur only if the polarization directions of the two time-reversed waves from the polarimeters match at the source as it emits, to verify the overall event.  Thus, by this forward-backward quantum handshake, Nature ensures that conservation of angular momentum is satisfied in the emerging quantum event between source and polarimeters.

In other words, the mechanism behind quantum entanglement is the quantum handshake, in which forward- and backward-going waves transfer energy, momentum, and angular momentum and satisfy all conservation laws.  This handshake mechanism also provides a deeper understanding of wave particle duality and of wave function collapse.  The mechanism of wave function collapse as a quantum handshake is demonstrated in mathematical detail in my recent paper with Carver Mead (see ref. below)

In this context, I note that in Chapter 6 of The Quantum Handshake, the transactional interpretation is used to explain in detail the "spooky" behavior of over twenty-six otherwise paradoxical and mysterious quantum optics experiments and gedankenexperiments (two-slit, Einstein's bubble, Schrödinger's cat, Wheeler's delayed choice, quantum eraser, black-hole information, ).  No other interpretation of quantum mechanics even attempts such a broad span of experiments/explanations.  If we cannot dismiss the plethora of competing QM interpretations using experimental testing, we can and should eliminate them when they fail (as almost all of them do) to explain the large number of paradoxical quantum optics experiments.


John G. Cramer's 2016 nonfiction book 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:  editions of John's hard SF novels Twistor and Einstein's Bridge are available online at:
https://www.amazon.com/Twistor-John-Cramer/dp/048680450X  and
https://www.amazon.com/Einsteins-Bridge-John-Cramer/dp/0380788314 .  
John's new hard-SF novel Fermi's Question, sequel to Einstein's Bridge, will be available soon from Baen Books.

Alternate View Columns Online: Electronic reprints of 222 or more of "The Alternate View" columns written by John G. Cramer and previously published in Analog are currently available online at:  http://www.npl.washington.edu/av .


References:

The EPR Paradox and Quantum Entanglement:
A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777-780 (1935);
N. Bohr, Phys. Rev. 48, 696-702 (1935);
E. Schrödinger, Proc. Camb. Philos. Soc. 31, 555-563 (1935);
E. Schrödinger, Proc. Camb. Philos. Soc. 32, 446-451 (1936).

Bell's Inequalities:
John S. Bell, Physics 1, 195-200 (1964);
John S. Bell, Reviews of Modern Physics 38, 447-452 (1966).

EPR Experiments:
Stuart J. Freedman and John F. Clauser, Phys. Rev. Lett. 28, 938-941 (1972);
A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. 49, 91-94 (1982);
A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. 49, 1804-1807 (1982).

The Transactional Interpretation of Quantum Mechanics:
John G. Cramer,
The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016);
John G. Cramer and Carver A. Mead, "Symmetry, Transactions, and the Mechanism of Wave Function Collapse," Symmetry 12(8), 1373-1416 (2020); https://www.mdpi.com/2073-8994/12/8/1373


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