"The Alternate View" columns of John G. Cramer

Published in the March-April-2023 issue of

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 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 othe*r 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

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

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

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:**
John's 1^{st} hard SF novel ** Twistor**
is available online at:

**Alternate
View Columns Online**: Electronic reprints of 226 or more of "The ** Analog**
are currently available online at:

.

**References:
**

__The EPR Paradox and
Quantum Entanglement:____
__A. Einstein, B.
Podolsky, and N. Rosen,

N. Bohr,

E. Schrödinger,

E. Schrödinger,

__Bell's
Inequalities:____
__John S. Bell,

John S. Bell,

__EPR Experiments:____
__Stuart J.
Freedman and John F. Clauser,

A. Aspect, J. Dalibard, and G. Roger,

A. Aspect, J. Dalibard, and G. Roger,

__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,"