"The Alternate View" columns of John G. Cramer

**Alternate View Column AV-37**

Keywords: nonlocality, Bell's Theorem, quantum mechanics,
Einstein, Podolsky, Rosen, Copenhagen interpretation

Published in the January-1990 issue of
**Analog Science Fiction & Fact Magazine;**

This column was written and submitted 6/23/89 and is copyrighted
© 1989, John G. Cramer. All rights reserved.

No part may be reproduced in any form without
the explicit permission of the author.

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Albert Einstein disliked quantum mechanics, the physical theory that deals
with matter and energy at the smallest possible scale. Quantum mechanics, as
developed by Heisenberg, Schrödinger, Dirac, and others, had many strange
features that ran head-on into Einstein's finely honed intuition and
understanding of how a proper universe __ought__ to operate. Over the years
he developed a list of objections to the various peculiarities of quantum
mechanics. At the top of Einstein's list of complaints was what he called
"spooky actions at a distance".

Einstein's "spookiness" is now called *nonlocality*, the mysterious
ability of Nature to enforce correlations between separated but entangled parts
of a quantum system that are out of speed-of-light contact, to reach
faster-than-light across vast spatial distances or even across time itself to
ensure that the parts of a quantum system are made to match. This column is
about nonlocality, and how, through Bell's theorem, the nonlocality implicit in
nature has been demonstrated in the laboratory.

In 1935 Einstein, with his collaborators Boris Podolsky and Nathan Rosen, published his list of objections to quantum mechanics in what has come to be known as "the EPR paper". The EPR paper lodged three main complaints against quantum mechanics, one of which was nonlocality. EPR argued that "no real change" could take place in one system as a result of a measurement performed on a distant second system, as quantum mechanics required. Einstein and his colleagues also found it unacceptable that in quantum mechanics the measurement of one variable often precludes any knowledge of a second "complementary" variable (for example momentum and position). They further objected to the intrinsic randomness and non-predictivity of quantum mechanics. They argued that the theory must be incomplete, and that it must eventually be replaced by a superior and more complete theory which would observe light's speed limits, would allow all physical quantities to have well-defined values, and would permit accurate prediction of the outcome of any quantum event.

A slow-motion uproar followed the publication of the EPR paper. The founders of quantum mechanics immediately tried to come to grips with the EPR criticisms. Niels Bohr focused this debate on the second of the EPR objections, the simultaneous "reality" of complementary variables like momentum and position. The arguments over this intellectual battleground washed back and forth for the next thirty years. During this ongoing controversy, EPR supporter David Bohm introduced the notion of a "local hidden variable" theory, a partially formulated theory that would replace quantum mechanics with a theoretical structure omitting the paradoxical features of quantum mechanics to which the EPR paper had objected. In Bohm's hidden-variable alternative to quantum mechanics, all correlation were established locally at sub-light speed. Position and momentum were permitted to have simultaneous values, values that were real, but were "hidden" and inaccessible to direct measurement.

Working physicists, however, paid little attention to hidden variable theories. Bohm's approach was far less useful than orthodox quantum mechanics for calculating the behavior of physical systems. Since it was apparently impossible to resolve the EPR/hidden-variable debate by performing an experiment, physicists tended to ignore the whole controversy. They continued to use and improve quantum mechanics without agonizing over whether there were underlying problems gnawing at the roots of the theory. The EPR objections were considered problems for philosophers and mystics, not Real Physicists.

In 1964 this perception changed. John S. Bell, a theoretical physicists
working at the CERN laboratory in Geneva, proved an amazing theorem which
demonstrated that certain experimental tests could distinguish the predictions
of quantum mechanics from those of any local hidden-variable theory. Bell,
following the lead of David Bohm, had based his calculations not on
measurements of position and momentum, the focus of Einstein's arguments, but
on measurements of the states of *polarization* of photons of light.

Before discussing Bell's theorem further, we should pause to develop some
background on the polarization of light. The phenomena we refer to as visible
light, infrared or ultraviolet rays, radio waves, X-rays, or gamma rays are all
aspects of the same basic physics. They are travelling waves produced when
electric and magnetic fields vibrate together at right angles to each other as
they move through space at the speed of light. The direction in which the
electric field of a light wave vibrates determines the *polarization* of
the wave. If the electric field vibrates always in the same plane, we say
that this is the plane of polarization, and that the wave has *linear
polarization* in that plane. If the electric field vibrates so as to trace
out a "cork screw" in space, a right or left handed helix as the wave travels
on its straight line path, we say that the wave has left or right *circular
polarization*. For the present discussion we will concern ourselves only
with linear polarization and will use the term *polarization* to indicate
linear polarization.

It is quite easy to measure polarization of visible light. Special optical filters, for example the lenses of Polaroid(TM) sunglasses, absorb light polarized in one direction while transmitting the light polarized in the perpendicular direction. There are also polarization-sensitive splitters (Nichol prisms) that will divide a beam of light into two beams, one, for example, with vertical polarization and the other with horizontal polarization.

Using such devices, light can be divided into two polarization components. For
example, light polarized at some angle to the vertical can be split into a
vertical and a horizontal polarization component. Similarly, both vertically
and horizontally polarized light can be split into a +45^{o} and
-45^{o} components of equal intensity. If a beam of unpolarized light
is passed first through one polarization filter and then another, the intensity
of the transmitted beam varies in accordance with Malus' Law, which states that
the light intensity **I**(**a**) is proportional to the square of the
cosine of the angle **a** between the polarization direction of the first
filter and that of the second filter, i.e.,
**I**(**a**)=**I**_{o}Cos^{2}(**a**), where
**I**_{o }is the intensity then the filters are parallel. This
equation tells us that when the planes of polarization of the two filters make
a right angle, the crossed filters look black and no light is transmitted.
When the planes of polarization make an angle of 45^{o}, half the light
is transmitted.

In an atom, if an orbital electron is kicked into a higher orbit by an
energetic photon or an electrical discharge, the electron returns to its lowest
energy state by a process called a *cascade*, a series of quantum jumps to
lower orbits, each jump producing a single light photon of a particular
wavelength. A two-photon cascade in which the atom as a whole begins and ends
with no net rotational motion is of particular interest, because the cascade
produces a pair of photons which have *correlated polarizations*. When
the photons from the cascade travel in opposite directions, the no-rotation
restriction requires that if one of the photons is measured to have any
definite polarization state, the other photon is required by quantum mechanics
to have exactly the same polarization state. Such photon pairs are said to be
in *entangled* quantum states. Experimental tests of Bell's theorem,
sometimes called EPR experiments, use entangled photons from such a cascade.

EPR experiments measure the coincident arrival of two such photons at opposite
ends of the apparatus, as detected by quantum-sensitive photomultiplier tubes
after each photon has passed through a polarizing filter. The photomultipliers
at opposite ends of the apparatus produce electrical pulses which, when they
occur at the same time, are recorded as a "coincidence" or two photon event.
The rate of such coincident events when the polarization directions of the two
filters have the values **a**_{1} and **a**_{2 }is
measured. Then one or both of the angles are changed and the rate measurement
is repeated, until a complete map of rate vs. angles is developed.

Bell's theorem deals with the way in which the coincidence rate of an EPR
experiment falls off when the two polarizing angles **a**_{1} and
**a**_{2} are not equal. Bell proved mathematically that for all
local hidden-variable theories the decrease in the coincidence rate must be
linear (or less) with the angular difference between the two filters. Suppose,
for example, that we misalign the angles of the two polarization filters so
that the angle between the polarization directions of the two filters is
**a**=**a**_{1}-**a**_{2} . We measure the
coincidence rate **R**(**a**), as compared to the rate **R**_{o
}when the filters are perfectly aligned. That rate drops by an amount
**D**_{1}=**R**_{o}-**R**(**a**). Now we double
the amount of the misalignment, so that the decrease in rate is
**D**_{2}=**R**_{o}-**R**(**2a**). For this
situation, Bell's theorem requires that **D**_{2} must be less
than or equal to twice **D**_{1} (**D**_{2 }<=
**2D**_{1}).

This prediction of Bell's theorem is one of the so-called "the Bell
inequalities". It can be thought of in the following way. Consider that the
coincidence rate **R**_{o }when the polarizing filters are aligned
(**a**=0) is a "signal", to which "noise" is added when a misalignment is
introduced. If the "noise" **D**_{1 }introduced by moving one
filter an amount q to the right is not correlated with the "noise"
**D**_{1 }introduced by moving the other filter by the same angle to
the left, then at most, when both sources of noise are present, the noise
**D**_{2 }from a **2a** misalignment should be twice
**D**_{1}. However, the two uncorrelated noise sources may
occasionally cancel, permitting **D**_{2 }to be less than twice
**D**_{1}. Therefore, this Bell inequality states that
**D**_{2} must be less than or equal to
twice **D**_{1}.

Quantum mechanics, on the other hand, predicts that the coincidence rate
**R**(**a**_{1},**a**_{2}) depends only on the
relative angle **a**=**a**_{1}-**a**_{2} between the
two polarization directions, and that **R**(**a**) obeys Malus' Law. In
other words, quantum mechanics predicts that
**R**(**a**_{1},**a**_{2})=**R**(**a**)=**R**_{o}Cos^{2}(**a**).
Therefore,
**D**_{1}=**R**_{o}[1-Cos^{2}(**a**)] and
**D**_{2}=**R**_{o}[1-Cos^{2}(2**a**)]. When
the misalignment angle **a** is fairly small, this means that
**D**_{2} is about four times **D**_{1 }and clearly
much larger than twice **D**_{1}
(i.e., **D**_{2} **4D**_{1} > **2D**_{1}). This is a
clear violation of Bell's theorem because the coincidence rate, as predicted by
quantum mechanics, falls off much too fast with increasing angle to be
consistent with Bell's theorem, which predicts an approximately linear
decrease.

When two theories make such distinctly different predictions about outcome of the same experiment, a measurement can be performed to test them. For quantum mechanics and Bell's theorem this crucial EPR experiment has now been performed a number of times. And we find that quantum mechanics always wins. The EPR experiments demonstrate very significant violations of the Bell Inequalities while confirming the predictions of quantum mechanics.

When the first experimental results from EPR experiments became available, they
were interpreted as a demonstration that hidden variable theories must be
wrong. This interpretation changed when it was realized that Bell's theorem
assumed a *local* hidden variable theory, and that *nonlocal*
hidden variable theories can also violate Bell's theorem and agree with the
experimental measurements. The assumption made by Bell that had been put to
the test was the assumption of *locality*, not hidden variables.
Locality was in conflict with experiment.

Or, to put it another way, the intrinsic nonlocality of quantum mechanics has been demonstrated by the experimental tests of Bell's theorem. It has been experimentally demonstrated that nature arranges the correlations between the polarization of the two photons by some faster-than-light mechanism that violates Einstein's intuitions about the intrinsic locality of all natural processes. What Einstein called "spooky actions at a distance" are an important part of the way nature works at the quantum level. Einstein's faster-than-light spooks cannot be ignored.

Readers and writers of science fiction will want to know what the nonlocality
of nature means for faster-than-light travel and faster-than-light
communication. Can we harness Einstein's spooks to drive our spaceships and
carry our messages? The answer, alas, seems to be no. Very clever people have
tried to exploit the seeming loophole in the lightspeed barrier implied by
nonlocality to design superluminal communication devices. See, for example, my
column "Paradoxes and FTL Communication"
[*Analog,* Sept-'88]. In every
case, including the Calcutta scheme mentioned in that article, these have been
shown to be unworkable. Nature seems to have reserved her faster-than-light
telephone line for her own private conversations.

**References:**

*EPR:*

Albert Einstein, Boris Podolsky, and Nathan Rosen, Physical Review
**47**, 777-780 (1935).

*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, Physical Review Letters
**28**, 938-941 (1972).

*This page was created by John G. Cramer
on 7/12/96.*