3. WHY MATTER ALONE IS NOT ENOUGH!
"Nonlocality gets more real". This is the provocative title of a bulletin in a recent
issue of "Physics Today." It reports some experimental results that imply that
causal influences must in some cases act over large distances faster than the
speed of light. These experiments, carried out in Switzerland, are similar to
many others performed over the past thirty years, but they are more spectacular
because the distance involved was not just a laboratory interval of a few meters,
but a geographic separation of more than ten kilometers. The results of these
experiments are incompatible with the materialist conception of nature that ruled
science from the time of Isaac Newton until the dawn of the twentieth century.
There is a theory that perfectly describes all of these experimental results, but it
is based on a non-material conception of the universe, and a new kind of
mathematical law.
According to Einstein's theory of relativity, any faster-than-light action would be,
from some point of view, instantaneous. But instant transfer of information is
anathema to many scientists, on aesthetic and intuitive grounds. Of course,
Newton's theory of gravity postulated a force that acted with no time delay over
a planetary scale, and gave no hint of what was transmitting this action. His
theory was severely criticized on that account, and even Newton himself was
troubled by this feature. In a letter to his friend Bentley, he expressed his own
skepticism about unmediated force, and by implication, I think, about any sort of
instantaneous action at a distance:
",...that one body may act upon another at a distance
through a vacuum, without the mediation of anything else, by
and through which their action and force may be conveyed
from one to another, is to me so great an absurdity, that I
believe no man, who has in philosophical matters a
competent faculty of thinking, can ever fall into it. Gravity
must be caused by an agent acting constantly according to
certain laws, but whether this agent be material or immaterial
I have left to the consideration of my readers."
Newton had, in fact, made huge efforts to find a satisfactory physical
explanation of this force, but failed. More than two centuries later Einstein
explained gravity as being due to the warping of space-time by the presence of
matter. According to this theory, the gravitational effect is indeed conveyed from
point to point by a local contact interaction that transfers information no faster
than the speed of light. Thus Einstein achieved what Newton had intuited, the
abolition of instantaneous action at a distance. His theory of relativity implied,
moreover, that no physical influence of any kind could act faster than the
speed of light.
But why should we be concerned here with this rather esoteric question of
whether faster-than-light influences exist? Our topic is human beings, and their
place in the causal structure of Nature. On the time scale of biological
processes in human brains and bodies the speed of light is so fast as to be
essentially infinite anyway. So why worry about this seemingly irrelevant
question?
There are three important reasons.
The first concerns the constitution of the world: the question of what the world is
made of. Neither matter nor energy can travel faster than the speed of light. Nor
could anything else in a world composed of matter and energy alone. Thus the
proved existence of such influences is a compelling and easy to understand
reason to abandon the tenets of materialism, and move on to the more
adequate quantum framework, which is relies on a causal interplay of the idea-
like and matter-like properties of nature.
The next reason pertains to size. It is often argued quantum theory concerns
only very small-scale phenomena, and hence can be ignored when dealing with
something as big as your brain, or even a neuron in your brain. But the faster-
than-light quantum effect entailed by the Swiss experiment acts over a distance
of more than ten kilometers: quantum effects are obviously not confined to small
regions. Indeed, in the von Neumann formulation of quantum theory to be
adopted here there is a brain-sized event associated with each of your
knowings: with each of your experiential graspings of a meaning. These
macroscopic brain events enter dynamically, by means of a well understood
quantum process that has no classical analog, into the formation of your
thoughts and actions.
The final reason concerns understanding. In the book John von Neumann and
the Foundations of Quantum Physics the philosopher Wesley C. Salmon, in a
contribution entitled Scientific Understanding in the Twentieth Century begins
his section on "The Possibility of Scientific Explanation" with the following
paragraph:
"Between the triumph of the atomic theory of matter early in the century and the
middle of the twentieth century it would not have been incoherent to claim that we
can describe the nature and behavior of atoms, molecules and subatomic
particles, and that we can make successful predictions on the basis of such
knowledge, but to deny that we have achieved anything that deserves the
honorific title of explanation or understanding. To appreciate the transition from
that position to our fin de siecle confidence in the possibility of scientific
explanation and understanding, we must turn to the work of philosophers."
He goes on to say that "According to an old doctrine, going back at least to
Aristotle, we seek to know, not only what, but also why."
Salmon is contrasting here to two different ideas of science. One claims
science is only about knowledge, description, and prediction; whereas the
other says science can provide also understanding.
During the first fifty years of the twentieth century the ascendant position of
philosophers of science was the first view, but now, according to Salmon,
philosophers are coming back to the old idea that science can provide also
understanding. That shift supports, philosophically, the aim of this book, which is
to provide not merely a description of the quantum world, but also an
understanding of it.
It is probably not coincidental that the ascendant views of philosophers during
that first half of the century dovetailed with those of the quantum physicists. The
essential core of Bohr's message was precisely that scientists should focus on
knowledge, description, and prediction, and forego the endeavor to understand
in terms of traditional concepts and categories.
But why should scientists, of all people, have abandoned the effort to understand
nature?
The reason is clear: Quantum theory, as a mathematical structure, is built on the
idea of non-microscopic events and instantaneous actions. Yet the scientist
were reluctant to admit that such things could actually exist: they preferred
abandoning understanding, to abandoning locality However, if understanding is
ever to be achieved, non-locality must surely be acknowledged.
No reasonable person should accept on hearsay a revolutionary new idea of
reality that overturns everything that has been believed for generations, and is,
moreover, wildly counter-intuitive: might not the physicists who are setting forth
this "craziness" be carried away by enthusiasm, or be so beguiled by the power
of their mathematical tools that they lose touch with reality. This abrogation of
the formerly well-established science has such far-reaching consequences that
serious thinkers need to understand for themselves the empirical evidence and
its logical implications. I shall therefore describe here the experiment performed
in Switzerland by members of the Applied Physics Group of the University of
Geneva, and then explain how their results contradict the basic idea that Nature
is built of matter and energy alone.
The general idea of the Swiss experiment is this: A sequence of pairs of
photons is generated in Geneva, and one member of each pair is sent by optical
fiber to the village of Bellevue, and the other is sent to Bernex. In each village a
random choice is made to perform one or the other of two alternative possible
experiments. Each performed experiment gives a result Yes or No. But the
operations are all carried out so fast that the information about which random
choice is made in a village cannot, even by traveling at the speed of light, get to
the other village before the result appears there.
It needs to be emphasized that the experiment does not demonstrate a direct
"mechanical" influence of the choice made in one regions upon the result
appearing in the other. The situation is more subtle than that. A "mechanical"
influence would be one such that, for an actually performed sequence of
measurements in the two villages, the answer Yes or No appearing in one
village is correlated to the choice made in the other village. (For example, each
time the "first" possibility is chosen in one region the result "Yes" appears in the
other region, and each time the "second" choice is made the result "No"
appears.) Such a correlation, if it existed, could be used to send a telegraph
message from one village to the other faster than light. But the possibility of
sending such messages faster-than-light is strictly excluded by quantum theory.
Correspondingly, the existence of such a "mechanical" faster-than-light
influence is not what this experiment demonstrates!
Classical physical theory imposes, however, also a stronger no-faster-than-light
condition. Because all casual connections are carried by matter or energy the
theory allows no influence of the choice made in one village on the outcome of
either one of the two experiments that could be chosen in the other village. It is
this stronger condition that is incompatible with the predictions of quantum
theory confirmed (to within the limits imposed by the experimental exigencies) by
the Swiss experiment.
I turn now to a more detailed description of the Swiss experiment, and to the
proof of the violation of this no-faster-than-light condition. Readers more
interested in general ideas than in detailed proofs can skip at any time to the last
paragraph of this chapter without loss of continuity.
The initial phase of the Swiss experiment occurs at a lab in downtown Geneva.
A pair of associated twin photons is born there. This birthing is achieved by
directing a laser beam at a crystal. Most of the laser light goes through the
crystal, but each laser photon in a small subset is split into a pair of photons,
with each member of the pair carrying about half the energy of its laser-photon
parent.
For some of these pairs one partner is sent by optical fiber to a lab in the village
of Bellevue, while the other partner is sent to a lab in the town of Bernex. These
two labs lie more than ten kilometers apart.
At each lab the arriving twin is sent into an "interferometer".
Interferometers are, themselves, very interesting devices, and they need to be
understood if the experiment is to be made clear.
There are different kinds of interferometers. To simplify the explanation without
altering the principle I shall consider one that is slightly different from what was
used in the Swiss experiment.
This interferometer involves two ordinary (i.e., fully silvered) mirrors, each of
which reflects all the light falling on it, and two half-silvered mirrors. In half-
silvered mirrors the layer of silver is so thin that it reflects (like a mirror) only half
the light incident upon it, and transmits (like a plate of clear glass) the other half.
The figure is missing from this plain text file.
AN INTERFEROMETER
[The light enters the device horizontally, and eventually exits either
horizontally, or vertically downward. Photon detectors H and V signal the
emergence of the photon in the horizontal and vertical exit beams,
respectively. The two 45-degree slanted lines on the lower side of the
rectangle represent half-silvered mirrors, the two upper 45-degree slanted
lines represent fully silvered mirrors. Thus half the light takes the short direct
path between the two half-silvered mirrors, whereas the other half takes the
longer roundabout path. Each detector, H or V, gets half of its light via the
direct path and half via the roundabout path.]
Experiments with an interferometer of this kind reveal an interesting
"interference" phenomena: the fraction of the photons detected in detector H
depends upon the difference between the lengths of the two alternative paths
available to the photon; i.e., on the difference of the lengths of short (direct) and
the long (roundabout) paths between the two half-silvered mirrors. This fraction
can easily be computed by imagining the photon to be a wave, like the wave on
the surface of a pond. This wave divides at the first half-silvered mirror into two
parts, which move along the two different paths to the second half-silvered
mirror. At the second half-silvered mirror the direct and roundabout parts of the
wave are reassembled, and one reconstituted combination is sent to H, and the
other reconstituted combination is sent to V.
The wave consists of a long regular sequence of crests and troughs, and the
"wavelength" of the light is distance between successive crests. The key point is
that the laws of wave optics say that the process of reflection off of a slanted
45-degree (half-silvered or fully-silvered) mirror shifts the crest of the reflected
wave backward by one quarter of a wave length, relative to the geometric
distance traveled by the wave. Transmission through the half-silvered mirror
generates no such shift.
The wave in, say, the horizontal exit beam will be the sum of a part coming via
the direct path and a part coming via the roundabout path. Suppose that the
difference in the lengths of these two paths is an integral (i.e., whole) number of
wavelengths. Then, without the quarter-wavelength shifts associated with the
reflections, the crests of the waves in this exit beams that come via the direct
and roundabout routes will exactly coincide: the extra distance traveled by the
light that takes the roundabout path would not produce any net shift in the
position of the crests, relative to the wave that takes the short path, because a
shift by an integral number of wave lengths just shifts each crest into
coincidence with another crest. Thus the contributions from the long and short
routes would, after being recombined at the second half-silvered mirror, be
exactly "in phase." The same would be true in the vertical exit beam.
But when the shifts at the 45-degree reflections are taken into account the
situation is more interesting. Consider first the light that goes to the detector H.
The light that travels the roundabout route to the detector H is reflected four
times and hence will have its crests shifted by four quarter-wavelengths (which
add up to one full wavelength). The light that travels the short direct route is not
shifted at all. Since a shift by a full wavelength keeps the crests aligned, the part
going to H via the roundabout route will be completely in phase with the light
going to H via the short (direct) route. Thus there will be complete constructive
interference between the two parts of the wave that go to H.
But consider next the two parts that go to V. The wave going via the roundabout
path to V is shifted backward by three quarters of a wavelength, whereas the
wave that goes via the short path to V gets shifted backward by one quarter of a
wavelength (because it is reflected only once.) Therefore the relative shift is
seven quarter-wavelengths minus one quarter-wavelength. This is six quarter-
wavelengths, or one and a half wavelengths, which is equivalent to a half
wavelength, since a shift by a full wavelength keeps the crests aligned. But a half
wavelength shift moves each crest of one part onto a trough of the other part,
and the two waves will cancel each other out. Thus there will be complete
destructive interference: no light will go to V. This "wave optics" calculation
matches the empirical facts.
Thus if the difference in the lengths of the long and short path lengths is an
integral number of wave lengths of the light, then all of the photons will get
detected in H, and none in V. But if, say, the roundabout path is now lengthened
by a half wave length the situation will be reversed and all of the light will go to V
and none to H.
These wave optics calculations are easy to do, and to understand, and they give
predictions about the fractions of the light going to H and to V, respectively, that
are in full accord with experiment. These results demonstrate clearly the wave
nature of light. This wave nature persists undiminished even when the beam is
attenuated so strongly that two photons are never (or at least hardly ever) in
transit at the same time.
Having thus establishing the wave nature of the light we arrive at an interesting
puzzle! If one places detectors in the two paths just before they reach the
second half-silvered mirror, then for each photon that enters the interferometer
only one or the other of the two detectors will fire, never both. This seems to
show clearly that the photon travels along one path or the other, not both.
But how can one reconcile this particle-type (single-path) behavior with the
empirically validated wave-like behavior just described, which depends upon the
interference between the light that travels the two paths?
This problem is, of course, the famous "wave-particle duality" puzzle.
The simplest answer is to assume that there is both a "particle of light", the
photon, and a wave. The wave obeys the laws of wave optics, but also guides
the photon to places where the waves interfere constructively, and away from
places where the waves interfere destructively. So there is no really serious
problem at this one-photon level. It is only when one considers two paired
photons that a real puzzle arises.
So let us return to the Swiss experiment. In that case there are two
interferometers in each village, and hence four altogether.
The figure is missing from this plain text file.
THE EXPERIMENTAL SET UP.
[The laser beam is split at D. The two R's indicate the two random processes,
each of which randomly sends the photon that arrives in its laboratory to
either the "upper" or the "lower" of the two interferometers in that village. H
and V label the photon detectors in the horizontal and vertical exit channels,
respectively. There are four alternative possible cases. In Case One the two
selected interferometers are the two lower ones, one in Bellevue and one in
Bernex. In Case Four the two selected interferometers are the two upper
ones. The two lower interferometers are mirror images of each other, and the
two upper interferometers are mirror images of each other. All four of the short
paths (between the two half-silvered mirrors in an interferometer) have the
same length, but the roundabout paths are slightly longer in the upper two
interferometers than in the lower two. In the lower two interferometers the
difference between the long and short paths is an integral numbers of
wavelengths.]
Some of the photons get lost along the way and do not reach a detector. But
there are many pairs whose two members both reach detectors, one in
Bellevue, the other in Bernex. Signals from those detectors are sent back by
ordinary wires to a central processor in Geneva.
Consider first Case One. In this case the two selected interferometers are the
two lower ones in the diagram. These two interferometers are mirror images of
each other. This means, in particular, that the length of the short path in the
Bellevue device is the same as the length of the short path in the Bernex device.
Likewise, the lengths of the two long paths are the same.
Each pair of photons is created at an event in Geneva. One member goes to
Bellevue the other member goes to Bernex, and then each generates a signal
that goes back to Geneva. Bellevue and Bernex do not lie at the same distance
from Geneva. Thus the signals from these two villages will not arrive in Geneva
simultaneously: there will be a time lag. This delay depends upon whether the
photons traverse the short or the roundabout routes inside the interferometers.
However, if both photons, one in each village, take the short route then this time
lag will be the same as when both take the long route. (This is because the
difference between the lengths of the long and short routes is the same for the
two photons, and hence the difference in transit times is the same.) But if one
photon of the pair takes a roundabout route whereas the other takes the direct
route then the time lag between signals from Bellevue and Bernex will be either
longer or shorter than the common lag time for the cases in which both photons
traverse the direct route or both traverse the roundabout route.
This difference in lag times allows the experimenters to keep only those pairs of
photons such that both members take the long path or both take the short path.
The slight lengthening of the long paths in the upper two interferometers (in our
diagram) is too small to upset this restriction of the data to the contributions in
which both of the two siblings take the roundabout route or both take the direct
route.
When coincidences of detection events, one in each village, are considered it is
the sum of the two phases that is pertinent. In Case One the long path in each
interferometer is longer than the short path by an integral (i.e., whole) number of
wavelengths. Consequently, there will be constructive interference if both
photons are detected in the H detectors, or if both are detected in the V
detectors, but destructive interference if one photon is detected by a V detector,
but the other is detected by an H detector.
These results are easy to deduce. Note that in the case where both photons are
detected in an H detector the contribution from the two long paths gives a total
shift of eight quarter wave lengths (there are altogether eight 45-degree
reflections on the path to the two detectors H) and the two short paths give no
shift. Thus we get a two-wavelength shift, and hence complete constructive
interference. In the case of two V's the two long paths give a backward shift of
six quarters (three reflections in each village) whereas the two short paths give
a total backward shift of two quarters, for a net difference of one full wavelength,
and hence, again, complete constructive interference. In the case of H in one
region but V in the other, the contribution from the two long paths will be shifted
back by seven quarters, whereas the contribution from the two short paths will
be shifted back by only one quarter of a wavelength, for a net difference of one
and a half wavelengths. Thus the crests coming from the long paths will coincide
with the troughs coming from the short paths, which means complete destructive
interference.
The rate at which the pairs are detected is slow enough so that each pair of
particles, one detected in Bellevue the other in Bernex, can be distinguished
from all the other pairs by fast electronics. A pair is classified as "matched" if
both members are detected in a horizontal exit channel or both are detected in a
vertical channel. They are "unmatched" if one partner is detected in a horizontal
exit channel and its mate is detected in a vertical exit channel.
Quantum theory predicts, and the empirical results confirm (to within the limits
imposed by experimental exigencies) that the fraction of the pairs that are
unmatched will be the sine squared of L/2 minus S/2, where L is the sum of the
two long paths, one in each village, and S is the sum of the two short paths. The
sine-squared function oscillates smoothly between zero and one, and touches
zero each time L/2 minus S/2 reaches some half-integral multiple of the
wavelength of the light. This agrees with the result in Case One that was just
described: there L/2 minus S/2 is an integral number of wavelenghts, and hence
the sine square of L/2 minus S/2 is zero.
For ease of explanation, I shall use just one simple property of this formula: if for
some original value of L/2 minus S/2 none of the pairs are unmatched then for
small shifts of L/2 minus S/2 away from this original value the number of
unmatched pairs will grow like the square of this small shift. In particular, if for
some small value of this shift in L/2 minus S/2 the value of this fraction of
mismatches is f, then a doubling of this small shift will multiply the fraction of
mismatches by about 4: the fraction of mismatches will more than double!
What is so astonishing about that?
What is puzzling and interesting is this. The experiment is done with very high-
speed equipment. The speed is so high that the information about which of the
two interferometer is randomly chosen for the photon in one village cannot get to
the other village before its twin photon is detected there, without that information
traveling faster than light. Under these conditions the principles of classical
physics ensure that the random choice of what is done to a twin in one village
can have no influence on the behavior of its faraway sibling. But this condition of
no faster-than-light influence cannot be reconciled with the quantum results just
described.
How is this remarkable result proved?
Case Two is the same as Case One up until the moment that the two random
choices are made, but the random choice in Bellevue goes the other way: the
upper interferometer is picked by the random process there, but nothing is
changed in Bernex. Now a small fraction f of the pairs will be "unmatched". Since
nothing has changed in Bernex, this small fraction f of unmatched events must
arise from a switching of this fraction f of the events in Bellevue from what they
were in Case One. That is, if in Case One the sequence of detection events is,
say (H, V, V, H, H, H, V, H, etc.) in both Bellevue and Bernex then in Case Two
the fraction f, say 1%, of these values will be reversed from their Case One
values in Bellevue, but none will be reversed in Bernex. This is the first key
consequence of the no-faster-than-light-influence condition: it ensures that the
random choice made in Bellevue does not disturb the outcomes in Bernex.
Case Three is the same as Case One in Bellevue, but the upper interferometer
is chosen in Bernex instead of the lower one. Hence the same fraction f of the
detection events, but now in Bernex, must be opposite to what they were in
Case One.
In Case Four the changes that were made in Bellevue in Case Two, and in
Bernex in Case Three are now made simultaneously in both Bellevue and
Bernex. Hence in this final case the changes that occur in Bellevue must be the
same as the changes made there in Case Two, since no influence of the choice
made in Bernex can be present in Bellevue. Similarly, in this Case Four, the
changes made in Bernex must be the same as the changes that were made
there in Case Three.
But then the total number of mismatches in Case Four can be no greater than
the sum of the number of mismatches in Cases Two and Case Three. Thus the
fraction f* of mismatches in Case Four can be no larger than 2f. But this
contradicts the empirically verified prediction of quantum theory that f* is roughly
4f.
This large-scale failure of the core causality idea of relativistic classical physics
suggests that we must be prepared for a profound revision of our conception of
the nature of the physical world. Bohr, Heisenberg, Pauli, and the other founders
of quantum theory partially achieved this by bringing conscious human
observers into basic physical theory in a way that permits the idea-like aspects
of reality to be more deeply involved in the causal structure of the Nature than
classical ideas allow. So let us look now more closely at what they did.