4. THE OBSERVER.
>From the time of Isaac Newton to the beginning of the
twentieth century science relegated consciousness to the
role of passive viewer: our thoughts, ideas, and feelings
were treated as impotent bystanders to a march of events
controlled wholly by contact interactions between tiny
mechanical elements. Conscious experiences, insofar as
they had any influences at all on what happens in the world,
were believed to be completely determined by the motions of
miniscule entities, and the behaviors of these minute parts
were assumed to be fixed by laws that acted exclusively at
the microscopic level. Hence the idea-like and felt realities
that make up our streams of conscious thoughts were
regarded as redundant, and were denied fundamental status
in basic theory of nature.
The revolutionary act of the founders of quantum mechanics
was to bring conscious human experiences into the basic
theory of physics in a fundamental way. In the words of Niels
Bohr the key innovation was to recognize that "in the drama
of existence we ourselves are both actors and spectators."
[Bohr, Essays 1958/1962 on Atomic Physics and Human
Knowledge]. After two hundred years of neglect, our
thoughts were suddenly thrust into the limelight. This was an
astonishing reversal of precedent because the enormous
successes of the prior physics was due in large measure to
the policy of keeping idea-like qualities out.
What sort of crises could have forced scientists to this
wholesale revision of their idea of the role of mind in their
description of Nature? The answer is the discovery and
integration into physics of the "quantum of action.'' This
property of matter was discovered and measured in 1900 by
Max Planck, and its measured value is called "Planck's
Constant." It is one of three absolute numbers that are built
into the fundamental fabric of the physical universe. The
other two are the gravitational constant, which fixes the
strength of the force that pulls every bit of matter in the
universe toward every other bit, and the speed of light, which
controls the response of every particle to this force, and to
every other force. The integration into physics of each of
these three basic quantities generated monumental shifts in
our conception of nature.
Isaac Newton discovered the gravitational constant, which
linked our understanding of celestial and terrestrial
dynamics. It connected the motions of the planets and their
moons to the trajectories of cannon balls here on earth, and
to the rising and falling of the tides. Insofar as his laws are
complete the entire physical universe is governed by
mathematical equations that link every bit of matter to every
other bit, and that moreover fix the complete course history
for all times from conditions prevailing in the primordial past.
Einstein recognized that the "speed of light" is not just the
rate of propagation of some special kind of wave-like
disturbance, namely "light". It is rather a fundamental
number that enters into the equations of motion of every kind
of material substance, and that, among other things,
prevents any piece of matter from traveling faster than this
universal limiting value. Like Newton's gravitational constant
it is a number that enters ubiquitously into the basic structure
of Nature. But important as the effects of two quantities are,
they are, in terms of profundity, like child's play compare to
the consequences of Planck's discovery.
Planck's "quantum of action" revealed itself first in the study
of light, or electromagnetic radiation. The radiant energy
emerging from a tiny hole in a heated hollow container can
be decomposed into its various frequency components.
Classical nineteenth century physics gave a clean prediction
about how that energy is should be distributed among the
frequencies, but the empirical facts did not fit that theory.
Eventually, Planck discovered that the correct formula could
be obtained by assuming that the energy was concentrated
in finite packets, with the amount of energy in each such
unit being directly proportional to the frequency of the
radiation that was carrying it. The ratio of energy to
frequency is called "Planck's constant". Its value is extremely
small on the scale of normal human activity, but becomes
significant when we come to the behavior of the atomic
particles and fields out of which our bodies and brains and
all large physical objects are made.
It took twenty-five years for Planck's "quantum of action" to
be integrated coherently into physics. During that interval
from 1900 to 1925 many experiments were performed on
atomic particles and it was repeatedly found that classical
laws did not work. They gave well defined predictions that
were contradicted by the empirical facts. But it was clear that
that all of these departures of fact from theory were linked to
Planck's constant.
Heisenberg finally discovered in 1925 the completely
amazing and wholly unsuspected and unprecedented
solution to the puzzle of the failure of the classical laws: the
quantities that classical physical theory was based upon,
and which were thought to be numbers, are not numbers at
all. Ordinary numbers, such as 2 and 3, have the property
that the product of any two of them does not depend on the
order of the factors: 2 times 3 is the same as 3 times 2. But
Heisenberg discovered that one could get the correct
answers out of the old classical laws if one decreed that the
order in which one multiplies certain quantities matters!
This "solution" may sound absurd or insane. But
mathematicians had already discovered that completely
coherent and logically consistent mathematical structures
exists in which the order in which one multiplies quantities
together matters. Ordinary numbers are just a very special
case in which A times B happens to be the same as B times
A. There is no logical reason why Nature should not exploit
the more general case, and there is no compelling reason
why our physical theories must be based exclusively on
ordinary numbers. Quantum theory exploits the more
general logical possibility.
An example may be helpful. In classical physics the center-
point of each object has, at each instant, a well defined
location, which can be specified by giving its three
coordinates (x, y, z) relative to some coordinate system. For
example, the location of a spider dangling in a room can be
specified by letting z be its distance from the floor, and
letting x and y be its distances from two intersecting walls.
Similarly, the velocity of that dangling spider as drops to the
floor, blown by gust of wind, can be specified by giving the
rate of change of these three coordinates (x, y, z). If each of
the three numbers that together specify the velocity are
multiplied by the weight (=mass) of the spider, then one gets
three numbers, say (p, q, r), that define the "momentum" of
the spider.
Now in classical mechanics the symbols x and p described
above both represent numbers: the symbol x represents the
distance of the spider from the first wall, measured in some
appropriate units, say inches; and the symbol p likewise
represents some number connected to the velocity and
weight of the spider. Because x and p both represent just
ordinary numbers, the product x times p is the same as p
times x, as we all learned in school. But Heisenberg's
analysis showed that in order to make the formulas of
classical physics describe quantum phenomena, x times p
must be different from p times x. Moreover, he found that the
difference between x times p and p times x must be Planck's
constant. [Actually, the difference is Planck's constant
multiplied by the imaginary unit i, which is a number such
that i times i is minus one.] Thus quantum theory was born
by recognizing, or declaring, that the symbols used in
classical physical theory to represent ordinary numbers
actually represented mathematical objects such that their
ordering in a product was important. The procedure of
creating the mathematical structure of quantum mechanics
from classical physics by replacing the ordinary numbers by
these more complex objects is called "quantization." That
process is an essentially straightforward mathematical
operation, but it needed to tied in some well-defined way to
empirical data before becoming part of science. Establishing
this link involves not just mathematics, in a narrow sense,
but involves also philosophy, in a broad sense.
By the year 1900 scientists believed that they had certainly
discovered the nature of the fabric of reality into which our
experiences are woven. External physical reality was
understood to be composed of moving atomic particles and
changing physical fields. The classical laws governing the
behavior of these physical realities had been proposed by
Isaac Newton, James Clerk Maxwell, and Albert Einstein.
What Heisenberg found out was that in order to
accommodate phenomena in which the value of Planck's
quantum of action is important the symbols, such as x and p,
that appear in the earlier theory have to be replaced by
mathematical objects such that their ordering in a series of
factors matters. What this mathematical change does,
conceptually, is to convert the conception of a particle as a
minute entity into the conception of a "particle" as an
extended cloud-like structure.
Physicists had, for more than two hundred years, imagined
Nature to be composed, at least in part, out of entities
resembling miniature planets. This idea of minute physical
entities had become so deeply entrenched the psyches of
scientists that it had acquired almost the status of an article
of faith: if you do not belief it your not a scientist. But Nature,
as she now reveals herself to us through our observations
and our mathematics, appears to be made out of a very
different kind of stuff. Careful analysis shows that atomic
particles can never reveal themselves to be the tiny moving
objects that they had been imagined to be since the time of
Isaac Newton. Nor is there any reason to believe that such
tiny objects exist at all. Each "particle", insofar as we can
ever know it, may be associated with a particular mass (e.g.,
the mass of an electron) and a particular charge (e.g., the
charge of the electron), but there is no evidence that it has a
particular location. All the empirical evidence is most
parsimoniously represented by taking each atomic particle to
be a cloud-like structure that has a strong proclivity to spread
out over ever-larger regions.
However, this diffusing tendency of the "clouds" does not
proceed unchecked forever. There is a counter process,
which consists of a sequence of "quantum jumps." These
events are sudden collapses of the cloud. At one moment
the form may extend over miles, but an instant later it is
reduced to the size of a speck. Yet how can we make good
scientific sense out of such a crazy idea of how the world
behaves?
Einstein described a simple situation that illustrates the
puzzling character of these quantum jumps. Suppose a
radioactive atom is placed in a detecting device that
responds to the decay of this atom by sending an electrical
pulse to a recording instrument that draws a line on a
moving scroll. A blip in this line will indicate the time at which
the electrical signal arrives. Next, suppose some scientists
are observing the instrument and reporting to each other
where the blip is located on the scroll. What we know is that
these observers will more or less agree amongst themselves
as to the position of the blip. But quantum theory has
stringent laws that govern in principle the behavior of all
physical systems. If one applies these rules to the entire
system under consideration here, which consists of the
radioactive atom, the detecting device, the electrical pulse,
the recording instrument, the bodies and brains of the
human observers, and all other physical systems that
interact with them, then one arrives at a contradiction. What
we know is that the blip seen by the observers occurs at a
fairly definite location. But according to the quantum laws the
full physical system will be a smeared out continuum of
possible worlds of the kind that occurred in classical physics.
In each of these classical-type worlds the blip will occur at
some particular location on the scroll, and all of the
observers will be reporting to each other that they see the
blip at that location. However, the full cloud-like quantum
state will include, for each of the infinity of possible locations
of the blip on the scroll, possible worlds in which the blip
occurs at that location, and in which all of the observers
report seeing the blip occurring at that particular location.
In short, the quantum law, or rule, that governs the behavior
of matter generates a whole continuum of possible worlds of
the kind that appear in our streams of conscious
experiences. The world that you experience is just one tiny
slice of the full world generated by the quantum laws
obtained by incorporating the correct measured value of
Planck's constant into the otherwise incorrect laws of
classical physics.
This mismatch, which lies at the central core of quantum
theory, is a discord between the two distinct parts of science,
the theoretical and the empirical: it is a disparity between
theory and (experienced) fact. These two interrelated
aspects of science are extremely different in character. Each
fact comes as a chunk of somebody's experience. But these
disjoint chunks are related to each other. At one moment you
see a chair, then look away. Upon looking back you see a
chair that resembles the one you saw before. You were
alone in the room, hence no continuous human experience
bridges the gap between these experiential moments. Yet
the two experiences are obviously linked together by
something.
How do we human beings, scientist and nonscientist alike,
deal with the manifest linkages between the disconnected
perceptual facts? The answer is this: we concoct theories!
We create ideas about persisting realities that exist even
when no one is watching them, and that bind the disjoint
facts together. Our physical theories are conceptual
frameworks that we create for the purpose not only of
organizing our perceptual experiences, but also of permitting
us even to have understandable and describable
experiences. We need at least a rudimentary "theory of
reality" even to grasp and describe the idea that some piece
of apparatus has been placed in a certain location and is,
itself, behaving in a certain way. As Niels Bohr succinctly
puts it: "The task of science is both to extend the range of
our experience and reduce it to order.'' [N. Bohr. Atomic
Physics and Human knowledge, p.1 ].
The unique quantum laws produced by the quantization
procedure make predictions about empirical data that are
accurate to as much as one part in a hundred million, and
they correctly describe various features of the behavior of
systems of billions of particles. But Einstein's example shows
that these quantum laws of motion lead also to cloud-like
physical states that are grossly discordant with the more
narrowly defined character of our actual experiences.
You might think that this huge conflict between the
mathematical theory and the empirical facts would render
the theory false and useless. But the amazing thing is that
the creators of quantum theory found that all of the
successes of classical physics and a great deal more could
be explained, without any contradiction ever arising, by
adopting the following dictum: assume that the quantum
generalization of the old classical laws do indeed hold, but if
they lead to a physical state that disagrees with your
empirical observation then simply discard the part of that
(mathematically computed) state that disagrees with your
observations, and keep the rest. This sudden resetting of the
physical state is the "quantum jump." By itself it would yield
nothing. But it is accompanied by a natural statistical law,
which will be described later, that produces all of the
wondrous results just described.
How can a theory of this kind make sense? Well, notice that
you, yourself, like all of us, are continually creating, on the
basis of the best information and ideas available to you a
theoretical image of the physical world around you: you have
an idea about the status of all sorts of things that you are not
currently experiencing. Each time you gain information you
revise that theoretical picture to fit the newly experienced
facts.
Quantum theory instructs the scientist to do the same. That
simple dictum (revise your theoretical picture of the world to
fit the empirical facts), together with its statistical partner,
produces not only incredibly accurate predictions, but every
successful result of the earlier classical physics, and all of
the thousands of successes of quantum theory where
classical physics fails. These impressive results are
achieved by simply allowing the beautiful, internally
consistent, and unique quantized version of the old classical
laws to hold whenever we are not actually acquiring
knowledge about a physical system, but incorporating
promptly any knowledge we acquire. The close connection
maintained in this way between what the mathematical
description represents and what we empirically know
underlies Heisenberg's assertion that the quantum
mathematics ``represents no longer the behavior of particles
but rather our knowledge of this behavior."
The shocker, however, is that Bohr and the other founders
have argued persuasively that no other description of nature
in terms of its atomic constituents can be more complete
than this one, in the scientific sense of telling us more about
relationships between human experiences. That is, this
theory, constructed by incorporating the measured value of
Planck's constant into the old and incorrect classical laws,
appears to tell us everything that a basic physical theory
could ever tell us about connections between empirical facts.
This claim of scientific completeness, made by Heisenberg,
Bohr, and the other founders of quantum theory, was
disputed by Einstein, who tried repeatedly to devise a
counter-example. But the quantum theorists shot down every
try. Thus it does indeed seem to be true that this fantastically
coherent quantization of the older laws generates everything
that is knowable about reality: this quantum description of
nature, crazy jumps and all, appears to be, from a narrow
scientific point of view, our best picture of nature. Any
attempt to add something more may please some
philosophers, but carries us outside of science, regarded
simply as a tool for "expanding our experience and reducing
it to order."
This apparent scientific completeness of quantum theory,
together with the fact that the "quantization" procedure totally
eliminates the classically conceived tiny entities, and
replaces them by cloud-like forms, make plausible the
conclusion that there simply are no classical-type or quasi-
classical-type realities lying behind our thoughts, and that
searching for them is a futile endeavor. The presumption that
such realities exist is therefore a gross philosophical blunder.
There is absolutely no empirical evidence that rationally
supports the notion that there is a physical reality out there
that is better defined than what quantum theory allows. The
assumption that such a quasi-classical type reality exists is
not justified by the scientific evidence, and is thus likely to
produce a conception of both nature and human beings that
is fundamentally incorrect.
But let us be clear about one thing: although quantum theory
is an endeavor to rationally order the empirical facts, and is
therefore erected upon human experience, it does not assert
that our thoughts are the only realities, and matter naught
but an invention of the mind. The founders did not espouse
the philosophy of idealism. (Everything is made out of ideas
alone: "To be is to be perceived.") Their position was the
more conservative one that science is about what we can
know, and that a physical theory must be judged not by
concordance with intuition, but rather by its rational
coherence, its capacity to accommodate the known facts,
and its power to make reliable predictions about future
experiences. This view liberates theoretical creativity: it
allows science, unfettered by ancient prejudice and fallible
intuition, to construct a practically useful and empirically
based new idea of the nature of reality.
Revamping the physics and the philosophy in this radical
way did not satisfy everyone, Einstein and Schroedinger
being the most notable hold-outs. But it did allow the
scientists who accepted it to get on with the business of
developing, testing, and using this immensely successful
theory.
I have stressed that the founders of quantum theory brought
human consciousness into basic theory of nature. But the
really essential point is that your mental life inserted in two
distinctly different ways. The first is as a passive stream of
conscious thoughts that constitutes a growing reservoir of
knowledge: each waking moment adds something new to
what you knew before. The second is as an active agent
endowed with a free will that can influence both how your
body moves and how your thoughts unfold. Explaining and
exploring that active aspect is the purpose of this book. But
to understand yourself as participant you must also
appreciate yourself as the intertwined expanding collection
of knowings upon which your actions are based.
As might be expected, this radical restructuring of physics is
not achieved without some rearrangements of old ideas. For
example, "The Observer" as understood in the original
"Copenhagen" formulation of quantum theory differs from
what one would normally mean by this term. In particular, it
involves an extension of the human observer outside his
physical body. Bohr mentioned several times the example of
a man with a cane: if he holds the cane loosely he feels
himself to extend only to his hand. But if he holds the cane
firmly then the outer world seems to begin at the tip of his
probing cane.
In analogy, "The Quantum Observer" is considered to
include not only the body and mind of the experimenter
himself, but also the measuring devices that he uses to
probe what is outside that extended "self". Thus the world is
imagined to be cleaved into two parts, which are described
in different ways. The outer "observed system" is described
in terms of the quantum mathematics, whereas the inner
"observing system'' is described as a collection of empirical
(i.e., phenomenal or experiential) facts. This way of dividing
the world implements the point, stressed already above, that
quantum physics --- like all of science --- rests on two
disparate kinds of descriptions, the first being of conscious
experiences that we can record, remember, and
communicate to our colleagues, and which form the
empirical database, and the second being of a theoretical
structure that we have invented for the purpose of
comprehending the structure of our experience.
Copenhagen quantum theory regards the measuring
instruments as part of the observer because these devices
are described not in terms of their atomic constituents but
rather in terms of our conscious knowings. Bohr repeatedly
points to this key feature of quantum theory, in statements
such as:
"The decisive point is that the description of the experimental
arrangement and the recording of the observations must be
given in plain language, suitably refined by the usual
terminology. This is a simple logical demand, since by the
word `experiment' we can only mean a procedure regarding
which we are able to communicate to others what we have
done and what we have learnt." (Essays 1958/1962….p.3)
I have described here the basic ideas of the Copenhagen
approach to physics, and explained its essential reliance
upon the experiences of the observers. This philosophical
framework is conceptual container for a rigid mathematical
structure, and this receptacle, or mold, was shaped in large
part by the rigid form that it was designed to hold. That
uncompromising structure, which was generated by
incorporating Planck's quantum of action into the old pre-
quantum laws of physics, captures and reveals aspects of
nature that supercede and negate all the scientific ideas
about the fundamental nature of reality that existed at the
dawn of the twentieth century. So having now described the
philosophical environment that was created to cradle the
new mathematics, and to connect it to empirical data, we are
in a good position to see what that new mathematical
structure is like. The ideas are basically simple, once old
prejudices and obscuring jargon are stripped away. With the
correct tools then in hand, we shall be able to describe the
mathematical rules that allow your thoughts, feelings, and
efforts to influence your mental and physical behavior.
5. THE UNSEEN.
Quantum theory represents our knowledge about the unseen
system being probed by means of a mathematical structure
called the quantum state. This state normally evolves
continuously in accordance with a deterministic law that is
closely connected to the "laws of nature" used in classical
physics. However, at certain instants this orderly progression
is suddenly interrupted by an abrupt "quantum jump". Such a
jump occurs each time one of the observers gains new
knowledge: the jump brings the quantum state into
concordance with the new state of our knowledge. Thus the
quantum state of the system being examined represents
always the evolving knowledge of the community of
communicating observers.
But how can a mathematically described state represent
human knowledge?. Our knowledge seems to be an
ephemeral and ineffable vagary, whereas the mathematically
described states of quantum theory are precise structures
that allow empirically observed numbers to be computed to
an accuracy of one part in a hundred million.
To explain this connection I need to introduce two
mathematical ideas: "Hilbert space", and "projection
operator". These names may sound intimidating, but the
ideas are basically simple, and understanding them will allow
you to grasp the essence of quantum theory.
A Hilbert space is a collection of vectors, and a vector is a
displacement by a specified amount in a specified direction.
Two vectors, A and B, can be added together to give a
vector C, which is formed by adding together the
displacements A and B.
Consider, for example, the displacement from the corner of a
room where two walls and the floor meet to a point on one of
these two walls. That displacement is the sum of a vertical
displacement up from the corner plus a horizontal
displacement along the wall that contains the point.
If the two vectors A and B that add to give C are
perpendicular to each other, as in this example, then the
theorem of Pythagoras asserts that the square of the length
of A plus the square of the length of B equals the square of
the length of C.
This celebrated theorem is tied to the probability rules of
quantum theory: If C is a vector of length one (i.e., unity) and
A and B are two perpendicular vectors that sum to C, then
the square of the length of A plus the square of the length of
B is unity (i.e., one). The two perpendicular vectors will
correspond to two alternative possible outcomes of a probing
action, and the square of the length of A will be the
probability for the event associated with A to occur, and the
square of the length of B will be the probability for the event
associated with B to occur. The sum of these two
probabilities is unity by virtue of the theorem. This accords
with the fact that the probabilities associated with alternative
possibilities must sum to unity.
In the example of the point on the wall, the space of vectors
is two-dimensional: any point on the wall can be reached
from the corner by a sum of just two displacements, one in
each of the two pre-specified perpendicular directions,
vertical and horizontal. We can also easily visualize
displacements in a three-dimensional space. But it is
possible to consider mathematically an N-dimensional vector
space in which there are exactly N mutually perpendicular
directions, and each vector in the space is a sum of N
vectors, one directed along each of these N directions. We
allow null displacements and also negative displacements,
which are the same as positive displacements in the reverse
direction.
A set of N vectors, each perpendicular to every other one, is
not easy to visualize, geometrically, for large N. But if one
uses an algebraic approach in terms of sets of numbers,
then the examples of vector spaces in one, two, and three
dimensions are easily generalized to spaces of arbitrarily
large but finite dimension N. With a little more effort one can
even go to the case where N is infinite. Hilbert spaces
include the infinite-N cases, but that is a technical matter that
need not concern us here. It will be enough to think of simple
cases where N in finite.
If a vector V is composed of a sum of N perpendicular
vectors then a generalization of the theorem of Pythagoras
shows that the square of the length of V is the sum of the
squares of the lengths of these N mutually perpendicular
vectors that add up to form V.
The second important concept is the idea of a projection
operator. A projection operator P acts on a vector V to give a
new vector PV. The action of P eliminates a specified subset
of a set of perpendicular vectors that add up to give the
vector V upon which it acts, but leaves unaffected the
remaining vectors in the sum. Thus, for example, the vector
V from the corner of a room to any point in the interior of the
room would be converted by a certain projection operator P
to the vector PV that is the displacement from the corner to
the point on the floor that lies directly under that point in the
room: the vertical vector is eliminated by the action of this
particular projection operator P.
That example is a very special case. For one thing the three
perpendicular vectors were very special, involving one
vertical vector and two particular horizontal ones. But one
can imagine replacing the room by a cubic box, and consider
the infinity of ways that this box could be oriented relative to
the room. For each of these orientations the three edges that
meet at a corner define three perpendicular directions. Then
one can go from N = 3 to arbitrary N, and select any subset
of the set of N perpendicular directions to be the set that is
not set to zero. This obviously gives a huge set of logically
possible projection operators P.
For each projection operator P there is a unique
complementary projection operator P' that does not set to
zero exactly the subset of the N perpendicular vectors that is
set to zero by P. Thus for any vector V, it is true that PV +
P'V = V. The vectors PV and P'V are two perpendicular
vectors that sum to V.
Given this simple idea of a vector, and how a vector in an N
dimensional space can be considered to be a sum of a set of
N vectors, each of which is perpendicular to every other one,
we can now state the basic idea of quantum theory: Our
knowledge about the unseen system, gleaned from earlier
experience about things we can see, is represented, under
certain ideal conditions, by a vector V of unit length. This
vector evolves under the action of a rule called "the
Schroedinger equation", which alters the direction that V
points, but leaves its length unchanged.
When the outcome of a probing action appears the vector V
suddenly jumps to the vector PV or to P'V, where P is the
projection operator associated with the probing action, and
P' is the complementary projection operator. The probability
of V jumping to PV is the square of the length of PV and the
probability that the jump will be to P'V is the square of the
length of P'V. These two probabilities add to unity, by virtue
of the theorem of Pythagoras. This property matches the
property of probabilities that their sum over any set of
alternative possibilities must be unity.
The essential point here is that our knowledge of the unseen
system being probed can, according to quantum theory, be
associated with a vector V in a Hilbert space, and this
association gives simple rules for the probabilities for the
alternative possible outcomes of our probing action to
appear, once the form of the projection operator P is known.
With this general picture in mind we can now return to the
question of how our knowledge is represented
mathematically.
According to quantum theory the polarization of a photon is
represented by a vector V in the two dimensional space that
is perpendicular to the photon's line of flight. Suppose a
photon is allowed to fall on a crystal that splits the beam so
that the part polarized along direction A1 is deflected to a
photon detector D1 and the part polarized in the direction
A2, perpendicular to A1, is deflected to a photon detector
D2. If the detectors are 100% efficient then one or the other
of the two detectors will fire, but not both.
In this example the probing action is associated with the
projection operator P such that the vector PV is directed
along A1 and P'V is directed along A2. The vectors PV and
P'V represent the alternative possible outcomes of the
probing action. If the observer sees detector D1 fire that he
knows that the system being probed is in state PV; if he sees
detector D2 fire then he knows that the system being probed
is in the state P'V. Thus quite accurate information about the
new state of the unseen system can be gleaned from the
empirically discernible fact of whether D1 fires or D2.
Discarding the part of the state V=PV +P'V that is
incompatible with the empirical fact that D1 fires and D2
does not, or vice versa, is non problematic.
The successive action upon a vector V, first of the projection
operator P1 and then of the projection operator P2 is
represented by V'=P2 P1 V. In general this vector is different
from V''=P1 P2 V: the order of in which the two operators P1
and P2 appear matters! This can be easily verified in simple
cases, and is not mysterious. All dependences of products
on the ordering of the factors in quantum theory can be
traced to this completely understandable dependence.
I specified at the beginning that V represented of our
knowledge of the system being probed. Thus there is no
problem with the fact that V suddenly changes when an
observer acquires new knowledge by seeing one of the two
the detectors, D1 or D2, fire and the other one not fire.
However, this facile way of speaking glosses over some
deep problems. This vector V seems to be connected more
closely to the state of the photon itself than to human
consciousness. The very fact that the photon could be
represented by a vector, and that this vector should evolve
normally in accordance with the Schroedinger equation was
a consequence of incorporating Planck's constant into the
equations of classical physics. That quantization procedure
converted the old classical-type of reality into the new cloud-
like (or vector-type) replacement. This transformation seems
to be an objective change, not related specifically to human
consciousness. Moreover, the stability of matter itself, and
the formation of the elements, are all understood in terms of
these quantum equations of motion. All of this structure and
process predates human existence. The original
Copenhagen pragmatic way of understanding the quantum
mathematics, while tremendously useful as a stepping stone,
closes the door to any real understanding of the reality that
replaces the one that empirical phenomena has ruled out.
6. THE PARTICIPANT
Niels Bohr, the principal architect of quantum philosophy,
wrote that we cannot forget "that in the drama of existence
we ourselves are both actors and spectators." [Essays
1958/62 on Atomic Physics and Human knowledge, p.15]
This comment succinctly captures a key point of quantum
theory: the human observers are no longer passive
witnesses to a flow of physical events that they cannot
influence. They are essential players in the action: their
"free" choices can influence the flow of physical events.
Quantum theory, in spite of its idealistic content, is
formulated in a completely realistic and practical way. It is
structured around the activities of human agents, who can
probe nature in any of many possible ways. Bohr
emphasized this freedom of the experimenters in passages
such as:
"The freedom of experimentation, presupposed in
classical physics, is of course retained and corresponds
to the free choice of experimental arrangement for which
the mathematical structure of the quantum mechanical
formalism offers the appropriate latitude."
The point here is that quantum theory, in its original form, is
set up in terms of an interaction between conscious human
agents and an invisible quantum system. As already
discussed, that system is represented in the theory by a
vector in Hilbert space. This vector usually evolves
according to the quantum law of motion, the Schroedinger
equation. But to get information about that system the
experimenter must ask specific questions by setting up
corresponding probes. For example, the experimenter can
orient the crystal in the photon experiment described earlier
in any way he chooses. Different choices correspond to
different choices of the two perpendicular directions A1 and
A2. Moreover, the human agent can choose to do or not do
the experiment, or to do it sooner or later. These choices
are, according to our basic physical theory, quantum theory,
not fixed by any yet-known laws of nature. Hence these
choices are, in that specific sense, "free choices".
We have now arrived at the crux of the matter! Quantum
theory, in its orthodox formulation, involves the human
observer not merely as a passive recipient of data, but also
as an active agent that enters into natural process in ways
that are not controlled by the known physical laws. His
specific role, as it appears in the world of experience, is to
select which experiment is to be performed: i.e., to choose
which aspect of nature will be probed. This role, as it
appears in the mathematics, is to select some one single
projection operator P. This P is the projection operator such
that the initial vector V will become PV if nature delivers the
affirmative answer 'yes' to the posed question, but will
become the vector P'V if nature delivers the negative answer
'no'. Here P' is the projection operator that keeps the vectors
that P eliminates, and hence satisfies the condition
PV+P`V=V for all V.
[Sometimes a complex question involving a combination of
several projection operators can be considered. But these
can be regarded as a sequence of individual P's, and I shall
adopt this simpler way of speaking.]
The essential point here is that, according to orthodox ideas,
nature's process of generating the experiences that appear
in our streams of consciousness cannot proceed without
particular questions being posed. But then the two key
questions become:
If the known physical laws do not determine the choices that
need to be made by the human agents in order for nature's
process of generating human experiences to proceed, then
what sort of considerations do influence or determine these
choices?
and
What effect do these "free" choices have on the course of
physical events?
The evolution of the unseen system involves a sequence of
questions with Yes or No answers. Hence the interaction
between nature and agent is like a game of twenty-
questions: the agent is free to choose a sequence of Yes-No
questions, and nature delivers an answer, Yes or No, to
each, in the form of an experience that answers the posed
question. The choice of question is represented within the
mathematical description as the selection of one projection
operator P from among an infinite continuum of possibilities.
Each possible P corresponds to particular way of orienting a
set of N mutually perpendicular vectors, and, then, a
particular choice of which of these N vectors will be
eliminated to form PV. The process of making these
particular choices of P's is not specified by the Schroedinger
equation, which controls the continuous evolution of the
physical state between observations, but neither the agent's
choices of the questions nor nature's choices of the answer.
In particular, a complete account of the dynamics needs to
explain an as-yet-unexplained process that picks a
sequence of particular P's from a continuum of possibilities.
This selection process is associated, according to orthodox
quantum theory, with consciously made free choices on the
part of human beings. And, according to the quantum rules
themselves, these "free choices" can influence the course of
physical events, as we shall presently see.