Quantum Quandries - Part 3
Bell's interconnectedness theorem
No one was
able to either refute or to confirm the foregoing sorts of thought experiments until
around the mid-1960s. Then, John Bell came forward with his theorem on
interconnectedness.
The problem
that initially attracted Bell's attention, and which would eventually lead to the
development of his theorem of interconnectedness, was David Bohm's counter-response to von
Neumann's 'irrefutable proof'. This proof allegedly showed how all hidden variable
theories were necessarily inconsistent with the results of quantum mechanics.
During the
mid-1960s, John Bell decided to investigate Bohm's model in order to try to determine how
it could succeed when, supposedly, von Neumann had proven that a model of the sort
proposed by Bohm could not possibly be successful. Bell discovered that von Neumann's
argument was not as ironclad as many physicists had believed it to be. More specifically,
von Neumann had claimed that if objects which had dynamic properties as an intrinsic part
of their nature were to be combined in ' reasonable' ways , then, one would not be able to
use such combinations in a way that would allow one to replicate the predictions of
quantum theory.
While Bohm's
combination of a pilot wave and a particle was quite reasonable (the signal problem aside)
and while his model was entirely capable of duplicating the results of quantum theory, it
fell outside the parameters of what von Neumann had in mind as being a reasonable sort of
combination. In other words, von Neumann's proof was faulty in as much as it rested on an
untenably narrow conception of what constituted a reasonable combination of objects.
Having laid
bare the limitations of von Neumann's proof, Bell continued to explore the issue of
whether or not there were necessary limitations to the character of the ontological ground
in which quantum facts were rooted. He subsequently put forth a proof, now known as Bell's
theorem, which claimed to show that all models of reality must necessarily be non-local
in character.
By the term
"non-local", Bell means the following. The values attributed to a given physical
event during the process of measurement are a function of not only local factors which are
contiguous or proximate to the event being measured, but such measured values are also the
result of non-local influences. Non-local influences are so distant from the measured
event they would have to travel faster than light in order to be considered contiguous or
proximate to the measured event.
Physicists
believe that whenever a particle moves, its associated field is distorted. The structural
character of the distortion initially occurs near the object which is moving, and, then,
the distortion spreads out through the field.
According to
Einstein's theory of special relativity, there is an inherent limit on how quickly not
only the field distortion, but, also, how quickly the associated particle, can move
through space. This limit is the speed of light.
This
inherent physical limitation on the rate of transmission or movement imposes constraints
on the idea of locality. Essentially, the constraint means locality has an upper limit
that is defined by the velocity of light. Anything which falls outside the so called light
cone in a given set of circumstances falls beyond the horizons of the conditions of
locality.
Generally
speaking, the notion of non-local influences is interpreted to mean that such influences
are transmitted instantaneously and would not fall off with distance. Furthermore,
non-local influences, unlike local forces or influences, do not require mediation.
Consequently,
according to Bell's theorem, any given physical event is subject to influences from many
different parts of the universe. Moreover, these influences occur irrespective of whether
they can be shown to be contiguous or proximate in any usual sense of these words.
The general
structure, in brief, of Bell's argument is as follows. He begins by accepting, at least
tentatively, the assumption of locality. This means that not only must interaction among
particles take place on a contiguous basis, it also means the transmission of influences
or signals cannot be superluminal in character. He, then, proceeds to show, by means of
simple arithmetic, that there is a certain inequality (which has come to be known as Bell's
inequality) which must be satisfied by all experiments of the sort proposed by EPR,
Bohm and others. Finally, he notes this inequality is not satisfied whenever such
experiments are run, and, therefore, he concludes the original assumption of locality is
not tenable.
If the
assumption of locality is not operable as a basis for interactions in the physical
universe, the only alternative seems to be maintain that interactions are governed, at
least in part, by the principle of non-locality in which influences, forces and so on are
transmitted through an action-at-a-distance process. Such processes are unmediated in the
sense that a given force or influence is transmitted from, say, one particle to the next
without requiring any intermediate steps.
Bell
maintained that irrespective of whether: (a) one advocated a model of reality which
presupposed that dynamic properties are intrinsic to an object's structural character (as
Bohm did in his pilot wave model), or, (b) one advocated a model of reality which
presupposed that dynamic properties arise external to the object (as the Copenhagen school
proposed), both models required the presence of non-local influences. These sorts of
influences are required in order to be able to account for the structural character of
quantum facts.
In other
words, there seems to be an aspect of any given ontological context which necessarily is
an expression of, and shaped by, faster than light transmission. Such influences are
manifested in the quantum facts which have arisen from the experimental data.
Therefore,
any model of reality, no matter what its position on the issue of dynamic properties, must
incorporate non-local influences into the model in order to be able to adequately reflect
the character of the actual facts of quantum phenomena. Stated in another way, Bell's
theorem stipulates that any attempt to introduce a hidden-variable approach to account for
the observed data of quantum physics cannot succeed unless it incorporates one or more
features that are superluminal (i.e., faster than light) in character.
The theorem
proposed by Bell emerges out of the same kind of modified version of the original EPR
experiment as had been devised by David Bohm. Essentially, the experimental set up
involves the following elements.
A light
source emits photons in opposite directions from one another. At some distance from the
light source there are calcite detectors. Calcite is a birefringent crystal which
is capable of distinguishing between photons according to whether their plane of
polarization is directed along the optical axis of the crystal or at right angles to that
optical axis. These detectors are capable of providing a polarization measurement at
various angles when the photons from the light source engages the detectors.
Finally,
although the states of polarization of any given pair of photons reflect one another
precisely when they are measured at the same angle at the different calcite
detectors, nonetheless, taken as a collective group, consisting of many pairs of emissions
over time, the photons are unpolarized. This is so since no matter what angle is selected
for measuring the various photons, one gets an unpredictable, 50-50 mixture of the two
possible orientations for their planes of polarization.
Bell focuses
on the property of correlated polarizations. Correlated polarizations are, in
contrast to the description given in the previous paragraph, independent of the angle at
which the two photons are measured by their respective calcite detectors. In other words,
although the angle at which polarization measurements are taken at the two calcite
detector sites may be different, if the measurements indicate the same state of
polarization in each of the photons, this is counted as a match, otherwise it is a
mismatch.
According to
quantum theory, the property of correlated polarization depends only on the relative angle
between the two calcite crystals and does not depend on the specific angle settings at the
two calcite detector sites. In other words, as long as one keeps the relative angle
between the detectors the same, one can choose any angle setting one likes at the two
calcite crystals, and quantum theory predicts the photon pairs will exhibit correlated
polarization states. Moreover, this prediction has been confirmed through a variety of
experiments.
Bell was
interested in looking at the character of the correlation patterns at different angles
(running from 0 to 90 degrees) for long runs of emitted photon pairs. Such correlation
patterns can be expressed as a fraction of matches to mismatches (i.e., correlation versus
no correlation) which ranges from perfect positive correlation of 1, when all pairs
exhibit correlation, to a correlation of 0, when there are no matches in the emitted
pairs.
Furthermore,
Bell wanted to examine the above mentioned variation in the correlation pattern at
different angles under the assumption of locality. Translated into the terms of the photon
experiment outlined previously, locality means one works on the assumption that what is
occurring at one calcite detector site cannot affect what is happening at the other
calcite detector site.
Thus, when
one varies the angle setting of one calcite detector, this should affect only the
measurement at the site where the angle setting has been altered. The measurement at the
other calcite detector site should be independent of such changes.
Bell's
inequality is rooted in the assumption of locality. Essentially, the inequality says: the
fraction of matches to mismatches one gets, when comparing the polarization states
measured at a given angle at the two calcite detection sites, should be equal to, or less
than, what one gets with measurements made when the calcite detectors are misaligned by a
factor of twice their current angle values. The possibility of coming up with a fraction
which is less than twice what one would expect at the larger angle is to acknowledge that
the way of counting matches and mismatches may overlap on some occasions as one varies the
angle of measurement.
The problem
with the predictions which are made on the basis of the assumption of locality, via the
Bell inequality, is that experiments do not confirm it. In fact, experiments indicate the
fraction of mismatches to matches will exceed the Bell inequality when the calcite
detectors are misaligned by a factor of twice the previous angle values at which
correlation values were recorded.
Since
experiments have shown that Bell's inequality is violated, one must consider what has to
be jettisoned as the problematic factor which leads to experimental results contrary to
what theory predicts. As it turns out, there is only one component of the theory
underlying the experimental set up which cannot be verified independently of Bell's
experimental proposal. The unconfirmed component is the assumption of locality.
Consequently,
in light of the experimental results, the assumption of locality seems not to be tenable.
Furthermore, this conclusion, apparently, forces one, in turn, to suppose the condition of
non-locality governs physical reality. That is, unless one assumes the condition of
non-locality prevails, how does one account for the experimental results which violate the
Bell inequality?
The
experimental basis for Bell's theorem concerning the interconnectedness of all aspects of
the universe lies with his demonstration that the inequality which is rooted in the
assumption of locality is not supported by experimental evidence. In other words, Bell's
demonstration is not based on having experimentally verified the existence of the
condition of non-locality. The nature of his argument is that he has shown something which
is consistent with the assumption of non-locality and, therefore, serves as a sort of
indirect verification of the assumption of non-locality.
Generalizing
the results of the photon polarization experiment to physical events, is based on the idea
of phase entanglements in configuration space. More specifically, assuming conditions of
non-locality have been established in a particular case, one might argue that phase
entanglements offer the perfect opportunity for the condition of non-locality to be given
expression across all manner of events. Thus, if one assumes the condition of non-locality
holds, then, when various influences and forces are passed on through phase entanglements,
events which are separated by distance, can, nonetheless, affect one another.
In effect,
Bell's theorem has raised the status of the idea of phase entanglement from one of
representation in the mathematical creation of configuration space, to an actual
ontological entity which has real, experimentally verifiable results. Although not all
physicists accept Bell's arguments or his conclusions, nonetheless, no one, to date, has
come up with a plausible alternative to Bell's position.
The ontology of quantum theory
Although
most quantum physicists claim not to be concerned about the actual character of quantum
reality and say their only interest is in being able to generate reliable methods for
solving various problems of prediction and calculation in relation to quantum events,
there is, nonetheless, an underlying ontological perspective which is tacitly held by the
vast majority of quantum physicists. Moreover, this perspective (which Herbert refers to
as the orthodox ontology) is rooted in a postulate about the character
of unmeasured quantum entities that is neither logically defensible nor experimentally
verifiable.
Essentially,
this fundamental postulate stipulates the following. Quantum entities represented by the
same wave function are not only in the same state, they also are identical to one another
in all physical respects.
However,
while quantum physicists contend there is a sameness of being among all quantum entities
which can be represented by a given wave function, this ' fact ' of the sameness of being
does not guarantee that a sameness of will ensue. Indeed, according to the tenets of
orthodox ontology, there is an inherent randomness in the character of reality such that
identical conditions are, nevertheless, capable of giving rise to variable results.
For example,
in electron diffraction experiments, from the point of orthodox ontology, all the
electrons released from the metal filament at a given setting of voltage, and so on, will
be precisely the same. However, the identical electrons will engage a variety of different
phosphor molecules at various points of the screen due to the element of intrinsic
randomness which is a characteristic of ontology at the quantum level of scale.
There is
another feature which follows from the two fundamental postulates of orthodox ontology
(i.e., quantum entities in the same state are ontologically identical and the
intrinsically random nature of ontology). This additional feature concerns the
relationship between the statistical character of quantum events and the character of any
given individual quantum entity among the entities being collectively tabulated by the
statistical description. In effect, from the point of view of orthodox ontology, there is
no real difference between a statistical description and an individual description. The
statistical description is merely the individual description writ large.
Consequently,
even if one cannot always deal with individual quantum entities, statistical descriptions
will permit one to have access to the same sort of information as if one were studying
individual quantum entities. In short, quantum statistical descriptions will accurately
reflect the character of individual quantum entities.
The feature
of intrinsic randomness plays a key role in the Copenhagen school's contention that the
quantum theory's statistical description of events is as complete as one is ever going to
get. The quality of intrinsic randomness leads the proponents of the Copenhagen school to
conclude there are no hidden variables which must be sought in order to get a more
complete and determinate account of the way things are.
For
instance, on the above view, there is no hidden cause why identical electrons turn up at
different points on the phosphor coated screen. The differences in are simply an
expression of the property of intrinsic randomness at work. As a result, the search for
hidden variables is really misguided and doomed to failure.
Dimensional dialectics: an alternative perspective
Neither
particles nor waves are the basic "stuff" of the universe. Both are effects of
an underlying spectrum of constraints and degrees of freedom that constitutes the
structural character of a given object, event, condition, process, or state as it unfolds
over time through engaging and being engaged by various aspects of ontology.
A spectrum
of ratios of constraints and degrees of freedom is the manifestation of a dialectic of
dimensions which is generated, set into motion, shaped and regulated by an order-field.
The dialectic of dimensions establishes the parameters, themes, currents, and so on, out
of which arise, on another level of scale, wave-effects and particle-effects of various
structural character.
Space, time,
consciousness, will, life, intellect, energy, emotion, and materiality are all examples of
dimensions. The foregoing list of 9 dimensions do not necessarily exhaust dimensionality,
but they are the ones with which we are most familiar. When they dialectically interact
with one another, they are capable of generating much of the physical, intellectual, and
emotional phenomena that are normally encountered during the course of day-to-day
experience.
Each of
these dimensions introduces a particular thematic orientation which is peculiar to that
dimension and not shared by any other dimension. The temporal dimension, for example, has
one kind of orienting influence, whereas space or consciousness have quite different
orienting influences.
One cannot
derive space from time or vice versa, nor can one derive consciousness from temporality or
spatiality, just as one cannot derive temporality or spatiality from consciousness. The
same is true of all the other dimensions. In short, each dimension is capable of being
expressed as a unique set of constraints and degrees of freedom.
Therefore,
on the view of the foregoing perspective, instead of treating space as being 1, 2, 3, or
n-dimensional (depending on how many different axes are used to set up a coordinate system
to represent the ordered n-tuples constituting the points of the various aspects of that
coordinate system) space can be considered to be just one dimension, consisting of
n-degrees of freedom. Thus, space which has breadth, width, and height would have
three degrees of freedom, whereas, space which required fewer or more axes to describe its
characteristics would have fewer or more degrees of freedom. Furthermore, associated with
each degree of freedom is one or more constraints which mark the limits of that degree of
freedom.
Similarly,
on the basis of the perspective outlined above, time is not the fourth dimension. This
terminology is often used because in scientific/mathematical descriptions time is usually
the fourth axis of a coordinate system or the fourth component of a given algebraic
n-tuple. However, time is just one dimension among a number of dimensions, and, like other
dimensions, it has a certain number of degrees of freedom and a certain number of
constraints that are associated with these degrees of freedom.
One of the
special characteristics of the temporal dimension is the way in which it interacts
with all the other dimensions. In a sense, time is a common currency (there may be other
common currency dimensions) of the multi-dimensional manifold that constitutes ontology.
By means of the phase relationships which time forms with every dimension, a common ground
arises through which different dimensions can dialectically interact with one another.
These phase relationships are like currents running through the temporal dimension.
The
dialectic of these temporal phase currents generates complex waveforms containing phase
information components from many different dimensions. Within these phase waveforms,
considered individually, and during the interaction of these waveforms, between and among
themselves, phase information is exchanged.
Phase
information has the capacity to bring about shifts or transitions in the way in which
those dimensions involved in the interaction express themselves. Through these shifts, a
given spectrum of constraints and degrees of freedom gives expression to a mode or facet
of its structural character which is different from the mode that was being manifested
prior to the exchange of phase information.
In effect,
the above position suggests human beings are rooted in phase space. In phase space, focal
awareness marks the point of origin of a multi-dimensional co-ordinate system or manifold.
This manifold consists of point-structures which give expression to ordered n-tuples of
phase relationships. These n-tuple point-structures combine together to form
neighborhoods, lattices, and latticeworks.
The
hermeneutical operator is capable of combining together different phase n-tuple point
structures and operating on these point-structures in a variety of ways. As a result of
the activity of the hermeneutical operator, complex structural waveforms can be generated,
shaped and modified in ways that alter the structural character of previously existing
point-structures, neighborhoods and latticeworks.
The modified
or new structures which are generated through the activity of the hermeneutical operator
give rise to a new set of phase relationships. Thus, the capacity of human beings to be a
multi-dimensional, multi-level-of-scale phase relationship processor, through the common
currency of the temporal dimension, allows qualitatively different kinds of dimensions to
be brought together to form various kinds of complex, structural, phase waveforms.
The
character of the dialectic of dimensionality is an expression of what goes on, on yet
another level of scale. This new level of scale is the order-field, and it
permeates all other levels of scale. Or, said in another way, all other levels of scale
are rooted in, generated by, and give differential expression to, the order field.
Thus, the
order-field forms an even more fundamental common currency basis for the exchange of
various kinds of information among different dimensions than do phase relationships. In
fact, phase relationships are a manifestation of this common currency aspect of the
order-field. On any given level of scale, and for any given point-structure, neighborhood
or latticework, a spectrum of ratios of constraints and degrees of freedom is, ultimately,
an expression of the different modes through which the order-field manifests itself.
Seen from
this perspective, although different dimensions have different spectra of ratios of
constraints and degrees of freedom associated with them, or to which they give expression,
the 'stuff' out of which the various structures of the world are constructed is an
expression of the manner in which the order-field, first, generates, and, then, brings
into dialectical interaction, the various dimensions. Thus, the exchange of information
takes place on the level of the common currency of ontology- the order-field, and is,
subsequently, given manifestation through the phase relationships which arise among
different ratios of constraints and degrees of freedom on a variety of levels of scale.
The
order-field (which generates, shapes and regulates the dialectic of dimensions)is somewhat
like a Turing machine that is completely self-regulating or autonomous. The order-field is
capable of spontaneously creating and reading out its own codes and, then, translating
these codes into dimensional attractors. Moreover, the order-field is capable of
establishing the sequence in which all of this is to be done, as well as: how, to what
extent, when, and for how long, different dimensional attractors are to engage one
another.
Seen from a
slightly different perspective, the order-field is like a fully integrated, but extremely
complex, genetic system consisting of all the necessary components for a full complement
of order-field counterparts to anabolic and catabolic functioning. Therefore, the
order-field can generate, support, maintain, regulate, dissolve and vector the dialectic
of dimensions in whatever way is indicated by the order-field itself.
In this
context, the dimensions are like genes which interact with one another to give expression
to various characteristics through different dimensional counterparts to the phenotypic
levels of scale, ranging from cell bodies (such as ribosomes, golgi complex, nucleus,
etc.), to simple cells, to tissues, to organs, to integrated organisms. Consequently,
wave-effects and particle-effects would be phenotypic-like manifestations on an
appropriate level of scale of dimensional ontology.
As a
particular kind of dialectic of dimensional 'genes' is turned on or activated, a
wave-effect manifests itself. As another kind of dialectic of dimensional genes is turned
on, a particle-effect manifests itself. Furthermore, under certain circumstances, both
sorts of dialectics of dimensional genes may be operational simultaneously.
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