Quantum Gauge Theory - Part 4
Semiotic quanta as vector bosons
In 1954 C.
N. Yang and Robert Mills proposed an isotopic-spin symmetry model. This
theory began as a model intended to account for interactions involving the strong force,
but after it was successfully re-normalized, investigators began to approach it as a
possible model of weak force interactions.
According to
Yang and Mills, when the rotational states of isotopic-spin are permitted to vary from one
point of the field to the other (i.e., when the field is given a local gauge character),
the laws of physics would remain invariant only if one introduces six, new, vector fields
of infinite range. These six fields involved three vector bosons (bosons are particles
that carry force).
Among the
new fields proposed by Yang and Mills, were two which were different from the photons
usually encountered in physics. Although the Yang-Mills 'photons' were spin-one, massless
particles, just like the normal photons carrying the force of an electromagnetic field,
they had the further property of carrying a charge. In other words, one of the new vector
fields involved positively charged photons, while the other new vector field involved
negatively charged photons, whereas 'normal' photons carried no charge.
If one
permitted photons to have charges of different character, this would set the stage for
photons, which are carriers of force, to interact with themselves and result in a variety
of strange phenomena that have not been experimentally observed. Consequently, the idea of
a charged-photon field tends to be ruled out as being unreconcilable with observable
reality.
Although
physics does not permit charged photons to interact because of the strange effects that
would arise when the carriers of electromagnetic force interact with one another,
hermeneutical field theory does not preclude semiotic quanta interacting with one another,
despite the fact that semiotic quanta are the carriers of hermeneutical force. Indeed,
neighborhoods, lattices and latticeworks are generated when semiotic quanta engage one
another - and this sort of phenomenon is not at all inconsistent with empirical
observation.
The
structural character of any given amalgamation of point-structures in the form of a
neighborhood or latticework depends on the dialectical character of the underlying set of
semiotic-semiotic quanta engagements, together with the sorts of phase relationship which
are established as a result of such dialectical engagements.
The idea of
a semiotic-semiotic quanta engagement seems to suggest it is a sort of mechanical process
which is, more or less, straightforward, without any need of conscious intervention or
without any room for an intentional shaping of the structural character of that
dialectical process. Nonetheless, while it is possible for such autonomous,
semi-consciousness or non-conscious kinds of hermeneutical activity to occur, the
component of reflexive consciousness is, to some extent, able to exert a directing,
orienting, limiting, shaping, modulating, and organizing influence on how the
semiotic-semiotic quanta dialectical interaction unfolds.
Reflexive
consciousness has the capacity to engage things at several different levels of scale. One
level of scale would be in relation to each of the components of the hermeneutical
operator (including itself).
For example,
when one is aware that an identifying reference of a particular kind is being made, and
one is aware that one is aware of this by reflecting on the character of the identifying
reference while it is being made, the component of reflexive consciousness is
dialectically interacting with the component of identifying reference. The same can be
true for all of the components of the hermeneutical operator. On this level of scale, the
reflexive consciousness/hermeneutical operator dialectic constitutes the primary
focal/horizonal event.
On another
level of scale, the component of reflexive consciousness reflects on the structural
character of the thematic currents which are being collectively contributed by all of the
other components of the hermeneutical operator. In this case, the component of reflexive
consciousness has the opportunity to integrate, or bring together, to some degree, the
character of that collective tensor-matrix as it engages, or is engaged by, the thematic
currents of certain aspects of the focal/horizonal dialectic of which the given semiotic
quantum is a part. On this level of scale, reflexive consciousness serves to bring
together a given semiotic quantum in the context of a broader or more complex
focal/horizonal dialectic.
On either of
the foregoing levels of scale, the component of reflexive consciousness brings together
the phase relationships linking a number of point-structures, neighborhoods, or
latticeworks. This is done in order to be in a position to apply, if appropriate and/or
required, various hermeneutical transformations to these phase relationships. Such
transformations would be an expression of the tensor-matrix character of a given semiotic
quantum that was engaging some aspect of the focal/horizonal dialectic.
In the
context of quantum electrodynamics, one can have an electron undergoing several,
successive phase transitions, such as, for example, the emitting and absorbing of a
photon. The end result of this sequence of phase transitions will be the same irrespective
of whether a photon is: first, emitted and, then, absorbed; or, first, absorbed and, then,
emitted. Thus, in such fields, symmetry is preserved with respect to phase shift
transformations irrespective of the order of sequence of such transformations.
In
Yang-Mills isotopic-spin local gauge fields, however, the order in which a sequence of
rotational transformation occurs does affect the outcome of the transformation process.
For instance, in one sequence of rotational transformations, the result might be a proton.
Yet, if one were to reverse the order of the sequence of rotational transformations, the
result might be a neutron.
A system in
which the order of sequence of a series of transformations makes no difference in the
outcome of such transformations is referred to as an Abelian system.
On the other hand, a system is known as non-Abelian when the order of sequence of a
series of transformations does make a difference in the character of the outcome of such
transformations.
Quantum
electrodynamics, general relativity theory, and Yang-Mills fields are all examples of
non-Abelian gauge field theories. In fact, apparently, all of the fundamental forces of
nature are expressions of non-Abelian gauge field theories
The
hermeneutical force which is carried by the semiotic quantum is also quite frequently,
though not necessarily always, non-Abelian in character. Thus, the order in which a
sequence of rotational transformations of the hermeneutical isotopic-spin component is
carried out often makes a difference to the structural character of the outcome of such
transformations.
For example,
if one asked several questions, the order in which the questions were asked might affect
the direction in which subsequent inquiry proceeded. Or, if one carried out a sequence of
inferential mappings, one might generate different outcomes, depending on the sequence in
which the mappings occurred, and so on.
The same
principle is also characteristic of the other components of the hermeneutical operator or
semiotic quantum. Therefore, like field theories involving the other fundamental forces of
nature, quantum hermeneutical-dynamics often give expression to a non-Abelian gauge field
theory.
The Higgs mechanism and the breaking of symmetry
As indicated
earlier, the idea of an electrically charged photon which was lighter than the electron
had physical ramifications capable of totally altering the structural character of
reality. Since such a reality is contrary to our experience, there were a number of
theoretical suggestions for dealing with these anomalous aspects of the Yang-Mills model.
These
suggestions had several goals. On the one hand, they wanted to avoid the problems entailed
by postulating the existence of electrically charged photons. On the other hand, theorists
wanted to retain those aspects of the Yang-Mills model which were quite attractive, both
heuristically, as well as, aesthetically.
Some of
these suggestions focused on finding a means of introducing mass into the fields
postulated by the Yang-Mills isotopic-spin model. One of the most fruitful and promising
of these theoretical suggestions concerns what is known as the Higgs mechanism.
Since the
Higgs field is characterized by only a magnitude, it is a scalar field with a zero spin
quantum. Moreover, unlike most fields, this field possesses the property of having a
non-zero energy in the vacuum state.
In physics,
a vacuum, generally, is construed as a state in which fields are in their lowest energy
mode. Usually, this means the energy value registers zero at any given point in the field.
When one
attempts to reduce the energy value of the Higgs field to zero, it requires energy. Yet,
when some non-zero energy value is uniformly distributed throughout the Higgs field, the
field assumes its lowest energy state. This capacity of the Higgs field not to disappear
in the vacuum state plays a central role in the contribution which it makes to resolving
some of the outstanding problems of the Yang-Mills model.
One of the
primary uses of the Higgs field concerns the manner in which it provides a frame of
reference for determining the state of isotopic-spin. Such a means of
determination was absent in the Yang-Mills model. As a result, one had no way to
distinguish neutrons from protons.
The gauge
character of the Higgs field provides an indicator of fixed length which can be
superimposed on the Yang-Mills field. The constancy of the gauge character of the Higgs
field is due to the non-zero value which that field has in the vacuum state.
Since the
Higgs field rotates, along with isotopic-spin, during any gauge transformation, one cannot
use the gauge character of the Higgs field to determine the absolute state of
isotopic-spin. On the other hand, one can use the constancy of the gauge character of the
Higgs field as a reference point against which one can detect transitions in the angle of
relative orientation between the gauge indicator of the Higgs field and the gauge
indicators of isotopic-spin. These differences in angle of relative orientation are used
to distinguish between protons and neutrons.
The way in
which the Higgs mechanism provides one with a means of distinguishing between protons and
neutrons is an example of spontaneous symmetry breaking. Although the
Yang-Mills fields preserve isotopic-spin across rotational transformations, the entities,
namely the neutrons and protons, which undergo these transformations, do not remain
invariant and, therefore, lose their symmetry.
The
hermeneutic fields generated by semiotic quanta seem to possess the property of
spontaneous symmetry breaking as well. More specifically, if one considers the
hermeneutical operator in and of itself, it shows no special preference for any particular
phenomenological or dimensional orientation or direction. However, when the semiotic
quantum comes under the influence of a given aspect of the phenomenological field, there
arises an axis of orientation in relation to the focal/horizonal dialectic that develops
with respect to the phenomenological field which is engaging and/or being engaged by the
semiotic quantum.
The
character of the aspect of the phenomenological field being engaged becomes the standard
against which the semiotic quantum is to be measured. Moreover, even though the semiotic
quantum may be able to preserve certain aspects of the field which it is engaging, by
accurately reflecting the structural character of those aspects in the organization of its
tensor-matrix, the quantum itself loses its pre-engagement symmetry.
In the above
comments, the phenomenological field is the region through which the results of
transduction activity can be given expression, provided that certain thresholds are
exceeded. In this respect, the phenomenological field mediates between the transduction
process and hermeneutical activity, just as the transduction process mediates between
ontology and phenomenology.
Although the
above comments focus on the phenomenological field, the structural character of different
aspects of that field are reflections of the transductional field. Therefore, by
implication, if symmetry has been maintained, the structural character of different
aspects of the phenomenological field are reflections of various aspects of the
ontological field which have been involved in dialectical engagement with the
transductional field.
What degree
of distortion exists in either the transductional reflection or the phenomenological
reflection (the latter being a reflection of a reflection) is not, at this point, the
issue. The emphasis, instead, is on the general character of the linkage between ontology
and phenomenology. The fact this linkage is somewhat circuitous or convoluted does not, in
and of itself, render the linkage useless as a source of accurate information with respect
to the structural character of some given aspect of ontology.
The above
point has parallels with the way in which telescopes and microscopes both are based on
utilizing a series of mirrors to generate an image of certain kinds of objects or
processes. The presence of mirrors, in and of themselves, do not render the observed image
inaccurate, although, to be sure, one must take into account the structural properties of
the mirrors in order to better appreciate the sources of distortion which can creep into
the observed image. Similarly, the fact the hermeneutical field introduces an additional
reflective manifold (making it a reflection of a reflection of a reflection) does not, in
principle, rule out the possibility that the linkage between the hermeneutical field and
the ontological field, circuitous and indirect though it may be, is capable of providing
an accurate reflection, within certain limits of resolution and so on, of various aspects
of the ontological field.
There is a
sense in which the link between ontological fields and hermeneutical fields gives
expression to a distributive property. In other words, various properties of the
ontological field are capable of being carried over, or distributed across, to the
phenomenological field. These properties subsequently become associated with, or entangled
with, certain aspects of the hermeneutical field.
Consequently,
under certain conditions, when one talks about the phenomenological or phenomenological
fields, one could be said to be speaking, in the foregoing distributive sense, about the
ontological field. This should be kept in mind throughout this discussion.
One
important difference between the Higgs field and its phenomenological counterpart is that,
unlike the Higgs field, the gauge character of the phenomenological field often does not
stay precisely the same from one situation to the next, even though the general structural
character of such situations may be very similar. This is because, quite frequently, the
principle (or set of principles) generating these sorts of situations is an expression of
one or more chaotic attractors.
Therefore,
the way in which a given situation will manifest itself over time will be characterized by
self-similar, rather than self-same, behavior. Nonetheless, despite the self-similar,
instead of self-same, gauge character of the phenomenological field, the phenomenological
structure (be it object, event, process, state, interaction, or condition) being engaged
over time, still serves as a gauge standard against which the semiotic quantum measures
itself in order to be able to accurately orient itself with respect to the character of
the structure being engaged.
In the
context of hermeneutical gauge field, spontaneous symmetry breaking also can occur in
another way. Instead of looking at the process of symmetry breaking from the point of view
of the semiotic quantum, one also can look at this process from the point of view of the
phenomenological field.
Considered
in and of themselves, ontological or phenomenological fields do not give any special
distinction to any of the isotopic-spin components of a particular semiotic quantum.
However, when such fields engage, or are engaged by, that semiotic quantum, there arises
an axis of orientation in relation to the focal/horizonal dialectic that develops with
respect to the engagement process.
Under such
circumstances, the structural character of the tensor-matrix of the semiotic quantum
becomes the standard of reference against which the structural character of a given aspect
of phenomenology or ontology is to be measured or assessed or evaluated. Although certain
aspects of the semiotic quantum's structural character may remain invariant during the
process of engagement, ontology and/or phenomenology lose their pre-engagement symmetry
since orienting phase relationships will emerge that are a function, in part, of the
character of the tensor-matrix to which the engagement process gives expression.
Point-structures,
neighborhoods and latticeworks of semiotic quanta can be linked together, through phase
relationships, in a manner that creates a theory, belief system, model, methodology, or
value system. Within these systems of phase relationships, there are certain spectra of
ratios of constraints and degrees of freedom (and, this will vary from theory to theory,
and so on) that arise. These key or essential or fundamental ratios become gauge standards
(irrespective of whether, ultimately, they have real heuristic value or not) against which
various aspects of the ontological or phenomenological are measured (irrespective of
whether accurately reflective measures are generated or not).
In effect,
the foregoing discussion suggests there is a mutual, spontaneous symmetry breaking that
occurs. One kind of symmetry breaking is phenomenological (and, by implication, involves
transductional and ontological fields). Another kind of symmetry breaking involves
hermeneutical fields. Furthermore, the point where each of these symmetries spontaneously
break is through the process of dialectical engagement - whether this is on the level of
scale of transduction, on the level of scale of phenomenology, or on the level of scale of
hermeneutical activity.
On this
latter level of scale, the focal/horizonal dialectic of the engagement process, which
marks a spontaneous breaking of symmetry, introduces a hermetical counterpart to the Higgs
field in physics. In other words, just as in physics, when the spontaneous breaking of a
symmetry is marked by the appearance of one or more fields (i.e., the Higgs fields), so
too, in hermeneutics, the spontaneous breaking of symmetry which is marked by the
dialectics of engagement gives rise to the field of semiotic quanta.
With each
focal/horizonal interaction, at least one semiotic quantum is generated. In other words,
at least one hermeneutical counterpart to a Higgs field is produced by the spontaneous
breaking of symmetry which occurs during the process of engagement.
There are a
variety of different directions in which this process of mutual symmetry breaking can go.
For example, when a semiotic quantum loses its pre-engagement symmetry, even though
certain symmetries in the interacting fields may be preserved, other symmetries in those
fields may not be preserved. Similarly, when ontological and phenomenological fields lose
their pre-engagement symmetry, even though certain symmetries may be preserved, the phase
relationships which do arise may distort various aspects of the structural character of
the interacting fields.
For mutual,
spontaneous symmetry breaking to lead to an accurate understanding, in which the relevant
symmetries- of, on the one hand, the hermeneutical field and, on the other hand, the
phenomenological and ontological fields are preserved, there must be a strong theme of
congruence established between, or among, the interacting fields. In the terminology of
'traditional' hermeneutics, there must be a "merging of horizons" of the fields
which are engaging one another.
Quantum chromodynamics
Quantum
chromodynamics (QCD) was introduced in an attempt to bring some semblance of
structural order to the proliferation of hadrons which had occurred during the
course of particle research. Although, initially, there were only three quarks (namely,
the up, down and strange quarks), eventually, six quarks were
necessary to account for the observed data ( the additional three quarks being: charm,
bottom and top).
Originally,
quarks were mathematical constructs. That is, while they constituted a
mathematical means of accounting for observed data, there was no experimental evidence
capable of demonstrating that they were anything more than a mathematical device.
In the
1960s, however, empirical evidence was forthcoming from a series of experiments which was
designed to probe the internal structure of protons. Examination of the decay
characteristics of the electron-proton collisions generated during these experiments
indicated the proton was made up of a number of elementary particles with properties that
were in agreement with what the quark model had predicted.
Despite the
fact there is considerable evidence to support the existence of quarks which are bound
together in pairs and triplets (and this also is true for their anti-particles), no one
has ever been able to put forth evidence indicating quarks or antiquarks can exist as
single (i.e., unpaired) entities. The inability to witness free quarks was rather
disturbing since the experimental evidence indicated that, within the proton, quarks did
seem to exist in a single state.
Scientists
began to wonder how there could be a force sufficiently strong to confine quarks within
the boundaries of the proton's structural character while, simultaneously, permitting the
quarks to have relatively free movement within those structural parameters. The lack of
success in producing isolated quarks has led theorists to search for an account of why
quarks are confined within the structural parameters of, say, a protein or neutron. This
is the problem of quark confinement.
According to
Pauli's exclusion principle, if two quarks are within a certain distance of one another,
they cannot each occupy the same quantum state. Prior to the ascendency of
the color hypothesis, the quark model permitted predictions which violated the
exclusion principle.
As a result,
the quantum property of color was developed as a means of getting the quark model to
conform to the Pauli exclusion principle. By postulating the quantum property of color,
one could have two quarks packed closely together since one could assume they had
different colors, and, therefore, they would be in different quantum states (the term
'quantum chromodynamics' gets the chromo- aspect of its name from the use of the color
property).
The quantum
property of color is never encountered in a single quark. This property manifests itself
when quarks are combined in pairs or triplets.
However, the
overall color property of the quark pair or triplet must be colorless. This requirement of
composite colorlessness was hypothesized in order to eliminate a certain amount of
particle redundancy which would occur if all color permutations were permitted.
Such
redundancy is inconsistent with the observed data. On the other hand, the color hypothesis
does indicate that as long as the quark pair or triplet is colorless, any combination of
colors is equally possible.
In 1973 a
number of investigators independently came up with the idea of a chromoelectric field.
This field was introduced in an attempt to account for some of the lacunae of the quark
model.
Essentially,
the chromoelectric field was believed to be generated by the color property. The field was
constructed in such a way that it permitted quarks to be weakly interacting when close
together, thereby providing an explanation for why quarks move freely within hadrons such
as protons and neutrons. At the same time, the constructed properties of the
chromoelectric field were of such a nature that the force between particles would remain
constant beyond a certain distance of separation.
Maintaining
the constancy of force between particles beyond a certain distance was accomplished by
taking the field between the particles and compressing the lines of force of that field
into a thin string of uniform cross section. This sort of compression permits the force
between the particles to continue to be constant irrespective of the distance between the
particles. Therefore, beyond a certain distance, no matter how much energy is
applied, one would not be able to separate the particles.
According to
the dynamics of the chromoelectric field theory, a hadron is not a point-particle. It is
thought of as a string. As indicated above, a string consists of a
compressed bundle of lines of force.
These
strings are believed to be capable of interacting with the structural character of the
vacuum. As a result, the propagation of color forces in the chromoelectric field can be
affected by the passage of such forces through the quantum vacuum. This kind of
interaction is not permitted in Newtonian physics since the Newtonian vacuum is believed
to be devoid of all matter and energy.
In an
electromagnetic field, the lines of force are densest in the area between two particles of
opposite charge. However, the lines of force which link the opposite charges also extend
in a variety of other directions as well, although they are not as dense as in the area
between the two charges.
The strength
of the force of a unit of electric charge impinging on any point in an electromagnetic
field will be a function of the number of lines of force crossing a given unit area of
surface which is orthogonal to the lines of force passing through that unit area of
surface. In the chromoelectric field, this is expressed in terms of the idea
of a string which constitutes a compressed bundle of lines of force.
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