Global and Local Gauge Symmetries in the "Tetrahedron Model": Part I
Abstract of the Unified Field Theory (Tetrahedron Model)
Introduction: Duality in Nature
From ancient times we have intuited and named a dual level of reality - it is a defining characteristic of abstract thinking, symbolic language, and the human condition. This recognition of abstract reality has its most explicit social expression in our religious (and political) systems of thought, the realm of the gods (and the State) vs the realm of humanity and the "citizen". Plato recognized it as the realm of ideal forms vs the realm of their material "shadows". Duality takes additional forms in philosophical, ethical, moral, and aesthetic conceptual systems. In our own physiology, in addition to the biological duality of gender, we seem divided between the intangible realm of thought and imagination and the realm of physical action and the body (mind-brain). In science we recognize dualities between the realm of physical or natural law vs the realm of phenomena, the theoretical vs the experimental, mathematics vs material reality, symbol vs substance, and virtual or potential vs actual or realized forms of energy, among many others.
A significant duality in mathematical physics is expressed as "global vs local gauge symmetry" - a methodology of treating the laws and phenomena of physics that is especially conducive to mathematical formulation ("group theory"), and is currently the favored theoretical approach in the ongoing search for the "Holy Grail" of physics, Einstein's dream of a unified field theory.
The world is a mysterious place, and not just in terms of the enduring question of humanity's role in the Cosmos. We find in all natural phenomena a variety of "hidden", relative, or emergent forces. This is nowhere more evident than in the paradoxes of relatively and quantum mechanics, enigmas at the very foundations of physics (spacetime warps, non-locality, etc.).
At the level of the four forces, we have the mysteries of gravitation, time, and magnetism in the long-range, "spacetime" forces. These are local effects set against and derived from the global invariants of electromagnetism: "velocity" c, the spatial metric, and electric charge. In the particle or short-range forces, we find the hidden "identity" or "number" charges of the massive leptons, Heisenberg's virtual vacuum "zoo" of particle-antiparticle pairs, and the strange realm of the weak force, with its massive IVBs, ghostly neutrinos, spontaneous symmetry-breaking, the creation and destruction of matter, etc. Finally, in the strong force we have the permanently confined and forever hidden quarks with their partial quantum unit charges, and the gluon field of "sticky light", exchanging color charges between quarks at velocity c.
The atomic realm is a hive of activity completely beneath our notice - the whirling electrons in their orbits, the frenzied exchange of gluons between quarks in the nucleus. The "vacuum" bubbles and froths with the creation and annihilation of Heisenberg's virtual particles; neutrino, gravitational, and electromagnetic waves of every description traverse the Cosmos unrecognized - either for lack of biological sensory apparatus or physical interaction. Yesterday, historical spacetime, and the "realm of the ancestors" is largely hidden from our view, even though its continuing reality in some alternative, causal form cannot be doubted - as it sustains our own today. (See: "A Spacetime Map of the Universe".)
These are just the documented, rational, "scientific" physical phenomena, and I have only mentioned the tip of the iceberg. Is it any wonder we have intuited a hidden, parallel, "occult" universe of paranormal effects and miracles, of gods, angels, and demons? Of "Paradise", a conservation domain of spirit and the eternal realm of invariant Divine Law - where all humanity finds itself in a globally symmetric state of universal spiritual equality?
Global vs Local Gauge Symmetries
The concept of symmetry is central to the modern effort to achieve Einstein's dream of a unified field theory of physics. I have used the concept extensively in my work (See: "Symmetry Principles of a Unified Field Theory"), but from a slightly different perspective than that of "establishment" physics. (See: "The Moment of Creation" by James S. Trefil, 1983, Macmillan, pages 87-125 for an expert, non-mathematical explanation of the use of symmetry concepts in the "standard model" of unification physics.)
Mathematical physics distinguishes between the concepts of "global" vs "local" symmetry: "local" gauge symmetries are derived from and represent individual examples of or variations upon universal or "global" gauge symmetries. The word "gauge" refers to a regulating property that establishes a magnitude or scale, as for example the value of the electromagnetic constant (c), a global gauge for electromagnetic energy and the spatial metric. The magnitude of the electric charge (e), Planck's energy constant h, the value of the universal gravitational constant (G), and the mass of the Higgs boson, also represent global gauge constants. On the other hand, a magnetic field, the time dimension, the massive IVBs (Intermediate Vector Bosons) of the weak force, and the gluon field of the strong force, are all local gauge "currents" of matter (field vectors of the forces) which establish and maintain local gauge symmetries. Cold, crystalline atomic matter is the prototypical example of local gauge symmetry established and maintained from global gauge symmetry - light.
Light (free electromagnetic energy) is a globally symmetric energy state from which locally asymmetric atomic matter (bound electromagnetic energy) is devolved. The charge neutrality and inertial stasis of cold atomic matter is the evidence of a locally symmetric energy state, involving charge conservation, alternative charge carriers, and inertial forces, which substitute for and replace the global symmetries. In many respects, the local symmetry state is just as invariant and conserved as the global one, and in fact the two regimes are in constant interaction and equilibration (through virtual particles, long-range fields, etc.).
The reason why we have a dual system of global vs local gauge symmetries in physical law and phenomena is because our Universe consists of massive, local energy forms in relative motion (matter), which are derived from light - a massless, non-local (global) energy form in absolute motion. Functionally, the local symmetries are embodied and enforced through the field vectors of the forces. The field vectors translate timeless global symmetries (such as the virtual charges of matter-antimatter particle pairs) into alternative, material, local, temporal forms (such as the real charges of atomic matter). These local charges conserve the invariant magnitude of the original global symmetries through time, until they can be returned (via the action of their associated forces) to their original symmetric form, light (typically via charge-anticharge annihilations).
Through an (as yet) unknown mechanism of "spontaneous symmetry-breaking", light produces matter which carries active charges (and spin) representing symmetry debts. The charges of matter are the symmetry debts of light. These charges produce forces which act to return matter (sooner or later) to its original symmetric form, light. Our Sun is a prototypical example of this universal phenomenon and natural agenda in action (symmetry conservation as required by Noether's Theorem).
While the ultimate role of the field vectors of the four forces is to return matter to light, their proximate role is to translate globally invariant symmetries into locally invariant charges. The reason why they bother to do this is because in the absence of antimatter (following "Big Bang" symmetry-breaking), local symmetry-keeping and charge conservation is a necessary first step in the pathway leading to the eventual and complete restoration of light's original symmetric non-local energy state - a restoration required by symmetry conservation and Noether's Theorem.
The charges of matter are derived from invariant global gauge symmetries, and their field vectors (including the graviton, or time) represent local gauge "currents" establishing and maintaining similarly invariant local gauge symmetries (local charge magnitudes, for example). The field vectors, in addition to transmitting the forceful effect of the charge, must also protect, conserve, or otherwise maintain the invariant magnitude of the charge. Symmetry conservation = charge conservation, which is why charge invariance is so important. Charge and symmetry conservation would have little meaning if charge invariance was not rigorously enforced. This is why all field vectors, in dealing with the relative energy state of matter, must have a flexible component or capability, like the photon's magnetic component, whose strength varies with the relative motion of electric charge.
Mathematical physics uses symmetry principles to obtain quantitative equations describing the operation of the forces, and for predictions and explanations of experimental results. I use the concepts of symmetry in a non-mathematical, qualitative way to understand why the forces act as they do, and why they must exist in nature. The concepts of symmetry, when properly applied, provide a broad avenue to the understanding of nature - equivalent to the fundamental and powerful ideas of entropy, causality, and energy conservation (See: "The Tetrahedron Model of Light and Conservation Law"). Both establishment physics and I have been successful in our own ways. This paper (and others in the global-local gauge symmetry series) is an attempt to join the perspectives of the "Tetrahedron Model" and the "Standard Model", not mathematically (because that desideratum is beyond my ability), but conceptually in English. (See also: The "Tetrahedron Model" vs the "Standard Model" of Physics: A Comparison.)
Although the global-local gauge symmetry "argument" is often couched in purely numeric terms of universal vs individual, for reasons of physical relevance I have broadened this usage to include the category of absolute vs relative. As I employ the terms, absolute stands to relative as global stands to local or as the universal stands to the individual. The absolute and the invariant are terms imposed upon the multitude, the general, the global. All photons travel with velocity c; all electrical charges are invariant in magnitude, all mass is gravitationally identical, all spatial locations are equivalent, etc. In contrast, the relative is unpredictable and peculiar to the individual. The task of local gauge symmetries is to maintain within the temporal, unpredictable, individual, and relative material domain some essential, conserved aspect of the global invariant - for example, the invariance of the magnitude of electric charge despite the freedom of relative motion of individual massive charge carriers (electrons, protons, mesons, etc.).
Global-Local Parameters in the Electromagnetic Force - General Considerations
The conversion of light to matter, free electromagnetic energy to bound electromagnetic energy, during the "Big Bang", represents the conversion of a globally symmetric form of energy (matter-antimatter symmetry, space, and massless non-local light) to a locally asymmetric form of energy (matter, time, and massive local particles). In purely energetic terms, this conversion is symbolized by DeBroglie's equation: hv = mcc. For simple reasons of conservation, a local form of energy (massive particles of matter) requires a local form of entropy (time), a local form of symmetry (charge), a local form of metric (gravitational spacetime), and a local connectivity domain (history, causality). Charge invariance; the invariance of velocity c, the "Interval", and causality (the Lorentz invariance of Special Relativity); and the invariance of elementary particle mass: all are conservation requirements with local gauge symmetry consequences ("currents") which follow upon the major transformation parameters (above) of free to bound electromagnetic energy during the "Big Bang".
The original and primordial global-local conversion of our primary electromagnetic cosmic energy form is accompanied by the gravitational conversion of globally symmetric space with its spatial entropy drive (the intrinsic motion of light) to locally asymmetric history with its historical entropy drive (the intrinsic motion of time). Finally, light's symmetric energy state, which is realized as globally symmetric matter-antimatter particle pairs, is converted (quantum mechanically through an asymmetry in the weak force), to locally asymmetric matter-only charges.
Charge conservation = symmetry conservation (Noether's Theorem), in which charges are carried by massive particles and conserved through time. The conserved charge-symmetry debt of matter is repaid when charges are eventually annihilated by antimatter charges. The entropy-interest on matter's symmetry debt is paid by gravitation, which creates the time dimension of matter by the annihilation of space and the extraction of a metrically equivalent temporal residue. The spatial expansion of the Universe is consequently slowed as it supplies energy for the historical expansion of matter's causal information domain - historic spacetime. Thus it is ultimately the spatial entropy drive of light's intrinsic motion which supplies the energy for the historical entropy drive of time's intrinsic motion. This energy cycle is completed by the conversion of bound to free energy (and the consequent conversion of the historical entropy drive of time to the spatial entropy drive of light) in the Sun and stars, and goes to completion in Hawking's "quantum radiance" of black holes.
Light is non-local, atemporal, acausal, massless, chargeless, and produces no gravitational field. Matter is local, temporal, causal, massive, charged, and produces a gravitational field. The conversion of globally symmetric light to locally asymmetric matter is succinctly characterized by matter's fundamental but local conservation parameters: mass, charge, time. (See: "The Tetrahedron Model of Light and Conservation Law".)
The Doppler Effect and Related Phenomena
The magnetic field associated with an electric charge in relative motion transforms the motion of the charge's electrical field to an alternative electrical form (magnetism) which does not alter the magnitude of electric charge. The magnetic field functions to protect the invariance of electric charge in relative motion, and hence also charge and symmetry conservation. In an analogous fashion, the Doppler effect associated with a luminous object in relative motion functions to transform the motion of the light source to an alternative luminous form (color, frequency) which does not alter the magnitude of velocity c. The Doppler effect functions to protect the invariance of velocity c and hence also the conservation of energy and all things gauged by the universal electromagnetic constant. We have two invariant constants, electric charge and velocity c, both defended by effects related to their specific forms of duality or global-local translation: electric charge through the electric vs magnetic duality associated with the electromagnetic field, and velocity c through the wavelength vs frequency duality associated with the propagation of light. A magnetic field tells us an electrically charged particle is in relative motion, and the Doppler effect similarly informs us of the relative motion of any luminous object. Both effects are related by the Lorentz invariance of Special Relativity, in which the flexibility of the time dimension is necessary to maintain the invariance of the "Interval", causality, and velocity c. Similarly, gravitational tidal forces, which also distort the dimensions, provide us with long-range information regarding the total bound energy associated with the relative motion of massive objects.
Related to these effects we note the fundamental quenching of an electric field by magnetic induction in the free electromagnetic wave, a balancing or compensation which results in the electrically neutral photon (a quantum unit of light), the field vector of the electromagnetic force. At the next level of material expression, we see the atomic combination of the election and proton, which also achieves electrical neutrality thanks to the magnetic field of the electron, despite the electron's orbital motion around the comparatively stationary proton. The universe is constructed in such a way (through global-local gauge symmetries and their transformations via the field vectors) that the invariant constants of the spatial and absolute realm of light can nevertheless subsist in the relative, temporal realm of matter, although in an altered (but also invariant) form (charge). In their completely global or universal symmetric form, charges are directly related to light's symmetry through the virtual matter-antimatter particle pairs that light's energy constantly creates and annihilates throughout the spatial "vacuum". Similarly, material local charges are constantly in communication and equilibrium with their global counterparts through the swarms of virtual particles that surround them. Thus the separation between global and local energy forms, charges, and symmetry states is more apparent than real.
Charge Invariance
The common factor or pivotal connection between my use of the notion of symmetry in the "Tetrahedron Model" and the mathematical formalism of the "Standard Model" is the idea of charge invariance. This notion is the rock to which both our systems are anchored: charge invariance is crucial to symmetry and charge conservation. Charges are invariant with respect to relative motion, entropy, age, or gravitational metric, protecting their symmetry conservation function. The charges (among other parameters) of elementary particles are quantized expressly to maintain their invariance and thus their conservation function. The case of electric charge and magnetism is paradigmatic: the magnetic field is the relativistic expression of the motion of an electric charge with respect to a stationary observer (see above).
The magnetic field is an alternative form of electrical energy which encodes and energetically accounts for the relative motion of electric charge, but which does not change the magnitude of electric charge. The existence of the magnetic field allows the relative (rather than absolute) motion of electric charge, conserving charge invariance, and therefore accomplishes the translation between the global, invariant gauge symmetry of electric charge and the local electromagnetic gauge symmetry of individual charge carriers. The local gauge symmetry is expressed through (for example) the electrical neutrality of (ground state) atomic matter, despite the large relative velocities of electrons in atomic orbits around the massive and essentially stationary protons.
Because of the compensating action of magnetic fields, local leptonic charges in relative motion have the same magnitude as the proton charge, and as the global, universal value of electric charge everywhere - a fact we ordinarily take for granted. We have the magnetic field to thank for the local phenomenon of electrically neutral, charge-balanced, quiescent atomic matter and chemistry (including biochemistry and life), and for the relative ease with which electromagnetic energy interacts with matter.
The smooth translation from global electrical gauge symmetry to local electromagnetic gauge symmetry depends upon the fact that light is an electromagnetic wave and that the photon is the field vector of electric charge. Thus the magnetic field is part of the electrical phenomenon and the electrical field vector from the beginning (maintaining the electrical neutrality of light), always ready to act in defense of the invariant value of electric charge, charge conservation, and hence symmetry and energy conservation. The magnetic field acts as the local gauge symmetry current, maintaining the invariant magnitude of massive electric charges in relative motion. Here we see that a portion of the electromagnetic field vector is "split out" to serve as the local gauge symmetry compensatory current, a notion which we can also apply to the gluon field of the strong force, apparently also a subdivision of the original electromagnetic field vector ("sticky light").
We furthermore take note of the fact that the photon is its own antiparticle, an internal or self-symmetry which is also found in the field vectors of all the other forces, either individually (as in the graviton), or as a group (in the IVBs of the weak force, and in the gluon field of the strong force). This is an important factor enabling the field vectors of the forces to translate a global symmetry into a local one - especially evident in the action of the gluon field of the strong force, where anticolor is used to cancel color so the transformation to a new color can occur. (Gluons are composed of color-anticolor charges in all combinations. In the case of the weak force IVBs, it is virtual particle-antiparticle pairs which become alternative charge carriers, facilitating particle decays and transformations (leptons, neutrinos, mesons). See: "Global and Local Gauge Symmetries in the Weak Force".)
Noether's Theorem
The concept of symmetry in physics is founded upon a great theorem formulated by Emmy Noether (in 1918), which states that in a multicomponent field, such as the electromagnetic field of light, or the metric field of spacetime, where one finds a symmetry one will find an associated conservation law, and vice versa. Hence the power of symmetry in physics derives from its intimate association with conservation laws. The mathematical field which addresses this association is known as "Group Theory".
Noether's Theorem states (in essence) that the symmetry of light must be conserved, no less than its raw energy. We have two outstanding examples of Noether's Theorem enforced in everyday experience: 1) charge conservation; 2) the inertial forces of the spatial metric. My own formulation of Noether's theorem is: "the charges of matter are the symmetry debts of light". Charge conservation (including spin) = symmetry conservation (symmetry as transferred from light and virtual particle-antiparticle pairs to massive elementary particles composed only of matter). Charges must retain their invariant, absolute values regardless of entropy, relative motion, gravitational metrics, alternative charge carriers, or the expansion (or contraction) of the universe. Otherwise, charges will not be able to cancel, balance, or annihilate each other upon demand, and charge conservation, symmetry conservation, and energy conservation will all fail.
The field vectors of the charges (the local symmetry "currents") all operate in some way to maintain the invariant, absolute value of charge, despite the relative environment of matter. For electric charge, this compensating factor in the field vector is the magnetic field of the photon; for the "location" charge of gravity it is the time component of spacetime; for the "identity" charge of the weak force it is the mass of the IVBs (and the virtual particle-antiparticle pairs of the "vacuum"); and for the strong force color charge it is the gluon field with its peculiar exchange rules ("asymptotic freedom"), producing the permanent confinement of the partial charges of quarks to particles (baryons and mesons) which display only whole quantum unit charge values ("white" color).
The usual electrical neutrality of the (low temperature) atomic realm, established through balancing charges, is an expression of the local gauge symmetry of individual carriers of electric and magnetic forces, despite the fact that the atomic realm is constantly in a state of relative motion (electron orbits, gluon exchange between quarks, thermal agitation, quantum excitations, gross relative motions, etc.) - and consists of alternative charge carriers which are not the antiparticles of their charge-balancing partners (the electron-proton pair is an obvious example).
Time - like magnetism - is a local gauge symmetry "current", in both Special and General Relativity. Causality, velocity c, Einstein's "Interval", and energy and symmetry conservation, are all invariant principles requiring the protection of the flexible time dimension and the gravitational force when massive particles and relative motions are involved. Electric charge, velocity c, and symmetry conservation are invariant principles in the case of magnetism and the electromagnetic force. Time is necessary to conserve matter's energy accounts because of matter's relative (rather than absolute) motion, and time is also necessary to conserve matter's causality and "Interval" for the same reason. Time is furthermore the critical dimension for charge conservation (charges, in the absence of immediate matter-antimatter annihilations, may be "stored" indefinitely in the temporal dimension until the debt is retired by charge annihilation). Finally, time is the primordial entropy drive of bound energy, creating and expanding history, the conservation domain of matter's causal information "matrix".
Gravity pays the interest on the symmetry debt of matter by creating time via the annihilation of metrically equivalent space, decelerating light's cosmic spatial expansion to fund matter's cosmic historical expansion.
Each of the four forces of physics is associated with a specific charge. ("Charge" can be regarded as a type of energetic asymmetry from which the associated force acquires its characteristic activity.) My method of unification (in the "Tetrahedron Model") is simply to show how these charges correspond to broken symmetries of light (broken originally when light is converted into matter or bound energy during the Big Bang.) This simple method leads to a qualitative understanding of how the forces are unified (they all originate as "symmetry debts" of light), and why they behave as they do (to restore the symmetric energy state of light - as per Noether's Theorem). It is not a quantitative, mathematical understanding, but because it is firmly based upon the physical principles of natural law - energy conservation, symmetry conservation, entropy, and causality - I expect it could be reformulated mathematically into a fully formal statement of the unified field theory. (See: "The Tetrahedron Model of Light and Conservation Law".)
The understanding gained through the development of the "Tetrahedron Model" is now considerably enlarged by the addition of the principle of charge invariance as evolved in the "global vs local gauge symmetry" theories of the "Standard Model". This particularly fruitful marriage between "alternative" and "establishment" physics is a union which is possible only because both models are based squarely upon the same conservation laws.
Summary: Rationale and Effects of Local Gauge Symmetries
The charges of matter are the symmetry debts of light (Noether's Theorem). These debts must be paid in full to satisfy energy, symmetry, and charge conservation (as through matter-antimatter charge annihilation or its equivalent). The function of local gauge symmetry, as effected by the field vectors of the four forces, is to ensure charge invariance (serving charge and symmetry conservation) and the invariance of the "Interval" (Lorentz invariance, serving causality and energy conservation) during and after the transformation of light to matter (as in the "Big Bang").
The conversion of the absolute, "global", non-local realm of light and space, gauged by the electromagnetic constant "c" and driven by the intrinsic motion of light (the entropy drive free energy), to the relative, local realm of matter and history, gauged by the gravitational constant G and driven by the intrinsic motion of time (the entropy drive of bound energy), requires the compensating mediation of local gauge "currents" (the field vectors of the forces), for reasons of energy, symmetry, and charge conservation, including charge invariance.
We find a distinct role for each of the four forces, ensuring the invariant magnitude of charge in the particle realm of matter, and in the case of gravity, through the creation of matter's time dimension, ensuring the invariance of matter's "Interval" (and therefore the invariance of causality and matter's energy accounts) in the metric realm of spacetime:
1) Electromagnetic force: relative motion and magnetism; magnetism and the magnetic force associated with the relative motion of electric charge. Invariance of electric charge despite the relative motion of massive charge-carrying particles - serving charge and symmetry conservation. Example: magnetic forces ensure the electrical neutrality of ground-state atomic matter despite the (relative) orbital motions of the electrons.
All electrical charges are the same in magnitude (charge invariance), a global symmetry within the electromagnetic force required by charge conservation and "Noether's Theorem". In atomic matter, charge invariance requires the existence of magnetic forces to achieve electrical neutrality (the local symmetry "current"), while simultaneously balancing the energy accounts of electric charges in relative motion - such that energy is conserved but without changing the invariant value of the electric charge. The photon is the field vector, whose magnetic component constitutes the compensating factor of the local gauge symmetry "current". The electrical neutrality of cold, "ground state" atomic matter is the evidence of the local symmetry state, achieved despite the relative (rather than absolute) motion of electrical charges (orbital electrons) - thanks to the compensatory action of magnetic force fields. The electromagnetic force provides a paradigm of global-local gauge symmetries for the other forces - either by similarity or contrast. Both magnetic fields and the Doppler effect are epiphenomena of the "Lorentz Invariance" of space and time (Special Relativity) in which the flexible dimensions form a local symmetry current simultaneously protecting the invariance of charge, velocity c, Einstein's "Interval", and causality.
2) Weak Force: Transformations of elementary particle "identity", including the creation, destruction, and swapping of elementary charges and associated mass-energy quanta. Just as charge invariance is a critical issue for charge and symmetry conservation, so also must be the mechanism of elementary charge carrier transformation (transformations of quarks and leptons). The role of the weak force and the massive IVBs is to ensure that charge invariance, charge conservation, and energy conservation are all scrupulously observed in any transformation of elementary particle charge, mass, and identity. To this end, the massive IVBs reprise the original energy density or electroweak force unification symmetric energy state in which these particles and charges were originally created and exchanged (during the "Big Bang"). (See: "The Role of the "W" IVB in Weak Force Transformations".)
The weak force IVBs are "metric" particles, catalytic particles composed entirely of a densely compressed and (perhaps) convoluted metric, similar to the densely energetic and compressed primordial metric of the early "Big Bang". The great mass of the IVBs consists of the binding energy required to compress and maintain a volume of spacetime metric in the particular configuration and density that we recognize as a weak force IVB.
The most significant feature of the massive IVBs is that they recreate the original conditions of the energy-dense primordial metric in which particles were first created and transformed during the early micro-moments of the "Big Bang". This recapitulation ensures that the original and invariant values of charge, mass, and energy are handed on to the next generation in the charge-transfer chain. The IVB mass not only provides a "conservation containment" where charge and energy transfers can take place, it simultaneously ensures that the appropriate alternative charge carriers are present (in the form of virtual particle-antiparticle pairs).
There is a crucial difference between the electromagnetic or strong force creation of particles via symmetric particle-antiparticle formation, and the weak force creation or transformation of asymmetric "singlet" particles to other elementary forms. ("Singlets" are matter particles without antimatter "mates".) In the case of particle-antiparticle pair creation, there can be no question of the suitability of either partner for a subsequent annihilation reaction which will conserve their original symmetry. Both particles are referenced against each other and gauged or scaled by universal electromagnetic constants such as c, e, and h. However, in the case of the weak force creation or transformation of a "singlet" elementary particle to another form, alternative charge carriers must be used to balance charges, since using actual antiparticles for this purpose can only produce annihilations. But how can the weak force guarantee that the alternative charge carriers - which may be a meson, a neutrino, or a massive lepton - will have the correct charge in kind and magnitude to conserve symmetry at some future date in some future reaction, or with an unknown partner which is not its antiparticle? Furthermore, quark charges are both partial and hidden (because they are confined), and number charges of the massive leptons and baryons are also hidden (because they are implicit) - they have no long-range projection (such as the magnetic field of electric charge) to indicate to a potential reaction partner the relative condition of their energy state. Conservation of energy, charge, and symmetry require that elementary particles created today, tomorrow, or yesterday be exactly the same in all respects as those created eons ago in the "Big Bang".
These problems are all solved by a return to the original conditions in which these particles and transformations were created, much as we return and refer to the Bureau of Standards when we need to recalibrate our instruments. The necessity for charge invariance in the service of symmetry conservation therefore offers a plausible explanation for the otherwise enigmatic large mass of the weak force IVBs. Weak force "singlets" can only be referenced against their original creation energy, as scaled by the universal Higgs boson. The IVB mass serves to recreate the original environmental conditions - metric and energetic, particle and charge - in which the reactions they now mediate took place, ensuring charge invariance and hence symmetry conservation regardless of the type of alternative charge carrier that may be required. (See: The Higgs Boson and the Weak Force IVBs.)
3) Strong force: partial quark charges and gluons. Invariance of whole, elementary quantum charge units despite the partial charges of the quarks - serving charge and symmetry conservation. Strong force color charges permanently confine quark partial charges to whole quantum unit charge values (baryons and mesons), so they may be canceled, neutralized, balanced, or annihilated by other elementary, whole quantum unit charges - such as those carried by the alternative charge carriers, the leptons and mesons.
Global Symmetry: whole quantum unit charges; also, all quarks are equivalent and interchangeable in terms of color charge.
The charges of matter are the symmetry debts of light and must remain whole to be payable on demand. But quarks must carry partial charges so they can assume electrically neutral combinations (such as the neutron) to allow symmetry-breaking in the "Big Bang". Hence the strong force is a compromise between the demands of manifestation (symmetry-breaking), and symmetry conservation via charge conservation (charges are symmetry debts). This compromise allows non-leptonic whole quantum unit charges (baryons and mesons) to exist provided their partial components (the quarks) can never become individually free. Baryons and mesons (the only allowed "white" quark combinations) must always express whole quantum unit charge values to the external world (in essence, as "seen" by the long-range forces) for purposes of charge balance (in atomic matter) and/or symmetry conservation (as via charge-anticharge annihilation). (Quarks only - hadrons: baryons and mesons.)
"Gluons" are the field vector of color charge, and the analog of the photon field vector of the electromagnetic force. Gluons are massless and move at velocity c; they are composed of color-anticolor charges in all possible combinations, and hence the field in total sums to zero or "white" color. Gluons have been compared to "sticky" light (because in "white" combinations gluons attract each other). Various processes such as fusion, the nucleosynthetic pathway in stars, and finally proton decay with color charge self-annihilation ("asymptotic freedom" - summing the gluon field to zero color by compression), and the cancellation of leptoquark identity charge via the leptoquark antineutrino ("proton decay"), returns the bound energy of the quarks and hadrons to light and whole quantum unit charge symmetry. (See: "Proton Decay and the 'Heat Death' of the Cosmos".)
The Strong Force - Two Expressions
The strong force has two structural levels of expression, quite different, one within the individual baryon (mediated by a gluon exchange field), and one between individual baryons (mediated by a meson exchange field). While the internal baryon level of the strong force consists of an interaction among three quarks carrying 3 "color" charges ("red, green, blue") exchanging a color-carrying gluon field, the strong force at the compound nuclear level consists of an interaction between two or more baryons carrying 2 quark "flavor" charges ("up, down"), exchanging a flavor-carrying meson field. The gluon field is composed of virtual color-anticolor charges, and the meson field is composed of virtual flavor-antiflavor charges, so the analogy is complete, except that the gluon field is massless while the meson field is massive. The massless gluon field nevertheless produces a short-range field because unlike photons, the gluons attract each other (gluons have been compared to "sticky light").
Two particle charges unique to the quarks, "flavor" and "color", each produce a version of the strong force, expressed at different structural levels of the nuclear material. The color version of the strong force is expressed within the baryon, producing absolute quark confinement, while the flavor version of the strong force is expressed between baryons in a compound atomic nucleus, producing a very powerful (but not absolute) binding of baryons within the nuclear boundary.
The role of the color charge is to protect charge invariance, charge conservation, and symmetry conservation by maintaining the integrity of whole quantum charge units, hence explaining the absolute character of the confinement of quark partial charges. The role of the flavor charge is also symmetry-keeping, but with respect to energy states rather than charge, which is a more variable function (since energy can be conserved in many forms - as mass, light, heat, linear and angular momentum, nuclear binding energy, chemical binding energy, kinetic and potential energy, magnetic and electrical energy, sound, information, etc.) The flavor charge role is to reduce the amount of bound energy (mass) contained in the baryon ground state as far as possible, while not violating the absolute parameters of charge conservation (electric charge, color charge, baryon number charge, spin).
It is the fact that we have two ground state flavor charges (up-down), that allows us to have two ground state baryons (neutron and proton), which can share their virtual meson fields and so bond together by reducing their total bound energy content. Because neutrons spontaneously decay into protons (half-life of about 15 minutes), and protons, given a sufficient energy boost, will revert to neutrons, we see that these two particles are in a real sense simply differently charged versions of one another. This close "family" relationship (as demonstrated by these weak force transformations) is the basic reason why these particles can form a combined "resonance" or "superposition" - the "nucleon" (as demonstrated by strong force bonding).
Flavor charges apparently exist to quantize and regulate, scale, or gauge the mass of quark and leptonic elementary particles. Flavor charges are associated with and identify the specific masses of quark and leptonic elementary particles. Inasmuch as massive particles must have an associated temporal entropy drive and gravitational field, we can say that the "agenda" of the flavor charge is revealed through the temporal entropy drive which is naturally associated with massive particles - that is, their gravitational field, with all its consequences for the release of bound to free energy in stars and other astrophysical phenomena.
The color charge of the strong force clearly has an "agenda" of quark confinement in the service of symmetry and charge conservation, through the protection of whole quantum charge units. The flavor charge of the strong force also has an agenda of symmetry conservation, but not through charge conservation, rather through the release of bound to free energy by funding the energetic mechanism of the nucleosynthetic pathway (through the release of bound energy). However, we must recognize the associated role of time and gravitation (the temporal entropy drive of bound energy) to comprehend the complete mechanism of the flavor charge in reducing the bound energy levels of the ground state nucleons within the compound atomic nucleus - this because nucleons will not bound spontaneously, but require the external force input of powerful gravitational fields, as in the stars. The spontaneous character of the flavor charge "agenda" is only apparent when we take into consideration the gravitational field which is naturally associated with any massive elementary particle carrying a flavor charge.
The miracle of the (nuclear level) strong force is of course the 92 elements of the periodic table (and their many isotopes). These exist only because the proton and neutron can coexist as a "doublet", a paired bound state of nuclear matter which achieves in its combined form (the "nucleon") a state of lower bound energy than either partner could alone. The origin of this miracle goes back to the paired quark families and the ground state "up, down" flavor pairs. Why do quarks come in paired families, anyway? The pairing phenomenon is also seen in the lepton families, and in the pairing of quark families with lepton families, of meson and gluon charge-anticharge pairs, of matter and antimatter, and even of space and time. The ultimate source of all this pairing is probably electrical, originating with the dipoles of both electric and magnetic fields in the primordial source of cosmic energy, light. When light interacts with the metric of spacetime to produce particles (during the Big Bang), the electromagnetic dipole of light, the tripole of space, and the quadrupole of spacetime are carried into the structural fabric of particles. (See: "Nature's Fractal Pathway".)
The "nucleon" is a combined state of both the proton and neutron, a "resonance" or "superposition" of these particles. Because in the combined state the baryons can share their load of "parasitic" virtual mesons, a significant reduction of their total bound energy is possible. This reduced energy is the "binding energy" of the atomic nucleus released in nuclear fusion. The quark composition of the proton is "uud+", while that of the neutron is "udd". The exchange of a (virtual) meson particle-antiparticle pair, ud+ or ud- (antiparticles underlined), changes a proton into a neutron and vice versa. If two protons and two neutrons combine, they can position themselves at the corners of a tetrahedron in which all partners are equidistant. In the tetrahedral configuration meson exchange is especially efficient, as each proton has two equidistant neutrons to play the round-robin exchange game with, and vice versa. This 4-baryon tetrahedron is the alpha particle or helium nucleus, an especially tightly bound and favored nuclear configuration (the "brick" of the nucleosynthetic pathway), and it is easy to see why. The exchange of mesons between neuton and proton is exactly the "sharing of differences" that epitomizes the third stage of the General Systems model. It leads directly to the 4x3 tetrahedral bonding of the alpha particle (4 nucleons each of 3 quarks), and thence to the carbon atom - 3 alpha particles each of 4 nucleons; and so on up the nucleosynthetic pathway in alpha particle increments. (See: "The Fractal Organization of Nature".)
The androgynous "nucleon" can also be seen as a state of higher symmetry than either the proton or neutron alone - the analog of a force unification symmetry state, but expressed at the particle level. This symmetry state was originally given the name of "isospin" symmetry or "isotropic spin" symmetry, and was conceived as a global symmetry state for which meson exchange formed the local symmetry "current" or field vector, and the proton and neutron were the local derivatives.
"Isotropic spin" symmetry or "isospin" symmetry leaves the strong force unaltered when protons and neutrons are interchanged. The name derives from assigning a completely imaginary state of "spin" to the nucleon ("up" for the proton and "down" for the neutron). This theoretical spin state is isotropic (invariant) insofar as the strong force is concerned, whether it is in the up or down "phase". Isospin symmetry was understood as a natural consequence of strong force meson exchange between the nucleons. When the quark model was developed by Gell-Mann and Zweig, the "up" and "down" designations were retained for the ground state quark flavors. The superseded isospin model was then applied to the actual (rather than virtual) weak force transformations of neutrons to protons. The weak force is also a short-range force with massive field vectors, the IVBs. Also like the strong force, meson exchange occurs in weak force baryon transformations, but is mediated by the much more massive IVBs. (See: "The 'W' IVB and the Weak force Mechanism".) (See: Robert Oerter: The Theory of Almost Everything. Penguin (Plume) 2006.) (See: James Trefil: The Moment of Creation. Macmillian (Collier) 1983.)
Local gauge symmetry is epitomized in the neutral, quiescent nature of the cold, crystalline, ground state of atomic matter, the state we normally occupy that is so life-friendly. The meson field of the strong force succeeds in reducing the energy level of most heavy atomic nuclei to a quiescent ground state. Radioactive decay is not a common phenomenon in our ordinary elements - one has to look rather hard to find it, as the Curies discovered. The local activity of the meson field provides us with a non-radioactive spectrum of stable heavy elements capable of producing and sustaining life.
4) Gravitation: a temporal metric and relative motion. Invariance of Einstein's "Interval" despite the variable dimensions and variable metrics of spacetime, and the variable relative motions of matter - serving energy conservation, causality, entropy, and (ultimately), symmetry conservation. Time is created by the gravitational annihilation of space and the extraction of a metrically equivalent temporal residue, decelerating light's spatial cosmic expansion to fund matter's historical cosmic expansion. Symmetry conservation is (ultimately) accomplished by the gravitational conversion of bound to free energy in stars, and by Hawking's "quantum radiance" of black holes. (See: "Entropy, Gravitation, and Thermodynamics".)
The invariance of the "Interval" is due to the flexible nature of time and space, and their interconvertibility. Flexible metric scales and the invariance of the "Interval" are both necessary to rescue energy conservation and causality from the fluid dimensionality of General Relativity, and from the relative motion of matter at less than "velocity c". Because of the invariance of the "Interval", energy conservation and causality is observed in all local metrics (on Jupiter, the Earth, the Moon, the Sun, etc.), despite the fact that time runs at a different rate on each, because length scales are also affected in a compensatory manner (Lorentz invariance in General Relativity). (See: "A Description of Gravitation".)
Global symmetry: The symmetric spatial metric gauged by c.
Gravity acts to conserve the non-local symmetric energy state of light, and light's entropy drive (light's intrinsic motion), by converting space and the embedded entropy drive of free energy (the expansive properties of space and light), to time and the entropy drive of bound energy (the intrinsic motion of time and the expansive properties of history). (See: "The Double Conservation Role of Gravitation".) Time, the entropy drive of bound energy, is also necessary to matter's causal relations and energy conservation (because the energy content of matter varies with its relative velocity).
Gravity introduces local time (and local causality) with the gravitational "location" charge, converting globally symmetric space to locally asymmetric time. This is a conversion from a global to a local entropy drive. The expansion of causal history replaces the expansion of acausal space; aging replaces cooling; the intrinsic motion of time (the local entropy drive of bound energy) replaces the intrinsic motion of light (the global entropy drive of free energy). Gravity is the conversion force for the primordial drives of global spatial vs local temporal entropy, in either direction.
Because the gravitational charge specifies a particular place (holds space constant), it must introduce movement in another dimension to satisfy entropy demands: matter's moving time dimension. Because matter does not expand or move in space (matter has no (net) intrinsic spatial motion), matter's time dimension must move - entropy increase is mandatory in some dimension, for all energy forms in our universe of electromagnetic energy.
Time is the local symmetry current which adjusts the energy accounts of matter in relative (rather than absolute) motion from place to place in space. Energy conservation is accomplished in systems of bound energy despite the relative (rather than absolute) motion of matter, and despite the lack of a globally symmetric spatial entropy drive. This is the conservation role of the local gauge metrical symmetry imposed by the gravitational force, whose field vector is time, spacetime, or the graviton. (See: "The Time Train".)
The function of the spatial metric is energy conservation, which requires a symmetry parameter (inertial forces) and an entropy parameter (the intrinsic motion of light or free energy as gauged by "velocity c"). This conservation function is globally gauged by c, and locally gauged by G, which introduces the asymmetric time parameter, necessary for matter's entropy drive, causality, and energy conservation. Time also indicates inertially (gravitationally) the spacetime coordinates of the distributional asymmetry of mass, including magnitude and density. A gravitational field is the spatial consequence of the intrinsic motion of time. Time and gravity induce each other endlessly. (See: "A Description of Gravitation"; and "Entropy, Gravitation, and Thermodynamics".)
The Material Cosmos is no Accident
If there is one conclusion we should draw from the global-local structure of our Cosmos, it is certainly that the appearance of matter (and by extension, life) in this Universe is no accident. The material Cosmos is a system of energy that was destined to manifest in its current life-friendly form from its beginning. It is not only the weak force asymmetry that is built into the laws of Nature, but the duality of the global-local structures of all the other forces as well. The magnetic field of the electromagnetic force, the gluon field of the strong force, the temporal metric of gravitation and spacetime - all these anticipate the creation or existence of matter, and are in addition to the weak force asymmetry parameter, the metric structure of the IVBs, and the alternative charge carriers of the leptonic field. And this is still to say nothing of the "life-friendly" values of the physical constants.
All these parameters are fixed at the level of the Multiverse, and once they are engaged as a self-consistent and self-referent set, capable of internal energy conservation, and requiring no net energy or charge to produce, the birth of our manifest Universe is assured. It is my assumption that our Universe is but one of perhaps infinitely many created in a similar fashion, each with its own unique set of physical parameters. Any notion of "Divinity" thus resides in the creative energies of the truly global Multiverse, of which our Universe is but one local example and subset. Other life-friendly Universes of our own type may be few or nonexistent, but we simply have no idea at all what creative possibilities are available to the Multiverse in this regard - the multifaceted exploration of itself.
For a summary of my own formulation of the force symmetries see: ("Symmetry Principles of the Unified Field Theory").
Weak Force Papers:
References:
http://www.people.cornell.edu/pages/jag8/gauge11.html
(Revised Feb., 2008)
(See also:
John A. Gowan
http://www.people.cornell.edu/pages/jag8/index.html
1) Noether's Theorem requires the conservation of light's symmetry no less than light's energy.
2) The charges (and spin) of matter are the symmetry debts of light.
3) Charge (and spin) conservation is a temporal, material form of symmetry conservation.
4) Paying (discharging) light's symmetry debt is the role of the forces.
5) Charge invariance in time and space (in the service of symmetry conservation) is the key to understanding the local action of the forces.
6) The field vectors of the forces act as local gauge symmetry "currents" which transform global and absolute charge invariance into local and relative charge invariance - serving charge and symmetry conservation, and in the case of gravity, time, and the "Interval", serving energy, symmetry, entropy, and causality conservation.
7) Gravity transforms the global spatial metric of absolute motion and light, as gauged by the electromagnetic constant c, into a local spacetime metric for relative motion and matter, as gauged by the gravitational constant G. (Gravity creates time by the annihilation and conversion of space.)
8) Gravity pays the entropy "interest" on matter's symmetry debt, creating time by the annihilation of metrically equivalent space, decelerating cosmic expansion in consequence. Conversely, the gravitational conversion of bound to free energy (as in the stars and Hawking's "quantum radiance" of black holes), pays all symmetry and entropy debts, accelerating the cosmic expansion. The radiance of our Sun and the stars represents a completed "circuit" of symmetry conservation. (See: "Currents of Entropy and Symmetry)".
Local Symmetry: partial charges of the quarks and their gluon field vectors; also, quark confinement and neutral ("white") color charge despite the partial charges carried by the quarks ("white" color also sums other partial charges to whole quantum unit values).
Local symmetry: The asymmetric historical metric gauged by G.
Non-local distributional symmetry of atemporal, acausal free energy (light) vs local distributional asymmetry of temporal, causal bound energy (matter). (Although G is a global gauge (invariant and universal), G nevertheless regulates a local metric - because of the time dimension gravity creates.)
Please use the URL http://www.webcitation.org/5YMk47HMc to access a cached copy of this page
If you have any questions, please feel free to contact the WebCite team at http://www.webcitation.org
