The Connection Between Symmetry and
(revised May, 2011)
John A. Gowan
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This paper is part of a set of five, listed below, examining various relationships between the four conservation principles of the Tetrahedron Model of Natural Law (these short papers are not intended to stand alone):
The connection between Symmetry Conservation
(manifesting as charge conservation) and Causality (historic
(This paper can also be seen in "Synopsis of the Tetrahedron Model".)
Charge conservation is a means of extending symmetry conservation into the time or historic dimension (in contrast to the inertial forces of the spacetime metric, which also conserve symmetry, but which have no mechanism allowing deferment in time) (just the difference between a credit card and a debit card). The charges of matter are the symmetry debts of light.
Because certain types of symmetry can be conserved through time in the form of charge, matter can have an historical (and necessarily causal) dimension, unlike light which bears no charges and is both atemporal and acausal. Unlike raw energy and entropy debts, which must be paid immediately, symmetry debts (when in the form of conserved charges), constitute the "credit card" of the Cosmos - "buy now, pay later". Gravity pays the "interest" on the symmetry debt of matter through the deceleration of the cosmic expansion via the gravitational conversion of space to time. It is therefore the entropy drive of free electromagnetic energy (light) and the expansion of space which (through gravity) funds the entropy drive of bound electromagnetic energy (matter) and the expansion of history. The charges of matter (symmetry debts) are eventually paid by matter-antimatter annihilations, the conversion of bound energy to free energy in stars, quasars, and Hawking's "quantum radiance" of black holes, and by particle and proton decay. Charge conservation, like the historical entropy drive (time's intrinsic motion) and the conversion of free energy to mass (hv = mcc), gives the Universe a life in the historical domain, in which energy can be converted to work, information, and material objects with relative rather than absolute motion, and yet all conservation laws are nevertheless observed. (See: "Global vs Local Gauge Symmetry and the 'Tetrahedron Model'".) The energy required to create matter's 4th dimension and entropy drive (time), is simply subtracted from the entropy drive of light and space (light's intrinsic motion), by the gravitational conversion of space to time, with the consequent deceleration of the spatial expansion of the universe. The expansion of pure space is gravitationally converted to the historical expansion of spacetime. (See: "The Conversion of Space to Time".)
Charge: the creation of fermions (quarks, leptons, neutrinos, and their charges) by symmetry-breaking during the "Big Bang". Fermions are the surviving matter half of light's particle-antiparticle form: charge conservation ensures that their symmetry debts, held through time as charges, will eventually be repaid. Charge conservation = symmetry conservation in the time dimension (hence the cardinal importance of charge invariance, with all the local gauge symmetry currents and forces required for its maintenance). The charges of matter are the symmetry debts of light - (Noether's Theorem). Charge conservation is a temporal form of symmetry conservation - made possible by the creation of the historical domain through the gravitational conversion of space to time. Fermions comprise the 92 naturally occurring elements, the information base of matter, created in the "Big Bang" and by the nucleosynthetic pathway in stars (and supernovas). Charges are held in the time or historical dimension where they are balanced or neutralized until they can be annihilated or otherwise canceled by their corresponding antimatter charges. Charge conservation is moot in the absence of a time dimension, as the mutual annihilations of virtual particle-antiparticle pairs attests.
This line (in the "Tetrahedron Model") is essentially the linkage between Causality and the source of Information, as Information is primarily supplied from the Symmetry pole, beginning with fermions, atoms, and charge conservation. In the chain of cause and effect, information must always be associated with the purely reactionary or mechanical aspects of the causal linkage - what, exactly, is the cause, and what, exactly, is the appropriate effect? In the classic notion of "Karma", the linkage of cause and effect with information is implicit: both the criminal and the crime are known, and "the punishment must fit the crime". Information is by its very nature asymmetric and begins with charge. The gravitational "location" charge of bound energy, and the "identity" or weak force "number" (or "flavor") charges of elementary particles (carried in their explicit form by neutrinos), are the most fundamental charges of matter; spin, electric charge, and color follow in descending order of importance or universality. Charges produce forces (carried by "field vectors" or "bosons") which act to pay the symmetry debts. Exactly what symmetries of light these charges represent is discussed in the paper "Symmetry Principles of the Unified Field Theory", among others.
Symmetry-breaking is necessary during the "Big Bang" to extract a residue of matter from the otherwise symmetric virtual particle "sea". Virtual particles (when not bound to an atom or other massive particle) do not exist in real time and hence do not produce a gravitational field (see: "Does Light Produce a Gravitational Field?"). Free virtual particles become manifest ("real", massive, temporal) only through the mediation of the weak force Intermediate Vector Bosons (IVBs). Acting in concert, the "Tetrahedron" of conservation principles allows the conversion of free energy to the mass, 4th dimension, and information of particles (bound energy, causal and entropic time, charge). But the weak force must still produce an asymmetry between particle vs antiparticle before the symmetry of the primordial pairs can be broken, isolating matter from antimatter. (See: "The Origin of Matter and Information".)
Charge conservation and atomic matter form the base of the "information pyramid". Most information originates in the atomic nucleus, but is vastly amplified in the chemical interactions, combinations, and permutations of the electron shells of atoms. (See: "The Information Ladder" and " The Information Pathway".) Molecular biologic information is carried by DNA and genes; symbolic information is carried by language and human writing, including math, music, and machine language, etc. Information is conserved permanently in the historic domain of spacetime (matter's causal web, net, field, or "matrix"), and conserved temporarily in the molecular genetic code of life, and symbolically through human agency (as in libraries). Time is a necessary dimensional parameter both to order information (as in abiotic cause and effect and in biotic development and evolution), to preserve information and matter's "causal matrix" through historic spacetime, and to produce the entropy drive of bound energy. Causality orders information just as it orders the spacetime metric and energy, providing evolutionary and developmental routes, abiotic and biotic, for the return of bound to free energy. Finally, time is the necessary dimensional parameter in which charge conservation has meaning.
The gravitational charge is complex in that it represents a double debt, one of entropy (intrinsic motion), and one of symmetry (immobile mass), both consequent upon the loss of light's intrinsic motion and non-local distributional symmetry (whenever free electromagnetic energy is converted to bound electromagnetic energy). (See: "The Double Conservation Role of Gravitation".) Due to the mixture of the entropy debt with the symmetry debt, the latter cannot be deferred in time; gravity can never be neutralized, unlike electric charge. Hence we see the gravitational debt being paid or satisfied in two modes, which it is convenient to think of as a payment of "interest", occurring at all gravitational energies (entropy debt - intrinsic motion, the gravitational conversion of space to time - as on planet Earth), and a payment of "principle", occurring only at high gravitational energies (symmetry debt - immobile mass, the gravitational conversion of bound to free energy - as in the stars).
Gravity pays the "interest" on the symmetry/entropy debt of matter by the conversion of space to time, creating a historical domain and a temporal entropy drive for matter and its charges. This action, however, only addresses the entropy debt (intrinsic motion), and does not diminish the actual symmetry debt (immobile mass) of matter (as in the familiar case of planet Earth), hence the analogy with "interest". The spatial expansion of the Cosmos is reduced nevertheless, supplying energy for the historical expansion. Therefore it is ultimately the intrinsic motion of light, the primordial entropy drive of free energy, which (through gravity) funds the intrinsic motion of time, the primordial entropy drive of bound energy. Gravity finally pays the "principle" on matter's symmetry/entropy debt by converting bound to free energy in stars, and by various other astrophysical processes, which go to completion in Hawking's "quantum radiance" of black holes. The gravitational force vanishes when mass vanishes - demonstrating the final repayment of the symmetry/entropy debt "principle", in complete satisfaction of Noether's Theorem. (See: "A Description of Gravitation".)
The "intrinsic" information inherently contained in free electromagnetic energy (light), and in the spacetime light creates, is expressed as the dimensional metric with its derivative, entropic regulatory gauges c, T, and G, its inertial forces conserving energy and symmetry, and finally as the "particle metric", the structural property of spacetime determining the species and masses of particles, charges, and force carriers that the "vacuum" is prepared to host, produce, and conserve (including the scaling property of the "particle mass gauge" or "Higgs" boson).
The realized possibilities we see in our Universe for quantized, bound energy forms are the 3 families of 4 elementary particles: 6 leptons and 6 quarks, and these determine the material parameters and characteristics of the Universe as we experience it (in our daily life, only 2 leptons and 2 quarks are found). The four dimensions of spacetime, the 3 energetic families each of 4 elementary particles, the four forces of physics, and the four major conservation laws, constitute the primary evidence of a 4x3 fractal algorithm inherent and operating in Nature, beginning with the electromagnetic "vacuum" of energized spacetime. This fractal algorithm is the fundamental and resonant "bit" or "Word" of Cosmic Information diagrammatically and symbolically represented by the "Tetrahedron Model". (See also: "Nature's Fractal Pathway"; "The Information Pathway"; and "The Fractal Organization of Nature".)
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