The Connection between Entropy and Symmetry (as Illustrated in the Tetrahedron Diagrams)
(revised April, 2006)
John A. Gowan
http://www.people.cornell.edu/pages/jag8/index.html
This paper is part of a set of four, 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 Entropy and Symmetry
The line connecting Entropy and Symmetry (see diagram) includes gravity and the spacetime metric. This line also indicates there is at least functionally a connection between charge conservation and the dimensional conservation domains of spacetime. The most fundamental expression of the connection between Entropy and Symmetry is velocity c, the electromagnetic constant, the intrinsic motion of light, which is both the entropy drive and the symmetry gauge of free electromagnetic energy. On the one hand, the intrinsic motion of light suppresses asymmetric time and maintains the symmetric status of the spatial metric, suppressing also "rogue" or sourceless gravitational fields. On the other hand, the intrinsic motion of light causes the expansion and cooling of the Cosmos, reducing its capacity to perform 'work". A related connection is that entropy and charge conservation play similar roles in the unfolding of the manifest, "real" world from "virtual" reality. Entropy allows the transformation of free energy to work, and charge conservation allows the transformation of free energy to information. Together with weak force symmetry-breaking and the conservation of light's raw energy as mass and momentum, this "trinity" of conservation effects brings the world of matter into reality. Finally, it is the existence of the time dimension which makes charge conservation a practical, functional option - producing a past, present, and future in which symmetry debts (charges) can be contracted, maintained, and eventually paid. Negentropic gravitational energy is the "interest" on bound energy's symmetry/entropy debt paid by the Cosmos, energy deducted from light's expansive entropy drive, creating instead the time dimension, entropy drive, and historic conservation domain of matter and information.
All forms of energy must have an entropy drive: Entropy (the 2nd law of thermodynamics) is required to protect the 1st law of thermodynamics, the Conservation of Energy. Primordial or "pure" entropy is an embedded characteristic of energy which creates a dimensional conservation domain for its energy type: space for free energy, historic spacetime for information (matter's "causal matrix") and the mixture of free and bound energy. The function of the pure entropy forms is produced by an entropy "drive", or intrinsic motion: intrinsic motion "c" for light, creating space, intrinsic motion "T" for time, creating history, and intrinsic motion G (gravitation) as the conversion force between the two entropy drives and domains, creating spacetime, the joint dimensional conservation domain of free and bound energy. The magnitude of G is determined by the small energy difference between the symmetric spatial entropy drive of light (S) (the intrinsic motion of light as gauged by "velocity c"), and the asymmetric temporal entropy drive of matter (T) (the intrinsic motion of time as gauged by "velocity T"): S - T = -G.
When free energy (light) is converted to bound energy (matter, mass, momentum), the positive entropy drive of free energy (intrinsic motion c, the "velocity of light") is transferred to the positive entropy drive of bound energy (intrinsic motion T, the "velocity of time"). Entropy is conserved and does not simply disappear when light or free energy is converted to matter or bound energy. The entropy of an isolated system always increases, whether in its temporal or spatial form and domain, or the mixture of both. Light's symmetric energy state is conserved as the charges and spin of matter, and the inertial and gravitational forces of the metric; light's raw energy is conserved as the mass and momentum of matter; light's entropy drive is conserved as the intrinsic motion of matter's time dimension and the gravitational field of matter (gravity is both a symmetry and an entropy debt of light). Light's positive spatial entropy (light's intrinsic motion), causing the expansion and cooling of space, reappears as matter's positive temporal entropy (time's intrinsic motion), causing the expansion and decay of history (historic spacetime).
The intrinsic motion of light, which is light's primordial expression of entropy (creating light's conservation domain, space, and causing the expansion and cooling of space), is conserved and transferred to matter as the intrinsic motion of time, which is bound energy's primordial expression of entropy (creating the conservation domain of information and matter's "causal matrix" - history - and causing the expansion and decay of historic spacetime as well as the aging of matter). Gravitation is the force which converts either form of entropy drive and domain to the other, converting some of light's dimensional conservation domain, space, into historic spacetime, the dimensional conservation domain of information and matter's causal matrix. Spacetime is a combined conservation domain where both light and matter can coexist, interact, and find conservation. Thus the function of entropy (in its primordial forms), whether positive or negative, spatial or temporal, is to create a dimensional conservation domain for energy, whether free or bound. This is the connection between the first and second laws of thermodynamics. (See: "Entropy, Gravitation, and Thermodynamics").
Gravity creates time by consuming space. By gravitationally linking to space (via time), matter retains an entropic connection to space, which light lost when it converted to bound energy and ceased its intrinsic motion. Hence gravity is the conserved entropy connection between bound energy and dimensionality. "Velocity T" and history substitute for "velocity c" and space as matter's connection to dimensionality. The intrinsic motion of matter's time dimension becomes the entropy drive for bound energy, and is the metric equivalent of light's intrinsic motion in space. Matter requires a time dimension as an entropy drive, to conserve causality, and to balance its raw energy accounts, since matter's energy content varies with its velocity and relative motion (momentum, kinetic energy). Light does not similarly require time, since unlike matter, light has but a single, constant, and absolute (non-relative) velocity; light's energy varies instead with its frequency. (See: "The Time Train".)
Symmetry-breaking changes light into the charges and mass of matter, space into historic spacetime, and spatial entropy (gauged as "velocity c") into temporal entropy (gauged as "velocity T"). Matter is an asymmetric form of light, 1/2 of light's particle form (being derived from the broken symmetry of particle-antiparticle pairs), and one-way time is similarly an asymmetric form of space, 1/2 of a spatial dimension (see quote below from the book "Trance, Art, Creativity").
"Analysis of this equation [Einstein's Interval] provides us with the proportion that time is to space as "i" (the square root of -1) is to 1. Now "i" multiplied by itself is negative 1, so that in a metaphoric sense we can say that the time dimension is "half" a space dimension. Curiously one finds this out intuitively. We have full intuition of the three spatial dimensions, but we cannot intuit the fourth dimension, so we experience it as "time." Furthermore this experience is not full; it is partial, for we are on a one way street indicated by "time's arrow" which allows us always to experience duration as getting later and later, but never the opposite." (Prof. John Curtis Gowan Sr. in "Trance, Art, Creativity" page 253-4)
The Connection Between Conservation and Entropy
Space is the conservation domain of light, created by the intrinsic motion of light (gauged as "velocity c"). Light's intrinsic motion is free energy's primordial expression of entropy, not only creating metric space, but also causing the expansion and cooling of space. Hence the connection between conservation and entropy is the creation of dimensional domains by entropy in which energy can be both used and conserved. Space is the dimensional conservation domain of light, created for light by the entropy drive (intrinsic motion) of light. This is the connection between the 1st and 2nd laws of thermodynamics and between the Entropy and Conservation poles of the tetrahedron diagrams.
All three forms of primordial entropy have (at least) two conservation roles. In the case of light's intrinsic motion, the connection between entropy and energy conservation is thoroughgoing. Light's intrinsic motion not only creates, but also expands and cools space, the dimensional conservation domain of free energy. "Velocity c" also gauges the energetic equivalence between mass and light through Einstein's most famous equation: E = mcc.
Furthermore, the entropy and symmetry keeping functions of free energy are also combined in the intrinsic motion of light: velocity c is both the entropy drive and the symmetry gauge of free energy. "Velocity c" regulates ("gauges") the metric symmetry of light's "non-local" energy state, suppressing time and sourceless or "rogue" gravitational fields.
In a similar way, the entropy and causality functions of bound energy are combined in the intrinsic motions of time: "velocity T" gauges the entropy drive of matter, and regulates and expands historic spacetime, the conservation domain of information and matter's "causal matrix".
Finally, gravity combines the entropy and symmetry debts of light with the causality of matter, creating time from space and converting bound to free energy in stars, etc.
It is the conservation role of light's entropy drive (the intrinsic motion of light) to create a dimensional conservation domain (space) in which action can occur, work can be done, and energy can be used and transformed while still being conserved. Similarly, the entropy drive of bound energy, the intrinsic motion of time, creates, expands, and decays (dilutes) history, the temporal analog of space. Gravitation, converting the drives and conservation domains of spatial entropy to the drives and conservation domains of temporal entropy, and vice versa, creates historic spacetime, the joint dimensional conservation domain of free and bound energy.
But if energy is used to create change, action, work, or transformed to another state, some price must be paid, some accounting must be made, in order to avoid violating energy conservation - as in the case of the perpetual motion machine. This price is entropy, whose increase allows energy to be used and yet conserved. The total energy of any system is conserved even as its capacity for performing work declines - its entropy increases.
Without entropy and the second law, energy conservation by the 1st law would be so completely rigid that energy could not be used for any purpose. Entropy frees energy from the miserly grasp of the 1st law by creating a dimensional conservation domain whose special character is just that in it, energy can both be used and conserved, through the additional accountability of entropy, the continual reduction in the capacity of the dimensional system to perform work. The increase of entropy provides an extra "degree of freedom" in the energy parameter - "capacity for work" - which allows energy to be conserved even while it is used and/or transformed.
The Connection Between Conservation and Symmetry
This connection has been rigorously established by Emmy Noether in her famous "Noether's Theorem": In a multi-component field (such as the electromagnetic field, or the metric field of spacetime), wherever one finds a symmetry one will also find an associated conservation law, and vice versa. We see this theorem demonstrated forcefully in two familiar areas - the forces associated with charge (and spin) conservation and the inertial and gravitational forces which regulate the symmetry of the spacetime metric.
We can visualize the line connecting the conservation and symmetry poles (see diagram) as filled with symmetric particle-antiparticle pairs (the vacuum "sea" of virtual particles), created by the interaction of light with the metric of spacetime, while the symmetry pole is the site of the general principle of symmetry conservation in all its forms (of which "Beauty" is one - an emergent property realized within the human metaphysical realm - see: "The Human Connection").
When the symmetry of particle-antiparticle pairs is broken, producing matter, the symmetry of the metric is also broken by the appearance of gravitation and its asymmetric dimensional product, time. The various symmetries of light are conserved as the various charges (and spin) of matter: the charges of matter are the symmetry debts of light. (This connection is evident from the fact that the functional role of the charges carried by particle-antiparticle pairs is to cause and facilitate annihilation reactions, restoring the perfect symmetry of the light which created them. When one member of such a pair vanishes, as in the creation of matter during the "Big Bang", the remaining member is left with all its charges intact and conserved, charges which were intended to protect light's symmetry via the annihilation reactions. Thus we see that the charges of matter do indeed represent the symmetry debts of light, frozen and conserved since the beginning of time in the "Big Bang".)
Uniquely among the charges, gravitation has two conservation roles, one as a symmetry debt, another as an entropy debt of light. Viewed as a symmetry debt, gravitation is a debt of light's "non-locality", whose charge is "location", and whose role is to restore the broken, non-local distributional symmetry of light by converting mass to light, as in stellar processes and Hawking's "quantum radiance" of black holes. Viewed as as an entropy debt, gravity's conservation role is to convert space into time, conserving light's spatial entropy drive by converting space into matter's temporal entropy drive. The two views and roles are compatible since the active principle of the "location" charge is time. That is, when gravity collapses space around a particle, it creates the particle's entropic time dimension, and by the same action establishes the particle's location in 4 dimensions. Finally, the gravitational conversion of bound energy to free energy (as in the stars) restores light's "non-local" energetic symmetry state and spatial entropy drive (intrinsic motion c), repaying both the symmetry and entropy debt simultaneously. See: "The Double Conservation Role of Gravitation".)
Connections to the Causality - Information Pole
The fermionic elements produced by symmetry-breaking provide the information realm with its major input, the information contained in the atomic nuclei and the electron shells of the elements of the periodic table. Organic and pre-biotic chemical processes create from these ingredients the replicating and information "remembering" molecule, DNA. The time dimension, created by the gravitational conversion of space, provides evolution with a necessary dimensional parameter. In the context of limited resources consumed by an exponentially replicating molecule, natural selection, through competition, differential death and reproduction, produces a self-interested biological entity with perceptual adaptations for fulfilling personal goals - food finding, mate finding, safety, etc. The variation in DNA information, produced randomly by copying errors and mutations, and purposely generated by sexual reproduction, is an example of positive entropy at work in the information dimension, as driven by time's one-way "arrow". Natural selection is a mechanism which uses this genetic variation to reverse the course of positive entropy, producing a negentropic evolutionary drive toward more complex biological information systems, culminating in humans, who in turn (as an iteration of the Universal Fractal) have created their own "artificial" information and evolutionary systems. (See: "The Information Ladder".)
The connection between Entropy and Causality-Information is of course through the time dimension of matter, produced by matter's gravitational field. Time provides the entropy drive of matter, as well as the historic domain (historic spacetime) which is the conservation domain for Information and matter's "causal matrix". Time also produces the necessary dimension in which evolutionary development can take place. Gravitation is the entropy-interest which the Cosmos pays for carrying matter's symmetry debts: charge conservation carries matter's symmetry debts indefinitely through time, but it is gravitation which creates the time dimension itself (from space), making this "buy now, pay later" strategy possible in terms of dimensions. The gravitational deceleration of the Cosmic spatial expansion provides the energy for matter's time dimension; thus it is that the temporal entropy drive and domain of bound energy is funded by the spatial entropy drive and domain of free energy.
Life is the conservation domain of information, because only life has a genetic system which allows the inheritance and accumulation of information through time. While at first this system of information conservation is wholly genetic or molecular, eventually, with the development of complex perceptual systems, conservation takes additional abstract and symbolic forms such as memory, language, mathematics, writing, books, libraries, cultural systems, schools, communication systems, money, the Media, computers and electronic networks, etc., all the refinements of the information dimension that human society, industry, technology, and science are now exploring.
The connection between the Conservation and Causality-Information poles is possibly the most interesting connection of the whole diagram, as we can see here on a metaphysical level Plato's realm of Ideal Forms, Jung's Archetypes, and the realm of Spirit, religion, and the soul; on the physical level it is raw energy conservation and causality; on the biological level it is photosynthesis, heritable genes and the genetic system; and on the human level it is abstract, symbolic, "artificial", social, mechanical, and electronic information systems, including such esoteric contacts or connections as inspiration, "the Muse", "revelation", ESP, psychic phenomena, genius, etc. For a discussion of the negentropic and information vector of the Universe, see: "Newton, Darwin, and the Abundance of Life in the Cosmos". For a discussion of psychic phenomena in the context of art, information, and religion, see my late father's book: "Trance, Art, Creativity".
The abstract information realm is the playground as well as the product of the human mind, whose imaginative and symbolic abilities enable our species to explore the dimension of art, science, religion, fantasy, meditation, technology, Natural Law, and the physical dimensions of the Cosmos itself in a manner inconceivable to any other animal. Unlike the other creatures of Earth, due to the abstracting ability of our minds, we live in 4 dimensions of Spacetime, and a 5th dimension of Information. See: "The Information Pathway", and "Chardin: Prophet of the Information Age".
Links:
