The Connection between
Conservation, Entropy, Symmetry, and Causality-Information (as
Illustrated in the Tetrahedron
(revised May, 2011)
John A. Gowan
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):
Connections Between Conservation and Entropy
Space is the conservation domain of light, created by the intrinsic motion of light (gauged by "velocity c"). Light's intrinsic motion is free energy's primordial entropy drive, 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 primordial forms of entropy in which energy can be used, transformed, and nevertheless conserved. Space is the entropic 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 Diagram.
All three forms of primordial entropy drive 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 entropic and symmetry-keeping functions of free energy are also combined in the intrinsic motion of light: "velocity c" gauges both the entropy drive and the metric and "non-local" distributional symmetry of light. "Velocity c" regulates ("gauges") the metric symmetry of light's "non-local" energy state, maintaining inertial symmetry among the dimensions, and suppressing time, virtual particles, 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: not only does time form the causal linkages of matter, but "velocity T" also gauges the entropy drive of matter, regulating the expansion of 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, all while simultaneously being conserved. Similarly, the entropy drive of bound energy, the intrinsic motion of time, creates, ages, 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 and entropic domain of free and bound energy.
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 (the same energy cannot be used twice to perform the same net "work"). 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 (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. Note again the functional similarity between entropy and charge: charge conservation allows symmetry to be conserved so that energy may be transformed to information (via atomic matter).
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 explicitly 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 Heisenberg/Dirac vacuum "sea" of virtual particles), created by the interaction of light with the metric of spacetime. The symmetry pole represents 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 charge symmetry of particle-antiparticle pairs is broken, producing matter, the inertial 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 weak force 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".) These conserved charges include "location", the charge which gives rise to the gravitational force.
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 and metric symmetry of light by converting mass to light, as in stellar processes and via Hawking's "quantum radiance" of black holes. Viewed as as an entropy debt, gravity's conservation role is to conserve light's spatial entropy drive by converting light's intrinsic motion into time's intrinsic motion. 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 coordinate position in 4 dimensions. Finally, the gravitational conversion of bound energy to free energy (as in the stars), restores light's "non-local" distributional and metric symmetry, and light's spatial entropy drive (intrinsic motion c), repaying both the symmetry and entropy debt simultaneously. The gravitational field of matter, which represents the demand for debt repayment, vanishes when mass vanishes. See: "The Double Conservation Role of Gravitation".)
Connections Between Conservation and Causality - Information
The 92 fermionic elements of the periodic table produced by symmetry-breaking provide the information realm with its major input, the information contained in the atomic nuclei and the electron shells of atoms. Organic and pre-biotic chemical processes create from these ingredients the replicating and information "remembering" molecule, RNA/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 ("agent") with perceptual and physical adaptations for fulfilling personal goals - food finding, mate finding, self-defense, 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 efficient, successful, and complex biological information systems, culminating in humans, who in turn (as an iteration of the Universal Fractal) have created their own abstract or "artificial" information and evolutionary systems. With the advent of humanity, we recognize the achievement of (at least) three goals of the Information Pathway: 1) humanity as a fractal iteration of the creative energy of the Cosmos (humanity as a co-creator); 2) humanity as the self-awareness and perceptual agent of the Cosmos (stardust awakened to life); 3) humanity as Nature's dispersal agent for Earth-Life into the Cosmos (via the creation of spaceships). (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" (temporal causal linkages). 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 actualized dimensions. The gravitational deceleration of the Cosmic spatial expansion provides the energy for matter's time dimension; thus (through gravitation), the spatial entropy drive and domain of free energy funds the historical entropy drive and domain of bound energy.
Life is the molecular 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 massive contribution of modern humans to Chardin's "noosphere").
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 immortal human soul - the essence of personal information. 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, the "Akashic Record", genius, etc. There is even a theorem in quantum mechanics to the effect that information can never be destroyed. We also recognize this fact in the permanence of the historic record and its "karmic" interconnections and consequences. (See: The Black Hole War by Leonard Susskind. Back Bay Books/Little, Brown and Co., 2008.) 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, available (free) on his memorial website: "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. Like the other dimensions, the 5th information dimension may be conceived as the product of the intrinsic motion of an entropic drive - the mixed spatio-temporal or "tertiary" entropy of Clausius, Boltzmann, and traditional thermodynamics, with a large negentropic input by gravity and natural selection. (See: "Nature's Fractal Pathway", and "Chardin: Prophet of the Information Age".)
(For more on this topic, see: "Entropy, Gravitation, and Thermodynamics" and "A Description of Gravitation".)