John A. Gowan
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The Function and Energetics of Entropy
Revised Nov., 2010
(See also: "Introduction to Entropy"; and "Spatial vs Temporal Entropy")
The function of entropy - its rationale or reason for existence - is to protect the conservation of energy and causality. The 1st law of thermodynamics (energy conservation) is protected by the second law (entropy) in that it is the function of the second law to create dimensional conservation domains in which energy can be used, transformed, and conserved simultaneously. For symmetric free energy (light), this domain is space, created by the entropic drive of free energy, the "intrinsic motion" of light, gauged by "velocity c", the electromagnetic constant. For asymmetric bound energy (matter), this domain is historic spacetime, created by gravity and the entropic drive of bound energy, the "intrinsic motion" of matter's time dimension, gauged by "velocity T", the one-way motion of time. (Time is also ultimately gauged by "c" as the duration required by light to travel a given distance. See: "The Time Train"). The historic component of spacetime is the conservation domain of information and matter's "causal matrix". History is the temporal analog of space, created by the intrinsic motion of time, partially visible in our great telescopes, and forming with gravitation the "causal matrix" of spacetime, upholding the effect of the "Universal Present Moment" for all bound energy forms in the Cosmos. (See: "A Spacetime Map of the Universe".)
Gravity is an entropy (and symmetry) conservation/conversion force, creating time from space and vice versa, the latter in conversions of bound to free energy, exampled by our Sun. Gravity and time induce each other in an endless cycle: gravity creates time from space (by the annihilation of space and the extraction of a metrically equivalent temporal residue); the intrinsic motion of time pulls space toward the center of mass and the beginning of the time line and the historic conservation domain of information. It is the connection between space and time, and the temporal (entropic) pull on space caused by time's intrinsic motion, that creates the spatial flow of gravity. Gravity is the spatial consequence of the intrinsic motion of time. (See: "A Description of Gravitation".)
Gravitation creates time and spacetime, and as a negative form of spatial entropy, causes the contraction and warming of space, rather than the reverse, as in the case of the intrinsic motion of light. The creation of dimensional conservation domains by the intrinsic, entropic motions c, T, and G (light, time, gravity), where energy can be both used, transformed, and yet simultaneously conserved, is the connection between the 1st and 2nd laws of thermodynamics. Consequently, wherever we find a form of energy, we will find an associated form of entropy (in entropy's primordial form, intrinsic dimensional motion).
Entropy is the guarantee made by the 2nd law of thermodynamics to the first law, that energy will be conserved while it is being transformed and used. The "teeth" of this guarantee is the effectively "infinite" velocity of both light and time, insuring that lost heat and opportunity cannot be recovered. Hence the "pure" or primordial forms of entropy not only establish the dimensional conservation domains of free and bound energy, but also protect and maintain their borders against violations of energy or causality by fast "space ship" or "time machine". Likewise, possible gravitational or inertial loopholes or breaches (such as "wormholes") in the metric fabric of spacetime are closed by the "event horizon" and central "singularity" of black holes - where g = c and time stands still. In the black hole, gravity takes over all energetic and entropic functions formerly provided by the electromagnetic metric.
-Gm: The Negentropic Energy of Gravitation
The effect of gravity is essentially to convert the spatial entropy drive of free energy (the intrinsic motion of light, as gauged by "velocity c") to the historical entropy drive of bound energy (the intrinsic motion of time, as gauged by "velocity T"), and vice versa. Gravity decelerates (or accelerates) the spatial expansion of the Cosmos in consequence. The increase in the historical conservation domain of matter (matter's causal information field - historic spacetime) is funded by a decrease in the spatial conservation domain of light. The process is reversed by the gravitational conversion of mass to light, as in the stars. Gravity pays the entropy-"interest" on the symmetry debt of matter by the creation of bound energy's time dimension. As we saw earlier, the gravitational conversion of space and the drive of spatial entropy (S) (the intrinsic motion of light) to time and the drive of historical entropy (T) (the intrinsic motion of time), can be represented by the "concept equation":
-Gm(S) = (T)m
-Gm(S) - (T)m = 0
Time is the universal driver of entropy, whether implicitly in free energy (as "frequency"), or explicitly in bound energy. The intrinsic motion of light is caused by the symmetric, "wavelength", or spatial component of an electromagnetic wave "fleeing" the asymmetric, "frequency", or temporal component, which is, however, an embedded characteristic of light's own nature: "frequency multiplied by wavelength = c". The intrinsic motion of light suppresses the time dimension to an implicit condition, maintaining the metric symmetry of space. (Light has no time dimension: light's "clock" is stopped - as discovered by Einstein.) When this process is reversed, time and gravitation are created (space is pulled by time into history, where space self-annihilates, creating more time). (See: " The Conversion of Space to Time".)
The intrinsic motion of light is ultimately caused by an embedded but implicit (as "frequency") temporal entropy drive. All forms of entropy serve the conservation of energy, causality, and symmetry. It should be no surprise that both spatial and temporal entropy are intrinsic to electromagnetic energy, ready to serve its free and bound expressions, massless light and massive particles. It is furthermore satisfying to our sense of the economy of nature to discover that gravitation arises as the mediating force between these two primordial forms of entropy, converting one to the other, with gravity itself conserving entropy, symmetry, causality, and energy. (See: "A Description of Gravitation".)
When light's entropy drive (implicit time) is converted to matter's entropy drive (explicit time), the very same temporal component of the electromagnetic wave is involved, simply switching from an implicit to an explicit condition. Space is gravitationally annihilated leaving a metrically equivalent temporal residue. (See: "Gravity Diagram No. 2".)
Time and gravity induce each other endlessly. We can think of this continuous process as the result of either: 1) the intrinsic motion of the time charge, dragging space after it to the point-like center of mass, where space self-annihilates as it tries to squeeze into the time line, exposing a new and metrically equivalent temporal residue (whose intrinsic motion continues the entropic cycle); or 2) the insatiable entropy-energy debt of matter, sucking in more space to pay its temporal expenses, which are endless because (instead of simply paying off the entropy debt) time is being used to create a continuously expanding history (the causal information domain of bound energy - historic spacetime). But these explanations are essentially the same, as both depend upon the intrinsic motion of time and the metric equivalence of the dimensions. Time is the active principle of the gravitational "location" charge. (See: "Entropy, Gravitation, and Thermodynamics".) (For a discussion of the weakness of gravity see: "The Half-life of Proton Decay and the 'Heat Death' of the Cosmos".)
"Spatio-Temporal" Entropy and the Third Law of Thermodynamics
The 3rd law of thermodynamics, by Nearnst (1918), states that at absolute zero (Kelvin scale), the entropy of every system is zero. At first there seems to be something strange here, since we are used to thinking of entropy increasing as things cool off, and here is something very cold with no entropy at all. However, at absolute zero, a cup of tea (for example) has no heat at all and hence no (thermal) entropy. Its frozen crystal lattice is maximally ordered and quiescent; information entropy (the decay of information) is also at a minimum. It does, however, have temporal and gravitational entropy associated with its rest mass energy, which is unaffected by (low) temperature (time and gravity continue to flow), and which will eventually be expressed through either the gravitational release of bound energy (culminating in the "quantum radiance" of a black hole), or radioactive decay (culminating in "proton decay"). The third law therefore addresses "tertiary" spatio-temporal entropy ("work" and thermal entropy associated with material systems), but not primordial temporal or gravitational expressions of entropy; nor does it affect the entropy associated with velocity c and the expansion of the Universe. (See: "Spatial vs Temporal Entropy".)
As the tea cools down, the entropy of the tea plus environment is increased, because radiant heat escapes from the tea to infinity, contributing to the expansion and cooling of the Universe. It is this escape of radiant or free energy which ultimately allows the tea to cool, and which actually requires an expanding Universe to be effective. The Universe is the grandest example of a closed expanding system in which T falls while Q (total heat) remains constant (by the conservation of energy), thus constantly increasing the entropy (S) of the Cosmos (dS = dQ/T).
Thermal entropy is gradually reversed in a collapsing Universe; temporal entropy, however, marches on. The Universe continues to age even as it collapses - time is always one-way (and the same way), and as the product of gravitation, time is "quite at home" in the contracting phase of the "Big Crunch".
The "Big Crunch" terminates in a cosmic-sized black hole, which cannot sustain itself because it uses up all the space with which it creates its gravitational binding energy. Hence the "Big Crunch" will "flash over" to a new "Big Bang" because light, unlike matter, can create its own conservation/entropy domain (space) from nothing, or rather from its own nature via its own intrinsic motion. (Due to proton decay in the interior, black holes contain nothing but gravitationally bound photons, poised to escape if ever the gravitational bonds relax.) In a cyclic, closed Universe, assuming no energy slips through the cusps, the cosmic entropy tally (temporal vs spatial) is reset to zero at every beginning. (See also: "The Connection Between Inflation and the "Big Crunch".)
The Conservation of Information
It is generally believed that our universe begins as a quantum fluctuation within the "multiverse", containing no net charge and no net energy - something like a scaled-up version of Dirac-Heisenberg virtual particle-antiparticle pair creation in the "vacuum" of spacetime. While the details of the process remain highly speculative, conservation principles argue for the general validity of such a conception. "No net charge" is achieved by the equal admixture of matter and antimatter, and "no net energy" is the consequence of the negative energy input of gravity - gravity is united with the other forces in the cosmic beginning. Scale or magnitude is due to initial conditions in the multiverse, as are the other life-friendly parameters of the physical constants of our cosmos - all a random choice among countless possibilities. "Inflation" from the state of a super-cooled "false vacuum" may also be involved.
George Gamow referred to the primordial substance or energy state as "Ylem", which we might conceive of today as a "soup" composed of equal parts of leptoquarks and antileptoquarks, whose positive energy is balanced by the negative energy of gravity in the initiating stage of the "Big Bang" or "Creation Event". Regardless of the details, given such a balanced initial condition, the universe contains at its beginning no net information, since it is symmetric in all respects, and information by definition is asymmetric. The Universe has the potential for information, but only if the initial symmetry of the universe can be broken and its energy converted into asymmetric particles (for example, matter in the absence of antimatter). It is thought that the initial symmetric energy state was broken by the asymmetric decay of electrically neutral leptoquarks vs antileptoquarks, a decay mediated by the weak force, and resulting in an excess of approximately one part per ten billion of leptoquarks, which subsequently decayed through a "cascade" of hyperons to the familiar protons and neutrons of the modern-day universe.
Because the Universe begins in a state of no net information, the Universe is not constrained to conserve some initial component of information in any ultimate sense; likewise, no initial limit is imposed (other than available energy) upon the amount of information the Universe may accumulate. But when all charges cancel, as for example in matter-antimatter annihilations, proton decay, or the "quantum radiance" of black holes, the information contained in these charges (and in their combinations and permutations) is canceled also.
Nevertheless, due to the temporal/causal nature of matter, information is conserved in the historical realm of spacetime, and this is permanent (if spacetime is permanent). With the expansion of history, information becomes attenuated as matter's causal matrix is diluted; the information does not disappear, it simply becomes increasingly harder to trace and resolve as its influence spreads into an expanding system of causal networks. This expanding causal web (expanding historically at the metric equivalent of "velocity c") also means the information becomes harder - in fact impossible - to destroy. Because black holes induce proton decay in their interiors, and also annihilate space, black holes destroy matter and matter's information content. In complete fulfillment of Noether's theorem, black holes gravitationally return matter and information to its original state as the completely symmetric free energy of Hawking's "quantum radiance". But only a cosmic-sized black hole (as in the "Big Crunch") is large enough to encompass the entire spacetime mesh of matter's historic domain of Information, the "causal matrix" of matter which is the source of the reality of today and the "universal present moment". Hence in the absence of a "Big Crunch", information is permanently stored in the historical domain of spacetime, regardless of what happens to its physical origins.
For a general introduction to the subject of entropy, see: "Introduction to Entropy".