Causality and Information
Revised Aug., 2014
John A. Gowan
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There is a natural interdependence between the invariance of causality, the invariance of velocity c, and the invariance of Einstein's "Interval". "Velocity c" is the invariant gauge of causality, the intrinsic motion of light (which is the entropy drive of free energy), and of the symmetric metric of space (suppressing the asymmetric time dimension): the conservation of energy, symmetry, and electric charge all require the invariance of "c". Time is one-way due to the imperative of causality; space and time warp and morph into one another to maintain the causal law in a gravitational spacetime where matter has relative rather than absolute motion. Einstein's Special Theory of Relativity and its cornerstone, the invariance of velocity c and the "Interval", is essentially concerned with rescuing causality in a material world of relative motion. The invariance of causality and the "Interval" is maintained in General Relativity as well, thanks to the "Equivalence Principle" and the flexibility of space and time ("Lorentz Invariance").
Gravitation and time provide the causal linkage for matter's "information matrix". Heisenberg's "Uncertainty Principle" limits our knowledge of the causal pathway, but it does not limit the causal principle anymore than it limits energy conservation. Causality is an attribute only of the material realm: light is non-local, a-temporal, and hence a-causal, lacking also a gravitational field. Matter is local, temporal, causal, producing a gravitational field which creates its temporal dimension via the annihilation and conversion of space to time. Light's "Interval" is zero; matter's "Interval" is always greater than zero (due to the inevitable presence of time, if nothing else).
History, created by the intrinsic motion of time, is the temporal analog of space, which is created by the intrinsic motion of light. Space is the entropic conservation domain of light, expanding and cooling; history is the entropic conservation domain of information, aging and decaying. Historic spacetime is the joint entropic conservation domain of light and matter's causal information matrix. (See: "Spatial vs Temporal Entropy".)
The equivalence relation between mass and energy discovered by Einstein: E = mcc, makes possible the conversion of free energy to mass and momentum (because energy is conserved in such a transformation). At very high energy, massive particles are apparently created by the entanglement of light's electromagnetic wave in the structural web of the spacetime metric, which is itself created by light's intrinsic motion. The Higgs boson is thought to be the scalar gauge particle responsible for the mass spectrum of elementary (leptonic) particles. Symmetry-breaking (by the "X" IVB?), and the services of leptonic alternative charge carriers are also necessary to prevent the heavy baryon (hyperon) particle-antiparticle pairs so created from simply self-annihilating. (See also: "The Higgs Boson vs the Metric of Spacetime".)
When matter is created from light (as during the "Big Bang"):
a) the raw energy of light is conserved as the mass and momentum of matter;
b) the intrinsic motion and entropy drive of light (as gauged by "velocity c") is conserved (in metrically equivalent units) as matter's entropy drive, the intrinsic motion of time (also gauged by "velocity c"). Time is gauged by "c" as the duration required by light to travel a standard distance.
c) the symmetry of light is conserved as the quantized charges and spin of matter, and by the inertial and gravitational forces of the spacetime metric.
It is the conservation function of the forces produced by matter's charges to return the asymmetric system of matter to its original symmetric state of light, either through antimatter annihilations, or by such secondary processes as chemical reactions, nucleosynthesis, fusion, fission, particle and proton decay, gravitational energy conversions, and finally, Hawking's "quantum radiance" of black holes. Nature's tendency to build interconnected material information systems (both biotic and abiotic) is motivated by matter's search for antimatter and a "memory" (stored as charge) of its former primordial symmetry and connective unity as free energy (light). Energetically, the Universe evolves through negative entropy (gravity); metaphysically, by transforming energy into information (symmetry-breaking, nucleosynthesis, chemistry, life, consciousness). (See: "The Information Pathway" and "Chardin: Prophet of the Information Age").
Causality vs Information in the Tetrahedron Model
I have decided to replace (or supersede) the "Information" designation of the "central" or 4th apex of the Tetrahedron Diagram with "Causality" (previously assigned to the time axis, or to a lesser position on the central point). This decision is due to a growing dissatisfaction with the "inert" or "passive" character of the word "Information" - the term refers to a characteristic or state of energy, whereas I want a more active indicator to compare with "Entropy" and the two conservation laws of the other vertices (energy and symmetry conservation). While "Information" does broadly characterize matter, and must be retained in a secondary or adjunct position, "Causality" identifies the most essential activity of matter - the intrinsic motion of matter's time dimension, matter's time-bound "karma" or causal connectivity. Matter is bound in time as light is bound in space. Because gravity creates time from space, "Causality" brings with it not only time, but gravity and historic spacetime as well, including the entire realm of Information which forms matter's causal, historic matrix. The principle of "Causality" is therefore certainly "large enough" to encompass the significance and scope of a primary "Tetrahedron Apex"; we furthermore find that we can more successfully integrate "Causality" with the other three vertices of the Tetrahedron than we could the term "Information", as "Causality" is more intimately connected with all three through time and energy relationships, as sketched below:
1) With Energy Conservation (via the relative motion of matter and the sequence of cause and effect). The laws of Special Relativity, Einstein's "Interval", and the interchange of time with space, the shrinking of meter sticks and the slowing of clocks, all are necessary to rescue causality in a spacetime where the absolute motion of light is mixed with the relative motion of matter. Causality conservation requires the "Lorentz Invariance" (the interchange of space with time) as formulated in Special and General Relativity.It is often proclaimed that Heisenberg's Uncertainty Principle has destroyed the principle of Causality. But this is not true: the principle of Causality remains valid, as does the principle of Energy Conservation, which depend upon each other. Heisenberg's Uncertainty Principle simply limits our ability to know the exact pathway of causality, but does not affect the operation of the principle itself. To quote Heisenberg on this issue: "In the strict formulation of the causal law - if we know the present, we can calculate the future - it is not the conclusion that is wrong but the premise". (As quoted in David Cassidy's book (page 228) Uncertainty: The Life and Science of Werner Heisenberg (W. H. Freeman and Co. 1992).
2) With Entropy (via the intrinsic motion of time and the expansion and decay of history). Causality is responsible for the one-way motion of time and for time's metric equivalence with velocity c; because causality requires a temporal parameter, the causal relations of matter are (partly) responsible for gravitation, the creator of time.
3) With Symmetry Conservation (via charge conservation and matter's causal information matrix in historic spacetime). Causality is responsible for ordering the "bits" and "events" of information into coherent threads and webs of indefinite length and complexity, which make the macroscopic, material Universe sensible, understandable, reasonable, reliable, and predictable. Causality produces the one-way order in the spacetime metric and in matter's historical information matrix which allows matter's eventual return to symmetry. The time dimension required by causality is also required by charge conservation; both make sense only in an historic domain, and both exist only if matter exists.
The Tetrahedron Model comprises a pairing of conservation laws: the Conservation of Energy and the Conservation of Symmetry; and an auxiliary pairing of energy principles, corollaries, or adjuncts to those laws - Entropy and Causality. I outline these connections in some further detail below.
1) Causality and Energy Conservation (the temporal sequence of cause and effect for matter in relative motion):
The order of cause and effect is a self-evident example of the connection between causality and energy conservation. Reversing the order of cause and effect violates energy conservation, because we have energy inputs without energy sources. The ordering of cause and effect is the primary reason for the linear and one-way progression of time. Time is required in any energy accounting of the motion of matter, since the energy content of matter varies with its velocity and is relative to the unpredictable motions of all other massive objects. Light does not require time for an accounting of its energy-in-motion (kinetic energy, momentum) since the motion of light is both absolute (non-relative) and invariant. The energy of light varies with its frequency, not its velocity.
Einstein's "Interval" and the interdigitation of space and time, in fact the whole of relativity theory, is constructed to rescue causality in a compound spacetime conservation/entropy domain where the relative motion of matter interacts with the absolute motion of light. The dimensions themselves shrink, expand, co-vary, and bend in exactly such a way that the invariance of causality, "velocity c", and the "Interval" are always preserved ("Lorentz Invariance"). Even Einstein's famous relation between the energy of light and mass, E = mcc, is an extension of the formula for matter's kinetic energy of motion: ke = 1/2mvv - as that formula must be modified to reflect the absolute character of light's intrinsic motion in which v = c with instantaneous acceleration (which eliminates the factor 1/2).
2) Causality and Entropy (time and gravitation):
The intrinsic motion of time is the entropy drive of bound energy. The intrinsic motion of time, as gauged by "velocity T", is the metric equivalent of the intrinsic motion of light, as gauged by "velocity c"; both are effectively "infinite" velocities, a distinction which is necessary for each to fulfill its role as the entropy drive of its particular energy form: free energy in the case of "velocity c", bound energy in the case of "velocity T". Only by means of an effectively "infinite" velocity can these entropy drives guarantee that energy conservation and/or causality will not be violated within the dimensional conservation domains they create, as by "time machine" or fast "spaceship". The dimensions of spacetime are created by the entropy drives of free and bound energy, the intrinsic motions of light and time. The dimensions are entropy domains created by electromagnetic energy for its own conservation. (See also: "The Time Train".)
Causality is responsible for the one-way linear intrinsic motion of time; and also for the metric equivalency between "velocity c" and "velocity T". Finally, because time is created by gravity, Causality, along with the conservation of light's energy, Symmetry, and Entropy, becomes a rationale for gravitation.
3) Causality and Symmetry (the temporal ordering of the metric and information - charge conservation through historic spacetime; Information and matter's causal matrix):
Causality, time, and history provide the dimensional arena and temporal parameter within which charge conservation has meaning; that is, symmetry debts (charges) incurred now can be redeemed later only if there is a time dimension which creates a distinction between "now" and "later", and therefore the possibility of conserving anything in a temporal dimension. Gravitation creates time and so pays the entropy-interest on matter's conserved charges or symmetry debts: the charges of matter are the symmetry debts of light. Because gravitation decelerates the expansion of the Cosmos, and because this expansion is driven by the intrinsic motion of light, we see that ultimately it is the entropy drive of free energy which funds the entropy drive of bound energy. The gravitational energy (-Gm) to create matter's temporal entropy drive (T) and historic dimension, comes directly from the expansive entropy-energy drive (S) creating light's spatial dimension:
-Gm(S) = (T)m;
-Gm (S) - (T)m = 0.
Therefore we can say that gravity is a conservation connection between the metric principles (and Tetrahedron Model poles) of Entropy and Symmetry: gravity converts symmetric space and a spatial entropy drive (the intrinsic motion of light as gauged by "velocity c") to asymmetric time and a temporal entropy drive (the intrinsic motion of time as gauged by "velocity T"), paying the entropy-interest on matter's symmetry debt via the creation of matter's time dimension. (See: "Gravity, Entropy, and Thermodynamics".) Causality provides the one-way temporal ordering of the metric which results in the gravitational conversion of bound to free energy in stars, quasars, and the "quantum radiance" of black holes, restoring the original symmetry of energy.
Matter's causal information matrix, historic spacetime, is created by gravitation and binds the material Universe together in time, gravitation, and causal linkages which remain historically active throughout the Cosmos, and are necessary and responsible for sustaining the effect we (and observers everywhere in the Cosmos) experience as the "universal present moment". We are all immortal in history. (See: "A Spacetime Map of the Universe".) Causality provides the temporal ordering of information which allows matter, through evolution, to find a conserved pathway back to its original symmetric form, light.
Causality, Symmetry-Breaking, and Information
Symmetry-breaking is the source of information; in the Tetrahedron Model, the symmetry pole supplies fermions (the particulate constituents of atoms), and their conserved spin and charge, to the causality pole and the Universe at large. It is the causality pole or relation that converts these charges and particles into sequentially ordered information. Information contains no ordering principle in and of itself. Without the ordering supplied by the causal relation, there is no meaningful information, just as without the ordering of letters, there is no meaningful writing or language, only randomized, chaotic, "alphabet soup". Conversely, without the supply of particles and charges, there are no letters or "bits" of information to order. (See: "The Origin of Matter and Information".)
Ordering is the essence of the relation between causality and symmetry, which is actually the relation between the broken symmetry represented by atoms and quanta ("bits" or "bytes") of information (without broken symmetry, the Universe consists only of light, which, being perfectly symmetric, contains no information in any case: light is non-local, a-temporal, and a-causal). This relation is not unlike that between causality and energy conservation, where the ordering of cause and effect among the energy, mass, momentum, or action quanta is necessary to insure the conservation of energy.
From such comparisons we deduce that the ordering of information is likewise necessary to the conservation of symmetry. The function of information (in the form of conserved charges) is to provide a pathway back to symmetry for the particles of matter, despite the absence of antimatter - as through the various forms of particle and proton decay, or the gravitational conversion of bound to free energy. All such pathways depend upon charge conservation, and we may presume, the ordering of information which these charges provide. An example that springs readily to mind is the "non-commutative" multiplication rules in the matrix algebra of quantum mechanics - where (a x b) is not the same as (b x a). Ordering matters in the realm of quantum information.
The famous "violations" of causality in quantum phenomena are due to the non-local, a-temporal, and a-causal character of light, and the persisting trace of this characteristic in subatomic particles depending upon their mass (DeBroglie "mass waves"). Furthermore, subatomic particles interact with other particles principally by means of electromagnetic or DeBroglie mass waves. The non-local character of light is why the Feynman "path integrals" are so successful in quantifying the behavior of photons and other subatomic particles in their interactions with matter. "Violations" of causality are restricted to quantum phenomena, are "virtual" in nature, and are contained and confined within the bounds of the Feynman "path integral" formulation.
The quantum "smearing" of probabilities and energy states (due to Heisenberg's uncertainty principle) is overcome in macroscopically observable states by the sheer weight of statistical probability and by the fact, noted earlier, that the causal path is favored because it has an energy source which all others lack. Insofar as information is conserved and associated with force - such relations are due to the primordial association of information with charge and charge conservation. When charges are annihilated in matter-antimatter annihilations, so too is the information associated with those charges. In an historical sense, information is never destroyed, as the influence or "karmic consequences" of information will propagated through time long after the originating impulse has vanished.
"Wrong-Way" Time and Heisenberg's Uncertainty Relation
Violations of causality in quantum mechanics may be compared to violations of energy conservation, which are allowed most notably in the formation and annihilation of virtual particle-antiparticle pairs. In quantum mechanics, energy may be borrowed if it is paid back so quickly that the process is not "noticed" by the usual conservation laws - Nature's "sleight of hand". This is the temporal component or interpretation of Heisenberg's "Uncertainty Principle": the quantity of energy borrowed multiplied by the quantity of time it is held must be approximately equal to Planck's constant divided by 2 pi. The more energy borrowed, the faster it must be paid back. This virtual component of time may be construed as "wrong-way" time, that is, time running into the future rather than the past. Thus virtual energy is borrowed from the future and immediately paid back (always faster than light speed, ct) in the present. This is the only physically acceptable way to think of time reversal, and it is strictly contained within Heisenberg's "Uncertainty Relation", which is also obeyed by Feynman's "path integrals" (where it is expressed as the canceling of oppositely directed vectors).
The "Spacetime Map" gives us a physical way to visualize "virtual time" as it borrows energy from the future, for in the Map we see that fully 1/2 of the Universe physically exists "now" in a future that is only revealed to us second by second at light speed. We can imagine that it is from this physically real "future" that energy is borrowed by "wrong-way" time. Because this future does not yet include us, but is already fully formed, it cannot be changed or affected by anything we do "here and now", so energy borrowed from it has to be paid back before that future becomes real for us, that is, at faster than light speed. In this sense only are causality violations allowed, but even virtual reality does have a physically real component which the "Spacetime Map" helps us to visualize.
The significance of this conception of virtual reality is that it exists not "outside" spacetime, but rather inside a portion of our Universe which is physically real, a future already formed which we are continually becoming part of. There is no difficulty in this conception of linking the virtual future with the appropriate locus of the "here and now", whereas in the conception of virtual reality as "outside" space and time, one does not know how to reconnect that virtual realm or transaction with a specific place and time in our Universe of experience.
Causality and "Karma"
The causal relation in energy, information, and historic spacetime is the rational or "scientific" equivalent of the ancient, intuitive, and metaphysical notion of "karma", of consequences, responsibility, and liability for our actions. "Vengeance is mine; I will repay, saith the Lord" (Romans 12:19). From this basis a rational or "scientific" parallel to the ethical or moral laws of social behavior found in most orthodox religious systems can be established, the first of which might be the "Golden Rule", which is both a symmetry statement regarding social behavior and a tacit acknowledgment of "karmic" or causal chains of social interaction which eventually "catch up" with their initiator, a notion also captured in the common phrase "what goes around comes around". There are always consequences to our actions, and we live forever in history. Applications of the Tetrahedron Model to human affairs and behavior might emphasize the traditional "Golden Rule" as a fundamental principle of causality and symmetry (justice, equity, responsibility, liability, harmony, beauty) in every situation.
Information and Entropy
The connection between Information and Entropy is time and temporal causality. The time component is necessary to link each piece of information (each bit) into the "causal matrix" of matter. Time is the entropy drive of matter and information, and creates the causal linkage of matter's information matrix or historic causal domain. Each quantum bit of information is associated with a quantum bit or link of time (like a chain link), which integrates the information bit into the general causal matrix or information field of matter. Entropy is always associated with energy, in this case bound energy, so a quantum unit of time or temporal entropy can be associated with a quantum unit of energy as well as of information. The gravitational conversion of space and the drive of spatial entropy into time and the drive of temporal entropy reaches a natural limit in the "event horizon" of a black hole where g = c. The surface area of a black hole's event horizon is proportional to its entropy, in terms of time or information (theorem of Bekenstein and Hawking).
A famous connection between Entropy and Information exists between Boltzmann's formulation of statistical thermodynamic entropy (1870s) and Shannon's parallel formulation of information entropy (1949). The two are computed by the same mathematical formula and when calculated for the same degrees of freedom (the same variables) are equal. The connection between elemental time and information in the Tetrahedron Model applies equally to both types of entropy, satisfying the condition that Shannon (or Boltzmann) entropy is not associated with meaning or significance, which is context dependent. The meaning or significance of information, with which we are of course very much concerned, is a characteristic of higher levels of the natural hierarchy, including information in the sense of complex organizational states, such as the functioning human body or society. See: Scientific American Aug. 2003 p. 58-65 "Information in the Holographic Universe" by Jacob D. Bekenstein.
The Destruction of Information
Is information destroyed in a black hole? This question is debated in Leonard Susskind's recent book: "The Black Hole War" (Little, Brown, and Co., 2008). From the overview of the "Tetrahedron Model" and Noether's principle of the conservation of symmetry, it appears that information should be destroyed in a black hole. There are several reasons to think so (contrary to the conclusions of Susskind's book). First, on the premise that the universe begins as light, devolves to matter, and finally evolves and resolves to light again, conserving the original perfect symmetry of free electromagnetic energy, information must be destroyed in any physical process which returns matter (and the information which matter contains) to light. Such final symmetry-restoring (conserving) reactions and processes include: 1) (actual) matter-antimatter annihilations due to the electromagnetic force; 2) (hypothetical) proton decay due to the strong and weak nuclear forces; 3) (theoretical) "evaporation" of black holes due to "Hawking radiation" (gravitational force); 4) (possible) "Big Crunch" gravitational collapse of the cosmos.
All four processes are driven by symmetry conservation acting through the charges of the four forces of physics. The charges of matter are the symmetry debts of light (Noether's Theorem). Light, as a perfectly symmetrical form of energy, does not contain any charge, any time dimension, any gravitational field, nor any information. Information is necessarily an asymmetric form or configuration of energy, and hence must be destroyed with charge when charges are annihilated and material energy forms are returned to their original symmetric state, light (in obedience to Noether's Theorem). If the universe begins with light (which contains no information) and returns to light, then information must be destroyed in the process of the final return. This is the long or generalized view of information destruction during the process of symmetry conservation as visualized in the "Tetrahedron Model".
A somewhat more detailed view of these same (above) processes takes note of the fact that even though a particle or a system is swallowed by a black hole, the prior history of that particle or system remains extant (except in the case of the "Big Crunch"). So both positions in the "black hole information war" may be correct - black holes do indeed destroy particular information systems, but those systems and the information they contain nevertheless survive in a real historical sense - if not as actual records, then as light visible to distant observers, and/or as influences and "karmic consequences" which propagate endlessly in causal chains and dendritic repercussions throughout spacetime.
This latter view is very similar to the "holographic boundary" vision of information conservation as put forward in Susskind's book. For example, light always travels in the "universal present moment", which forms the spacetime boundary of our universe - the outermost spatial line of the "Spacetime Map of the Universe". The boundary 2-D holographic surface which contains all the information necessary to reconstruct the "bulk" 3-D universe (including its historical development) is apparently stored in the 2-D light waves which propagate forever throughout the "universal present moment" of the cosmos (see: "A Spacetime Map of the Universe". Hence there is no need to "rescue" Quantum Mechanics from a crisis caused by the destruction of information in black holes - the information lives on anyway in causal history and in the propagating light waves of the "universal present moment" of spacetime.
Reconstituting the original information from such historical records or from propagating causal effects or light rays is certainly no less improbable or challenging than decoding the hidden messages in Hawking radiation, as Susskind suggests is possible. Furthermore, if the holographic principle is true to the model, then only a fragment of the original hologram is necessary to reconstitute an image of the whole, and such fragments should be abundantly present in the historical record. For example, we have been able to reconstruct the age of the dinosaurs from fossils, the evolutionary history of the cosmos from starlight, and the ontogeny of humanity from DNA.