If the objection round completes with no objections surfaced, the decision is made and the process ends. Integration: If objections surface, once the objection round completes the group enters open dialog to integrate the core truth in each into an amended proposal.
As soon as an amended proposal surfaces which might work, the facilitator cuts off dialog, states the amended proposal, and goes back to an objection round. So what we can do is be integrating; we canbecome an agent for the natural evolutionary impulse at the heart of reality, byriding the emerging moment here and now and integrating what actually arises into that present moment. In Holacracy, we strive to integrate what needs integrating as it needs integrating — no more, no less, no sooner, no later.
The more we can find the discipline and skill required to do this, the more value we can integrate into our reality. Check-in : The check-in is a brief go-around, where each person gives a short account of their current mindset and emotional state, to provide emotional context for others in the meeting and to help the speaker let go of any held tensions. Agenda Setup : The facilitator solicits agenda items for the meeting on the fly agenda items are never carried over from prior meetings!
Participants state agenda items briefly, as just a title, and the facilitator charts them on the board. Once all agenda items are listed, the facilitator proposes an order to tackle them in and quickly integrates any objections to the order. Specific Items : The group proceeds through each agenda item until the meeting time elapses or until all items have been resolved.
Each agenda item uses one of the integrative decision-making processes e. Closing : The closing is a brief go-around, where each person reflects and comments on the effectiveness of the meeting, providing feedback for the facilitator and others about the meeting process itself. Describe the Role : The facilitator announces the role the election is for, and the accountabilities of that role. Fill Out Ballots : Each member fills out a ballot, without any up-front discussion or comment whatsoever. Everyone must nominate exactly one person—no one may abstain or nominate more than one person.
The facilitator collects all of the ballots. Read Ballots : The facilitator reads aloud each ballot and asks the nominator to state why he or she nominated the person shown on their ballot. Each person gives a brief statement as to why the person they nominated may be the best fit for the role. Nomination Changes : The facilitator asks each person in turn if he or she would like to change his or her nomination, based on new information that surfaced during the previous round.
Changed nominations are noted, and a total count is made. Proposal : The facilitator proposes someone to fill the role, based on the information that surfaced during the process most notably the total nomination counts. Objection Round : This is identical to the objection round for the general integrative decision-making process, however the nominee in question is asked last. If objections surface, the facilitator may either enter dialog to integrate them, or simply propose a different nominee for the role and repeat the objection round.
Lightning Round : One by one, each participant states what they plan to work on in the coming week, with no discussion.
Swami Satyananda Saraswati
Each person has 60 seconds max, and the facilitator cuts off anyone who runs over time. Metrics Review : Each circle member with accountability for providing a metric presents that metric. Agenda Setup : Identical to the governance meeting agenda setup again, the agenda for tactical meetings is always built on-the-fly, with no carry-over from prior meetings. Specific Items : The group proceeds through each agenda item, with the goal of completing the entire agenda before time elapses these are swift-moving meetings. Typically, each item is a brief free-form discussion—tactical meetings do not use the integrative decision-making process, unless someone has an explicit accountability to integrate perspectives around a specific issue before taking action.
Most people spend a massive percentage of their waking time involved in a business of some sort; it is the container for much of the culture we exist within and it has a dramatic impact on our lives and our personal development. Business is the first type of truly global social organization to emerge in the world—it crosses geopolitical and ethnic boundaries, and has the real potential to unite our world in a truly global communion.
None of this is meant to ignore or excuse the atrocities committed in the name of business, and there have been many. If we threw out early nations once we saw their dark side we would be back to living in tribes, warring with and enslaving our neighbors. What is needed is to move forward, not backward, and that means embracing the business world and helping it evolve.
Holacracy effectively integrates most of the distinctions between for-profit and non-profit companies. It's one thing to identify analogies between processes on different levels; I have done exactly this, of course, throughout this book. It's quite another to argue on the basis of these analogies that the processes are identical, one and the same thing. Still another problem with quantum models of consciousness is that the relationship of the one to the other--that is, of quantum collapse to consciousness--is not very clear. Some theorists, such as Amit Goswami, contend that consciousness causes the collapse: However, in terms of any holarchical view of existence, it's extremely difficult to understand how something above the brain and mentality could act on subatomic processes see also Chapter 6.
It's also difficult to understand, again, why the brain itself is there. And in any case, if consciousness causes the collapse then consciousness is still unexplained. The theory only explains what consciousness does , not what it is --it doesn't even explain how consciousness does what it does. One could just as well say that consciousness causes neurons to fire. On the other hand, if one is to argue that consciousness is the collapse of the wave function, then one is back to a grossly reductionist view of the phenomenon.
Consciousness is somehow made identical to a subatomic process, with no real explanation of how, other than that both are indeterminate. Worse, it now seems that consciousness is a rather capricious phenomenon, because the collapse of the wave function is usually considered to be a random process. Whichever way one puts the relationship, quantum models of consciousness, like other materialistic theories, really do not explain the gap between consciousness and other phenomena--the hard problem of experience.
To say that consciousness is the collapse of the wave function no more explains the mystery of experience then to say that consciousness is the recurrent activity in neural pathways in the brain. So regardless of the other merits of quantum theories of consciousness, they aren't complete. While the most widely accepted monistic theories of consciousness are some variant of materialism, alternative monistic theories exist which are idealistic. Whereas materialism, in effect, says that everything is ultimately matter, idealism says everything is consciousness.
Thus the material world has no reality, but is in some sense a creation of consciousness. In Western thought, the most famous proponent of idealism was George Berkeley, who held that nothing exists except as it's experienced by some observer Darcy To account for the continued existence of the material and biological world when it wasn't being observed by some human or animal, Berkeley proposed that God is an eternal observer. Thus everything comes into existence through the observational consciousness of God. Human beings, in this view, participate in God's consciousness to some extent.
Berkeley's philosophy has often been described as a denial of matter, but one could argue that it depends on how one defines matter. If a higher form of being exists which is always conscious, and if what that being is conscious of has some permanence and continuity, then there is a kind of matter in the world. This matter is not the ultimate stuff of the world, but as we have just seen, neither is it in quantum theory. In quantum theory, the ultimate nature of the world seems to be fields, in networks of processes.
Matter only emerges when we focus our attention on certain points or aspects of these networks. In Berkeley's idealism, the ultimate nature of the world is God. Matter is that which is observed by God, upon which we also focus our attention. The practice of science, or any other systematic form of knowledge, doesn't necessitate that matter be the ultimate basis of existence. All that a scientifically viable theory of existence requires is that what we perceive as matter exists and changes through certain rules which can be reproducibly observed. Quantum theory satisfies this requirement, and so, perhaps, does Berkeley's idealism.
Though Berkeley reached his idealistic view through some philosophical arguments that have generally been discredited since Russell ; Nagel ; Darcy , the view itself is perhaps not really disprovable. There seems to be no definitive argument or evidence against the possibility that everything we call the world is the product of a single mind. Yet this view does seem at odds with some commonplace observations.
For example, if everything we call the world is the consciousness of God, why do we see more and more the further we penetrate this world? Why are organisms composed of cells and tissues and we know now, atoms and molecules? If the world is just God's vision, why was it necessary for this world to contain anything beyond gross appearances? If we are figments of God's imagination, why do we need cells and tissues to function? And even odder is why we had to evolve, though of course evolution was not generally accepted in Berkeley's time. Berkeley's idealism might fare better against such arguments with a somewhat different understanding of God.
This is the kind of God described by mystics, a universal consciousness. In the mystic worldview--expressed by Plotinus in the West, for example, and by Aurobindo in the East--consciousness has always existed, and created the physical, biological and mental world with which are familiar O'Brien ; Wilber The mystic view is not as pure a form of idealism as Berkeley's, for it does not make an either-or distinction between matter and consciousness. It might be better put to say that there are degrees of consciousness; matter, life, and mind each represent increasingly higher degrees or manifestations of it.
Earlier, I touched on the possible role of higher levels of existence in manifesting our own consciousness, and I will have more to say about them in the following chapter, and later in this book. For now, however, I want to point out that while these higher levels are frequently not taken very seriously by scientists and philosophers interested in consciousness, the existence of a higher state of being is broadly compatible with most other theories of consciousness. This is because a higher state can be viewed as either an emergent phenomenon or a fundamental phenomenon.
If it's an emergent phenomenon, then higher consciousness appears with a certain level of organization or complexity of humanity on earth. In this view, it could be quite compatible with some forms of materialism, including, as I noted earlier, functionalism. On the other hand, in the traditional view of mystics, as I said earlier, consciousness is considered to be fundamental, something that existed prior to other forms of life.
This idea is obviously very closely related to Chalmer's in some respects, as well as with receiver models of consciousness. Yet it could also be consistent with functionalism or with quantum models of consciousness. Functionalism, in the eyes of its adherents, makes consciousness emergent from, and therefore ultimately rooted in, material processes.
But it's possible to adopt something resembling a functionalist view without assuming emergence. One could, for example, assume that the programs in the brain are what enable it to tune in to a field of consciousness, if one accepts the possibility of such a field. One could also argue that these programs, rather than emerging from the random asssemblies of physical and biological processes, are the result of organization imposed on these systems from above. Quantum models of consciousness also may seem to explain the phenomenon as emerging from the brain.
Presumably that has been the intention of most of those who have proposed them. But at the very least, a quantum theory of consciousness can be made compatible with the idea that consciousness is fundamental. This is what Goswami has attempted to do, and if consciousness causes the collapse of the wave function, there seems to be no other way to understand it. On the other hand, if consciousness is somehow understood as identical to the collapse--ignoring the obvious problem of transparency--then consciousness is associated with something very primordial.
So even the most reductionistic, materialistic quantum models have some affinity for the notion of a universal consciousness. We have seen that there are a number of theories of consciousness which don't fall clearly into the traditional categories of monism or dualism. Each of these theories has certain attractive features, and while they may seem quite different from one another, there are definitely areas of consistency, which opens up the possibility of some kind of synthesis.
Nevertheless, none of these theories, any more than the traditional monistic and dualistic ones, accounts for the hard problem of consciousness. Viewing these failures, some philosophers, such as Colin McGinn and Thomas Nagel, throw up their hands and surrender. We will never have a complete theory of consciousness, they decide, so we should stop worrying about the problem and get on with what we can do--solving the softer problems. To some scientists and philosophers--perhaps a growing number of them--this is an attractive position, for it neither underestimates the magnitude of the hard problem, as many who propose theories of consciousness seem to do, nor explains it away by proposing something even more mysterious, as traditional religions do.
Furthermore, cognitive scientist Steven Pinker contends, not being able to explain the hard problem which he refers to as "sentience" in the passage below is no real loss for science:. It's not just that claims about sentience are perversely untestable; it's that testing them would make no difference to anything anyway. Our incomprehension of sentience does not impede our understanding of how the mind works in the least.
Generally the parts of a scientific problem fit together like a crossword puzzle When any part of the puzzle is blank, such as a lack of chimpanzee fossils or an uncertainty about whether the climate was wet or dry, the gap is sorely felt and everyone waits impatiently for it to be filled.
But in the study of the mind, sentience floats in its own plane, high above the causal chains of psychology and neuroscience. If we ever could trace all the neurocomputational steps from perception through reasoning and emotion to behavior, the only thing left missing by the lack of a theory of sentience would be an understanding of sentience itself. Philosophers and scientists who take this view of the hard problem, however, don't necessarily agree on why consciousness should be beyond our understanding.
Pinker, it seems, believes that consciousness in this sense has no connection to any of our scientific understanding. It really belongs to another domain entirely. This is a rather remarkable concession for a scientist to make, yet it's strongly implied by the zombie argument, which we saw that Chalmers and many other philosophers accept.
On the other hand, philosophers like McGinn and Nagel, and functionalists like Douglas Holfstadter , believe there has to be a relationship between brain and consciousness, which if properly understood, would illuminate how the one emerges from the other.
What they doubt is whether the human mind, as it's so constructed, is capable of this understanding. Philosophers who take this latter view seem to believe that our inability to understand consciousness is just an accidental or contingent result of the way we evolved. Thus McGinn suggests that a species could have evolved lacking some aspects of human intelligence, but with the ability to understand the relationship of consciousness to the brain. This understanding, in McGinn's view, would be neither superior nor inferior to ours. It would be just a different kind of understanding, much, I suppose, as an artist's or musician's insights need not be ranked as greater or lesser than those of a scientist, but just of a different nature.
There is a great deal of evidence for different kinds of intelligences Gardner , and I agree with McGinn that there is no reason to imagine that another species could not have evolved with intelligences different from our own. The question, though, is whether this would have given it any more insight into consciousness than we have. As I emphasized earlier, in the holarchical view, any form of life's view of existence is limited by its position in the holarchy. It can have little or no appreciation of anything occurring on levels of existence above its own.
If the experiential, first person aspects of consciousness are really beyond our understanding, this strongly suggests that consciousness is a higher-level phenomenon. Our inability to understand it has nothing to do with the contingencies of evolution up to our present status. Our ignorance derives from the fact that we haven't evolved far enough. We don't simply need a different kind of understanding; we need a different level of understanding. McGinn, ironically, appeals to an analogy that supports exactly this understanding of the hard problem.
He discusses the story of Flatland, a two-dimensional world whose inhabitants live entirely within the contraints of these dimensions Abbott ; see also Rucker They can have no real understanding of three-dimensional forms, which exist outside of the plane, literally, of their own existence. Thus when a three-dimensional form does enter their world, they see only a cross-section of it, where it intersects their plane.
Barron's Educational Series, Inc. Conversations on Mind, Matter and Mathematics. Thought Control in Democracies. The Engine of Reason, the Seat of the Soul. An Introduction to Evolutionary Ecology. The Human Genome Project. Of Molecules and Men. University of Washington Press. The Problem of Consciousness. The Origin of the Genetic Code. The transfer of viable microorganisms between planets.
In Science and Beyond. The Birth of Complex Cells. In Molecular Origins of Life. How Big is the Universe of Exons? The Design of Life. Socialization Among Human and Non-human Animals. In Companion Encyclopedia to Anthropology. Political Dominance and Social Evolution. A Molecular Basis for Animal Form. The Causes of Consequences of the Disappearance of Species.
Archaebacteria Come of Age. Life in the Balance: Humanity and the Biodiversity Crisis. An Alternative to Phylectic Knowledge. In Models in Paleobiology. The Strange Theory of Light and Matter. The Lexus and the Olive Tree. Information Theory and the Living System. Cells, Embryos and Evolution. Protein Folding in the Cell. The Exon Theory of Genes. Cold Spring Harbor Sympos. On the Ancient Nature of Introns. University of Arizona Press. The Charm of Physics. American Institute of Physics. Darwinism and the Expansion of Evolutionary Theory.
The two major premises of this study—the informaton particle and field-process theories of information for organization evolution and dynamics—will heavily utilize and generalize concepts borrowed from this section. Along with these discussions will be the introduction of a robust generalization to probability and causal analysis as applied to physical phenomena, namely the causaloid structure Hardy, In particular, my interest laid in the past work done to promote any development of an information-based theory of physics from first principles.
The literature reviewed was generally of abstract models of information, proposed novel physical theories, abstract field theories, general discussions on emergent sciences such as complexity, evolution, adaptive systems, holarchies, and finally, higher order mathematical representations of abstract objects. The concept of a universal hyper-computer which computes the evolution of the universe in existential real time lies at the foundation of this proposal.
Fredkin and Zuse were the first to publish general hypotheses of universal computers using reversible automaton to achieve this.
Fredkin generalized the concept to cover a discretized version of the philosophy of scientific development known as digital philosophy and digital mechanics, an atomism reducing all of life to categories of finite automata. This idea has been most recently championed by Wolfram , utilizing his taxonomy of cellular automaton and his principle of computational equivalence PCE which describes a concept of computational categorization. Lloyd a, b followed up on this line of thought with quantum and black-hole versions of universe-wide computers.
See Appendix B for my version of a quantum-gravity universe hyper-computer and chapter 4 for a higher-order computation based on generalized fields—morphic and informaton computation, that dramatically extend the traditional information bit representation. Wheeler conceived a gedankenexperiment by devising a quantum version of the popular questions game. In this game, a participant is allowed to ask 20 questions regarding an entity that they must then guess by the end of the twentieth question or sooner. The answers must be Boolean: yes or no.
The entity selected may be different from the others prior to each question. In this manner, the ensemble of 20 people emulates a quantum superposition of information on the state of an entity. Each question then imitates a measurement or observation of the experiment. Conceptually, this quantum binary or qubit game could be the basis for finding an answer to any informational question as presented in the universe.
His emphasis on the physical ubiquity of qubit information motivated work into the possible discrete representations of the universe via quantum computation with generalized qubits. Quantum entropy will be generalized later in this chapter and in chapter 4 utilizing the GTU and other generalizations to classical entropy. The observables can have possible values in the spectrum S A , the eigenstates of A. This is a continuum problem although a quantization can take place for physical quantities of the system especially at the Planck scale Madore, Digital physics states that a quantum system is manifested in a complete or a spectrum of discrete spaces instead.
The quanta in a physical system move in an unknown potential V x. At best only incomplete information about V x is possible. Enter perturbative techniques for finding local approximations via a quantization of the system. Quantization is the separation of classical and quantum parts of the system around these locales using large numbers of quanta representing a condensate state Rozali, Long evolutions are hard to compute away from these locales and so these methods are used to approximate the quantum states locally.
Consequently, an important property that a physical system should retain is that of background independence BI. BI is satisfied if the system has gauge invariance with respect to spatial-temporal transformations active diffeomorphisms Rovelli, BI systems then have invariant fields within spatial- temporal diffeomorphisms or as smooth topological mappings change the structure.
Essentially one aspires to a physical system theory that takes into account global effects in generality. In order to also satisfy general relativistic mechanics a physical theory must satisfy local Lorentz invariance. Simple discretization of spatial-temporal c2 structures via a lattice representation unfortunately does not posses Lorentz invariance. In this regard, the idea of a fuzzy sphere was devised to represent space at or under the Planck scale with generalized fuzzy points that resemble cells while maintaining a usual continuous approximation at super-Planck scales.
Within this representation is the notion of fuzzy points on a sphere that in fact satisfy these conditions while retaining Lorentz invariance. The classical container of discrete information is the bit, the abstract representation of a Boolean state variable. In quantum mechanics this abstract container is generalized for the possibility of superimposed states to be discussed next.
These containers are called qubits and were first coined by Schumacher In the next chapter a generalization of a minimal or atomic discrete information container along the lines of a generalized uncertainty concept will be introduced. In addition, later in this chapter, it will be pointed out that a physical system described by a fuzzy probabilistic logic further generalizes a quantum system. Qubits represent idealized quantum states of 1 an attribute or observable of a quantum system.
In a quantum physical system, a qubit can be used to measure any Boolean state attribute of a quanta. A point on the surface of the Bloch sphere represents a general mixed quantum state of a single qubit with 2D spherical or 3D Cartesian coordinates representing the probabilities respectively of each pure state part of that superimposed state, i. Figure 1. By Smite-Meister, Copyright by Smite- Meister. However, the classical realization of a qubit is the collapse to a bit. The Bloch sphere will be revisited when projections of states are considered in qubit computations.
There are many such superimposed states. This represents the gist of the nonlocality of quantum mechanics. Bell established inequalities of measureable physical quantities that real and local-based physical theories must satisfy. Quantum mechanics violates these conditions in addition to not feasibly requiring hidden variables, hence the nonlocality of quantum causality Bell, On the other hand, separable quantum states involving local hidden variables with independent observers satisfy Bell-type inequalities Loubenets, ; Loubenets, Nonetheless, recently, it was shown that three possibilities can be had by quantum states.
Quantum states a do not allow for a local realistic model, b do not possess the required EPR-type correlations, or c satisfy both a and b Zukowski, Entanglement is sometimes referred to as stronger-than-classical correlations because of this seemingly nonlocal causality. Superpositions for bi-partite systems can be generalized to multiqubit systems. In these multiqubit states, coalitions of qubits may be entangled with other distinct coalitions, but not individually within each.
Combinatorial entanglement and unentanglement in and outside of subsets of qubits ensues. A subset of the component states in a superposition could be entangled or each one could be entangled in the case of a fully entangled superposition state. Otherwise it is an entangled state. An information container or system that is in an entangled state is referred to as an e-bit.
Computation and information manipulation with an e-bit can be achieved and will be reviewed and further enhanced. In the case of an e-bit, the act of decoherence is detrimental to an end computational result being realized. Decoherence is the leakage of information from a qubit that has been coupled to a neighboring environment. This is expressed as the degeneration of the coherency of an entangled state.
It is evolutionary since decoherence happens over a period of time. Subsequently, the operators, E1 t and E0 t approach mutual orthogonality with time. This implies that multiple qubits coupled with each other would reduce decoherence, i. Quantum noise may also be introduced into the evolution of a qubit in a quantum channel, as noise is introduced in a classical bit stream. Quantum noise is manifested by the quantum uncertainty in the position of a particle and hence an unknown or unwanted change in the density matrix operator of a quantum system.
Further generalizing multipartite quantum systems are n-qudits. Partial separability and entanglement as well, can come in subset combinations. To review, entanglement comes when a state cannot be expressed as a product of mixed or pure states. Because of subset entanglement, entanglement swapping can be actuated when partial entanglement between subsystems of qudits leads to the allowance of entanglement with other subsystems of qudits.
One result illustrates the variety of possibilities in such swapping schema. An is the minimum 1 n i average entropy over all decompositions of the multipartite system. The case for bipartite systems is given in Jaeger, , p. Forming the difference defines a bound entanglement measure Jaeger, , p. Essentially an entropic measure of entanglement is a measure of the amount of information that is available to be entangled.
However, in general, surmising if a state is entangled in a general multipartite system is difficult because of the combinatorial possibilities involving multiple dimensions and large numbers of quanta. It seems that in a multipartite qudit system, too strong of an entanglement between any two quanta prevent entanglement sharing among other quanta. However, under submaximal or partial entanglement, this monogamy condition can be relaxed.
This tendency is called entanglement promiscuity in the limit. Entanglement is referred to as a super-correlative theory of causality, that is, a basis for causality that is stronger than probabilistic correlations. No-signal theories are those which posit that information cannot be transferred between quanta at superluminal speeds, though correlations can be made. In a generalization to this description of information transfer limitation, the concept of Information Causality was introduced— transmission of m classical bits can cause an information gain of at most m bits Pawlowski, et al.
Information causality describes a principle that is applicable to theories of physics that are more general than QM in the sense of possessing stronger correlations, i. Super- quantum correlative systems violate the information causality principle, while those of classical and quantum systems do not. One point this dissertation will question—is there some form of intelligible information transferred where only super-correlations are present? Just as statistical correlation does not imply physical causality, does super- correlation imply a version of super-causality in the universe?
Information in a quantum e-bit situation is classically reached by collapsing a quantum e-bit to a classical bit. There are intermediate levels of communication strength that depict mixed degrees of classical and quantum causality and there are super quantum causalities as well. Stronger than quantum correlations are produced by relaxing the constraint of relavistic causality, that is, admitting superluminal classical communication. Label such theories as s-quantum or super-quantum theories and their information containers as s-bits superluminal.
The maximal bound on the CHSH inequality is 4 in the case of independent correlations. For quantum correlations it is 2 2. It was posited that the condition of relativistic causality prevents a version of a quantum theory from reaching this upper bound. In this experiment J is spacelike separated from both A and B and produces a jamming of the measurements made by A and B in the following manner. Without jamming, the entangled event measured by A and B violates the CHSH inequality, while with jamming it is classically correlated.
Additionally, the jamming mechanism must satisfy the conditions of unarity and binarity which prevent J from senting superluminal signals to A or B individually or jointing in such a way that it can be informationally read, i.
These are the so- called PR-box or nonlocal information channels. In other words, quantum mechanics is not the only theory that reconciles relativistic causality with nonlocality. Moreover, stronger correlative theories exist which are consistent with general relativity and quantum mechanics. We label such theories as nl-correlative and the participating information containers as nl-bits.
- A response to Mark Edwards.
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Superluminal signal communication, while being contradictory in a classical sense, is possible, in a quantum mechanical and relativisitic realm, if the signal propagated is not comprehended until after the trailing light is received. Essentially, this means that super- quantum signals abound from all corners of the universe to each abstract brain, but its classical understanding lags behind its light cone. Generalized entanglement in multipartite systems based on a notion of a generalized uncertainty system which, in turn, is based on composites of different notions of uncertainty is a key component in forming a new model of super-information and communication.
Quantum and fuzzy systems generalize probabilistic ones. Would systems based on general uncertainty and super-quantum theories generalize quantum and fuzzy systems? What of the notion of macroscopic development of larger systems from smaller ones that follow such rules? One must first look at theories of formation of microsystems and macroorganization. Quantum gravity as seen through the lens of loop quantum gravity LQG spinfoam models, a version of a topological quantum theory which combines in a consistent and physically plausible way the structural laws of general relativity and quantum mechanics, will be reviewed as the preferred approach to unifying QM and GR.
This will be followed by a review of the concept of information fields as a manner in which signal processing can be combined with physical field theory to compute and view ensemble information flow. Penrose had developed the spin network formalism for representing states of quanta and their fields as an abstract directed graph with nodes representing states of a quanta and edges representing fields between quanta.
LaFave first developed the formalism for spinfoams as path histories for spin networks analogous to Feynman path histories and diagrams for particle path histories. These ideas were followed up for the more general case of quantum gravity spinfoams as histories of spin networks by a group of physicists; most notably Ashtekar and Rovelli Specifically, these graphs are embedded spin-networks ESNs. These states represent the polymeric excitations of the gravitational field.
Two members of the same equivalence ESN class are gauge equivalent because the diffeomorphism gauge values are shared. ESNs define the abstract reference global structure for space. Figure 2. Rovelli, , p. Copyright by Cambridge University Press. Reprinted with permission. Since one can take as one example of a field configuration that of a gravitational field, then utilizing relativistic dependence of spacetime on that field, the propagator will remain dependent only on the combined spatial-temporal separation of the points, not the underlying geometric structure.
These are separated measurements in a background-dependent QFT. In spin-foam geometry, an ESN replaces the spatial-temporal coordinates, x, t. Furthermore, in a quantum experiment, one can rig measurements so that the starting ESN, s, is the state to measure and the ending ESN, s ' , is the observed state measurement. In this way, the propagator, W s , s ' , gives the correlational probability of observing s ' , given that the actual state was s. Spinfoams represent a generalization of Feynman diagrams for discrete quantum gravity in the following sense.
The surface faces, denoted by f, of a spinfoam are the world surfaces and denote the links in the graph. The edges, denoted by e, are the worldlines of the nodes of the graph. This amplitude can be extended and expressed as a separable product. This is the general form of the computation of a spinfoam model propagator. To this effect, triangulation of a spinfoam is constructed. Vertices of a spinfoam are embedded in each 4-simplex of a triangulation. This is a 2-complex. Note that 4-simplices of the triangulation can be generalized to n-simplices of n-polyhedra in a tile covering of the spinfoam model.
To greatly simplify the development of an expression for the calculation of the sum-of-paths, an intermediate theory of models called BF-Theory will be used to setup the terms. Generally, a holonomy is a relative measure of how much geometrical information is preserved from the curvature of a connection during its parallel transports, i. Holonomies are closely related to the curvature of forms of the manifold by the Singer-Ambrose Theorem. Hence, the group of holonomies of a connection of a manifold gives information about the geometric curvature of the surface.
This, in turn, will give an indication of the effect of the curvature of the surfaces of the triangulations to preserving the geometry of the underlying spacetime manifold. At each vertex there are four contracting tensors resulting in a function of six spins of the six faces that bound the vertex point. Crane and Yetter give a variation on this model that bypasses the condition of infrared divergence, that is, of the divergence of the sum integral in the sum of paths expression due to high energies or phenomena happening at large distances and Barrett gives a formalism for the graph invariant for relativistic spin networks over 4-simplices.
The above partition function involves an infinite number of degrees of freedom. In order to capture the situation for a true 4-D spacetime spinfoam model, a sum over 2- complexes must be made in the partition function. We review the general approach taken by the method of group field theory. What is needed for a relativistic version is a Lorentzian model. Spin networks, in this framework, will be associated with a richer structure that represents information field values with respect to observers and transmitters event generators of information, i.
We next consider the role information can play in LQG. Specifically, since the mechanisms of LQG and spinfoam networks carry the states of quanta through a relativistic constraint in the geometry, quantum information will be investigated in such settings. For a spin network and hence a spinfoam, the goal will be to develop a definition for the partial trace operator acting on a bipartite subsystem so that standard manipulation of entangled elements can be performed.
This will give an indication of the potential for accommodating entangled information in spinfoams and spin networks. Let Tv be the total number of ingoing edges to v and Sv the total number of outgoing edges to v. Ev as a function of v is gauge invariant and preserves its value under the SU 2 gauge group of v. In this way, the functions Ev are the analogy of the wave functions for quantum geometry and are called gauge invariant cylindrical functions.
In the rest of the discussion, it will be assumed that the intertwiner functions are normalized, i. These will, in turn, be defined in terms of partial tracing, an operation that defines quantum information and entanglement between two quantum subsystems in general see 3. Course- graining in a spin network is the procedure in which a larger region in the spin network is patched from smaller ones and the dynamics are redefined to the larger region from the smaller patch areas.
This turns out to be the space of states of B when one course-grains B to a single vertex. The integration of the tensor product integrand in 3. This is a formal definition of the partial trace operation for entangled subsystems acted upon by a general operator on a spinfoam. We consider the case of Schwarzchild nonrotating black holes and a spinfoam representation with qubits on its surface patches.
A case for rotating black hole computation is given at the end of Appendix B. The case for relativistic quantum information independent of the quantum gravity framework was reviewed and investigated in Adami and Bais and Farmer However, LQG information theory, as discussed here, provides a subsuming conception to that of relativistic quantum information. Black-hole information theory, as discussed in Appendix B, is done so in the context of quantum gravity and hence serves as a basis for general information in moving information containers and organisms.
We are interested in computing the entropy of such spinfoams and hence of the information dynamics on such devices. Spin-s systems which represent the patches on the 1 surfaces of spinfoams are considered, starting with the spin- qubit systems. These are 2 akin to quantum computer registers residing on spinfoams. In effect, they are LQG spinfoam computers. We are interested in the general information flow in such devices as a model for information flow in bi-partite systems such as our informaton model in this paper.
The informaton model is a system of bipartite-entangled event-observer pairs and as such represent information particles that live by entanglement. This is the qubit black hole model of information. This has possible implications 4 8n for the hypothesis of information loss in black holes and the evaporation model. The consequences of this are that information loss is possible because of the lessening of entanglement in such limited segregated start up qubit black hole models. It should be noted that these results are generalizable to the qudit case where the dimension of the state space for each spin particle on a surface patch is d.
The qudits then become SU d invariant. This means that under a condition of marginal pairwise entanglement i. In this method quantum information decoheres into the environment. Mutual information, I S : F is then a partial measurement of the information from S. Decoherence is normally the killer of entanglement. In this general case of a qubit and its environment, mutual information can be recovered as an indicator of the original quantum information from S. In the case of informatons in chapter 4, the mutual pairs of entities within each informaton can recover mutual information from other informaton subsystems that are considered part of their respective environment.
This is considered a form of quantum Darwinism because observers get information about quantum systems through their imprint on its environment. Haziness then determines the capacity to store information about a qubit in an environment or part thereof containing it. We next consider a model for information fields using generalized Bayesian signal processing in the form of an information field theory constructed in the tradition of QFT. Faraday originally defined the concept of physical fields to accommodate the spatial dynamics of electromagnetism Faraday, These vectors represent arrays of values relating to observables of an entity.
The underlying space may be Einstienian and quantum in nature and hence a creditable physical field theory must take into account the constraints of such frameworks. Additionally, only one data observation is taken and so this technique is not an ensemble statistical decision problem as in the derivation of an estimator based on a repeated iid sampling.
Let s depict the signal of interest and d the data sample collected by the observer. By this definition, the noise component is linearly uncorrelated to s, given the data d, i. Criteria must then be used in order to differentiate the performance of such transformations of data to construct spaces of response functionals. What is desirable is the maximization of the response function, RT s corresponding to the data transformation T on d. This mapping should also recover or be as nearly invariant to s as much of the signal as possible, i. This was made unclear and could be further crystallized through the use of optimal statistical estimators such as complete and minimally sufficient statistical estimators.
These, however, require repeated quantum experiments. Nonetheless, in general, a signal operator could be a filter applied to an input stream in producing an output or in a quantum mechanical setting, a measurement operator of the quantum state producing an observation. The authors give as their example a Gaussian data model in a free theory free of interactions. Feynman diagrams are constructed from the symbols of lines, vertices with line attachments and without line attachments according to the Feynman rules: 1.
Open-ended lines represent external coordinates. The propagators, D are represented by a line connecting the coordinates defining D. All internal coordinates are integrated over external coordinates are not 6. Each diagram is divided by its symmetry factor which is the number of permutations of vertex attachments leaving the topology invariant. This model of an information field presumes a design that involves a linear response function, single observation experiments, and a separate signal operator as a outside process.
Furthermore, the Hamiltonian operators that are derived from these extensions as generators of an information field will be applied in the more general spinfoam formalism. These quantities may be calculated using the Feynman diagrams rules as defined above. Their similarity is the fidelity of the signal reconstruction. This may also be measured by the quantity Q and reframed in the context of F , U , and L above in the following sense.
The corresponding expressions for fidelity and quality of information measurement will follow as well. Can one construct evolutionary rules for complex adaptive systems development from general rules for spacetime and information fields?
Consciousness – Viewpoints which Matter
Towards this end, the next section will review complex adaptive systems CASs and their most currently practical models, multiagent ensembles. To a lesser extent, holonic systems have become attractive as a means of describing the organizational behavior of natural complex systems. This will set the stage for the proposals to be made in the next chapter that attempt to pull together information field models as a calculus for constructing general computational holonic multiagent complex adaptive systems as models for realistic ensembles and organization. In the vernacular of complex systems theory, a system consisting of multiple agents or entities is complex if it exhibits collective behavior that cannot be explained by the microlevel rules of its components.
This behavior is at times self-referential, emergent, evolutional, self-organized or adaptive. Therein lay ambiguities to the technical definitions of complex systems. Does one characteristic causally link to another or are all of these properties linked to a separate mechanism? These authors used classical definitions of entropy to define categories of complexity.
Here quantum and more general extensions of entropy will be used in that context. Complex or at least a measure of complexity may be viewed as the amount of information needed to describe a system. Shannon entropy was proposed to measure this concept for signals in a noisy channel defining his famous entropy quantity Shannon, Additive entropies can be classified under this very general form.
These general entropy measures are examples of functionals defined on the space of probability distributions of the underlying random variables. Tsallis studied and developed functionals in this manner using the principle of maximum entropy. Tsallis generalized Shannon entropy for nonadditive entropies using a parameter q.
M acting as the moment functions. Extensive systems are those in which total system energy is proportional to system size. Criticisms of Tsallis statistics as a means of thermodynamic construction of systems mainly point to certain nonphysical conclusions reached by them. It continues to be a controversial theoretical construct with some successful implementations. Since complex systems consist of multiple entities, their interactions are as important as each individual action and as such one would like to utilize the concepts of joint and conditional entropies and mutual information of two or more quantum random variables.
Divergences will be used in the definition of the info-macrodynamics of the informaton model to be developed in chapter 4. Prior to embarking on quantum communication theory, we mention a concept that runs antecedent to that of entropy, that of extropy. Extropy has been popularly defined as negentropy or the information content as disorder in a system decreases. For molecular systems this is similar to the concept of potential for life expectation. More specifically, extropy has been defined for systems as the entropy of a Markov chain that describes the states of the system.
These definitions are motivated by the setup for a digital probabilistic approach to physics Stonier, , , We extend this to quantum systems. A similar extropy definition may be based on such general structures. We now turn to a discussion on abstract communication channels. The channel capacity is an upper bound for the rate of communication that is possible over a quantum noisy channel and is given by maximizing the quantum mutual information over all distributions on the source quantum system. When information is transmitted classically, as in electronic signal transmission through a wire, radio waves, or light waves, the medium is quantum mechanical.
In the case the transmitting of a classical bit stream through a quantum transmission channel requires two additional processes — the encoding of the classical information into a quantum state and the decoding of the message by a quantum measurement on output Hayashi, , p. This situation is referred to as a c-q classical-quantum channel. Returning to the discussion on proposals to define a common structural framework for complex systems, Prokopenko, et al. In the glossary of network theory, assortiveness between two nodes, x1 and x2 is a measure of reciprocity in the sense that highly connected nodes connect with other highly connected nodes or in the opposite side of this spectrum with other low connected nodes.