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arXiv:1603.01879

Emergence time, curvature, space, causality, and complexity in encoding a discrete impulse information process

Vladimir S. Lerner

Published Mar 6, 2016• 3 citations
arXivHTMLPDF

Abstract

Interacting random field of probabilities links Kolmogorov law 0-1 and Bayesian probabilities observing Markov diffusion process under Yes-No actions of random impulse. These objective probabilities measure virtual probing impulses processing the interactions in observable process. The impulse observation increases each posteriori correlation reducing conditional entropy measures from finite uncertainty up to certainty of real impulse. The reduced entropy conveys probabilistic causality with time course and temporal memory in collecting correlations, which interactive impulse innately cuts exposing hidden process entropy. The natural cut of this entropy reveals information hidden in the correlation connections. Inside the merging probing impulse emerges reversible microprocess with yes-no conjugated entangled entropy, curvature and logical complexity. Within the impulse time interval, entanglement starts before its space is formed and ends with beginning the space during reversible relative time interval being small part of impulse time interval. Merging impulse curves and rotates the impulse interactive actions in microprocess whose space interval measures this transitive movement.The cutting entropy sequentially converting to information memorizes the probes logic in Bit, participating in next probe conversions and encoding which memorizes information causality. The complexity and mass appears after the space emerges from the entanglement.The cognition assembles common units through the multiple attraction and resonances at forming network (IN) of triplet hierarchy, which accept only units that concentrates and recognizes each triplet IN node. The ended triplet of hierarchical INs measures level of the observer intelligence. The synthesized optimal process minimizes the observations time in Artificial designed information Observer with intellectual searching logic.

DOI
10.48550/arxiv.1603.01879

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Interacting random field of probabilities links Kolmogorov law 0-1 and Bayesian probabilities observing Markov diffusion process under Yes-No actions of random impulse. These objective probabilities measure virtual probing impulses processing the interactions in observable process. The impulse observation increases each posteriori correlation reducing conditional entropy measures from finite uncertainty up to certainty of real impulse. The reduced entropy conveys probabilistic causality with time course and temporal memory in collecting correlations, which interactive impulse innately cuts exposing hidden process entropy. The natural cut of this entropy reveals information hidden in the correlation connections. Inside the merging probing impulse emerges reversible microprocess with yes-no conjugated entangled entropy, curvature and logical complexity. Within the impulse time interval, entanglement starts before its space is formed and ends with beginning the space during reversible relative time interval being small part of impulse time interval. Merging impulse curves and rotates the impulse interactive actions in microprocess whose space interval measures this transitive movement.The cutting entropy sequentially converting to information memorizes the probes logic in Bit, participating in next probe conversions and encoding which memorizes information causality. The complexity and mass appears after the space emerges from the entanglement.The cognition assembles common units through the multiple attraction and resonances at forming network (IN) of triplet hierarchy, which accept only units that concentrates and recognizes each triplet IN node. The ended triplet of hierarchical INs measures level of the observer intelligence. The synthesized optimal process minimizes the observations time in Artificial designed information Observer with intellectual searching logic.
What is information originating in observation? Until now it has no scientifically conclusive definition. Information is memorized entropy cutting in random observations which processing interactions. Randomness of various interactive observations is source of entropy as uncertainty. Observation under random 1-0 impulses probabilities reveals hidden correlation which connects Bayesian probabilities increasing each posterior correlation. That sequentially reduces relational entropy conveying probabilistic casualty with temporal memory of correlations which interactive impulse innately cuts. Within hidden correlation emerges reversible time space microprocess with conjugated entangled entropy which probing impulse intentionally cuts and memorizes information as certainty. Sequential interactive cuts integrates cutting information in information macroprocess with irreversible time course. Memorized information binds reversible microprocess within impulse with irreversible information macroprocess. Observer probes collect cutting information data bits of observing frequencies impulses. Each impulse cuts maximum of impulse minimal information performing dual max-min principle of converting process entropy to information through uncertain gap. Multiple naturally encoding bits moving in macroprocess join triplet macrounits which logically organize information networks encoding macrounits in structures enclosing triplet code. Network time space distributed structure self renews and cooperates information decreasing its complexity. Integrating process entropy functional and bits information in information path integral embraces variation minimax law which determines processes regularities. Solving problem mathematically describes micro macro processes, network, and invariant conditions of observer network self replication.
Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states. Information appears phenomenon of interaction cutting correlations carrying entropy. Each inter action models Kronicker impulse, delta impulse models interaction between the Kronicker impulses. Each impulse step down action cuts maximum of impulse minimal entropy and impulse step up action transits cutting minimal entropy to each step up action of merging delta function. Delta step down action kills delivering entropy producing equivalent minimax information. The merging action initiates quantum microprocess. Multiple cutting entropy is converting to information micro macroprocess. Cutting impulse entropy integrates entropy functional EF along trajectories of multidimensional diffusion process. Information which delivers ending states of each impulse integrates information path functional IPF along process trajectories. Hidden information evaluates Feller kernel whose minimal path transforms Markov transition probability to probability of Brownian diffusion. Each transitive transformation virtually observes origin of hidden information probabilities correlated states. IPF integrates observing Bits along minimal path assembling information Observer. Minimax imposes variation principle on EF and IPF whose extreme equations describe observing micro and macroprocess which describes irreversible thermodynamics. Hidden information curries free information frozen from correlated connections. Free information binds observing micro macro processes in information macrodynamics. Each dynamic three free information composes triplet structures. Three structural triplets assemble information network. Triple networks free information cooperate information Observer.
Up to now both information and its connection to reality have not scientifically conclusive definitions neither implicit origin. They emerge in observing multiple impulses interactive yes-no actions modeling information Bits. The observed information process connects reality, information, and creates Observer. Interaction is fundamental reality building structure of Universe from quantum physics up to brain neurons interactive actions. Merging action and reaction joins probabilistic prior and posterior actions on edge of the observed predictability and begins microprocess. Its time of entanglement starts space interval composing two qubits or Bit of reversible logic in the emerging information process. The impulse interacting action curves impulse geometry creating asymmetrical logic Bit as logical Maxwell demon. With approaching probability one, the attracting interaction captures energy memorizing asymmetrical logic in information certain Bit. Such Bit is naturally extracted at minimal quality energy equivalent ln2 working as Maxwell Demon. The memorized impulse Bit and its free information self-organizes multiple Bits in triplets sructuring macroprocess. Memorized information binds reversible microprocess with irreversible information macroprocess along multidimensional observing process. The macroprocess self-forming triplet units UP attract new UP through free Information. Multiple UP adjoin hierarchical network whose free information produces new UP at higher level node and encodes triplets in multi-levels hierarchical organization. The interactive information dynamics assemble geometrical and information structures of cognition and intelligence in double spiral rotating code. Information Path Functional integrates multiple interactive dynamics in finite bits which observe and measure reality. The time and space of reality exists only as units of information as Wheeler predicted.
Bayesian integral functional measure of entropy-uncertainty (EF) on trajectories of Markov multi-dimensional diffusion process is cutting off by interactive impulses (controls). Each cutoff minimax of EF superimposes and entangles conjugated fractions in microprocess, enclosing the captured entropy fractions as source of an information unit. The impulse step-up action launches the unit formation and step-down action finishes it and brings energy from the interactive jump. This finite jump transfers the entangled entropy from uncertain Yes-logic to the certain-information No-logic information unit whose measuring at end of the cut kills final entropy-uncertainty and limits unit. The Yes-No logic holds Bit Participator creating elementary information observer without physical pre-law. Cooperating two units in doublet and an opposite directional information unit in triplet forms minimal stable structure. Information path functional (IPF) integrates multiple hidden information contributions along the cutting process correlations in information units of cooperating doublets-triplets, bound by free information, and enfolds the sequence of enclosing triplet structures in the information network (IN) that sequentially decreases the entropy and maximizes information. The IN bound triplets release free information rising information forces enable attracting new information unit and ordering it. While IPF collects the information units, the IN performs logical computing using doublet-triplet code. The IN different levels unite logic of quantum micro- and macro- information processes, composing quantum and/or classical computation.
Every vertex of the magic cube of physics discussed so far introduced a major element in the development of physics and the whole of science. Mechanics introduced the basic concept of equations of motion, or time-evolution of a physical system given certain initial condition and the associated idea of determinism, even with its generalization in the form of chaos, the dependence of the outcomes of the temporal evolution on the initial conditions. These concepts taken for many particles, or elements of a physical system, led to the probabilistic description of many particle systems, in the realm of statistical physics and thermodynamics, whereby the averages over time of various observable quantities were related to the ensemble averages, that involve classical, so-called Kolmogorov, probability measures, at least for certain “equilibrium” situations. The second law of thermodynamics introduced the concept of entropy and its probabilistic increase, the first truly emergent, probabilistic law in physics (temperature and pressure, being other emergent quantities, apart from entropy, the measure of disorder of a statistical system). In the context of Newtonian gravity, one gets, at least in retrospect the geometric description of gravity in non-relativistic, Galilean spacetime. Galilean relativity, based on the asymmetric mixing of space and time, with the absolute, universal time, true for all observers, gets generalized in special theory of relativity to observer dependent space and observer dependent time, viewed as “slices” of a new concept of spacetime, with the new concept of causal structure, that distinguish timelike, null and spacelike events. This in turn is made into a full dynamical geometric structure of spacetime with a relativistic description of gravity stemming from curvature of spacetime, and a dynamical causal structure, tied to gravity. In our next story, the story of quantum theory, we will encounter fundamental, intrinsic probabilities, that can interfere, unlike the classical probabilities of statistical thermodynamics, and which are consistent with equations of motion of individual elements, and not, as in statistical thermodynamics, with temporal averages over the time evolution of many elements. This is the big new lesson of quantum theory, that transcends the lessons of classical spacetime physics.
It is not solid physical structures and interactions that lie in the basis of objective reality, but merely probabilities and superposition among them. The solid structures of our sensorial and practical experience are an outcome of the collapse of probability functions as a result of physical measurement and even – sensory observation. While in causal processes energy is applied to alter the existing spatial structures, information processes employ energy for the conversion of the probability distributions of the systems’ dynamical states. There are equivalences and mutual conversion of mass, energy and information. Mass, energy and information are just three appearances under which probability communicates with us. From the above ontological frame of reference, we will consider and offer a hypothetical answer to the questions: What is probability? What is and what does the processes viewpoint on information disclose? What is the cognitive (the mental) image? What are the equivalences and mutual conversions of mass, energy, and information? How do our thoughts bring about our actions?