Applications of The Information Model of The Collapse Phenomena: The Mathematical Model of Everett's Worlds in The Case of The Measurement of A Spin 1/2 Projection
The information model of the collapse phenomena is further advanced. We discover an important property of the model - the death point effect. The P function approach is presented to construct the manifest form of the function of risk. We clarify a close connection of the model with the Extended Everett Concept. The model is also reformulated as an automaton. Examples are considered.
The information model of the collapse phenomena is further advanced. We discover an important property of the model - the death point effect. The P function approach is presented to construct the manifest form of the function of risk. We clarify a close connection of the model with the Extended Everett Concept. The model is also reformulated as an automaton. Examples are considered.
The mathematical representation of the universe consists of sequences of symbols, rules and operators containing Gödel's undecidable propositions: information and its manipulation, also with Turing Machines. Classical information theory and mathematics, ideally independent from the medium used, can be interpreted realistically and objectively from their correspondence with quantum information, which is physical. Each representation of the universe and its evolution are, in any case, physical subsets of the universe, structured sets of observers and their complements in the universe made with spacetime events generated by local quantum measurements. Their description becomes a semantically closed structure without a global object-environment loss of decoherence as a von Neumann's universal constructor with a semantical abstract whose structure cannot be decided deterministically a priori from an internal observer. In a semantically closed structure, the realization of a specific event that writes the semantical abstract of the constructor is a problem of finding "which way" for the evolution of the universe as a choice of the constructor's state in a metastructure, like the many-world Everett scenario, from a specific result of any quantum measurement, corresponding to a Gödel undecidable proposition for an internal observer.
Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the sphere of life.
We discuss mathematical models describing the action of consciousness and super-consciousness as these phenomena are defined in the Extended Everett's Concept (EEC) proposed by the author. According to the Everett's interpretation of quantum mechanics, the state of the quantum world is a superposition of various classical pictures of the world (classical realities, or alternatives). Humans, due to their ability called consciousness, perceive the alternatives separately: all alternatives are perceived, but subjectively perceiving one of them is accompanied by the sensation of the remaining alternatives as if being invisible. This causes the impression that only one of the alternatives really exists, but this is an illusion of consciousness. When consciousness (separating the alternatives) is turned off (in sleep, trance or meditation) or weakened, another ability arises called super-consciousness. Due to super-consciousness, the human gets access to the set of all alternative realities taken as a whole, selects those alternatives that are favorable, and ensures that just these selected alternatives are experienced after consciousness is turned on again. Thus, EEC explains, on the basis of quantum mechanics, those features of consciousness which are usually treated as mystical. It is shown in the paper how these features of consciousness and super-consciousness can be presented by simple mathematical models.
Extended Everett's Concept (EEC) recently developed by the author to explain the phenomenon of consciousness is considered. A mathematical model is proposed for the principal feature of consciousness assumed in EEC, namely its ability (in the state of sleep, trance or meditation, when the explicit consciousness is disabled) to obtain information from all alternative classical realities (Everett's worlds) and select the favorable realities. To represent this ability, a mathematical operation called postcorrection is introduced, which corrects the present state to guarantee certain characteristics of the future state. Evolution of living matter is thus determined by goals (first of all by the goal of survival) as well as by causes. The resulting theory, in a way symmetrical in time direction, follows from a sort of antropic principle. Possible criteria for postcorrection and corresponding phenomena in the sphere of life are classified. Both individual and collective criteria of survival are considered as well as the criteria providing certain quality of life and those which are irrelevant to the life quality. The phenomena of free will and direct sighting of truth (e.g. scientific insight) are explained in these terms. The problem of artificial intellect and the role of brain look differently in the framework of this theory. Automats may perform intellectual operations, but not postcorrection, therefore artificial intellect but not an artificial life can be created. The brain serves as an interface between the body and consciousness, but the most profound level of consciousness is not a function of brain.
Abstract The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.