An anhomomorphic logic A * is the set of all possible realities for a quantum system.Our main goal is to find the "actual reality" φ a ∈ A * for the system.Reality filters are employed to eliminate unwanted potential realities until only φ a remains.In this paper, we consider three reality filters that are constructed by means of quantum integrals.A quantum measure µ can generate or actualize a φ ∈ A * if µ(A) is a quantum integral with respect to φ for a density function f over events A. In this sense, µ is an "average" of the truth values of φ with weights given by f .We mainly discuss relations between these filters and their existence and uniqueness properties.For example, we show that a quadratic reality generated by a quantum measure is unique.In this case we obtain the unique actual quadratic reality."Reality is merely an illusion, albeit a very persistent one.
An anhomomorphic logic A * is the set of all possible realities for a quantum system.Our main goal is to find the "actual reality" φ a ∈ A * for the system.Reality filters are employed to eliminate unwanted potential realities until only φ a remains.In this paper, we consider three reality filters that are constructed by means of quantum integrals.A quantum measure µ can generate or actualize a φ ∈ A * if µ(A) is a quantum integral with respect to φ for a density function f over events A. In this sense, µ is an "average" of the truth values of φ with weights given by f .We mainly discuss relations between these filters and their existence and uniqueness properties.For example, we show that a quadratic reality generated by a quantum measure is unique.In this case we obtain the unique actual quadratic reality."Reality is merely an illusion, albeit a very persistent one.
An anhomomorphic logic $\ascript ^*$ is the set of all possible realities for a quantum system. Our main goal is to find the "actual reality" $ϕ_a\in\ascript ^*$ for the system. Reality filters are employed to eliminate unwanted potential realities until only ϕa remains. In this paper, we consider three reality filters that are constructed by means of quantum integrals. A quantum measure μ can generate or actualize a $ϕ\in\ascript ^*$ if μ(A) is a quantum integral with respect to ϕ for a density function f over events A. In this sense, μ is an "average" of the truth values of ϕ with weights given by f. We mainly discuss relations between these filters and their existence and uniqueness properties. For example, we show that a quadratic reality generated by a quantum measure is unique. In this case we obtain the unique actual quadratic reality.
Anhomomorphic logic is a new interpretation of Quantum Theory (due to R. Sorkin). It is a histories formulation (c.f. consistent histories, quantum measure theory). In this approach, reality is a co-event, which is essentially an assignment of a truth value {True, False} to each question. The way this assignment is done mimics classical physics in as much as possible allowing however for sufficient flexibility to accommodate quantum 'paradoxes', as is shown by the analysis of Kochen-Specker theorem. In this contribution, after briefly reviewing the approach, we will examine how probabilistic predictions can arise. The Cournot principle and the use of approximate preclusions will play a crucial role. Facing similar problems in interpreting probability as in classical probability theory, we will resort to the weak form of Cournot principle, where possible realities will be preclusive co-events and the quantum measure is used to obtain predictions. Examples considered, includes the fair coin and the double slit pattern arguably one of the most important paradigms for quantum theory.
A classical logic exhibits a threefold inner structure comprising an algebra of propositions , a space of "truth values" V , and a distinguished family of mappings ϕ from propositions to truth values. Classically is a Boolean algebra, V = 2 , and the admissible maps ϕ: 2 are homomorphisms . If one admits a larger set of maps, one obtains an anhomomorphic logic that seems better suited to quantal reality (and the needs of quantum gravity). I explain these ideas and illustrate them with three simple examples.
Although various schemes for anhomomorphic logics for quantum mechanics have been considered in the past we shall mainly concentrate on the quadratic or grade-2 scheme. In this scheme, the grade-2 truth functions are called coevents. We discuss properties of coevents, projections on the space of coevents and the master observable. We show that the set of projections forms an orthomodular poset. We introduce the concept of precluding coevents and show that this is stronger than the previously studied concept of preclusive coevents. Precluding coevents are defined naturally in terms of the master observable. A result that exhibits a duality between preclusive and precluding coevents is given. Some simple examples are presented.
We modify the Relative State Interpretation (RSI) of Quantum Mechanics so that it does not imply many worlds and parallel realities. We drop the assumption that probability amplitudes correspond one-to-one with reality: Not all information is contained in amplitudes, and not all amplitudes need be realized. Amplitudes do not "collapse" after a measurement, but evolve continuously, including unrealized ones. After each "event" only one possible outcome is realized. Therefore, if a value is measured, that value is real, all others are not; there is only one reality and one world. Reality content is "quantized" : unity for realized outcomes, zero for all others. It is "conserved": can move along any possible sequence of events, but only one at a time. The modified RSI is is strictly deterministic in the sense that the "global" probability amplitudes of the universe are determined for all times by the laws of physics and the initial conditions. They guide all events. But it is not deterministic in the sense that from the amplitudes one can not predict which outcome actually happens; that represents new information that accumulates as history unfolds. To the extent that information is part of the physical world, the coming into being of the universe is ongoing, even after the Big Bang. All predictions of the two versions agree, except possibly in esoteric, untested cases.
Several experiments have suggested that the complete indistinguishability of quantum systems is to be considered a real phenomenon. Experiments such as the HOM effect, the existence of BECs, the path identity cases, and many others are physical realities of today. Physicists `explain’ these phenomena using different models, such as Bohmian mechanics, relational quantum mechanics or the QBism approach. Most of these models are constructed within a standard mathematical framework, meaning standard mathematics, where all things can, even if only in principle, be distinguished from one another, so complete indistinguishability can only be mimicked. These approaches may work for physical purposes but are debatable regarding logical and metaphysical questions. If we accept that such questions are at least part of the philosophical aspect of quantum physics, then we are authorised to analyse them and try to offer an alternative. Looking for an alternative, we consider Alain Aspect’s and Anton Zeilinger’s views about quantum realism, opting for Aspect’s acceptance of some kind of reality behind the wave-function, while Zeilinger suggests that everything comes from information. In our opinion, the case is the opposite: it is information that comes from the existence of things. The aim of this paper is to justify why we think that the underlying reality (in Aspect’s sense) can be seen as a quantum ontology of non-individuals.