The Axioms of the Theory of Local Observables

Guang-Liang Li

The Copenhagen interpretation presumes the legitimacy of quantum superpositions, attaches ``the probabilistic nature'' to quantum mechanics, brings observers into axioms of the theory, and claims that quantum mechanics is already a complete theory. Einstein disagreed with this interpretation; he argued against the legitimacy of quantum superpositions, worried about observers in the axioms, and considered quantum mechanics incomplete. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. They derived Bell inequalities, tested them by experiments, and proved Bell's theorem to interpret the experimental results. Regrettably, the experimental results are misinterpreted. This article introduces a new principle, the general principle of measurements, and provides its mathematical proof. Based on this principle, quantum mechanics can be completed within the framework of local realism by using disjunction (``or'') as the logical relation between orthonormal vectors spanning any given Hilbert space while keeping its general definition unchanged. Probabilistic predictions given by the completed theory and the current theory are exactly the same. Furthermore, by eliminating observers from the axioms and precluding inexplicable collapses of wave-functions, the completed theory alleviates much difficulty in understanding quantum mechanics and is intuitively comprehensible. In conclusion, Einstein's local-realist world-view is correct.

H. J. Borchers

Etang Chen

Francisco Calderón Ossa

The axiomatic formulation of an Algebraic Relativistic Quantum Field Theory leads naturally -via the Haag-Kastler axioms- to the fact that operators representing observables generate a von Neumann algebra localized in a space-time region in which said observations are made. I present and explain the axioms, as well as the mathematical preliminaries needed to understand them and apply them to the so-called causal diamond and Fermi's Two-Atom System. The latter shows the importance of formulating axioms concerning causality that try to make compatible the requirement from Special Relativity according to which no causal influence can travel faster than the speed of light and the quantum mechanical theory of measurement and preparability of states. For a relativistic field-theoretic setting, these concepts must be re-formulated, and this reasoning suggests that the operator algebra must be a type III von Neumann factor. I also introduce some philosophical problems concerning our usual notion of causality from Hume to contemporary theories of counterfactual causation and show how the algebraic structure of the theory is deeply related to the causal one and how this theory can be extended if we change the way we think about causality, measurements, and local preparability of states.

Lawrence J. Landau

Daegene Song

Based on the standard axioms of quantum theory, we provide a counter-example which invalidates the full compatibility between consciousness and quantum theory. In particular, we present an example of a natural phenomenon in which an observer's the mental state can be fully described in mathematical terms analogous to the state vector that is being observed. This mathematical description of the observer's mental state enables us to examine consciousness within the standard axioms of quantum theory. The separation between the observing party and the physical system being observed, imposed by the axiom of quantum theory, poses a problem when the observer is observing his own mental state, i.e., self-observing consciousness.