Essentials of Quantum Theory

Enrico G. Beltrametti, Gianni Cassinelli

We are concerned with the formulation of the essential features of quantum theory in an abstract way, utilizing the mathematical language of proposition lattice theory. We review this approach giving a set of consistent axioms which enables to achieve the relevant results: the formulation and the essential role of the superposition principle is particularly examined.

Amretashis Sengupta

Osvaldo Frota Pessoa Junior

When asking whether consciousness is an “essentially quantum effect”, one must first lay down criteria for considering an effect quantum mechanical. After a brief survey of the interpretations of quantum theory, three such sufficient criteria are proposed and examined: wave-particle duality (or collapse), entanglement (“non-locality”), and quantum condensation (involving “identical ” particles). A fourth criteria could involve the use of quantum field theories, but this problem is left open. If a quantum effect played an essential role in the brain, it would probably follow the first criterion, since the entanglement of many particles would be rapidly washed out by decoherence, and there is no strong evidence for the existence of biological condensates.

Shiv R. Vatsya, Shiv R. Vatsya

Rudolf Haag

A discussion of fundamental aspects of quantum theory is presented, stressing the essential role of “events.”