The Complementary Nature of the Quantum Theory

George Frederick James Temple

Javier M. Magán, Diego Pontello

We approach the physical implications of the noncommutative nature of complementary observable algebras (COAs) from an information theoretic perspective. In particular, we derive a general entropic certainty principle stating that the sum of two relative entropies, naturally related to the COA, is equal to the so-called algebraic index of the associated inclusion. Uncertainty relations then arise by monotonicity of the relative entropies that participate in the underlying entropic certainty. Examples and applications are described in quantum field theories with global symmetries, where the COAs are formed by the charge-anticharge local operators (intertwiners) and the unitary representations of the symmetry group (twists), and in theories with local symmetries, where the COAs are formed by Wilson and t'Hooft loops. In general, the entropic certainty principle naturally captures the physics of order and disorder parameters, a feature that makes it a generic handle for the information theoretic characterization of quantum phases.

Ahmet Orun

We have managed to observe the magnitudes of atomic exchange [3] activities between the chemical substances by quantization of interferometric (Mach-Zehnder) quantum eraser pattern’s motions caused by photonic wave-particle duality shifting [1]. Such characteristic shiftings substantially support our Natural Quantum Communication theory which indicates that the Interferometer’s photons attempt to access or gain complementary information provided by “naturally communicated” substances in the chemical reaction tube located along the lower arm of interferometer, which consequently exhibit characteristic wave-particle duality shifting [2]. The proposed theory may explain, how medications provide curing effect on "diseased organic tissues" via transmitting a complementary quantum information that is normally missing in the receiver domains, or natural quantum communication between vaccine and immune system. Furthermore, in the future some related advance technique would be expected to replace natural substance style supplements (e.g. human cells’ need of Oxygen) with only (Oxygen atom’s) quantum information provision instead.

George Frederick James Temple

Ronald F. Peierls

Sandro Petruccioli

At the beginning of the paper presented at Como in 1927 Bohr stated: ‘On the one hand, the definition of the state of a physical system, as ordinarily understood, claims the elimination of all external disturbances. But in that case, according to the quantum postulate, any observation will be impossible, and, above all, the concepts of space and time lose their immediate sense. On the other hand, if in order to make observation possible we permit certain interactions with suitable agencies of measurement, not belonging to the system, an unambiguous definition of the state of the system is naturally no longer possible, and there can be no question of causality in the ordinary sense of the word. The very nature of the quantum theory thus forces us to regard the space-time coordination and the classical theories, as complementary but exclusive features of the description, symbolizing the idealization of observation and definition respectively’. The contrast effectively illustrated between possibilities of definition and conditions of observation thus expresses the cognitive scope of quantum theory and summarizes the complementary and irreducible aspects of the description of objects belonging to the microworld. In Bohr's view, this contrast is the direct consequence of two general assumptions: the postulate regarding the discontinuity or individual nature of atomic processes, symbolically represented by the quantum of action, and an epistemologically binding judgement on the system of concepts whereby such processes may be described.