Quantum Theory, Part I: Elements

Uri Haber‐Schaim

Xin Guo

The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains diagonal elements of Fock space from the interacting terms, which is different from the standard procedure of previous perturbation method. In this letter, we use the adaptive perturbation theory to extract the solvable elements in the two-particle system and obtain the energy spectrum of the solvable part. Then, we diagonalize the Hamiltonian to obtain the numerical solution. Finally, we compare two kind of values. The results show that the adaptive perturbation theory can be well applied to the strong coupling regime of two-particle system, and on the whole, with the increase of quantum number, two values are closer.

William T. Dixon

Frederico Rodrigues Pfrimer

What is the nature of reality? How should be an answer to this question? At this level, we are so deep that all our concepts are obscure. Quantum theory (QT) is at this level. The quest for interpreting it fails because the clarity of our actual fundamental concepts in ordinary language cannot match the precision of the theory's mathematical formalism. The interpretation of quantum mechanics should define and bring clarity to fundamental concepts; not simply rely over them. Quantum theory requires a new worldview, the one that will make it understandable. We discuss on the formulation and interpretation of closed, and final theories, in other words, completely axiomatic theories that define their own conceptual framework, and closed theories that cannot be made simpler. We claim that everything we can properly say about a theory follows from its interpretation, and that interpreting is saying the meaning of each of its mathematical statements. We argue that quantum mechanics is a closed theory; and, therefore, that part of it is part of the final or fundamental theory of physics (FTP). We propose a new entirely axiomatic formulation of part of quantum theory (including all its mathematical framework) in which new powerful and useful elements are added to the existing formalism. Our interpretation is straightforward: it allows us reading or saying the meaning of each of the theory's axiom, theorem or element. We state that the proposed theory is the FTP. Its interpretation may dissolve most of the existing paradoxes around QT. The principle of excluded middle is not valid in general. Both epistemic and ontic elements are present in the theory since it is a theory of knowledge and truth. This and other fundamental concepts are defined by the theory, which can represent both reality and our knowledge about it. Aesthetics is one of its key features.

Klaus Hasselmann