A New Approach to Quantum Theory

Yoshifumi Ito

Even if there was a pioneering work [1], it becomes about 11 years since we really began to investigate the new quantum theory. Thus, in this article, we wish to summarize the research of the new quantum theory in these 11 years. In the section 1, we give a more clear and evident formulation of Ito [2], [3]. In the section 2, we give a more precise representation of Ito-Kayama [6], [7]. In the section 3, we summarize the papers [8], [9], [10]. In the section 4, we mention the philosophical consideration of the new quantum theory. In the section 5, we mention several problems of the new quantum theory.

Yakir Aharonov

Jonathan Ben‐Artzi, Anders C. Hansen, Olavi Nevanlinna +1 more

We report on new barriers in the theory of computations. These barriers show that the standard theory of computations and complexity theory is insufficient for many core problems in computational theory. Thus we are in need for a new extended complexity theory. The new theory settles the long-standing computational spectral problem and also provides new fundamental algorithms for quantum mechanics.

Kunwar Jagdish Narain

Arkady Plotnitsky

This article offers a new argument concerning the relationships between mathematics and physical reality in quantum theory. While, as dedicated to the centenary of Heisenberg's invention of quantum mechanics, the article contains a historical discussion, it is not historical, but physical and philosophical. Heisenberg's thinking leading him to QM and beyond is only part of the genealogy of this argument, which also differs from that of Heisenberg and builds on the previous work of the present author. Among the contributions in the article are a new conception of the ultimate reality responsible for quantum phenomena; a new understanding, based on this conception, of the role of mathematics in physics in quantum theory; a critique of Heisenberg's and all Platonism in quantum theory and beyond; a new perspective on the role of symmetries in quantum field theory; and a new understanding of the relationships between continuity and discontinuity in quantum physics.