Related papers: Editor's column (on an article by Jaffe and Quinn)
In this paper we give a reasonable explanation (not proof) to the Copenhagen interpretation of Quantum Mechanics from the view point of decoherence theory. Mathematical physicists with strong mission must prove {\bf the Copenhagen…
Invited contribution to the inaugural issue of {\em Physics Educator.}
Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the $relational$ perspective on the theory, and a comment on its philosophical implications.
I contrast the profound differences in the ways in which algebra and analysis are used in physics. In particular I discuss the fascinating phenomenon that theoretical physicists devote almost all their efforts to algebraic problems even…
Reply to the Comment physics/0307134 by A. Helmstetter and D. Sornette
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
Jaynes' criticism of Bell's theorem is examined. It is found that Bell's reasoning leading to his theorem is sound when properly interpreted. The nature of physical influence and logical inference in quantum mechanics, and its relationship…
Mathematical physics has many facets, of which we shall briefly give a (very partial) description, centered around those of main interest for Elliott and us (Moshe Flato and I). In our case these aspects had as a corollary a variety of…
The paradoxes of thermodynamics and statistical physics are unavoidable in the study of physical paradoxes because of their importance at the time they came to be as well as the frequency of their appearance in historical studies of…
This is a reply to the comment by J. L. Alonso et al. (arXiv:1302.6146; to appear in J. Chem. Phys) on our paper A. Abedi, N. T. Maitra, and E. K. U. Gross, J. Chem. Phys. 137, 22A530 (2012) [arXiv: 1208.4388]
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
The paper contains critical comments to the paper mentioned in the title from the mathematical point of view
I advocate an extreme "shut-up-and-calculate" approach to physics, where our external physical reality is assumed to be purely mathematical. This brief essay motivates this "it's all just equations" assumption and discusses its…
The purpose of this note is to discuss some of the questions raised by Dunn, J. Michael; Moss, Lawrence S.; Wang, Zhenghan in Editors' introduction: the third life of quantum logic: quantum logic inspired by quantum computing.
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
This viewpoint relates to an article by Jorge Kurchan (1998 J. Phys. A: Math. Gen. 31, 3719) as part of a series of commentaries celebrating the most influential papers published in the J. Phys. series, which is celebrating its 50th…
We present evidence for an undiscovered link between N=2 supersymmetric quantum field theories and the mathematical theory of helices of coherent sheaves. We give a thorough review for nonspecialists of both the mathematics and physics…
The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as `duality' is understood in physics and (ii) equivalence of theories, as `equivalence' is understood in logic and philosophy. The…