Related papers: Editor's column (on an article by Jaffe and Quinn)
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…
We sketch some connecting relations involving fractional and quantum calculi, fractal structure, thermodynamics, and quantum mechanics.
The first part of this paper is a summary of a hypothesis previously advanced, suggesting the existence of a close link between thermodynamics and relativity. The second part is a preliminary comment about some possible consequences in the…
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
A connection between fractional supersymmetric quantum mechanics and ordinary supersymmetric quantum mechanics is established in this Letter.
I review a number of the open questions about neutrino properties, critique recent hints of neutrino mass, and discuss one recently proposed neutrino mass matrix to illustrate the direction in which we may be headed. I also present one…
The Weltanschauung emerging from quantum theory clashes profoundly with our classical concepts. Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our…
In this reply, we hope to bring clarifications about the reservations expressed by Floyd in his comments, give further explanations about the choice of the approach and show that our fundamental result can be reproduced by other ways. We…
Do we have two kinds of reality: physical and mathematical? What is the role of mathematics in physics? These fundamental questions have intrigued original and brilliant minds since ancient times. A recent article (Aharonov, Cohen and…
Based on new experiments about the "macroscopic Schrodinger's cat state" etc., a self-consistent interpretation on quantum mechanics is presented from the new point of view combining physics, philosophy and mathematics together.
Contrary to claims about the irrelevance of philosophy for science, I argue that philosophy has had, and still has, far more influence on physics than is commonly assumed. I maintain that the current anti-philosophical ideology has had…
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The…
We argue that several apparently distinct responses to the hole argument, all invoking formal or mathematical considerations, should be viewed as a unified "mathematical response". We then consider and rebut two prominent critiques of the…
We discuss some methodological aspects of the relation between physics and metaphysics by dealing specifically with the case of non-relativistic quantum mechanics. Our main claim is that current attempts to productively integrate quantum…
These notes have been triggered by physicist's considerations on (1)'Pre-quantized wave equations' for matter fields, (2) Conservation laws, (3) Gauge Field extensions. All starting from variational principles. These notes do not contain…
This reply contains a brief response to the comment by R. Howl, D. R\"atzel, and I. Fuentes [arXiv:1811.10306]
This manuscript is written for students in introductory physics classes to address some of the common difficulties and misconceptions of the normal force, especially the relationship between normal and friction forces. Accordingly, it is…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…