Related papers: Four Departures in Mathematics and Physics
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
We argue that most advances in science and technology during the past and the present centuries rely on modern physics concepts developed in the early $20$th century. The reliance is so profound that any improvement of literacy of science…
We analyse the implications of the closure of the physical for experiments in the scientific study of consciousness when all the details are considered, especially how measurement results relate to physical events. It turns out that the…
Whoever has to learn or to teach thermodynamics is confronted with conceptual difficulties which are specific to this field of physics ([1],[2]). It seems that they can be eliminated by inserting relativity in the thermodynamic theory. The…
We acuminate the idea of a final theory of physics in order to analyze its logical implications and consequences. It is argued that the rationale of a final theory is the principle of sufficient reason. This implies that a final theory of…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
In this paper, we argue that there are foundational dilemmas in theoretical physics related to the concept of reality and the nature of mathematics in physics. Physical theory is treated as a conceptual organism which develops under the…
Even after over 150 years of discussion, the interpretation of the second law of thermodynamics continues to be a source of confusion and controversy in physics. This confusion has been accentuated by recent challenges to the second law and…
A system's apparent simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and…
Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
(transcript of a talk given by Prof.~Feshbach:) Nuclear physics has been and will be a major factor in science and technology. It makes unique and important contributions to medicine, to industry and to other sciences. Interaction with…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
Most of the logical objections against the classical laws of motion, as they are usually presented in textbooks, centre on the fact that defining force in terms of mass and acceleration, the first two laws are mere assertions of concepts to…
We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as the supergeometric setting. The review is supplemented by a…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.