Related papers: Four Departures in Mathematics and Physics
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
We explain the solution of the following two problems: obtaining of Kepler's laws from Newton's laws (so called two bodies problem) and obtaining the fourth Newton's law (the formula for gravitation) as a corollary of Kepler's laws. This…
Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…
Physics is considered as one of the most prevailing and problematic subjects by the students in the realm of science. Students perceived physics as a difficult subject during high school days and become more evasive when they reach college.…
This chapter, from the Routledge Companion to the Philosophy of Physics (Eleanor Knox and Alastair Wilson, eds., 2021), is an overview of the constraints that relativity places on interpretations of quantum theory. It focuses on four main…
In contemporary physics space and time are intertwined entities so that kinematical and dynamical quantities are expressed in the four-dimensional space-time. This formulation seems to contradict our every-day experience and perception…
The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
Paradoxes are a very frequent phenomenon in processes of thought which strive towards the intelectual and cognitive shifts. They occur in all areas of human spiritual activites. What we are interested here in, are the paradoxes in physics.…
In a recent article, M. Tegmark poses the hypothesis that our known universe is a ``baggage free'' mathematical structure among many other possible ones, which also correspond to other physical universes --Mathematical Universe Hypothesis,…
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…
The electromagnetic interaction is characterised by discrete states for bound systems in contrast to continuous states for unbound systems. The difference merely arises because the characteristic equations do not exhibit the same behaviour…
The laws of quantum mechanics are couched in subtle mathematical language. The laws are not usually stated in a compact pedagogical form. Here I present a possible way to correct this. Essential facts can be distilled into seven statements…
Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore,…
Astrophysical paradoxes are the paradoxes of physics. The main motivation of a formulated paradox is clearly recognized in the scientific environment because the phenomenon of a paradox itself has become interesting. There is an explanation…
The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might…
The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However,…
We point out four problems which have arisen during the recent research in the domain of Combinatorial Physics.