Related papers: Nobody needs equations
The Free Lunch Principle: Nature thrives on freebies. She chooses nothing, and no one helps Her. She must use canonical mathematical structures as there is no one to tell Her otherwise. With this I show where variational principles are…
The development of the trigonometric functions in introductory texts usually follows geometric constructions using right triangles or the unit circle. While these methods are satisfactory at the elementary level, advanced mathematics…
I propose that Physics should be formulated using minimal mathematical structure, beginning with its foundational arena: spacetime. This paper opens with a concise overview of several research directions explored in previous work. Among…
In this paper, we prove that the algebra of an \'etale groupoid with totally disconnected unit space has a simple algebra over a field if and only if the groupoid is minimal and effective and the only function of the algebra that vanishes…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing the boundedness of a set. The dual principle, although known to the analyst and despite its…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
Understanding geometric relationships with little mathematical knowledge can be challenging for today's students and teachers. A new toolset is introduced that is able to create a proof without words by combining the benefits of the…
An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.
We have recently showed that it is possible to deal with collections of indistinguishable elementary particles (in the context of quantum mechanics) in a set-theoretical framework by using hidden variables, in a sense. In the present paper…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
Galilean Relativity and Einstein's Special and General Relativity showed that the Laws of Physics go deeper than their representations in any given reference frame. Thus covariance, or independence of Laws of Physics with respect to changes…
We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals…
The procedure used to "do physics" in the macroscopic world is familiar: You take an object, start it off with a particular position and velocity, subject it to known forces (say gravity or friction, or both), and follow its trajectory. You…
The need to describe abrupt changes or response of nonlinear systems to impulsive stimuli is ubiquitous in applications. Also the informal use of infinitesimal and infinite quantities is still a method used to construct idealized but…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
We present a fully relational definition of inertial systems based in the No Arbitrariness Principle, that eliminates the need for absolute inertial frames of reference or distinguished reference systems as the "fixed stars" in order to…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria,…
We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any…