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We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
There is a substantial curricular overlap between calculus and physics, yet introductory physics students often struggle to connect the two. We introduce a quantity-based framing of the Fundamental Theorem of Calculus (FTC) to help unify…
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
Recent experiments appear to have revealed the possibility of quantum entanglement between spatially separated human subjects. In addition, a similar condition might exist between basins containing human neurons adhering to printed circuit…
There is a contemporary trend toward geometrizing all mathematical theories, as proposed by the Langlands program, and, by extension, physical theories as well. Within this paradigm, it becomes possible to represent physical objects as…
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of…
This article is an attempt for a new vision of the basics of Physics, and of Relativity, in particular. A new generalized principle of inertia is proposed, as an universal principle, based on universality of the conservation laws, not…
This book invites readers to see mathematics not just as formulas and rules, but as the deepest expression of human thought. It begins by exploring the timeless idea of mathematics as a universal language, contrasting its precision with the…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…
Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current…
The problem of fundamental units is discussed in the context of achievements of both theoretical physics and modern metrology. On one hand, due to fascinating accuracy of atomic clocks, the traditional macroscopic standards of metrology…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
Even simplified models of quantum many-body systems can be difficult to analyse. However, taking inspiration from the foundations of physics, one may wonder whether there are practical advantages to constructing alternative beyond-quantum…
Maxwell's mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as "dynamical systems". That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly…
We argue that Anton Zeilinger's "foundational conceptual principle" for quantum mechanics according to which an elementary system carries one bit of information is an idealistic principle, which should be replaced by a realistic principle…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
In this paper we are going to introduce a new dynamical postulate in Quantum Mechanics. This new principle is defined using path integrals over the set of normalized wave functions. We will show in a qualitative way that this postulate is…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
The aim of this paper is twofold: First, we give a formal introduction to the basics of the mathematical framework of classical mechanics. Along the way, we prove a Hamiltonian and a Lagrangian version of Noether's Theorem, an important…