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Even though the concepts of time and space are basic concepts of physics, they have not been vouchsafed a constructive definition. As to space, this is no wonder because a correct notion of space cannot be formed in the frame of the…

Two people may claim both to be naturalists, but have divergent conceptions of basic elements of the natural world which lead them to mean different things when they talk about laws of nature, or states, or the role of mathematics in…

Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…

Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…

The traditional pedagogical paradigm in physics is based on a deductive approach. However, with the recent advances in information technology, we are facing a dramatic increase in the amount of readily available information; hence, the…

The most striking observable feature of our indeterministic quantum universe is the wide range of time, place, and scale on which the deterministic laws of classical physics hold to an excellent approximation. This essay describes how this…

Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…

In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…

Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…

A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…

Can mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at…

This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…

As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…

The paper puts forward a conceptual framework in which the phenomenon of time can be presented and discussed in a proper way. We argue that change is ontologically and epistemologically a more basic phenomenon than time. Time is an abstract…

A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…

This contribution argues that the notion of time used in the scientific modeling of reality deprives time of its real nature. Difficulties from logic paradoxes to mathematical incompleteness and numerical uncertainty ensue. How can the…

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…

The notion of time in cosmology is revealed through an examination of transition matrix elements of radiative processes occurring in the cosmos. To begin with, the very concept of time is delineated in classical physics in terms of…