Related papers: Axiomatization of Mechanics
The notorious `measurement problem' has been roving around quantum mechanics for nearly a century since its inception, and has given rise to a variety of `interpretations' of quantum mechanics, which are meant to evade it. We argue that no…
It has been shown that the criticism of Pauli as well as of Susskind and Glogover may be avoided if the standard quantum-mechanical mathematical model has been suitably extended. There is not more any reason for Einstein's citicism, either,…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
Quantum mechanics is now 100 years old and still going strong. Combining general relativity with quantum mechanics is the last hurdle to be overcome in the "quantum revolution".
On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of…
The present discussion concerning certain fundamental physical theories (such as string theory and multiverse cosmology) has reopened the demarcation problem between science and non-science. While parts of the physics community see the…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
In this paper, we point out that there are at lest six theorems in physics sharing common virtue of Pythagoras theorem, so that it is possible to string these theorems together with the Pythagoras theorem for physics teaching, the six…
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…
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…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
The problem of whether or not the equations of motion of a quantum system determine the commutation relations was posed by E.P.Wigner in 1950. A similar problem (known as "The Inverse Problem in the Calculus of Variations") was posed in a…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
The twentieth century saw two fundamental revolutions in physics -- relativity and quantum. Daily use of these theories can numb the sense of wonder at their immense empirical success. Does their instrumental effectiveness stand on the rock…
Obtaining a rigorous justification of the kinetic theory of gases from Newton's second law of dynamics for a large number of identical spheres interacting by elastic binary collisions, is a problem formulated by Hilbert in 1900 (Hilbert's…
We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is…
It was generally believed throughout the 20-th century that irreversibility is a purely classical event without operator counterpart. However, a classical irreversible system cannot be consistently decomposed into a finite number of…