A fundamental postulate of quantum mechanics states that a measurement of a quantum system causes the collapse of the wave function. This is in contrast to the smooth, continuous, deterministic time evolution of the wave function in between measurements, governed by the Schrodinger equation. The latter is similar to classical physics; the former is unique to quantum mechanics. (Note that many ...

Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that natural phenomena have a connection with intangible reality which cannot be measured directly. Futhermore, the intangible reality is supposed as vacuum particles –...

These lectures fall into two distinct, although tenouously related, parts. The first part is about fuzzy and noncommutative spaces, and particle mechanics on such spaces, in other words, noncommutative mechanics. The second part is a discussion/review of twistors and how they can be used in the calculation of Yang-Mills amplitudes. The point of connection between these two topics, discussed in ...

It is shown that the wave function describes the state of the statistical ensemble E [S] of individual particles, or the statistical average particle 〈S〉. This result follows from the fact that in the classical limit h̄ = 0 the Schrödinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an in...

We apply methods of quantum mechanics for mathematical modeling of price dynamics at financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven. Our model expresses complexit...

We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space. The wavefunction gives not the density of stuff, but giv...

Historically the starting point of wave mechanics is the Planck and Einstein-de Broglie relations for the energy and momentum of a particle, where the momentum is connected to the group velocity of the wave packet. We translate the arguments given by de Broglie to the case of a wave defined on the grid points of a space-time lattice and explore the physical consequences such as integral period,...

This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the Dirac equation, operators and monogenics, the Hydrogen atom, propagators and scattering theory, spin precession, tunnelling times, spin measurement, multipartic...

Jeffrey Bub himself once mentioned that whenever someone arrives at a position in the philosophy of quantum mechanics s/he seems to lose momentum. Here we have a clear counterexample: since his first book on the subject in 1974, which pioneered many of the subsequent development, Bub has gained a great deal of momentum. His position today has the additional virtue of providing sufficient condit...