Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum physics: the quantum wave equation, de Broglie equations, uncertainty relation, statistical result of quantum wave-function. This shows us a possible new way to interpret quantum physics. We will also prove that physics with multiple proper time does not cause causality problem.
If time has three dimensions, how does a particle move? This paper demonstrates that quantum physics naturally emerges from a framework of three-dimensional time. We present the equations governing the motion of 0-spin, 1-spin, and 1/2-spin particles within this three-dimensional time model. Phenomena such as quantum non-locality, spin, gauge transformation invariance, Bose-Einstein condensation, the exclusion principle, and Schrödinger's cat problem are shown to arise due to the presence of two additional time dimensions. We will explore how causality is maintained in this multi-dimensional time framework. Additionally, we will demonstrate that gravitational and electromagnetic fields can be unified within the 3+3 space-time Kaluza-Klein (KK) equations. Furthermore, a strong-interaction equation based on the
σ−ω model is derived from the geometry of three-dimensional time for fermions. Finally, we show that gravitational, electromagnetic, and strong interactions can be unified within the same six-dimensional Kaluza-Klein equation. Key words: Three dimensional time, What is spin, Interpreting of quantum physics, Dirac equation, unified theory
As part of a probabilistic reconstruction of quantum theory (QT), we show that spin is not a purely quantum mechanical phenomenon, as has long been assumed. Rather, this phenomenon occurs before the transition to QT takes place, namely in the area of the quasi-classical (here better quasi-quantum) theory. This borderland between classical physics and QT can be reached within the framework of our reconstruction by the replacement
p→M(q,t), where
p is the momentum variable of the particle and
M(q,t) is the momentum field in configuration space. The occurrence of spin, and its special value
1/2 , is a consequence of the fact that
M(q,t) must have exactly three independent components
Mk(q,t) for a single particle because of the three-dimensionality of space. In the Schrödinger equation for a "particle with spin zero", the momentum field is usually represented as a gradient of a single function
S. This implies dependencies between the components
Mk(q,t) for which no explanation exists. In reality,
M(q,t) needs to be represented by three functions, two of which are rotational degrees of freedom. The latter are responsible for the existence of spin. All massive structureless particles in nature must therefore be spin-one-half particles, simply because they have to be described by
4 real fields, one of which has the physical meaning of a probability density, while the other three are required to represent the momentum field in three-dimensional space. We derive the Pauli-Schrödinger equation, the correct value
g=2 of the gyromagnetic ratio, the classical limit of the Pauli-Schrödinger equation, and clarify some other open questions in the borderland between classical physics and QT.
Spin of elementary particles is the only kinematic degree of freedom not having classical corre- spondence. It arises when seeking for the finite-dimensional representations of the Lorentz group, which is the only symmetry group of relativistic quantum field theory acting on multiple-component quantum fields non-unitarily. We study linear transformations, acting on the space of spatial and proper-time velocities rather than on coordinates. While ensuring the relativistic in- variance, they avoid these two exceptions: they describe the spin degree of freedom of a pointlike particle yet at a classical level and form a compact group hence with unitary finite-dimensional rep- resentations. Within this approach changes of the velocity modulus and direction can be accounted for by rotations of two independent unit vectors. Dirac spinors just provide the quantum description of these rotations.
A great effort has been devoted to formulate a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in order to connect classical and quantum theories rests in finding a parameter which plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneer works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi [Phys. Rev. Lett. 52, 2009 (1984)]. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail. 1