Related papers: Physics in discrete spaces (A): Space-Time organiz…
Recent progress in quantum gravity and string theory has raised interest among scientists to whether or not nature behaves discretely at the Planck scale. There are two attitudes twoards this discretenes i.e. top-down and bottom-up…
After more than a century of concerted effort, physics still lacks basic principles of spontaneous self-organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics…
The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space…
Discussion of some aspects of the concept of time for a general audience: nature of time, A- and B-series, time in physics, the "now", measurement of time, definition of time units, time's arrow, relativity of time, relativity of…
The often-asked question whether space-time is discrete or continuous may not be the right question to ask: Mathematically, it is possible that space-time possesses the differentiability properties of manifolds as well as the ultraviolet…
We propose the quantum mechanical description of complex systems should be performed using two types of causality relation: the ordering relation ($x\prec y$) and the subset relation ($A\subseteq B$). The structures with two ordering…
A modified version of the bilocal particle is presented in terms of complex space time. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac's conjecture.…
In considering the nature of the basic mathematical structures appropriate for describing the fundamental elements of particle physics a significant role for the octonions, as an extension from the complex numbers and uniquely the largest…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
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. In this way, a physical clock with discrete…
A system of $N$ particles in a chemical medium in $\mathbb{R}^{d}$ is studied in a discrete time setting. Underlying interacting particle system in continuous time can be expressed as \begin{eqnarray} dX_{i}(t) &=&[-(I-A)X_{i}(t) +…
We show that discretization of spacetime naturally suggests discretization of Hilbert space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that…
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
We proved that under quantum mechanics a momentum-energy and a space-time are dual vector spaces on an almost complex manifold in position representation, and the minimal uncertainty relations are equivalent to the inner-product relations…
With the theory of special relativity, time has been linked with space into a four-dimensional space-time from which a basic question must be asked: can space be really transformed into time and vice-versa? The response is affirmative if…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is…