Related papers: Mathematical Structure of Discrete Space-time
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational…
It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
A particular science is not only defined by its object of study, but also by the point of view and method under which it considers that same object. Taking space and time as an illustrative example, our main aim here is to bring out an…
We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system…
Our purpose here is to introduce the idea of viewing the spacetime as a macroscopic complex system which, consequently, cannot be directly quantized. It should be thought of as a collection of more fundamental "microscopical" entities…
We discuss the problem of determining the spacetime structure. We show that when we are using only topological methods the spacetime can be modelled as an R- or Q-compact space although the R-compact spaces seem to be more appropriate.…
A review of new aspects concerning time-symmetry in Quantum Mechanics.
Planck-scale physics challenges the classical smooth-spacetime picture by introducing quantum fluctuations that imply a nontrivial spacetime microstructure. We present a framework that encodes these fluctuations by promoting local scale…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
Recent discoveries in differential topology are reviewed in light of their possible implications for spacetime models and related subjects in theoretical physics. Although not often noted, a particular smoothness (differentiability)…
In contemporary physics space and time are intertwined entities so that kinematical and dynamical quantities are expressed in the four-dimensional space-time. This formulation seems to contradict our every-day experience and perception…
We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…
In this thesis the cosmological constant is investigated from two points of view. First, we study the influence of a time-dependent cosmological constant on the late-time expansion of the universe. Thereby, we consider several combinations…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…
While Quantum Gravity remains elusive and Quantum Field Theory retains the interpretational difficulties of Quantum Mechanics, we have introduced an alternate approach to the unification of particles, fields, space and time, suggesting that…
We show that a recent proposal for the quantization of gravity based on discrete space-time implies a modification of standard quantum mechanics that naturally leads to a loss of coherence in quantum states of the type discussed by Milburn.…
In classical physics, a single measurement can in principle reveal the state of a system. However, quantum theory permits numerous non-equivalent measurements on a physical system, each providing only limited information about the state.…