Related papers: Mathematical Structure of Discrete Space-time
A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity ($\Scri{}^+$)…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…
The nature of quantum nonlocality, as exemplified by entanglement, remains one of the deepest mysteries in quantum physics, challenging classical notions of causality and locality. In this work, we introduce the concept of dark space-time,…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…
Space-time symmetries and internal quantum symmetries can be placed on equal footing in a hyperspin geometry. Four-dimensional classical space-time emerges as a result of a decoherence that disentangles the quantum and the space-time…
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
In this paper we show that, via an extension of time, some metric structures naturally appear in both classical and quantum mechanics when both are formulated via path integrals. We calculate the various Ricci scalar and curvatures…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
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…
Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…
The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
Symbolic data structures for model checking timed systems have been subject to a significant research, with Difference Bound Matrices (DBMs) still being the preferred data structure in several mature verification tools. In comparison,…
We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that break discrete time translation symmetry in driven quantum many-body systems…
Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set…
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…
This essay is a tour around many of the lesser known pregeometric models of physics, as well as the mainstream approaches to quantum gravity, in search of common themes which may provide a glimpse of the final theory which must lie behind…