Related papers: Special Relativity in a Discrete Quantum Universe
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…
We discuss the issue of unitarity in particular quantum cosmological models with scalar field. The time variable is recovered, in this context, by using the Schutz's formalism for a radiative fluid. Two cases are considered: a phantom…
In the underlying Planck scale theory we introduce a certain type of discrete symmetry, which potentially brings the stability of the weak-scale hierarchy under control. Under the discrete symmetry the $\mu $-problem and the tadpole problem…
The field theory quantized on the {\it light-front} is compared with the conventional equal-time quantized theory. The arguments based on the {\it microcausality} principle imply that the light-front field theory may become nonlocal with…
The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection…
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…
Besides the two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the one-way velocity of light in all inertial frames of reference, the special theory of relativity employs another assumption. This…
A common misconception is that Lorentz invariance is inconsistent with a discrete spacetime structure and a minimal length: under Lorentz contraction, a Planck length ruler would be seen as smaller by a boosted observer. We argue that in…
Recently there have been several studies devoted to the investigation of the fate of fundamental relativistic symmetries at the foreseen unification of gravity and quantum regime, that is the Planck scale. In order to preserve covariance of…
This paper presents an approach to the creation of a variant of Extended Special Relativity that takes into consideration the existence of limiting relativistically invariant quantities (Planck parameters). It shows the possibility of…
Hardy's theorem states that the hidden variables of any realistic theory of quantum measurement, whose predictions agree with ordinary quantum theory, must have a preferred Lorentz frame. This presents the conflict between special…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
A new relativistic transformation in the velocity space (here named the differential Lorentz transformation) is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
A major challenge at the interface of quantum gravity and cosmology is to explain the emergence of the large-scale structure of the Universe from Planck scale physics. In this letter, we extract the dynamics of scalar isotropic cosmological…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on…
The implications of an Evolutionary Quantum Gravity are addressed in view of formulating a new dark matter candidate. We consider a Schr\"odinger dynamics for the gravitational field associated to a generic cosmological model and then we…