Related papers: Space and time transformations with a minimal leng…
Relativity and quantum mechanics are generalized by considering a finite limit for the smallest measurable distance. The value a of this quantum of length is unknown, but it is a universal constant, like c and h. It depends on the total…
Inspired in metamaterials, we present a covariant mechanics for particles in Kleinian spacetime and show some of its effects, such as time contraction and length dilatation. We present the new expressions for relativistic momentum and…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…
The effects of the IR aspects of gravity on quantum mechanics is investigated. At large distances where due to gravity the space-time is curved, there appears nonzero minimal uncertainty $\Delta p_{0}$ in the momentum of a quantum…
We present a simple proof of the minimum time for the quantum evolution between two arbitrary states. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based…
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…
Quantum-gravity renders the space-time dimension to depend on the size of region; it monotonically increases with the size of region and asymptotically approaches four for large distances. This effect was discovered in numerical simulations…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…
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…
We have performed an experimental test under the conditions of which quantum mechanics predicts a spatially-discontinuous single-particle transport. The transport is beyond the relativistic paradigm of movement in Cartesian space and…
The existence of a minimum time uncertainty is usually argued to be a consequence of the combination of quantum mechanics and general relativity. Most of the studies that point to this result are nonetheless based on perturbative…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
In this work, we consider effects of the dynamical vacuum in quantum cosmology in presence of a minimum length introduced by the GUP (generalized uncertainty principle) related to the modified commutation relation $[\hat{X},\hat{P}] :=…
The concepts of space, time, and matter are of central importance in any theory of the gravitational field. Here I discuss the role that these concepts might play in quantum theories of gravity. To be concrete, I will focus on the most…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \delta_{ij} + g(P^2) P_i P_j $ for any…
According to most inflationary models, fluctuations that are of cosmological size today started out much smaller than any plausible cutoff length such as the string or Planck lengths. It has been shown that this could open an experimental…
We attempt to find new symmetries in the space-time structure, leading to a modified gravitation at large length scales, which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified…
It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…