Related papers: Minimal Length and Small Scale Structure of Spacet…
The starting point of this work is the axiomatic existence of a smallest measurable interval, viz. the Planck time $t_P$, set by quantum fluctuations in the vacuum metric tensor. By the Relativity Principle, the same limit must then apply…
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…
It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time…
Lie-type deformations provide a systematic way of generalising the symmetries of modern physics. Deforming the isometry group of Minkowski spacetime through the introduction of a minimal length scale $\ell$ leads to anti de Sitter spacetime…
The narrow and subtle difference between the Hilbert spaces of operators corresponding to the purely quantum mechanical momentum and the generalized momentum that includes minimal length effects is polished. Additionally, the existence of…
The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as a phenomenological modification of Heisenberg's uncertainty relation. We show that this modification is equivalent to a…
The existence of a fundamental zero-point length, $l_0$, a minimal spacetime scale predicted by T-duality in string theory or quantum gravity theories, modifies the entropy associated with the horizon of spacetime. In the cosmological…
The time separation function (or Lorentzian distance function) is a fundamental object used in Lorentzian geometry. For smooth spacetimes it is known to be lower semicontinuous, and in fact, continuous for globally hyperbolic spacetimes.…
Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The…
The possibility of a minimal physical length in quantum gravity is discussed within the asymptotic safety approach. Using a specific mathematical model for length measurements ("COM microscope") it is shown that the spacetimes of Quantum…
In this paper, we clarify a foundational loose end affecting the phenomenological approach to quantum gravity centered around the generalization of Heisenberg uncertainty principle. This misconception stems from a series of recently…
I propose that Physics should be formulated using minimal mathematical structure, beginning with its foundational arena: spacetime. This paper opens with a concise overview of several research directions explored in previous work. Among…
We show that the two-point function \sigma(x,x')=\sqrt{<[\phi(x)-\phi(x')]^{2}>} of a scalar quantum field theory is a metric (i.e., a symmetric positive function satisfying the triangle inequality) on space-time (with imaginary time). It…
Considering that a position measurement can effectively involve a momentum-dependent shift and rescaling of the "true" space-time coordinates, we construct a set of effective space-time coordinates which are naturally non-commutative. They…
This is an extended version of the first part of a forthcoming paper where we will study the local Zeta functions of the minimal spherical series for the symmetric spaces arising as open orbits of the parabolic prehomogeneous spaces of…
The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…
I propose a general class of space-times whose structure is governed by observer-independent scales of both velocity ($c$) and length (Planck length), and I observe that these space-times can naturally host a modification of…
Newtonian gravity arises as the nonrelativistic, static, weak-field limit of some Lorentzian spacetime geometry solving the generally covariant Einstein equations for a given matter field configuration. Spacetime geometry has a local…
A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further…
The purpose of this article is to prove that, under suitable constrains on the electrovacuum spacetime $M$, if $\Sigma\subset M$ is an embedded strictly stable minimal two-sphere which locally maximizes the charged Hawking mass, then there…