Quantum gravity and minimum length

Broad arguments indicate that quantum gravity should have a minimal length scale. In this essay we construct a minimum length model by generalizing the time-position and energy-momentum operators while keeping much of the structure of quantum mechanics and relativity intact: the standard position-momentum commutator, the special relativistic time-position, and energy-momentum relationships all remain the same. Since the time-position and energy-momentum relationships for the ...

The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure which underlies this uncertainty relation.

The relevance of the Planck scale to a theory of quantum gravity has become a worryingly little examined assumption that goes unchallenged in the majority of research in this area. However, in all scientific honesty, the significance of Planck's natural units in a future physical theory of spacetime is only a plausible, yet by no means certain, assumption. The purpose of this article is to clearly separate fact from belief in this connection.

The existence of a fundamental length scale in Nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg uncertainty principle may be expected. Despite the attention given to this possibility in the past decades, there has been no common framework for a systematic investigation of so called generalized uncertainty principles (GUP). In this work we provi...

According to a number of arguments in quantum gravity, both model-dependent and model-independent, Heisenberg's uncertainty principle is modified when approaching the Planck scale. This deformation is attributed to the existence of a minimal length. The ensuing models have found entry into the literature under the term Generalized Uncertainty Principle (GUP). In this work, we discuss several conceptual shortcomings of the underlying framework and critically review recent deve...

The fundamental physical description of the Universe is based on two theories: Quantum Mechanics and General Relativity. Unified theory of Quantum Gravity (QG) is an open problem. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed position-momentum commutator. Relativistic Generali...

The Karolyhazy uncertainty relation is the statement that if a device is used to measure a length $l$, there will be a minimum uncertainty $\delta l$ in the measurement, given by $(\delta l)^3 \sim L_P^2\; l$. This is a consequence of combining the principles of quantum mechanics and general relativity. In this note we show how this relation arises in our approach to quantum gravity, in a bottom-up fashion, from the matrix dynamics of atoms of space-time-matter. We use this r...

We give six arguments that the Planck scale should be viewed as a fundamental minimum or boundary for the classical concept of spacetime, beyond which quantum effects cannot be neglected and the basic nature of spacetime must be reconsidered. The arguments are elementary, heuristic, and plausible, and as much as possible rely on only general principles of quantum theory and gravity theory. The paper is primarily pedagogical, and its main goal is to give physics students, non-...

The notions of minimum geometrical length and minimum length scale are discussed with reference to correlation functions obtained from in-in and in-out amplitudes in quantum field theory. Whereas the in-in propagator for metric perturbations does not admit the former, the in-out Feynman propagator shows the emergence of the latter. A connection between the Feynman propagator of quantum field theories of gravity and the deformation parameter $\delta_0$ of the generalised uncer...

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 $[\hat{X},\hat{P}] := \frac{i\hbar}{ 1 - \beta\hat{P}^2 }$ . We determine the wave function of the Universe $ \psi_{qp}(\xi,t)$, which is solution of the modified Wheeler-DeWitt equation in the representation of the quasi-position space, in the limit where the scale...