[Paper Review] Remarks on DSR and Gravity

Franz Hinterleitner|arXiv (Cornell University)|Jun 4, 2007

Noncommutative and Quantum Gravity Theories9 references4 citations

TL;DR

This paper investigates the relationship between Doubly Special Relativity (DSR) and classical gravity by comparing DSR corrections to Newtonian gravity and Generalized Uncertainty Principle (GUP) effects. It finds that DSR's low-energy limit must be quadratic in momentum over Planck mass to reproduce Newtonian gravity, while GUP induces an effective repulsion, contrasting with DSR's attraction and aligning with quantum gravity effects like those in loop quantum cosmology.

ABSTRACT

Modifications of Special Relativity by the introduction of an invariant energy and/or momentum level (so-called Doubly Special Relativity theories, DSR) or by an energy-momentum dependence of the Planck constant (Generalized Uncertainty Principle, GUP) are compared with classical gravitational effects in an interaction processes. For the low energy limit of the usual formulations of DSR to be equivalent with Newtonian gravity, a restrictive condition is found. GUP yields an effective repulsion, in analogy to the gravitational repulsion in loop quantum cosmology.

Motivation & Objective

• To assess whether Doubly Special Relativity (DSR) can reproduce classical gravitational effects in the low-energy limit.
• To examine the physical consistency of DSR with Newtonian gravity by analyzing energy-momentum conservation and reaction thresholds.
• To compare DSR with the Generalized Uncertainty Principle (GUP), particularly regarding their effective gravitational behavior.
• To determine under what conditions DSR corrections align with the correspondence principle, i.e., recover classical gravity at low energies.
• To explore whether GUP, unlike DSR, describes intrinsic quantum gravity effects independent of classical gravity.

Proposed method

• Uses momentum space formalism to analyze DSR, distinguishing physical energy-momentum (E, p) from pseudo-variables (ε, π) related by nonlinear transformations.
• Applies the correspondence principle to require DSR’s low-energy limit to match Newtonian gravity, leading to a constraint on the form of DSR corrections.
• Derives an effective scattering angle correction from DSR using a perturbative expansion in p/m_P, assuming a power-law dependence on momentum.
• Compares DSR to GUP by modeling GUP via energy-momentum-dependent Planck constant ̃ℏ(E,p), leading to modified de Broglie relations and effective forces.
• Analyzes the sign of quantum corrections: DSR yields attraction, GUP yields repulsion, due to different roles of physical vs. pseudo-variables.
• Considers the implications of reversed variable roles (E,p) ↔ (ε,π) in DSR, showing that threshold anomalies would reverse sign but remain small.

Experimental results

Research questions

• RQ1 Under what conditions does the low-energy limit of DSR reproduce Newtonian gravity?
• RQ2 How do DSR corrections compare to classical gravitational effects in a scattering process?
• RQ3 What is the nature of the effective force generated by the Generalized Uncertainty Principle (GUP)?
• RQ4 Why does GUP produce a repulsive effect while DSR produces an attractive one, despite both modifying quantum gravity at the Planck scale?
• RQ5 Can the DSR framework be reconciled with classical gravity if the correction terms are not quadratic in p/m_P?

Key findings

• For DSR to reproduce Newtonian gravity in the low-energy limit, its corrections must be quadratic in p/m_P, a restrictive condition derived from the correspondence principle.
• GUP leads to an effective repulsive force, in contrast to DSR’s effective attraction, due to the lower bounds it imposes on space and time intervals.
• The repulsive nature of GUP is analogous to gravitational repulsion in loop quantum cosmology, suggesting GUP describes intrinsic quantum gravity effects.
• In contrast to DSR, which may conflict with classical gravity, GUP counteracts Newtonian gravity and thus qualifies as a description of pure quantum gravity effects.
• If the roles of physical and pseudo-variables were interchanged in DSR, the sign of threshold anomalies would reverse, but the magnitude would remain small.
• The lowest-order correction in GUP must be of higher than quadratic order to avoid conflict with classical gravity, unlike in DSR.