[Paper Review] Comment on 'Large-scale non-locality in "doubly special relativity" with an energy-dependent speed of light'

Michele Arzano|ArXiv.org|Sep 17, 2003

Black Holes and Theoretical Physics6 references3 citations

TL;DR

This paper challenges key conclusions from a prior study on doubly special relativity (DSR) with an energy-dependent speed of light, arguing that the reported large-scale non-locality and loss of wave packet coincidence stem from invalid assumptions. It demonstrates that the Fourier transformation formalism used in the original work fails under DSR's non-commutative spacetime and generalized uncertainty principles, invalidating the derived non-local effects and wave packet decoherence claims.

ABSTRACT

We show that some of the recent results reported in gr-qc/0308049 are based on assumptions which are in contrast with general properties of ``Doubly Special Relativity'' and/or with Planck-scale physics models.

Motivation & Objective

• To challenge the validity of large-scale non-locality and wave packet coincidence loss reported in a prior DSR study.
• To identify inconsistencies in the field-theoretic framework used, particularly the application of standard Fourier transforms in non-commutative DSR spacetime.
• To highlight the incompatibility of standard quantum mechanical relations (e.g., p → iħ∂/∂x) with Planck-scale physics and generalized uncertainty principles.
• To argue that operational definitions of velocity and trajectory for Planck-scale particles are physically meaningless due to measurement limitations.
• To clarify the domain of applicability of DSR transformations, restricting them to elementary particles rather than composite systems.

Proposed method

• Analyzes the field-theoretic construction in the original paper, focusing on the use of Fourier transforms to relate space-time and momentum-space fields.
• Identifies that the standard Fourier transform procedure fails in DSR due to non-commutative spacetime structures, such as κ-Minkowski space, requiring normal ordering prescriptions.
• Applies the concept of non-trivial integration measures in non-commutative geometry, showing that standard measures violate invariance under DSR symmetries.
• Demonstrates that the DSR transformation's non-linear structure necessitates a modified integration measure, invalidating the equality in equation (10) of the original paper.
• Uses the generalized uncertainty principle (GUP) to argue that standard p → iħ∂/∂x relations break down at Planck scales.
• Argues that the operational definition of velocity via macroscopic trajectories is infeasible for Planck-scale particles due to measurement constraints and non-local interactions.

Experimental results

Research questions

• RQ1 Can the standard Fourier transform formalism be consistently applied in doubly special relativity (DSR) with non-commutative spacetime?
• RQ2 Does the energy-dependent speed of light in DSR theories lead to large-scale non-locality as claimed in the original study?
• RQ3 Are the conclusions about wave packet coincidence loss valid under the constraints of non-commutative spacetime and generalized uncertainty principles?
• RQ4 Can macroscopic trajectories of Planck-scale particles be operationally defined in DSR frameworks?
• RQ5 What is the correct domain of applicability of DSR transformations—elementary particles or composite systems?

Key findings

• The standard Fourier transform procedure used in the original paper is invalid in DSR due to non-commutative spacetime, requiring normal ordering and altering integration measures.
• Equation (10) in the original paper, which claims wave packet coincidence loss, is invalid because it ignores non-trivial integration measures and normal ordering in non-commutative geometry.
• The generalized uncertainty principle (GUP) invalidates the standard quantum mechanical relation p → iħ∂/∂x at Planck scales, undermining the field-theoretic model.
• The operational definition of velocity via macroscopic trajectories is physically meaningless for Planck-scale particles due to measurement limitations and non-local interactions.
• DSR transformations are only applicable to elementary particles with energies bounded by the Planck scale, not to composite systems.
• The claim of large-scale non-locality from energy-dependent light speed is unfounded due to the incompatibility of trajectory-based definitions with Planck-scale physics.