[Paper Review] A note on DSR

Carlo Rovelli|arXiv (Cornell University)|Aug 29, 2008

Noncommutative and Quantum Gravity Theories3 references12 citations

TL;DR

This paper proposes that Deformed Special Relativity (DSR) arises from a physical effect—gravitational time dilation due to a massive particle's potential well—even in regimes where gravity and quantum mechanics are negligible. By analyzing this self-interaction effect, the author derives the Girelli-Livine DSR formalism, providing a physical basis for the 5D spacetime structure and a concrete derivation of DSR from classical gravitational dynamics.

ABSTRACT

I study the physical meaning of Deformed, or Doubly, Special Relativity (DSR). I argue that DSR could be physically relevant in a certain large-distance limit. I consider a concrete physical effect: the gravitational slowing down of time due to the gravitational potential well of a massive-particle, and its effect on the dynamics of the particle itself. I argue that this physical effect can survive in a limit in which gravitation and quantum mechanics can be disregarded, and that taking it into account leads directy to the Girelli-Livine DSR formalism. This provides a physical interpretation to the corresponding 5d spacetime, and a concrete physical derivation of DSR.

Motivation & Objective

• To explore whether DSR can have physical relevance beyond formal symmetry considerations.
• To identify a classical physical mechanism that naturally leads to DSR in a regime where quantum gravity effects are negligible.
• To provide a physical derivation of the Girelli-Livine DSR formalism through a self-consistent gravitational effect.
• To interpret the 5D spacetime structure in DSR as arising from a physical, rather than purely mathematical, origin.

Proposed method

• Analyzing the gravitational potential well of a massive particle and its effect on the particle's own time evolution.
• Focusing on the self-induced gravitational time dilation as a key physical effect in the large-distance limit.
• Applying the formalism of relativistic dynamics to a particle interacting with its own gravitational field.
• Deriving the DSR structure by requiring consistency of the particle's dynamics under this self-gravitational effect.
• Connecting the resulting symmetry structure to the Girelli-Livine DSR model via geometric and algebraic analysis.

Experimental results

Research questions

• RQ1 Can DSR emerge from a classical gravitational effect without requiring quantum gravity?
• RQ2 What physical mechanism underlies the 5D spacetime structure in DSR?
• RQ3 Does self-gravitational time dilation persist in a regime where gravity and quantum effects are negligible?
• RQ4 How does the self-interaction of a massive particle lead to deformed Lorentz symmetry?

Key findings

• The gravitational time dilation due to a particle's own potential well survives in the large-distance limit where gravity and quantum mechanics are negligible.
• This self-interaction effect naturally leads to the Girelli-Livine DSR formalism through consistency of the particle's dynamics.
• The 5D spacetime structure in DSR is physically interpreted as arising from the self-gravitational potential of the particle.
• The derivation provides a concrete physical origin for DSR, moving beyond abstract symmetry postulates.