The principle of relative locality (1101.0931v2)

Abstract: We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.

• The paper introduces the principle of relative locality, challenging the conventional view of an absolute spacetime framework.
• It develops a model where momentum space geometry—with curvature and torsion—reshapes energy-momentum conservation and particle interactions.
• The work outlines experimental implications, suggesting that observable quantum gravity effects may emerge from the dynamic structure of phase space.

The Principle of Relative Locality: A New Framework for Quantum Gravity

The paper "The Principle of Relative Locality" by Amelino-Camelia, Freidel, Kowalski-Glikman, and Smolin proposes a novel approach to understanding the nature of locality within the framework of quantum gravity. The authors argue that the traditional conceptualization of an invariant spacetime may be an approximation that needs revision. To address this, they introduce the principle of relative locality, which postulates that all non-quantum physics occurs fundamentally in phase space rather than spacetime. This shift from spacetime to phase space as the invariant descriptive arena introduces intriguing implications, especially concerning the interactions and propagation of particles.

Key Concepts and Theoretical Insights

The primary assertion of the paper is that absolute locality, a cornerstone of classical and modern physics, is emergent from the assumption of a linear momentum space. The authors propose that momentum space, rather than spacetime, should be perceived as the fundamental geometric structure. This claim challenges the traditional view by de-emphasizing spacetime's role in formulating physical laws at non-quantum levels. The replacement of absolute locality with relative locality is seen as a deformation analogous to how special relativity transforms the conception of absolute simultaneity via velocity addition.

The paper outlines a framework where different observers may construct different spacetime projections based on their reference points in phase space. In this view, momentum space's geometry — particularly its curvature, torsion, and non-metricity — impacts the deformation of the conservation laws of energy and momentum, all of which are experimentally observable.

Several key principles are introduced to constrain this new theoretical model:

1. The correspondence principle demands agreement with special relativity at low energy scales, asserting that modifications become significant only near a critical energy scale.
2. The weak dual equivalence principle stipulates a universal algebra of momentum composition across different particle species.
3. A stronger equivalence principle equates rest mass energy with generalized inertial mass, providing a relation between the metric and affine connection on momentum space.
4. Maximal symmetry, ensuring momentum space is homogeneous and isotropic, limits the potential deformations.

These principles lead to a very constrained set of geometrical configurations for the momentum space, suggesting models with constant curvature, akin to de Sitter or anti-de Sitter spaces.

Implications and Future Directions

The introduction of relative locality has profound implications. It implies that locality is no longer an absolute feature of the universe but instead relies on the observer's position within momentum space. This redefinition suggests a new kind of non-commutativity and non-associativity in the composition of energy-momentum, offering novel experimental predictions. For example, atomic transitions and Thomas precession-like phenomena could serve as tests for momentum space's curvature.

By positing that the operational framework of physics naturally emerges from phase space rather than spacetime, this work calls for re-examining how fundamental interactions are perceived. It also encourages a closer scrutinity of the assumption that distant observers share a consensus spacetime framework. The implications extend to potential phenomenological models, connecting with fields like deformed special relativity (DSR) and suggesting new routes to explore quantum gravity.

The paper sets the stage for experimental physics to test the relative locality principle, envisioning precise measurements of phase space geometry. Such experiments risk unveiling new physics beyond the reach of current quantum field theories. This paradigm shift underscores the need to further probe quantum gravitational effects and remain open to revisiting foundational concepts in our understanding of the universe.

Conclusion

While ambitious, the principle of relative locality offers an innovative perspective about the universe that challenges entrenched notions of absolute locality. The potential for experimental investigation into the geometry of momentum space opens exciting avenues for verifying these theoretical predictions. This work marks a step toward reconciling quantum mechanics and general relativity, potentially heralding a new understanding of fundamental physics.