Relative Locality

§1 · The claim, in one sentence

The shared arena of physics is phase space, and each observer builds a spacetime from it, so distant observers can disagree about whether an interaction happened at a single point.

§2 · Why it might be true

The family stance

Spacetime keeps a relativity principle down to the Planck scale, but its rules are deformed there. All inertial observers agree on the speed of light and on a Planck-scale length or energy, and none of them is preferred. What that Planck scale means mathematically varies between formulations, and none is established by experiment. In a later geometric version, relative locality, the arena every observer shares is phase space. Each observer builds a spacetime from it, and distant observers can disagree about whether an interaction happened at one point.

§2.5 · Evidence

• The framework turns apparent non-locality for distant observers into an expected feature, which gives DSR's non-locality problem a principled reading.
• Amelino-Camelia, Matassa, Mercati and Rosati showed in 2011 that a worldline analysis with deformed symmetries avoids some previously conjectured pathologies.
• The 2011 paper identifies a natural set of physical hypotheses that singles out momentum spaces with a metric-compatible connection and constant curvature, narrowing the options.

§3 · What you'd need to test it

• Momentum space has a geometry set by the Planck mass, which can modify how energy and momentum are defined and conserved
• These deformations of the conservation laws are in principle measurable by appropriate experiments
• An interaction that is local for a nearby observer appears non-local to a distant one, by an amount tied to the energies involved, while locality is kept in phase space
• Astrophysical observations could measure the geometry of momentum space

§4 · Where it breaks

• Giving up absolutely coincident events is a large conceptual price. Hossenfelder argued in 2010 that models with an energy-dependent speed of light produce non-locality that conflicts with known particle physics, and later work tried to answer her.
• Curvature, torsion and non-metricity are free choices, so the geometry of momentum space rests on extra physical hypotheses instead of a derivation.
• The principle is formulated for a regime in which Planck's constant and Newton's constant are neglected, so its link to a full quantum theory of gravity is still missing.