Principle of relative locality

Abstract

We propose a deepening of the relativity principle according to which the invariant arena for nonquantum 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 energy-momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of energy-momentum space geometry, such as its curvature, torsion and nonmetricity, 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 energy-momentum space with a metric compatible connection and constant curvature

The Extended Relativity Theory in Clifford Phase Spaces and Modifications of Gravity at the Planck/Hubble Scales

“…This type of limit in (2.12) has also been studied by [15] pertaining to the notion of "relativity of locality" in curved phase space.…”

Five dimensional formulation of a deformed special relativity

“…In the context of Relative Locality, see Refs. [4] and [5], where the momentum space is supposed to be curved, the value of the mass of a particle with momentum p is defined as the value of the geodesical distance from the origin of the momentum space to the point, over the momentum space itself, identified by the coordinates of p. We want now to take this intuition and move it into the context of this paper.…”

“…(18) must always hold, so, combining it with Eq. (26), we deduce that dχ 4 dλ must also be a constant during a free motion, i.e.,…”

Physics with Curved Momentum Space

“…Indeed virtually all physical measurements can be reduced to measurements of energies and momenta of incoming particles of various kinds (probes) performed by measuring devices located at the origin of a coordinate system, and therefore we deal with momentum space, not spacetime, measurements. It is only by observing the incoming probes that we can infer the properties of distant events [8,9]. Therefore, momentum space measurements should be seen as physically more fundamental than space-time measurements.…”

“…However, one can imagine a regime of quantum gravity, in which the Planck length is negligible, while the Planck mass remains finite. This formally means that both and G go to zero, so that both quantum and local gravitational effects become negligible, while their ratio remains finite [8,9,11]. In more physical terms this regime is realized if the characteristic length scales relevant for the processes of interest are much larger than l Pl , so that the spacetime quantum foamy effects can be safely neglected, while the characteristic energies are comparable with the Planck energy.…”