Machian Dynamics
Barbour also researches Machian physics, a related field. The Machian approach requires physics to be constructed from directly observable quantities. In standard analytical dynamics a system's future evolution can be determined from a state consisting of particle positions and momenta (or instantaneous velocities). The Machian approach eschews the momenta/instantaneous velocities, which are not directly observable, and so needs more than one "snapshot" consisting of positions only. This relates to the idea of snapshots, or "Nows" in Barbour's thinking on time.
Along with physicist Bruno Bertotti, Barbour developed a technique called "best matching" for deriving gravitational equations directly from astronomical measurements of objects’ spatial relations with each other. Published in 1982, the method describes gravitational effects as accurately as Einstein's general relativity, but without the need for a "background" grid of spacetime. According to physicist David Wiltshire at the University of Canterbury in New Zealand, such a truly Machian or relational approach could explain the appearance of an accelerated expansion of the universe without invoking a causative agent such as dark energy.
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