My laws make more precise Carlo Rovelli’s two principles: time does not exist, space does not exist. He argues that the universe is a network of relations and not a game played out on some invisible arena of absolute space and time such as Newton postulated. I agree but believe it is important to formulate precisely the manner in which the universe is relational.

Barbour’s First Law

The change of a physical field at a given point is not measured by time but by the changes of all the other physical fields at the same point. To determine a rate of change, one does not divide an infinitesimal change by an infinitesimal time interval but by the weighted average of all the other changes at the same point. This ensures that an invisible time can play no role in the dynamics of the universe.

Barbour’s Second Law

Geometry is founded on congruence, dynamics on minimisation of incongruence.

This requires amplification. Suppose just three particles in space. Newton defined their motions relative to absolute space. In relational dynamics, this is not allowed. Instead, the motions (changes) between two instantaneous states of the three particles are completely determined by the intrinsic changes of the triangles that they form. Real change will happen when a triangle becomes incongruent with itself. To determine the intrinsic change between one triangle and another ever so slightly incongruent with it, move one relative to each other until the position of best matching, in which they coincide more closely than in any other possible relative positioning, is achieved. The corresponding displacements (changes) determined by this minimisation of incongruence are the true physical displacements. The notion of best matching can be applied universally to both particles and fields.

Barbour’s Third Law

Space is Riemannian.

Spelled out in the appropriate mathematical detail, these three laws seem to explain the structure of all currently known physical fields as well as the existence of the universal light cone of Einstein’s special relativity and gauge theory.