SciamaRelation

The Sciama relation is a concept in theoretical physics that attempts to provide a quantitative formulation of Mach's Principle. Mach's Principle, broadly speaking, suggests that the inertia of a body is somehow related to the distribution of matter in the universe. It proposes that local physical phenomena, like the inertia of objects, are influenced by the large-scale structure of the universe.

In this context, Dennis Sciama proposed a specific relation to express this idea. He suggested that the inertial forces experienced by a body are related to the distribution of distant matter in the universe through a scalar potential. The scalar potential in this case represents the gravitational potential contributed by all the matter in the universe.

According to Sciama's relation, the acceleration $\vec{a}$ of a body in an inertial frame is given by the negative gradient of the scalar potential $\Phi$, i.e.

$$ \vec{a} = -\nabla \Phi $$

This scalar potential $\Phi$ is determined by the distribution of matter throughout the universe. Sciama's idea was an attempt to formalize the concept of Mach's principle in the language of classical field theory, connecting the local inertial properties of a body to the global properties of the universe.

However, it's important to note that Sciama's formulation, while influential, is not universally accepted or validated by empirical evidence. It remains a theoretical construct that has inspired further research in gravitation and cosmology, particularly in the context of general relativity and alternative theories of gravity.