Galileo vs. Aristotle, Principles of Equivalence and the Gravitational Acceleration of Atoms according to General Relativity

We derive the gravitational acceleration of atoms according to general relativity. Our results show that elements differ in the gravitational acceleration they experience, which means that the principles of equivalence are not valid for atoms. Bulk matter consists of atoms. Therefore, bulk matter also violates the principles of equivalence. The primary cause of the violation is the gravitational effect of the electric field energy of the charged particles that constitute atoms. A secondary cause is the gravitational field energy associated with each atom. However, the influence of the electric field energy on gravitational acceleration is very small for uranium atoms, which have one of the largest values among the natural elements found on Earth. It is only −3.4× 10 −23 g N , where g N is the Newtonian acceleration of gravity. This value is orders of magnitude smaller than current experimental precision.