The theory of special relativity applies only to inertial observers, who are related through a relative speed along some straight line direction. [As soon as there is some acceleration between the observers, either as a change in speed or a change in direction, the descriptions from special relativity are no longer valid.] Or putting it in a slightly different way, special relativity says that no physical experiment can be used to distinguish between one state of uniform motion and another. Is it possible to devise a more general theory where the form of physics is the same for all states of free motion, inertial or accelerated?

In considering this, one of the other facts found by Galileo and Newton comes to mind. The concept of mass is introduced by each of them in two forms. On the one hand, we are aware of mass by virtue of weight - the force that gravity exerts on a massive object. This is known as gravitational mass. On the other hand, we know of mass through the force we must exert to get an object to move and accelerate independent of gravity. That is inertial mass. What Galileo and Newton realized is that gravitational mass and inertial mass are exactly equal. You might call this the Galilean Principle of Equivalence. It is just that neither one had any explanation for it.

For Einstein, though, the equality between inertial and gravitational mass was not accidental. It pointed to a way of extending the Principle of Relativity to noninertial systems.