L E C T U R E A T P O L Y T E C H N I C O F R I O D E J A N E I R O 1 0 0 3 The theory of relativity considers the world of physics as a continuum of four dimen- sions, where space and time are connected in an indissoluble manner. By contrast, in pre-relativity science, events were arranged objectively in time, indepen- dent of a notion of space. In classic science, geometry—Euclidean geometry—was studied before physics, independent of physics and as a real basis for the same. The systems of reference furnished by geometry and indispensable to the description of any physical phenomenon are implicitly considered solid bodies. In the case of two dimensions, for example, Euclidean geometry presupposes, from the physicist’s point of view, the possibility of forming a mesh with regular, equal juxtapositions. If this construction is not possible, the geometry will not be Euclidean. In the restricted theory of relativity, geometry is still Euclidean, and time is defined with- in the geometry, taking into consideration the principle of the constancy of the speed of light, thus allowing the synchronization of all clocks in one system, whose time is conse- quently defined. Moving, however, from one system to another, both inertial, one can verify the conse- quences already noted in the contraction of rods and the slowing of time in the direction of the movement, when observed from the first reference system. Seen thus, as explained, there is no privileged inertial system of reference, all being equal, as expressed by the laws of nature. Would the independence of systems of reference be peculiar only to inertial systems? Would all states of motion not be equal from the physicist’s point of view? The principle of inertia, as formulated in classical science, prevents the extension of the already demonstrated reference systems to inertial systems. In classical mechanics, inertial mass is defined, that is, mass is the quantity intrinsic to the material that manifests as its resistance to acceleration. It is an inert mass. But mass can also be defined by its effect in the gravitational field. It is a heavy mass. The constant acceleration for all bodies in motion under the action of a gravitational field shows the equality of two masses, factually registered, but not interpreted by classical me- chanics. There must be, therefore, a profound relationship between gravitation and inertia. A possible explanation for a simple case may be gleaned from the next example: We suppose an isolated mass, at rest, or endowed with rectilinear and uniform motion in relation to the inertial system. We will study its movement, as if judged from another system—we say a box inside which there is an observer—endowed with accelerated motion in relation to the first inertial reference. The movement will be accelerated relative to the box’s acceleration. We suppose now that the box is at rest, and that the material point will be subject to the action of the field of gravity in the opposite direction to the accelerated motion referred to above.