"That sounds very hopeful," I remarked, "for then it should also be possible to describe very briefly the theory of relativity."
"Let us rather say its essentials—the heart of the matter. Well, then, get your Kirchhoff page ready. We shall see whether we can set out on it the special theory of relativity."
The totality of our experience compels us to assume that light travels with a constant velocity in empty space. Likewise, our whole experience in optics compels us to recognize that all inertial systems are equivalent; these are systems that are produced from an allowable one by means of a uniform translation. An allowable system is one in which Galilei's and Newton's Law of Inertia holds. (This law states that a moving body that is left to itself retains its direction and velocity permanently.)
Now, the law of the constancy of light propagation seems to conflict with the classical principle of relativity, according to which the velocity of a ray of light assumes different values in the moving system according to the direction of the ray.
This apparent incompatibility arises from the following unproved assumptions:
(a) If two events are simultaneous with regard to one inertial system, they are also simultaneous with regard to any other inertial system.
(b) The length of a measuring-rod, the shape and size of a rigid body, and the rate of a clock are independent of their motion with respect to the system of reference used, provided this motion is rectilinear and non-rotational.
These assumptions must be discarded if this disagreement is to be eliminated. If we substitute for them the assumption that all inertial systems are equivalent and that the velocity of light in vacuo is constant, we get:
(1) That the dimensions of bodies and the rate of clocks have a functional relation to the motion.
(2) That the equations of motion of Newton require to be modified; this modification leads to results that, for rapid motions, differ appreciably from those of Newton.