Albert Einstein

“ If a material point be at rest in this system, then its position in this system can be found out by a measuring rod, and can be expressed by the methods of Euclidean Geometry, or in Cartesian co-ordinates.
If we wish to describe the motion of a material point, the values of its coordinates must be expressed as functions of time. It is always to be borne in mind that such a mathematical definition has a physical sense, only when we have a clear notion of what is meant by time. ”

“ The introduction of a "Lightäther" will be proved to be superfluous, for according to the conceptions which will be developed, we shall introduce neither a space absolutely at rest, and endowed with special properties, nor shall we associate a velocity-vector with a point in which electro-magnetic processes take place.
3. Like every other theory in electrodynamics, the theory is based on the kinematics of rigid bodies; in the enunciation of every theory, we have to do with relations between rigid bodies (co-ordinate system) , clocks, and electromagnetic processes. ”

“ The observer finds out, by means of clocks placed in a system at rest (the clocks being synchronous as defined in § 1) , the points of this system where the ends of the rod to be measured occur at a particular time t. The distance between these two points, measured by the previously used measuring rod, this time it being at rest, is a length, which we may call the "length of the rod."
According to the Principle of Relativity, the length found out by the operation a) , which we may call "the length of the rod in the moving system" is equal to the length l of the rod in the stationary system. ”

“ If the electron moves from the origin of co-ordinates of the system K with the initial velocity 0 steadily along the X-axis under the action of an electromotive force X, then it is clear that the energy drawn from the electrostatic field has the value . Since the electron is only slowly accelerated, and in consequence, no energy is given out in the form of radiation, therefore the energy drawn from the electro-static field may be put equal to the energy W of motion. ”

“ We see that in the theory developed the electromagnetic force plays the part of an auxiliary concept, which owes its introduction in theory to the circumstance that the electric and magnetic forces possess no existence independent of the nature of motion of the co-ordinate system. ”

“ For v = c, all moving bodies, when considered from a stationary system shrink into planes. For a velocity larger than the velocity of light, our propositions become meaningless ; in our theory c plays the part of infinite velocity. ”

“ Transformation of the Maxwell-Hertz Equations. Let us start from the equations :—
where , denotes times the density of electricity, and are the velocity-components of electricity. If we now suppose that the electrical masses are bound unchangeably to small, rigid bodies (Ions, electrons) , then these equations form the electromagnetic basis of Lorentz's electrodynamics and optics for moving bodies. ”

“ All problems of optics of moving bodies can be solved after the method used here. The essential point is, that the electric and magnetic forces of light, which are influenced by a moving body, should be transformed to a system of co-ordinates which is stationary relative to the body. In this way, every problem of the optics of moving bodies would be reduced to a series of problems of the optics of stationary bodies. ”

“ If in addition to the systems K, and k, we introduce the system k', of which the initial point moves parallel to the ξ-axis with velocity w, then between the magnitudes, x, y, z, t and the corresponding magnitudes of k', we obtain a system of equations, which differ from the equations in §3, only in the respect that in place of v, we shall have to write,
We see that such a parallel transformation forms a group. ”

“ We have to take into consideration the fact that those of our conceptions, in which time plays a part, are always conceptions of synchronism. For example, we say that a train arrives here at 7 o'clock ”