The Principle of Relativity · Albert Einstein
I.—KINEMATICAL PORTION.
1. The laws according to which the nature of physical systems alter are independent of the manner in which these changes are referred to two co-ordinate systems which have a uniform translators motion relative to each other. 2. Every ray of light moves in the “stationary co-ordinate system” with the same velocity _c_, the velocity being independent of the condition whether this ray of light is emitted by a body at rest or in motion.[6] Therefore velocity = Path of Light/Interval of time, where, by ‘interval of time’ we mean time as defined in §1. Let us have a rigid rod at rest; this has a length _l_, when measured by a measuring rod at rest; we suppose that the axis of the rod is laid along the X-axis of the system at rest, and then a uniform velocity _v_, parallel to the axis of X, is imparted to it. Let us now enquire about the length of the moving rod; this can be obtained by either of these operations.— (_a_) The observer provided with the measuring rod moves along with the rod to be measured, and measures by direct superposition the length of the rod:—just as if the observer, the measuring rod, and the rod to be measured were at rest. (_b_) 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.”
We suppose that the space is measured by the stationary measuring rod placed in the stationary system, as well as by the moving measuring rod placed in the moving system, and we thus obtain the co-ordinates (_x_, _y_, _z_) for the stationary system, and (ξ, η, ζ) for the moving system. Let the time _t_ be determined for each point of the stationary system (which are provided with clocks) by means of the clocks which are placed in the stationary system, with the help of light-signals as described in § 1. Let also the time τ of the moving system be determined for each point of the moving system (in which there are clocks which are at rest relative to the moving system), by means of the method of light signals between these points (in which there are clocks) in the manner described in § 1. To every value of (_x_, _y_, _z_, _t_) which fully determines the position and time of an event in the stationary system, there correspond a system of values (ξ, η, ζ, τ); now the problem is to find out the system of equations connecting these magnitudes. Primarily it is clear that on account of the property of homogeneity which we ascribe to time and space, the equations must be linear. If we put _x′_ = _x_ - _vt_, then it is clear that at a point relatively at rest in the system _k_, we have a system of values (_x′_ _y_ _z_) which are independent of time. Now let us find out τ as a function of (_x′_, _y_, _z_, _t_). For this purpose we have to express in equations the fact that τ is not other than the time given by the clocks which are at rest in the system _k_ which must be made synchronous in the manner described in § 1.
Text from Project Gutenberg, public domain in the United States.