Translation
On the Electrodynamics of Moving Bodies
Zur Elektrodynamik bewegter Körper
I. Kinematical Part.
§ 1. Definition of Simultaneity.
Let there be given a coordinate system in which Newton’s mechanical equations hold. To distinguish it in words from coordinate systems to be introduced later, and to make the idea precise, we call this coordinate system the “stationary system”.
If a material point is at rest relative to this coordinate system, its position relative to the latter can be determined by rigid measuring rods, using the methods of Euclidean geometry, and expressed in Cartesian coordinates.
If we wish to describe the motion of a material point, we give the values of its coordinates as functions of time. Now it must be borne well in mind that a mathematical description of this kind has a physical meaning only when one has first become clear about what is to be understood here by “time”. We have to take into account that all our judgements in which time plays a part are always judgements about simultaneous events. If, for example, I say: “That train arrives here at 7 o’clock,” this means roughly: “The pointing of the small hand of my clock to 7 and the arrival of the train are simultaneous events.”[1)]
It might seem that all the difficulties concerning the definition of “time” could be overcome by my putting “the position of the small hand of my clock” in place of “time”. Such a definition does indeed suffice when it is a matter of defining a time exclusively for the place at which the clock is located; but the definition no longer suffices as soon as it is a matter of connecting with one another, with respect to time, series of events that occur at different places, or — what amounts to the same thing — of evaluating, with respect to time, events that occur at places remote from the clock.
We could, it is true, content ourselves with evaluating events with respect to time by having an observer, located together with the clock at the origin of coordinates, assign the corresponding position of the clock’s hands to each light signal that gives evidence of an event to be evaluated and reaches him through empty space. But such an assignment has the drawback that it is not independent of the standpoint of the observer provided with the clock, as we know from experience. We arrive at a far more practical stipulation through the following consideration.
If there is a clock at the point of space, an observer located at can evaluate, with respect to time, the events in the immediate vicinity of by finding the positions of the clock’s hands that are simultaneous with these events. If there is also a clock at the point of space — we wish to add, “a clock of exactly the same constitution as the one located at ” — then an evaluation, with respect to time, of the events in the immediate vicinity of by an observer located at is also possible. But without a further stipulation it is not possible to compare, with respect to time, an event at with an event at ; so far we have defined only an “-time” and a “-time”, but no “time” common to and . The latter time can now be defined by stipulating by definition that the “time” which light requires to travel from to is equal to the “time” which it requires to travel from to . For let a ray of light start at the “-time” from towards , let it be reflected at the “-time” at towards , and let it arrive back at the “-time” at . The two clocks run synchronously by definition if Time in the stationary systemTime in the stationary systemTime in the stationary systemExplain this equation
We assume that this definition of synchronism is possible without contradiction, and indeed for arbitrarily many points, and that therefore the following relations hold in general:
1. If the clock at runs synchronously with the clock at , then the clock at runs synchronously with the clock at .
2. If the clock at runs synchronously both with the clock at and with the clock at , then the clocks at and also run synchronously relative to each other.
In this way, with the help of certain (imagined) physical experiences, we have established what is to be understood by synchronously running clocks at rest that are located at different places, and have thereby evidently obtained a definition of “simultaneous” and “time”. The “time” of an event is the reading, simultaneous with the event, of a clock at rest located at the place of the event, which runs synchronously with a specified clock at rest, and indeed with the same clock for all determinations of time.
In accordance with experience we further stipulate that the quantity Distance between two eventsTime in the stationary systemTime in the stationary systemSpeed of lightExplain this equation is a universal constant (the velocity of light in empty space).
It is essential that we have defined time by means of clocks at rest in the stationary system; because of this association with the stationary system we call the time just defined “the time of the stationary system”.
II. Electrodynamical Part.
In conclusion I remark that in working on the problem treated here my friend and colleague M. Besso stood loyally by my side, and that I owe him several valuable suggestions.
Bern, June 1905.
(Received 30 June 1905.)