By A. EINSTEIN June 30, 1905
It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on therelative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric ﬁeld with a certain deﬁnite energy, producing a current at the places where parts of theconductor are situated. But if the magnet is stationary and the conductor in motion, no electric ﬁeld arises in the neighbourhood of the magnet. In the conductor, however, we ﬁnd an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as thoseproduced by the electric forces in the former case. Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the ﬁrst order of smallquantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.1 We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light isalways propagated in empty space with a deﬁnite velocity c which is independent of the state of motion of the emitting body. These two postulates suﬃce for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies. The introduction of a “luminiferous ether” will prove to be superﬂuous inasmuch as the view here to bedeveloped will not require an “absolutely stationary space” provided with special properties, nor
preceding memoir by Lorentz was not at this time known to the author.
assign a velocity-vector to a point of the empty space in which electromagnetic processes take place. The theory to be developed is based—like all electrodynamics—on the kinematics of the rigid body, since theassertions of any such theory have to do with the relationships between rigid bodies (systems of co-ordinates), clocks, and electromagnetic processes. Insuﬃcient consideration of this circumstance lies at the root of the diﬃculties which the electrodynamics of moving bodies at present encounters.
I. KINEMATICAL PART
§ 1. Deﬁnition of Simultaneity
Let us take a system of co-ordinates in which theequations of Newtonian mechanics hold good.2 In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the “stationary system.” If a material point is at rest relatively to this system of co-ordinates, its position can be deﬁned relatively thereto by the employment of rigid standards ofmeasurement and the methods of Euclidean geometry, and can be expressed in Cartesian co-ordinates. If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by “time.” We have to take into...