Lecture delivered to the Nordic Assembly of Naturalists at Gothenburg,[1]July 11, 1923.
If we consider that part of the theory of relativity which may nowadaysin a sense be regarded as bona fide scientific knowledge, we note twoaspects which have a major bearing on this theory. The whole developmentof the theory turns on the question of whether there are physicallypreferred states of motion in Nature (physical relativity problem).Also, concepts and distinctions are only admissible to the extent thatobservable facts can be assigned to them without ambiguity (stipulationthat concepts and distinctions should have meaning). This postulate,pertaining to epistemology, proves to be of fundamental importance.
These two aspects become clear when applied to a special case, e.g. toclassical mechanics. Firstly we see that at any point filled with matterthere exists a preferred state of motion, namely that of the substanceat the point considered. Our problem starts however with the questionwhether physically preferred states of motion exist in reference toextensiveregions. From the viewpoint of classical mechanics theanswer is in the affirmative; the physically preferred states of motionfrom the viewpoint of mechanics are those of the inertial frames.
This assertion, in common with the basis of the whole of mechanics as itgenerally used to be described before the relativity theory, far frommeets the above "stipulation of meaning". Motion can only be conceivedas the relative motion of bodies. In mechanics, motion relative to thesystem of coordinates is implied when merely motion is referred to.Nevertheless this interpretation does not comply with the "stipulationof meaning" if the coordinate system is considered as something purelyimaginary. If we turn our attention to experimental physics we see thatthere the coordinate system is invariably represented by a "practicallyrigid" body. Furthermore it is assumed that such rigid bodies can bepositioned in rest relative to one another in common with the bodies ofEuclidian geometry. Insofar as we may think of the rigid measuring bodyas existing as an object which can be experienced, the "system ofcoordinates" concept as well as the concept of the motion of matterrelative thereto can be accepted in the sense of the "stipulation ofmeaning". At the same time Euclidian geometry, by this conception, hasbeen adapted to the requirements of the physics of the "stipulation ofmeaning". The question whether Euclidian geometry is valid becomesphysically significant; its validity is assumed in classical physics andalso later in the special theory of relativity.
In classical mechanics the inertial frame and time are best definedtogether by a suitable formulation of the law of inertia: It is possibleto fix the time and assign a state of motion to the system ofcoordinates (inertial frame) such that, with reference to the latter,force-free material points undergo no acceleration; furthermore it isassumed that this time can be measured without disagreement by identicalclocks (systems which run down periodically) in any arbitrary state ofmotion. There are then an infinite number of inertial frames which arein uniform translational motion relative to each other, and hence thereis also an infinite number of mutually equivalent, physically preferredstates of motion. Time is absolute, i.e. independent of the choice ofthe particular inertial frame; it is defined by more characteristicsthan logically