Albert Einstein’s book *Relativity: The Special and General Theory* was originally published in German and translated into English in 1920. In the second chapter he introduces “The System of Co-ordinates”. The following post gives Einstein’s text followed by a revision that exchanges length with duration and space with time. First, Einstein’s text, with alternative wordings in square brackets:

End of Chapter I – If, in pursuance of our habit of thought, we now supplement the propositions of Euclidean geometry by the single proposition that two points on a practically rigid body always correspond to the same distance (line-interval), independently of any changes in position to which we may subject the body, the propositions of Euclidean geometry then resolve themselves into propositions on the possible relative position of practically rigid bodies.

Chapter II – On the basis of the physical interpretation of distance which has been indicated, we are also in a position to establish the distance between two points on a rigid body by means of measurements. For this purpose we require a “distance” (rod S) which is to be used once and for all, and which we employ as a standard measure. If, now, A and B are two points on a rigid body, we can construct the line joining them according to the rules of geometry; then, starting from A, we can mark off the distance S time after time [again and again] until we reach B. The number of these operations required is the numerical measure of the distance AB. This is the basis of all measurement of length.

Every description of the scene of an event or of the position of an object in space is based on the specification of the point on a rigid body (body of reference) with which that event or object coincides. This applies not only to scientific description, but also to everyday life. If I analyse the place specification “Times Square, New York,” I arrive at the following result. The earth is the rigid body to which the specification of place refers; “Times Square, New York,” is a well-defined point [place], to which a name has been assigned, and with which the event coincides in space.

This primitive method of place specification deals only with places on the surface of rigid bodies, and is dependent on the existence of points on this surface which are distinguishable from each other. But we can free ourselves from both of these limitations without altering the nature of our specification of position. If, for instance, a cloud is hovering over Times Square, then we can determine its position relative to the surface of the earth by erecting a pole perpendicularly on the Square, so that it reaches the cloud. The length of the pole measured with the standard measuring-rod, combined with the specification of the position of the foot of the pole, supplies us with a complete place specification. On the basis of this illustration, we are able to see the manner in which a refinement of the conception of position has been developed.

(a) We imagine the rigid body, to which the place specification is referred, supplemented in such a manner that the object whose position we require is reached by the completed rigid body.

(b) In locating the position of the object, we make use of a number (here the length of the pole measured with the measuring-rod) instead of designated points of reference.

(c) We speak of the height of the cloud even when the pole which reaches the cloud has not been erected. By means of optical observations of the cloud from different positions on the ground, and taking into account the properties of the propagation of light, we determine the length of the pole we should have required in order to reach the cloud.

From this consideration we see that it will be advantageous if, in the description of position, it should be possible by means of numerical measures to make ourselves independent of the existence of marked positions (possessing names) on the rigid body of reference. In the physics of measurement this is attained by the application of the Cartesian system of co-ordinates.

This consists of three plane surfaces perpendicular to each other and rigidly attached to a rigid body. Referred to a system of co-ordinates, the scene of any event will be determined (for the main part) by the specification of the lengths of the three perpendiculars or co-ordinates which can be dropped from the scene of the event to those three plane surfaces. The lengths of these three perpendiculars can be determined by a series of manipulations with rigid measuring-rods performed according to the rules and methods laid down by Euclidean geometry.

In practice, the rigid surfaces which constitute the system of co-ordinates are generally not available; furthermore, the magnitudes of the co-ordinates are not actually determined by constructions with rigid rods, but by indirect means. If the results of physics and astronomy are to maintain their clearness, the physical meaning of specifications of position must always be sought in accordance with the above considerations.

We thus obtain the following result: Every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for “distances;” the “distance” being represented physically by means of the convention of two marks on a rigid body.

What follows is a revision, with changes in italics, for three-dimensional *motion*, with a monorail transportation system over a rigid frame. Note: a *rigid body clock* is a linear clock, which measures duration in proportion to distance moved.

End of Chapter I – Let us supplement the propositions of Euclidean geometry by the single proposition that two *instants* on *an inertial monorail moving over* a practically rigid body always correspond to the same *distime* (*time*-interval), independently of any changes in position to which we may subject the *monorail*, the propositions of Euclidean geometry then resolve themselves into propositions on the possible relative *time* position of practically rigid body *clocks*.

Chapter II – On the basis of the physical interpretation of a *a time*-interval which has been indicated, we are also in a position to establish the *time*-interval between two *instants* on an inertial monorail over a practically rigid body by means of measurements. For this purpose we require a “*distime*” (*rod clock T*) which is to be used once and for all, and which we employ as a standard measure. If, now, A and B are two *instants* on a rigid body *clock*, we can construct the line joining them according to the rules of geometry; then, starting from A, we can mark off the *distime T* *over and over* until we reach B. The number of these operations required is the numerical measure of the *distime* AB. This is the basis of all measurement of length-*duration*.

Every description of the *context* of an event or of the position of an object in *time* is based on the specification of the *instant* on an inertial monorail over a practically rigid body (body of reference) with which that event or object coincides. This applies not only to scientific description, but also to everyday life. If I analyse the *time* specification “*New Year’s Eve,* Times Square, New York,” I arrive at the following result. The earth is the rigid body *clock *to which the specification of *time* refers; “*New Year’s Eve,* Times Square, New York,” is a well-defined *time*, to which a name has been assigned, and with which the event coincides in *time*.

This primitive method of *time* specification deals only with *times* on the surface of rigid body* clocks*, and is dependent on the existence of *instants* on this surface which are distinguishable from each other. But we can free ourselves from both of these limitations without altering the nature of our specification of position. If, for instance, a *hot air balloon* is *rising *over Times Square, then we can determine its position relative to *an instant on* the monorail over a rigid body by erecting a *pole clock* perpendicularly on the Square, so that it reaches the *hot air balloon*. The length-*duration* of the pole *clock* measured with the standard measuring-rod *clock*, combined with the specification of the position of the foot of the pole, supplies us with a complete *time* specification. On the basis of this illustration, we are able to see the manner in which a refinement of the conception of time position has been developed.

(a) We imagine the rigid body *clock*, to which the *time* specification is referred, supplemented in such a manner that the object whose *time position *we require is reached by the completed rigid body *clock*.

(b) In locating the *time position *of the object, we make use of a number (here the *duration-*length of the pole measured with the measuring-rod *clock*) instead of designated *instants* of reference.

(c) We speak of the *duration-*height of the cloud even when the pole *clock* which reaches the cloud has not been erected. By means of optical observations of the cloud from different *time positions *on the ground, and taking into account the properties of the propagation of light, we determine the *duration-*length of the pole *clock* we should have required in order to reach the cloud.

From this consideration we see that it will be advantageous if, in the description of *time position*, it should be possible by means of numerical measures to make ourselves independent of the existence of marked *time positions *(possessing names) on the rigid body *clock* of reference. In the physics of measurement this is attained by the application of the Cartesian system of co-ordinates.

This consists of three plane surfaces perpendicular to each other and rigidly attached to a rigid body *clock*. Referred to a system of co-ordinates, the *context* of any event will be determined (for the main part) by the specification of the *duration-*lengths of the three perpendiculars or co-ordinates which can be dropped from the *context* of the event to those three plane surfaces. The *duration-*lengths of these three perpendiculars can be determined by a series of manipulations with rigid measuring-rod *clocks* performed according to the rules and methods laid down by Euclidean geometry.

In practice, the rigid surfaces which constitute the system of co-ordinates are generally not available; furthermore, the magnitudes of the co-ordinates are not actually determined by constructions with rigid rod *clocks*, but by indirect means. If the results of physics and astronomy are to maintain their clearness, the physical meaning of specifications of *time positions *must always be sought in accordance with the above considerations.

We thus obtain the following result: Every description of events in *time* involves the use of a rigid body *clock* to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for “*distimes*;” the “*distime*” being represented physically by means of the convention of two marks on a rigid body *clock*.