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Book by David Michalets

Review of Einstein's 1920 Book on Relativity  (from Translation)

An (original) line precedes original content from the source.

A (remark) line precedes my remark from my review of the preceding original content.

My remark applies to only this section of the original.

Section III. of 35



THE purpose of mechanics is to describe how  bodies change their position in space with  time." I should load my conscience with grave sins against the sacred spirit of lucidity were I to formulate the aims of mechanics in this way, without serious reflection and detailed explanations. Let us proceed to disclose these sins.
It is not clear what is to be understood here by "position" and "space." I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the embankment, without throwing it. Then, disregarding the influence of the air resistance, I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices that the stone falls to earth in a parabolic curve. I now ask: Do the "positions" traversed by the stone lie "in reality" on a straight line or on a parabola? Moreover, what is meant here by motion "in space"? From the considerations of the previous section the answer is self-evident. In the first place, we entirely shun the vague word "space," of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by "motion relative to a practically rigid body of reference." The positions relative to the body of reference (railway carriage or embankment) have already been defined in detail in the preceding section. If instead of "body of reference" we insert "system of co-ordinates," which is a useful idea for mathematical description, we are in a position to say: The stone traverses a straight line relative to a system of coordinates rigidly attached to the carriage, but relative to a system of co-ordinates rigidly attached to the ground
(embankment) it describes a parabola. With the aid of this example it is clearly seen that there is no such thing as an independently existing trajectory (lit. "path-curve" That is, a curve along which the body moves), but only a trajectory relative to a particular body of reference. In order to have a complete description of the motion, we must specify how the body alters its position with time; i.e. for every point on the trajectory it must be stated at what time the body is situated there. These data must be supplemented by such a definition of time that, in virtue of this definition, these time-values can be regarded essentially as magnitudes (results of measurements) capable of observation. If we take our stand on the ground of classical mechanics, we can satisfy this requirement for our illustration in the following manner. We imagine two clocks of identical construction; the man at the  railway-carriage window is holding one of them, and the man on the footpath the other.
Each of the observers determines the position on his own reference-body occupied by the stone at each tick of the clock he is holding in his hand.
In this connection we have not taken account of  the inaccuracy involved by the finiteness of the velocity of propagation of light. With this and with a second difficulty prevailing here we shall have to deal in detail later.


Einstein is concerned that any single observer will describe a physical behavior differently than another observer.

He describes one person dropping a stone from a moving train. Einstein believes an observer who is on thembankment will observe the stone on a parabolic path. This is because the stone begins vertically static, but after its release, it accelerates at free fall until its velocity settles.

Einstein neglects the person dropping the stone from the train. He sees it falling with an increasing distance, with no lateral motion.

This is the only observer in the set who measures a relative distance. All others measure a position using a coordinate system having a physical reference point.

It is true that the trajectory is based on an observer, and how they measure any observed positions. Any instrument doing an automated observation or measurement  must use a specific coordinate system and fixed reference point for those data tobe analyzed and compared with another data set.

Relativity cannot get around a technique of measuring the position of an object.

Physics, a science about motion,  is based on measurements. That accumulated data are analyzed to draw conclusions.

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last change 05/07/2022