*Reference: Einstein’s 1920
Book*

*This paper presents Part 1, Chapter 3 from the book **RELATIVITY: THE SPECIAL AND GENERAL
THEORY by A. EINSTEIN.
The contents are from the original publication of this book by Henry
Holt and Company, New York (1920).*

*The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.*

*The heading below is linked to
the original materials.*

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**Space and Time in Classical Mechanics**

“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
co-ordinates 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”^{1}),
but only a trajectory relative to a particular body of reference.

^{1} That is, a curve along which the body moves.

*Einstein is pointing out that we see trajectory of a body relative to another body only and not independently.*

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.

*Just like space co-ordinates, each reference body must have its own time co-ordinates as well to complete the picture of motion. *

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## FINAL COMMENTS

*Einstein notices that a reference system should provide not only its unique space co-ordinates but also its unique time co-ordinate. Time co-ordinate enters the picture because the reference bodies are themselves moving. The problem in classical mechanics has been that it has not been able to figure out a way to measure space and time in absolute co-ordinates.*

*But there may be a way if we look at time as endurance of change, and inertia as resistance to change. The lesser is the inertia the more rapidly the changes shall occur. A reference body shall move faster on its own if its inertia decreases. This is actually observed when we compare the material domain to the field domain. The material domain has high inertia and low velocity, whereas, the field domain has low inertia and high velocity. If inertia could be measured in absolute terms, velocity may also be measured in absolute terms. This will allow absolute co-ordinates to be assigned to space and time.*

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