*Reference: **Einstein’s 1920 Book*

*This paper presents Part 1, Chapter 10 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.*

.

## On the Relativity of the Conception of Distance

Let
us consider two particular points on the train^{1} travelling along the
embankment with the velocity ** v**, and inquire as to their distance
apart. We already know that it is necessary to have a body of reference for the
measurement of a distance, with respect to which body the distance can be
measured up. It is the simplest plan to use the train itself as the
reference-body (co-ordinate system). An observer in the train measures the
interval by marking off his measuring-rod in a straight line (

*e.g.*along the floor of the carriage) as many times as is necessary to take him from the one marked point to the other. Then the number which tells us how often the rod has to be laid down is the required distance.

^{1} *e.g.* the middle of the
first and of the hundredth carriage.

It
is a different matter when the distance has to be judged from the railway line.
Here the following method suggests itself. If we call ** A’ **and

**the two points on the train whose distance apart is required, then both of these points are moving with the velocity**

*B’***along the embankment. In the first place we require to determine the points**

*v***and**

*A***of the embankment which are just being passed by the two points**

*B***and**

*A’***at a particular time**

*B’***—judged from the embankment. These points**

*t***and**

*A***of the embankment can be determined by applying the definition of time given in Section 8. The distance between these points**

*B***and**

*A***is then measured by repeated application of the measuring-rod along the embankment.**

*B**A priori* it is by
no means certain that this last measurement will supply us with the same result
as the first. Thus the length of the train as measured from the embankment may
be different from that obtained by measuring in the train itself. This circumstance
leads us to a second objection which must be raised against the apparently
obvious consideration of Section 6. Namely, if the man in the carriage covers
the distance ** w** in a unit of time—

*measured from the train*,—then this distance—

*as measured from the embankment*—is not necessarily also equal to

**.**

*w**Since
time changes with the motion of the body, a distance may appear different
depending on the motion. *