contraction being just sufficient to compensate for the difference in
time mentioned above. Comparison with the discussion in Section XII
shows that also from the standpoint of the theory of relativity this
solution of the difficulty was the right one. But on the basis of the
theory of relativity the method of interpretation is incomparably more
satisfactory. According to this theory there is no such thing as a
specially favoured (unique) co-ordinate system to occasion the
introduction of the ther-idea, and hence there can be no ther-drift,
nor any experiment with which to demonstrate it. Here the contraction
of moving bodies follows from the two fundamental principles of the
theory, without the introduction of particular hypotheses; and as the
prime factor involved in this contraction we find, not the motion in
itself, to which we cannot attach any meaning, but the motion with
respect to the body of reference chosen in the particular case in
point. Thus for a co-ordinate system moving with the earth the mirror
system of Michelson and Morley is not shortened, but it _is_ shortened
for a co-ordinate system which is at rest relatively to the sun.
XVII.
MINKOWSKI S FOUR-DIMENSIONAL SPACE
The non-mathematician is seized by a mysterious shuddering when he
hears of four-dimensional things, by a feeling not unlike that
awakened by thoughts of the occult. And yet there is no more
common-place statement than that the world in which we live is a
four-dimensional space-time continuum.
Space is a three-dimensional continuum. By this we mean that it is
possible to describe the position of a point (at rest) by means of
three numbers (co-ordinates) _x, y, z_, and that there is an indefinite
number of points in the neighbourhood of this one, the position of
which can be described by co-ordinates such as _x1, y1, z1_, which may
be as near as we choose to the respective values of the co-ordinates
_x, y, z_, of the first point. In virtue of the latter property we
speak of a continuum, and owing to the fact that there are three
co-ordinates we speak of it as being three-dimensional.
Similarly, the world of physical phenomena which was briefly called
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