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12
Relativity: The Special and General Theory
from amongst all possible Galileian co?ordinate systems, we should have chosen one (K
0
)
of a
particular state of motion as our body of reference. We should then be justified (because of its
merits for the description of natural phenomena) in calling this system " absolutely at rest," and all
other Galileian systems K " in motion." If, for instance, our embankment were the system K
0
then
our railway carriage would be a system K, relative to which less simple laws would hold than with
respect to K
0
.
This diminished simplicity would be due to the fact that the carriage K would be in
motion (i.e."really")with respect to K
0
.
In the general laws of nature which have been formulated
with reference to K, the magnitude and direction of the velocity of the carriage would necessarily
play a part. We should expect, for instance, that the note emitted by an organpipe placed with its
axis parallel to the direction of travel would be different from that emitted if the axis of the pipe were
placed perpendicular to this direction.
Now in virtue of its motion in an orbit round the sun, our earth is comparable with a railway carriage
travelling with a velocity of about 30 kilometres per second. If the principle of relativity were not
valid we should therefore expect that the direction of motion of the earth at any moment would
enter into the laws of nature, and also that physical systems in their behaviour would be dependent
on the orientation in space with respect to the earth. For owing to the alteration in direction of the
velocity of revolution of the earth in the course of a year, the earth cannot be at rest relative to the
hypothetical system K
0
throughout the whole year. However, the most careful observations have
never revealed such anisotropic properties in terrestrial physical space, i.e. a physical
non?equivalence of different directions. This is very powerful argument in favour of the principle of
relativity.
Next: The Theorem of the Addition of Velocities Employed in Classical Mechanics
Relativity: The Special and General Theory