nevertheless regard the chest as being at rest. We have thus good
grounds for extending the principle of relativity to include bodies of
reference which are accelerated with respect to each other, and as a
result we have gained a powerful argument for a generalised postulate
of relativity.
We must note carefully that the possibility of this mode of
interpretation rests on the fundamental property of the gravitational
field of giving all bodies the same acceleration, or, what comes to the
same thing, on the law of the equality of inertial and gravitational
mass. If this natural law did not exist, the man in the accelerated
chest would not be able to interpret the behaviour of the bodies around
him on the supposition of a gravitational field, and he would not be
justified on the grounds of experience in supposing his reference-body
to be at rest.
Suppose that the man in the chest fixes a rope to the inner side of the
lid, and that he attaches a body to the free end of the rope. The
result of this will be to stretch the rope so that it will hang
vertically downwards. If we ask for an opinion of the cause of
tension in the rope, the man in the chest will say: The suspended body
experiences a downward force in the gravitational field, and this is
neutralised by the tension of the rope; what determines the magnitude
of the tension of the rope is the _gravitational mass_ of the suspended
body. On the other hand, an observer who is poised freely in space
will interpret the condition of things thus: The rope must perforce
take part in the accelerated motion of the chest, and it transmits this
motion to the body attached to it. The tension of the rope is just
large enough to effect the acceleration of the body. That which
determines the magnitude of the tension of the rope is the _inertial
mass_ of the body. Guided by this example, we see that our extension
of the principle of relativity implies the _necessity_ of the law of
the equality of inertial and gravitational mass. Thus we have obtained
a physical interpretation of this law.
From our consideration of the accelerated chest we see that a general
theory of relativity must yield important results on the laws of
gravitation. In point of fact, the systematic pursuit of the general
idea of relativity has supplied the laws satisfied by the gravitational
field. Before proceeding farther, however, I must warn the reader
49