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44
Relativity: The Special and General Theory
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 strech 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 against a misconception suggested by these considerations. A
gravitational field exists for the man in the chest, despite the fact that there was no such field for the
co?ordinate system first chosen. Now we might easily suppose that the existence of a gravitational
field is always only an apparent one. We might also think that, regardless of the kind of gravitational
field which may be present, we could always choose another reference?body such that
no gravitational field exists with reference to it. This is by no means true for all gravitational fields,
but only for those of quite special form. It is, for instance, impossible to choose a body of reference
such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes.
We can now appreciate why that argument is not convincing, which we brought forward against the
general principle of relativity at theend of Section 18. It is certainly true that the observer in the
railway carriage experiences a jerk forwards as a result of the application of the brake, and that he
recognises, in this the non?uniformity of motion (retardation) of the carriage. But he is compelled by
nobody to refer this jerk to a " real " acceleration (retardation) of the carriage. He might also
interpret his experience thus: " My body of reference (the carriage) remains permanently at rest.
With reference to it, however, there exists (during the period of application of the brakes) a
gravitational field which is directed forwards and which is variable with respect to time. Under the
influence of this field, the embankment together with the earth moves non?uniformly in such a
manner that their original velocity in the backwards direction is continuously reduced."
Next: In What Respects are the Foundations of Classical Mechanics and of the Special Theory of
Relativity Unsatisfactory?
Relativity: The Special and General Theory