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Relativity: The Special and General Theory
Albert Einstein: Relativity
Part II: The General Theory of Relativity
The Equality of Inertial and Gravitational Mass
as an argument for the General Postule of Relativity
We imagine a large portion of empty space, so far removed from stars and other appreciable
masses, that we have before us approximately the conditions required by the fundamental law of
Galilei. It is then possible to choose a Galileian reference−body for this part of space (world),
relative to which points at rest remain at rest and points in motion continue permanently in uniform
rectilinear motion. As reference−body let us imagine a spacious chest resembling a room with an
observer inside who is equipped with apparatus. Gravitation naturally does not exist for this
observer. He must fasten himself with strings to the floor, otherwise the slightest impact against the
floor will cause him to rise slowly towards the ceiling of the room.
To the middle of the lid of the chest is fixed externally a hook with rope attached, and now a " being
" (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest
together with the observer then begin to move "upwards" with a uniformly accelerated motion. In
course of time their velocity will reach unheard−of values — provided that we are viewing all this
from another reference−body which is not being pulled with a rope.
But how does the man in the chest regard the Process ? The acceleration of the chest will be
transmitted to him by the reaction of the floor of the chest. He must therefore take up this pressure
by means of his legs if he does not wish to be laid out full length on the floor. He is then standing in
the chest in exactly the same way as anyone stands in a room of a home on our earth. If he
releases a body which he previously had in his land, the accelertion of the chest will no longer be
transmitted to this body, and for this reason the body will approach the floor of the chest with an
accelerated relative motion. The observer will further convince himself that the acceleration of the
body towards the floor of the chest is always of the same magnitude, whatever kind of body he may
happen to use for the experiment.
Relying on his knowledge of the gravitational field (as it was discussed in the preceding section),
the man in the chest will thus come to the conclusion that he and the chest are in a gravitational
field which is constant with regard to time. Of course he will be puzzled for a moment as to why the
chest does not fall in this gravitational field. just then, however, he discovers the hook in the middle
of the lid of the chest and the rope which is attached to it, and he consequently comes to the
conclusion that the chest is suspended at rest in the gravitational field.
Ought we to smile at the man and say that he errs in his conclusion ? I do not believe we ought to if
we wish to remain consistent ; we must rather admit that his mode of grasping the situation violates
neither reason nor known mechanical laws. Even though it is being accelerated with respect to the
"Galileian space" first considered, we can 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