View source for Einstein:Book chapter20 - The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity

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==20: The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity==
<p class="NOINDENT">{{Boldword|W|E}} 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.</p>

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 house on
our earth. If he releases a body which he previously had in his hand, the acceleration 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 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 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 the end 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:

<blockquote>'''"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." '''</blockquote> 

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