Talk:PlanetPhysics/Equality of Inertial and Gravitational Mass As an Argument for the General Postulate of Relativity

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%%% Primary Title: The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity
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\begin{document}

 \subsection{The Equality of Inertial and Gravitational Mass
as an Argument for the General Postulate of Relativity}
From \htmladdnormallink{Relativity: The Special and General Theory}{http://planetphysics.us/encyclopedia/SpecialTheoryOfRelativity.html} by \htmladdnormallink{Albert Einstein}{http://planetphysics.us/encyclopedia/AlbertEinstein.html}
We imagine a large portion of empty space, so far removed from stars
and other appreciable \htmladdnormallink{masses}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html}, 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
\htmladdnormallink{motion}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} 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 \htmladdnormallink{force}{http://planetphysics.us/encyclopedia/Thrust.html}. 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 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 \htmladdnormallink{The Gravitational Field}{http://planetphysics.us/encyclopedia/GravitationalField.html}, and this
is neutralised by the tension of the rope; what determines the
\htmladdnormallink{magnitude}{http://planetphysics.us/encyclopedia/AbsoluteMagnitude.html} of the tension of the rope is the \htmladdnormallink{gravitational mass}{http://planetphysics.us/encyclopedia/Mass.html} 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 \htmladdnormallink{acceleration}{http://planetphysics.us/encyclopedia/Acceleration.html} of the body. That
which determines the magnitude of the tension of the rope is the
\htmladdnormallink{inertial mass}{http://planetphysics.us/encyclopedia/Mass.html} 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 \htmladdnormallink{general theory}{http://planetphysics.us/encyclopedia/GeneralTheory.html} 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 \htmladdnormallink{field}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html} exists for the man in the chest, despite the
fact that there was no such field for the co-ordinate \htmladdnormallink{system}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html} 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 \htmladdnormallink{section}{http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html} 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 \htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html} in the
backwards direction is continuously reduced."

\subsection{References}
This article is derived from the Einstein Reference Archive (marxists.org) 1999, 2002. \htmladdnormallink{Einstein Reference Archive}{http://www.marxists.org/reference/archive/einstein/index.htm} which is under the FDL copyright.

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