Principle Of Equivalence
Relativity, The Special and The General Relativity
Part: THE EQUALITY OF INERTIAL AND GRAVITATIONAL
Animated Flash Figures
Principle of Equivalence
We imagine a large portion of empty space, so far removed
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.
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 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 generalized postulate of relativity.
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 neutralized 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
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
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
We can now appreciate why that argument is not convincing, which we brought forward against
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