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.If hereleases a body which he previously had in his land, the accelertion of the chest will no longer betransmitted to this body, and for this reason the body will approach the floor of the chest with anaccelerated relative motion.The observer will further convince himself that the acceleration of thebody towards the floor of the chest is always of the same magnitude, whatever kind of body he mayhappen 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 gravitationalfield which is constant with regard to time.Of course he will be puzzled for a moment as to why thechest does not fall in this gravitational field.just then, however, he discovers the hook in the middleof the lid of the chest and the rope which is attached to it, and he consequently comes to theconclusion 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 ifwe wish to remain consistent ; we must rather admit that his mode of grasping the situation violatesneither 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 havethus good grounds for extending the principle of relativity to include bodies of reference which areaccelerated with respect to each other, and as a result we have gained a powerful argument for ageneralised postulate of relativity.We must note carefully that the possibility of this mode of interpretation rests on the fundamentalproperty of the gravitational field of giving all bodies the same acceleration, or, what comes to thesame thing, on the law of the equality of inertial and gravitational mass.If this natural law did notexist, the man in the accelerated chest would not be able to interpret the behaviour of the bodies43 Relativity: The Special and General Theoryaround him on the supposition of a gravitational field, and he would not be justified on the groundsof 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 abody 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 thechest will say: "The suspended body experiences a downward force in the gravitational field, andthis is neutralised by the tension of the rope ; what determines the magnitude of the tension of therope is the gravitational mass of the suspended body." On the other hand, an observer who ispoised freely in space will interpret the condition of things thus : " The rope must perforce take partin the accelerated motion of the chest, and it transmits this motion to the body attached to it.Thetension of the rope is just large enough to effect the acceleration of the body.That whichdetermines the magnitude of the tension of the rope is the inertial mass of the body." Guided by thisexample, we see that our extension of the principle of relativity implies the necessity of the law ofthe equality of inertial and gravitational mass.Thus we have obtained a physical interpretation ofthis law.From our consideration of the accelerated chest we see that a general theory of relativity must yieldimportant results on the laws of gravitation.In point of fact, the systematic pursuit of the generalidea 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.Agravitational field exists for the man in the chest, despite the fact that there was no such field for theco-ordinate system first chosen.Now we might easily suppose that the existence of a gravitationalfield is always only an apparent one.We might also think that, regardless of the kind of gravitationalfield which may be present, we could always choose another reference-body such thatno 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 referencesuch 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 thegeneral principle of relativity at theend of Section 18.It is certainly true that the observer in therailway carriage experiences a jerk forwards as a result of the application of the brake, and that herecognises, in this the non-uniformity of motion (retardation) of the carriage.But he is compelled bynobody to refer this jerk to a " real " acceleration (retardation) of the carriage.He might alsointerpret 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) agravitational field which is directed forwards and which is variable with respect to time.Under theinfluence of this field, the embankment together with the earth moves non-uniformly in such amanner 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 ofRelativity Unsatisfactory?Relativity: The Special and General Theory44 Relativity: The Special and General TheoryAlbert Einstein: RelativityPart II: The General Theory of RelativityIn What Respects are the Foundations of Classical Mechanics and of theSpecial Theory of Relativity Unsatisfactory?We have already stated several times that classical mechanics starts out from the following law:Material particles sufficiently far removed from other material particles continue to move uniformlyin a straight line or continue in a state of rest.We have also repeatedly emphasised that thisfundamental law can only be valid for bodies of reference K which possess certain unique states ofmotion, and which are in uniform translational motion relative to each other.Relative to otherreference-bodies K the law is not valid.Both in classical mechanics and in the special theory ofrelativity we therefore differentiate between reference-bodies K relative to which the recognised "laws of nature " can be said to hold, and reference-bodies K relative to which these laws do nothold.But no person whose mode of thought is logical can rest satisfied with this condition of things.Heasks : " How does it come that certain reference-bodies (or their states of motion) are given priorityover other reference-bodies (or their states of motion) ? What is the reason for this Preference? Inorder to show clearly what I mean by this question, I shall make use of a comparison.I am standing in front of a gas range
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