Chapter 7 z
The General Theory of
z z z z
Relativity
Thez Generalz Theoryz ofz Relativityz is,z asz thez namez indicates,z az generalizationz
ofzthezSpecialzTheoryzofzRelativity.zItziszcertainlyzonezofzthezmostzremarkablez
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hyzarezinertialzframeszofzreferencezsozspecial?zWhyziszitzwezdoznotzfeelzgravity
’szpullzwhenzwezarezfreelyzfalling?zWhyzshouldzabsolutezvelocitieszbezforbidde
nz butz absolutez accelerationsz byz accepted?
Figurez 7.1:zEinstein
151
,152
7.1 The happiest thought of my life.
z z z z z
Inz1907,zonlyztwozyearszafterzthezpublicationzofzhiszSpecialzTheoryzofzRel-
zativity,zEinsteinzwrotezazpaperzattemptingztozmodifyzNewton’sztheoryzofzgra
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outzofzthiszproblemziszbyzconcludingzthatzNewton’szgravitationalzequationszar
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ez involvedz cannotz bez describedz accuratelyz byz thesez equations.
Inz1920zEinsteinzcommentedzthatzazthoughtzcamezintozhiszmindzwhenzwri
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nz observerz freelyz fallingz fromz thez roofz ofz az housez –
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gzbehind.zIfzhezwereztozpushzthezbombzawayzhezwouldzseezitzmovezwithzconst
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diesz(wezhavezgoodzevidencezforzthis:zthezApolloz10–
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Mr.zCoyoteziszfatedztozrepeatzthezexperiencezwithzmanyzotherzthings:zrock
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withz respectz toz himz allz objects,z irrespectivez ofz composition,z mass,
1Iz ignorez airz resistance
, 153
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ThisziszreminiscentzofzGalileo’szargument:zthezobserverzletszgozofzsomezob
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Whatz doesz thisz imply?z Well,z fromz Newton’sz equationsz wez get
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Sozthezequalityzofztheztwozm’szwaszupgradedzbyzEinsteinztozazpostulate:zth
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mz inz mMG/r2z arez identical)z impliesz anz incrediblez amountz ofz newz and
2Thez reasonsz behindz thez requirement z that z thez boxz bez small z willz becomez clearz soon.
, 154
surprisingzeffects.zThezmzinzFz=zmaziszcalledzthezinertialzmasszandzthezmzinz
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z
Thez wholez ofz thez Generalz Theoryz ofz Relativityz restsz onz thisz postulate,z
Thezinertialzandzgravitat
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ThezcompletedzformulationzofzthezGeneralzTheoryzofzRelativityzwaszpub-
zlishedz inz 1916z (Fig.zz7.2).
Figurez 7.2:z Einstein’sz Generalz Theoryz ofz Relativityz paper.
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allz inertialz framesz ofz referencez arez equivalent.
The General Theory of
z z z z
Relativity
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ofzthezSpecialzTheoryzofzRelativity.zItziszcertainlyzonezofzthezmostzremarkablez
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Figurez 7.1:zEinstein
151
,152
7.1 The happiest thought of my life.
z z z z z
Inz1907,zonlyztwozyearszafterzthezpublicationzofzhiszSpecialzTheoryzofzRel-
zativity,zEinsteinzwrotezazpaperzattemptingztozmodifyzNewton’sztheoryzofzgra
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nz observerz freelyz fallingz fromz thez roofz ofz az housez –
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Let’szimaginezthezunfortunatezWilezE.zCoyotezfallingzfromzanzimmensezhei
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Mr.zCoyoteziszfatedztozrepeatzthezexperiencezwithzmanyzotherzthings:zrock
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withz respectz toz himz allz objects,z irrespectivez ofz composition,z mass,
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, 153
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ThisziszreminiscentzofzGalileo’szargument:zthezobserverzletszgozofzsomezob
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Whyzwouldzthiszbeztrue?zThezanswerzcanzbeztracedzbackztozthezwayzinzwh
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Whatz doesz thisz imply?z Well,z fromz Newton’sz equationsz wez get
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Sozthezequalityzofztheztwozm’szwaszupgradedzbyzEinsteinztozazpostulate:zth
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2Thez reasonsz behindz thez requirement z that z thez boxz bez small z willz becomez clearz soon.
, 154
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lativityz isz az gemz 3.
ThezcompletedzformulationzofzthezGeneralzTheoryzofzRelativityzwaszpub-
zlishedz inz 1916z (Fig.zz7.2).
Figurez 7.2:z Einstein’sz Generalz Theoryz ofz Relativityz paper.
3Thez Specialz Theoryz ofz Relativityz isz equallyz nice,z itz isz basedz onz thez onez statement z thatz
allz inertialz framesz ofz referencez arez equivalent.
