Understanding Relativity 1996

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1、ThispageintentionallyleftblankThispageintentionallyleftblankThispageintentionallyleftblankThispageintentionallyleftblank20/GalileanRelativitywithm'themassappropriatetoframe5'.Inclassicalmechanics,however,massisconsideredanintrinsicpropertyofabodyandmustbeinvariant.HencewecanputnI'==m.Weshow

2、edearlier(eq.[1.13])thataccelerationisinvariantunderaGalileantransformation:a'==a.Henceequation(1.18)followsfrom(1.17)ifandonlyiftheforceFisalsoinvariant,12thatis,ifF'==F(1.20)Onehastoinvestigatecasebycasewhethertheforcesthatexistinnaturesatisfytheinvariancerequirement(eg.[1.20]).Forexample

3、,thegravitationalattractionbetweentwobodiesisgivenbyNewton'slawofgravity:(1.21)Herem1andm2arethemassesofthebodies,risthedistancebetweenthem,andGisaconstant.Wehavealreadyshownthatdistanceisinvari•antunderaGalileantransformation.Hencethegravitationalforceisin•deedinvariantandthelawofgravityis

4、consistentwiththeprincipleofrelativity.ThemostimportantexampleofaforcelawthatisnotcovariantinGalileanrelativityiselectromagnetism.Thelawsofelectricityandmagne•tismwerecodifiedinthelatenineteenthcenturyinasystemknownasMaxwell'sequations.Ifoneassumesthattheseequationsholdinsomeframe5andmakesa

5、Galileantransformationtoanotherframe5',theequationsin5'donothavethesameform:Maxwell'sequationsarenotcovariantunderaGalileantransformation.ThiswasverytroublingtoEinsteinandmotivatedhisquestforanewtheory.Therewerethreelogicalpossibilities:(i)Therelativityprincipledoesnotapplytoelectromagnetis

6、m;Max•well'sequationsarevalidonlyinonespecialframeofreference.(ii)Therelativityprincipledoesapplytoelectromagnetism,butMax•well'sequationsareonlyapproximatelycorrect;theymustbereplacedbyamoregeneralsetofequationsthatarestrictlycovariant.12.Ifeveryterminarelationisinvariant,asinthepresentexa

7、mple,therelationisobviouslycovariant.Thisisnotanecessarycondition,however.Covariancerequiresonlythatbothsidesoftheequationtransforminthesameway.Suppose,forexample,thatundersomehypotheticaltransformation,a'=2aandF'=2F.Eq.(1.18)wouldbesatisfiedandthelawwou