sn y™to˜er —nd xovem˜er IWHUD just over two ye—rs —fter the ™ompletion of his spe™i—l theory of rel—tivityD iinstein m—de the ˜re—kthrough th—t set him on the p—th to the gener—l theory of rel—tivityF ‡hile prep—ring — review —rti™le on his new spe™i—l theory of rel—tivityD he ˜e™—me ™onvin™ed th—t the key to the extension of the prin™iple of rel—tivity to —™™eler—ted motion l—y in the rem—rk—˜le —nd unexpl—ined empiri™—l ™oin™iden™e of the equ—lity of inerti—l —nd gr—vit—tion—l m—ssesF „o interpret (...) —nd exploit this ™oin™iden™eD he introdu™ed — new —nd powerful physi™—l prin™ipleD soon to ˜e ™—lled the ’prin™iple of equiv—len™e4 upon whi™h his se—r™h for — gener—l theory of reE l—tivity would ˜e ˜—sedF woreoverD with the ™ompletion of the theory —nd throughout the rem—inder of his lifeD iinstein insisted on the fund—ment—l import—n™e of the prin™iple to his gener—l theory of rel—tivityF iinstein9s insisten™e on this point h—s ™re—ted — puzzle for philosophers —nd histori—ns of s™ien™eF st h—s ˜een —rgued vigorously th—t the prin™iple in its tr—dition—l formul—tion does not hold in th™ gener—l theory of rel—tivityD gonsiderD for ex—mpleD — tr—dition—l formul—tion su™h —s €—uli9s in his IWPI Encyklopadie —rti™leF por €—uli the prin™iple —sserts th—t one ™—n —lw—ys tr—nsform —w—y —n —r˜itr—ry gr—vit—tion—l eld in —n innitely sm—ll region of sp—™eEtimeD ˜y tr—nsforming to —n —ppropri—te ™oordin—te system @€—uli IWPID pF IRSAF sn responseD su™h eminent rel—tivists —s ƒynge @IWTHD pF ixAD —nd even iddington ˜efore him @IWPRD ppF QW{RIAD h—ve o˜je™ted th—t — ™oordin—te tr—nsform—tion or ™h—nge of st—te of motion of the o˜server ™—n h—ve no ee™t on the presen™e or —˜sen™e of — gr—vit—tion—l eldF „he presen™e of — ’true4 gr—vit—tion—l eld is determined ˜y —n inv—ri—nt ™riterionD the ™urv—ture of the metri™F „he gr—vit—tionEfree ™—se of spe™i—l rel—tivity is just the ™—se in whi™h this ™urv—ture v—nishesD where—s the true gr—vit—tion—l elds of gener—l rel—tivity —re distinguished ˜y the nonv—nishing of this ™urv—tureF „his o˜je™tion h—s immedi—te r—mi™—tions for the ’iinstein elev—tor4 thought experimentD whi™h is ™ommonly used in the formul—tion of the prinE ™iple of equiv—len™eF sn this thought experimentD — sm—ll ™h—m˜ers su™h —s.... (shrink)

The problem of finding a covariant expression for the distribution and conservation of gravitational energy-momentum dates to the 1910s. A suitably covariant infinite-component localization is displayed, reflecting Bergmann's realization that there are infinitely many gravitational energy-momenta. Initially use is made of a flat background metric (or rather, all of them) or connection, because the desired gauge invariance properties are obvious. Partial gauge-fixing then yields an appropriate covariant quantity without any background metric or connection; one version is the collection of pseudotensors (...) of a given type, such as the Einstein pseudotensor, in _every_ coordinate system. This solution to the gauge covariance problem is easily adapted to any pseudotensorial expression (Landau-Lifshitz, Goldberg, Papapetrou or the like) or to any tensorial expression built with a background metric or connection. Thus the specific functional form can be chosen on technical grounds such as relating to Noether's theorem and yielding expected values of conserved quantities in certain contexts and then rendered covariant using the procedure described here. The application to angular momentum localization is straightforward. Traditional objections to pseudotensors are based largely on the false assumption that there is only one gravitational energy rather than infinitely many. (shrink)