T_NAKÄ[uO

ɁuȂFCURVED SPACE-TIMEvǂށBiRj

<<   쐬 F 2016/10/21 00:01   >>

 "Remarks on the Equivalence of Inertial and Gravitational Masses and on the Accuracy of Einstein's Theory of Gravity." CURVED SPACE-TIME ̍ŌɂȂ܂B [ȂFCURVED SPACE-TIMEiRj]========================================================== The curved space-time metric and the relativistic Lagrangian for a test body moving in the static gravitational field of the central gravitating body, when converted to spherical coordinates, are thus as follows: (36) (37) ɍWɕϊASɏd͌̂鋅Ώ̂ȐÓId͏̋ȂvʂƎ̂̑Θ_IOWA͎̒ʂłF @$ds^{2}= \left ( 1-\frac{2\kappa M_{s}}{c^{2}r} \right )c^{2}dt^{2}-\left ( 1-\frac{2\kappa M_{s}}{c^{2}r} \right )^{-1}dr^{2}-r^{2}(d\vartheta^{2}+\sin ^{2}\vartheta d\varphi^{2})\; \; \; \; \; (36)$ @$L= \left ( 1-\frac{2\kappa M_{s}}{c^{2}r} \right )c^{2}\left ( \frac{dt}{d\tau } \right )^{2}-\left ( 1-\frac{2\kappa M_{s}}{c^{2}r} \right )^{-1}\left ( \frac{dr}{d\tau } \right )^{2}-r^{2}\left \{\left ( \frac{d\vartheta}{d\tau } \right ) ^{2}+\sin ^{2}\vartheta \left ( \frac{d\varphi}{d\tau } \right )^{2} \right \}\; \; \; \; \; (37)$ This is exactly the Schwarzschild solution of Einsteinfs theory of gravitation for an empty space. ́Amɋ̋Ԃ̂߂̃ACV^Cd͗_̃VcVgłB It is important to note that it was not necessary to use assumptions from which the Einsteinfs field equation is derived. ACV^Co鉼肪KvłȂ_ɒӂ邱Ƃ͏dvłB The key factor in finding the correct space-time metric was Newtonfs gravitation law written with the proper time as given in Eq.27. (27)ŗ^悤ɁǍvʂtɂČƂȂv͌ŗLŏj[g̏d͖@łB This was enabled by the use of the new mass equivalence principle. ́AVʓpĉ\ƂȂB It is also apparent that for a different gravitational law a different metric would be obtained. قȂd͖@̂߂ɁAقȂvʂ邱Ƃ́A炩łB These facts thus establish a strong link between Newtonfs gravitation law and the Schwarzschild metric of the curved spacetime. ̎́Aj[g̏d͖@ƋȂ̃VcVgvʂ̋֘Â悤ɎB This result thus justifies the choice made in Eq.14 about the gravitational mass dependency on velocity, instead of introduction of gravito-magnetic fields or other theories of gravity, and proves its correctness. ̌ʂ́Aigravito-̓܂͑̏d͗_̑Ɂjd͎ʂ̑xˑɂ(14)łȂI𐳓A̐ؖB The Einsteinfs theory of gravity is therefore consistent with Newtonfs gravitation law if the new mass equivalence principle is used. Vʂ̓g΁AACV^C̏d͗_̓j[g̏d͖@ƈvB The presented derivation of the Schwarzschild solution from the new mass equivalence principle should thus be a successful conclusion to the new theory and a crowning moment. ꂽVʓVcVg̓óÂ悤ɐV_̐_łȂ΂ȂȂB However, there is a subtle flaw in the derivation even when a presumably correct result was obtained. A炭ʂ͓ꂽƂłAoɔȌׂB When the transfer to the curved coordinate system was made, by using Lagrangian for the curved space-time, Newtonfs gravitation law was left unchanged. ȂWnւ̍WϊȂꂽƂAȂ̂߂̃OW֐pāAj[g̏d͖@͕sς̂܂܂ɂꂽB It is extremely unlikely that Newtonfs gravitational law would hold in coordinate distances. j[g̏d͖@Wx邱Ƃ͂肻ȂB The coordinate distances in curved space-time, unlike in the flat space-time, are not physical quantities but only scaffolding for mapping the space. Ȃ̍ẂAȎƈقȂAIȗʂłȂԂ̒n}邽߂̑łB This casts a great suspicion on the validity of the Schwarzschild solution and the whole concept of Einsteinfs theory of gravity. ́AVcVg̗LƃACV^C̏d͗_ׂ̂Ă̊TOɊւđ傫ȋ^𓊂B =============================================================================================== ƁA|\tg̏؂肽ɋ߂̂ɂȂĂ܂AӖǂȂƂ̂܂B Ȃꂽ󕶂v珑܂B ͂̕ӂŁBB

uOC

NbNċC`悤I
OCăNbN΁ÃuOւ̃Nt܂B
OC

^Cg i{j uO^

 ^Cg {@

e jbNl[^

Rg

 jbNl[ {@
ɁuȂFCURVED SPACE-TIMEvǂށBiRj T_NAKÄ[uO/BIGLOBEEFuuO
TCYF