On Achievements, Shortcomings, and Errors of Einstein_T.doc

8/13/2019 On Achievements, Shortcomings, and Errors of Einstein_T.doc

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On Achievements, Shortcomings and rrors o! instein

C. Y. Lo

Applied and Pure Research Institute

" Taggart #rive, $nit , %ash&a, %H 030'0

A(STRA)T

The e*ectromagnetic energ+ is not e&iva*ent to mass Th&s, instein.s !orm&*a / mc 2 is on*+ conditiona**+ va*id

erimenta**+, it is non that the hotons are e&iva*ent to mass Hoever, to satis!+ / mc 2, the hotons m&st

inc*&de not on*+ e*ectromagnetic ave energ+, 4&t a*so gravitationa* ave energ+ or the d+namic case ith massive

so&rces, it is i**&strated thro&gh e*icit ca*c&*ations that the non-*inear instein e&ation has no 4o&nded d+namic

so*&tions Th&s, the ositive mass theorem o! Ya& 6 Schoen 7and 8itten9 is mis*eading in h+sics A*so, the 2011

Sha Pri:e to )hristodo&*o& is act&a**+ toard his errors against honora4*e ;&**strand, )hairman o! the %o4e* Pri:e

)ommittee !or Ph+sics Y8OR#S? d+namic so*&tion@ gravitationa* radiation@ rinci*e o! ca&sa*it+@

PA)S? 020)v@ 050-h@ 050>d@ 0B0)c

Unthinking respect for authority is the greatest enemy of truth. A. !instein

". Introduction.

instein is common*+ recogni:ed as a geni&s 4eca&se he created ne theories and *ed &s ith acc&rate redictions

to ne areas o! h+sics, name*+, secia* re*ativit+, &ant&m mechanics and genera* re*ativit+ In secia* re*ativit+, he

revo*&tioni:ed the notion o! sace-time and esta4*ished a !orm&*a 4eteen energ+ and mass / mc2 The notion o!

hoton *a+s a centra* ro*e in &ant&m mechanics In genera* re*ativit+, he ama:ed &s 4+ his three acc&rate redictions

Th&s, a !aith in instein as deve*oed

1


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Hoever, as time has gone 4+ the shortcomings o! his theories are grad&a**+ shon and even inc*&de mistaes 8e

admire instein not 4eca&se he as er!ect as e revio&s*+ 4e*ieved, 4&t rather !or his ingen&it+ in starting ne

chaters o! h+sics In hat !o**os, e sha** oint o&t the ro4*ems that e no This *eads to the necessar+

recti!ication o! his theories, in artic&*ar, genera* re*ativit+ 19%everthe*ess, it a*so 4ecomes c*ear that his conCect&re o!

&ni!ication 4eteen gravitation and e*ectromagnetic is esta4*ished Th&s, !ina**+ instein.s conCect&re t&rns o&t to 4e

correct at the end It is & to &s to e*ore !&rther hat he has started that remains !or o&r !&t&re investigation

#. $pecial Relati%ity and the &ormula ! ' mc#

8hi*e secia* re*ativit+ t&rns o&t to have the *east ro4*ems, the &nconditiona* va*idit+ o! the !orm&*a / mc 2is on*+ a

sec&*ation that has never 4een veri!ied D1E In !act, instein had tried ver+ hard !or +ears 71=05-1=0=9 to rove this

!orm&*a to 4e genera**+ va*id, 4&t !ai*ed D2E

The !orm&*a can 4e traced 4ac to secia* re*ativit+, hich s&ggested a rest inertia* mass m0has the rest energ+ o!

m0c2 This is s&orted 4+ the n&c*ear !issions ith F / Fmc2, here Fm is the mass di!!erence a!ter the !ission and

F the tota* energ+ created and is &s&a**+ a com4ination o! di!!erent t+es o! energ+ Hoever, !or an ar4itrar+ energ+

, the re*ation m / Gc2 is not on*+ an &nveri!ied sec&*ation, 4&t a*so an o4stac*e !or rogress in h+sics D1E

According to genera* re*ativit+, s&ch a c*aim is incorrect !or e*ectromagnetic energ+ The instein !ie*d e&ation is,

;R1

2

gR / > T , 719

here the energ+ stress tensor Tis the s&m o! an+ t+e o! energ+-stress tensor The e*ectromagnetic energ+-stress

tensor, 4eing trace*ess, cannot a!!ect R in e 719 There!ore, the e*ectromagnetic energ+ is not e&iva*ent to mass


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8hen instein roosed the notion o! hoton, it consists o! a &ant&m o! e*ectromagnetic energ+, and it acts *ie a

artic*e in the hotoe*ectric e!!ect It has 4een o4served that the artic*e 0meson deca+s into to hotons 7ie, 0

9 This as mistaen*+ considered as evidence that the e*ectromagnetic energ+ is e&iva*ent to mass Hoever, there

o&*d 4e a con!*ict i! a hoton inc*&des on*+ e*ectromagnetic energ+ since the e*ectromagnetic energ+-stress tensor is

trace*ess There!ore, the hotons m&st consist o! non-e*ectromagnetic energ+

Since a charged artic*e a*a+s has mass, it is nat&ra* that the non-e*ectromagnetic energ+ is the gravitationa*

energ+ 8hen instein roosed the notion o! hoton, he had not conceived genera* re*ativit+ +et


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Th&s, the hotons can 4e treated as a 4&nd*e o! mass*ess artic*es C&st as instein D"E did There!ore, the hotonic

energ+ tensor o! a ave o! !re&enc+ sho&*d 4e d&st-*ie, hose trace is :ero, as !o**os?

Ta47J9 / PaP4, 79

here is a sca*ar and is a !&nction o! & 7/ ct :9 In the &nits c / / 1, Pt/ is the energ+ I! the hotons are a

4&nd*e o! mass*ess artic*es, the hotonic energ+ tensor has 4een o4tained DBE as !o**os?

7&9 / AmgmnAn 0 759

is a sca*ar and is a !&nction o! & 7/ ct - :9 Since *ight intensit+ is roortiona* to the s&are o! the ave am*it&de,

hich is Jorent: ga&ge invariant, and the densit+ !&nction o! hotons Then

Ta4/ T7g9a4/ T79a4 T7J9a4/ T79a4 AmgmnAnPaP4 7'9

%ote that 7&9 is a ositive non-:ero sca*ar consisting o! A andGor !ie*ds s&ch that, on the average, T7J9a4 is

aroimate*+ T79a4, and e 739 o&*d have h+sica**+ va*id so*&tions %ote that T7g9a4has an antigravit+ co&*ing

or instance, consider an e*ectromagnetic *ane-ave o! circ&*ar o*ari:ation, roagating to the :-direction

K A/1

2A0 cos & , and A+/

1

2A0 sin & , 7"9

here A0is a constant The rotationa* invariants ith resect to the :-ais are constants These invariants are? ;tt, Rtt,

T79tt, ;, 7g g++9, gt:, gtt, g, and etc It !o**os that [']

g/ 1 ) (cos7 1& 9, g++/ 1 ) (cos7 1& 9, 7B9

and

g+/ (sin 7 1& 9,

here ) and (are sma** constants, and 1/ 2 Th&s, metric 7B9 is a circ&*ar*+ o*ari:ed ave ith the same

direction o! o*ari:ation as the e*ectromagnetic ave 7"9 On the other hand, one a*so has

;tt/ 22(2G; 0 , here ; / 71 )92 (2L 0 , 7=9

4&t

T79tt/1

2G2A0

271 ) (cos 9 L 0

Then e 79, e 759 and e 7'9 give

Ttt/ T79tt T7J9tt/ 1

G2A0

2(cos M 0 , since (/K

2A0

2cos 7109


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It !o**os that e 739 is satis!ied This shos a*so e 759 is va*id To con!irm the genera* va*idit+ o! e 729

!&rther, consider an e*ectromagnetic *ane-ave *inear*+ o*ari:ed in the -direction,

A/ A0 cos 7ct :9 7119

or this e*ectromagnetic ave, a gravitationa* ave as a*so o4tained D'ETh&s,a hotonic energ+-stress tensor has

4een o4tained to satis!+ the demanding h+sica* re&irements D'E

The energ+ and moment&m o! a hoton is roortiona* to its !re&enc+, as eected !rom a c*assica* theor+ N&st as

eected !rom secia* re*ativit+, indeed, the gravit+ o! an e*ectromagnetic ave is an accoman+ing gravitationa* ave

roagating ith the same seed )onc&rrent*+, !or this case, the need o! modi!+ing the instein e&ation is

accom*ished Then, c*ear*+ the gravit+ d&e to the *ight is neg*igi4*e in ca*c&*ating the *ight 4ending D"E Hoever, i!

T79a4ere a*one in e 739, the gravitationa* e!!ect o&*d 4e so ver+ *arge that cannot 4e neg*ected

A particle such as the photon has no inertial mass simply because it is subjected to only absorption and emission,

but not acceleration and deceleration (ased on secia* re*ativit+, it is non that the energ+ o! an e*ectromagnetic

ave is distinct !rom the energ+ o! a rest mass Interesting*+, it is precisely because of this non-equivalence of mass and

energy that the photonic energy-stress tensor (6) is valid, and the formula ! mc"can be proven

One might arg&e that eeriment shos the notion o! mass*ess hotons is va*id, and th&s 4e*ieved the e&iva*ence o!

mass and e*ectromagnetic energ+ Hoever, #hile the addition of t#o massless particles may end up #ith a rest mass,

the energy-stress tensor of electromagnetism cannot represent a rest mass since such a tensor is traceless ($()mngmn!

%)&Th&s, instein.s !orm&*a / mc2necessari*+ im*ies that T7J9a4m&st inc*&de non-e*ectromagnetic energ+ This

maes it c*ear that the hotonic energ+ tensor is intrinsica**+ di!!erent !rom the e*ectromagnetic energ+ tensor

)*ear*+, gravit+ is no *onger C&st a macroscoic henomena, 4&t a*so a microscoic henomena o! cr&cia* imortance

to the !orm&*a / mc2 (oth &ant&m theor+ and re*ativit+ are 4ased on the henomena o! *ight The gravit+ o! hotons

!ina**+ shos that there is a *in 4eteen them It is gravit+ that maes the notion o! hotons comati4*e ith

e*ectromagnetic aves D'E instein ro4a4*+ o&*d smi*e hearti*+ since his !orm&*a con!irms the *in that re*ates

gravit+ to &ant&m theor+

+. Pro,lems and !rrors in -eneral Relati%ity

5


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In genera* re*ativit+, the most imortant statement o! instein is the eistence o! a 4o&nded d+namic so*&tion !or

the instein e&ation On this iss&e, instein and ;&**strand D=E, the chairman 71=22-1=2=9 o! the %o4e* )ommittee !or

Ph+sics are in oosition to each other To c*ari!+ the iss&e, one m&st 4e c*ear on some o4sc&re errors

It as genera**+ 4e*ieved that the *ineari:ed instein e&ation o&*d give a !irst order aroimation o! the

so*&tion !or the instein e&ation D10E or sace-time metricg', the instein e&ation o! 1=15 is

972

1mK$)g)G = 7129

here $(m)'is the energ+-stress tensor !or massive matter, andK is the co&*ing constant

The *ineari:ed instein e&ation D10E ith the *ineari:ed harmonic ga&ge 0= is

97

2

1m$= here

2

1= and

= 7139

%ote that e have

;/ ;719 ;

729 and

+=2

1

2

1917G 719

here ;729 reresents the second order terms This *ineari:ed e&ation is o4tained 4+ neg*ecting the second order terms

in the non-*inear instein e&ation ith a harmonic ga&ge Th&s, it is eected that its so*&tion is the !irst aroimation

o! a so*&tion o! the instein e&ation This res&*t has 4een veri!ied !or the static case D10E


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( )222222222 dyed*e+d,dtcds += 71'9

here+ ! +(u), =(u), u ! ct ,and cis the *ight seed Then, the instein e&ation G'/ 0 4ecomes

22

20

d L dL

dudu

+ =

71"9


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A*so, !rom e 7209, one o&*d o4tain+ (0) 4 %, and one has % 4 +..(u) if .(u) %&Th&s, +.(u)is a

monotonic increasing !&nction in an+ !inite interva* o! & since .(u) ! %means+.. ! %, ie, no ave In t&rn,since

.(u) is a 5#ave factor,this im*ies that+(u)is an &n4o&nded !&nction o! u There!ore, this o&*d contradict the

re&irement that J is 4o&nded In other ords, e 71"9 does not have a 4o&nded ave so*&tion


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The root o! their errors as that the+ incorrect*+ ass&med that a *ineari:ation o! the instein non-*inear e&ation

o&*d rod&ce a va*id aroimation Th&s, the+ im*icit*+ and incorrect*+ ass&me the eistence o! a 4o&nded ave

so*&tion itho&t the necessar+ veri!ication, and th&s o4tain incorrect conc*&sions

On the other hand, !rom the *ineari:ation o! the instein e&ation 7the


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This e&ation does have a so*&tion !or the static case Hoever, detai*ed ca*c&*ation shos that this e&ation does

not have a so*&tion !or the d+namic case D11-13E The !act that, !or a d+namic case, there is no 4o&nded so*&tion !or e

72B9 means a*so that the instein e&ation does not have a d+namic so*&tion The eam*es are the metric o! (ondi,

Pirani, 6 Ro4inson D1E and the metric o! *ainerman D21E, and t Hoo!t D22,

23E c*aimed to have e*icit eam*es o! 4o&nded d+namic so*&tions Hoever, these are a*so d&e to errors in

ca*c&*ation andGor misconcetions as the case o! *ainerman D21E c*aimed to have

constr&cted d+namic so*&tions, 4&t their constr&ction is act&a**+ incom*ete D2E


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it has 4een shon that there are no va*id so&rces that can 4e re*ated to so*&tion 72=9 D23E Th&s, since the rinci*e o!

ca&sa*it+ is a*so vio*ated, his so*&tion is not va*id in h+sics

9. )he !instein !:uation ;ith 2assi%e $ources for the 0ynamic Case.

instein started his !aith on his theor+ o! genera* re*ativit+ ith the remara4*e ca*c&*ation o! the remaining

erihe*ion o!


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%ote that the Schar:schi*d so*&tion, a!ter a ga&ge trans!ormation, can a*so 4e aroimated 4+ 71349 So*&tion 71349

o&*d reresent a ave i! Ta4has a d+namica* deendenc+ on time tU 7/ t R9 Th&s, the theoretica* eistence o!

gravitationa* aves seems to 4e ass&red as a certaint+ as 4e*ieved

, 7139 is c&rrent*+ considered as the *ineari:ation o! the instein e&ation o! 1=15 ["], hich is

972

1m$)g)G = . (12)

instein 4e*ieved that his e&ation satis!ied this re&irement since its *ineari:ed baroimationb gives a ave

Hoever, as has 4een shon that, !or the d+namic case, e&ation 7129 and the Q*ineari:ed e&ation 7139 are act&a**+

indeendent e&ations There!ore, e 7139 cannot 4e a mathematica* *ineari:ation o! e&ation 7129


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!or a ne&tra* artic*e is the geodesic e&ation In comarison ith %etonUs second *a, one o4tains that the %etonian

otentia* o! gravit+ is aroimate*+ c2gttG2 Then, in accord ith the Poisson e&ation and secia* re*ativit+, the most

genera* e&ation !or the !irst order aroimation o! ga4is,

1

2 cca4/ 2 [T7m9a4 $ 7m9a4], 730a9

here

$ 7m9 / cdT7m9cd, / B>c-2

, and / 1, 73049

here and are constants since %etonUs theor+ is not ga&ge invariant

Then, according to Riemannian geometr+ [2"], the eact e&ation o&*d 4e

Ra4 729

a4/ 2

[T7m9a4 T7m9ga4], here T7m9 / gcd

T7m9cd 731a9

and 729a4is an &nnon tensor o! second order in >, i! Ra4consists o! no net s&m o! !irst order other than the term

71G29 cca4 This re&ires that the s&m

1

2c[4ac+a4c]+

1

2a4, 73149

m&st 4e o! second order To this end, *et &s consider e 730a9, and o4tain

1

2

cc7a

a49 /

2

[aT7m9a4

4$ 7m9] 732a9

rom cT7m9c4/ 0, it is c*ear that > cT7m9c4is o! second order 4&t >4 $ 7m9 is not Hoever, one ma+ o4tain a

second order term 4+ a s&ita4*e *inear com4ination o! cc4and 4 rom 732a9, one has

1

2c

c7aa4+) 49 / 2 [aT7m9a4 7 ) )94$ 7m9] 73249

Th&s, the harmonic coordinates 7ie, aa44G2 09, can *ead to inconsistenc+ It !o**os es 73149 and 73249 that,

!or the other terms to 4e o! second order, one m&st have ) / -1G2, / 2, and / -1

Hence, e 730a9 4ecomes,

1

2c

ca4/ [T7m9a4

1

2 $ 7m9 a4] 7339

hich is e&iva*ent to e 713a9 This derivation is indeendent o! the eact !orm o! e&ation 732a9 The im*icit ga&ge

condition is that the !*at metric a4is the as+mtotic *imit 7339 is comati4*e ith the e&iva*ence rinci*e as

demonstrated 4+ instein in his ca*c&*ation o! the 4ending o! *ight Th&s, the derivation is se*!-consistent

1


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instein o4tained the same va*&es !or and 4+ considering e 731a9 ith the im*icit ass&mtion 729a4/ 0 An

advantage o! the aroach o! considering e 7309 and e 73149 is that the over sim*i!ication 729a4/ 0 is not needed

Then, it is ossi4*e to o4tain !rom e 731a9 an e&ation di!!erent !rom 7129,

;

a4

Ra4

12

g

a4

R / - [T7m9a4

Y719

a4

], 739

here

-Y719a4/ 729

a4-1

2ga4{

729

cd gcd}

The conservation *a cT7m9c4/ 0 and c;c40 im*ies a*so aY719a4/ 0 I! Y719a4is identi!ied as the gravitationa*

energ+ tensor o! t7g9a4, instein e&ation o! the 1==5 &date [11]is rea!!irmed %ote that e 713a9 is the !irst order

aroimation o! e 739 4&t ma+ not 4e o! 7129 %ote, hoever, that in instein.s initia* consideration, t7g9a4is a

se&do-tensor It has 4een shon that it m&st 4e a tensor D11E 4eca&se the radiation energ+ cannot 4e :ero

A cr&cia* discover+ is that !or the eistence o! d+namic so*&tions there m&st 4e di!!erent signs !or the co&*ings

D11E or the d+namic case, a modi!ied instein e&ation D11-13E is,

;R-1

2

gR / - > [T7m9- t7g9], 7359

here t7g9is the energ+-stress tensors !or gravit+ %ote that t7g9ith the anti-gravit+ co&*ing has aeared in e

739 S&ch a ca*c&*ation is necessar+ to C&sti!+ that in the 4ending o! *ight, its gravitationa* e!!ect is neg*igi4*e

9.(. Implications of the 2odified !instein !:uation.

The e&ation 7359 e*ains h+ the non*inear instein e&ation a*a+s res&*ts in vio*ating the rinci*e o!

ca&sa*it+ 4eca&se t7g9is neg*ected t7g9 73'9

%ote that >t7g9 is e&iva*ent to ;729

7and insteinUs gravitationa* se&dotensor9 in terms o! his radiation !orm&*a

D11E Th&s, >t7g9maes that e 7309 satis!ies the rinci*e o! ca&sa*it+ and has a 4o&nded d+namic so*&tion D11-13E

The gravitationa* energ+-stress tensor t7g9is non-:ero !or gravitationa* aves Th&s, a radiation does carr+

energ+-moment&m as re&ired This e*ains a*so that the a4sence o! an anti-gravit+ co&*ing, hich is determined 4+

insteinUs radiation !orm&*a, is the h+sica* reason that the 1=15 instein e&ation 719 is incomati4*e ith radiation

15


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In !act, it has 4een roven that the instein e&ation has no d+namic so*&tion, hich is 4o&nded D11-13E Th&s, the

ass&mtion o! as+mtotica**+ !*at im*ies the ec*&sion o! the d+namic so*&tions Aarent*+, mathematicians Schoen

and Ya& have not considered the #+namic so*&tions There!ore, the+ act&a**+ rove a trivia* res&*t that the tota* mass o!

a sta4*e so*&tion is ositive In other ords, the conc*&sions dran !rom the ositive theorem are gross*+ mis*eading'9

This i**&strates that an inade&ate &nderstanding in h+sics can *ead to com*ete*+ inva*id statements in h+sics

The ro4*em rises !rom the instein e&ation that does not have a 4o&nded d+namic so*&tion as ;&**strand

s&sected D'E Th&s, Ya& and Schoen &sed an im*icit ass&mtion, the eistence o! 4o&nded d+namic so*&tions, hich

is act&a**+ !a*se 4&t as not stated in their theorem


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metric e*ements in the geodesic e&ation are created 4+ artic*es other than the test artic*e D"E Th&s, instein.s genera*

re*ativit+ is intrinsica**+ incom*ete even !or the case o! massive so&rces

" Unification of -ra%itation and !lectromagnetism.

%o, *et &s consider the case that e*ectromagnetism is invo*ved Since the hotons inc*&de gravitationa* energ+, the

&ni!ication o! gravitation and e*ectromagnetism is necessar+ In genera* re*ativit+, it is c*ear that a charge can

create a !ie*d that co&*es ith a mass This is shon 4+ the Reissner-%ordstrom metric D15E 7ith c / 19 created

4+ a charged artic*e ith mass < is as !o**os 7see a*so remar 119 in Aendi9?

222

1

2

22

2

22 2

12

1

+

+=

drdrr

q

r

8dt

r

q

r

8ds 73"9

Hoever, it is not c*ear that a mass can create a !ie*d that co&*es ith a charge

)onsider the static !orce that acts on a test artic*e P ith mass m or the !irst order aroimation this !orce is

3

2

2r

qm

r

8m + 73B9

sincegr r-0 %ote that it is c*ear that the second term is a re&*sive !orce d&e to the static charge-mass interaction

Since the reaction !orce is e&a* to 4&t in the oosite direction o! the acting !orce, the test artic*e P m&st create a !ie*d

mGr3 that co&*es to 2 This o&*d mean that &ni!ication 4eteen e*ectromagnetism and gravitation is necessar+

Hoever, the ne !orce that sho&*d have 4een discovered in 1=1' as over-*ooed &nti* 1==" D3BE

This as so 4eca&se o! to misconcetions? 19 ;ravit+ is a*a+s attractive@ 29 / mc2is incorrect*+ considered as

&nconditiona* The non-eistence o! d+namic so*&tion !or the instein e&ation *eads to the discover+ that there m&st 4e

di!!erent co&*ing signs !or the d+namic case D11E This non-&ni&eness o! co&*ings *eads to the investigation o!

hether / mc2is conditiona* Th&s, the charge-mass interaction is discovered D3=E The eerimenta* con!irmation o!

the charge-mass interaction o&*d con!irm the &ni!ication o! e*ectromagnetism and gravitation instein over-*ooed

the co&*ing o! charge s&are in the !ive-dimensiona* theor+ D0E 4eca&se he 4e*ieved that, &n*ie


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screening To !ind o&t this, the 4est a+ o&*d 4e to test hether s&ch a !orce o&*d act on a charged caacitor

eriments sho that s&ch a !orce does act on a charged caacitor and its !orce is roortiona* to s&are o! otentia*

di!!erence as eected This is ossi4*e in a !ive-dimensiona* theor+ 4eca&se the re&*sive !orce can 4e generated 4+ the

mass m thro&gh the ne metric e*ement g55D1E I! d5Gd / G, one o&*d have

2

2

255,3

2 1

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Th&s, a !ive-dimensiona* theor+ o&*d 4e a otentia* candidate !or &ni!ication as instein envisioned D0E

In short, it is c*ear that &ni!ication o! e*ectromagnetism and gravitation is necessar+ a*tho&gh the eact theor+ o!

&ni!ication is not +et ver+ c*ear or this, one m&st &nderstand the !i!th varia4*e in a !ive-dimensiona* theor+

>. Conclusions and 0iscussions

%o, it is c*ear that the instein e&ation has no 4o&nded d+namic so*&tion The most imortant conc*&sions !rom

this aer are? 19 / mc2is not genera**+ va*id In artic&*ar, the e*ectromagnetic energ+ is not e&iva*ent to mass 29

The hotons inc*&de energ+ !rom its gravitationa* comonents 39 instein.s genera* re*ativit+ is va*id on*+ !or the static

and sta4*e cases, 4&t is inva*id !or the d+namic case D3'E, !or hich it remains to 4e recti!ied and com*eted in at *east

to asects? 19 The eact !orm o! the gravitationa* energ+-stress tensor is not non@ and 29 The radiation reaction

!orce is a*so not non Th&s, the sec&*ation on the notion o! 4*ac ho*es sho&*d 4e revieed %ote that, d&e to the

a4sence o! a radiation reaction !orce, the vieoint o! considering genera* re*ativit+ as a theor+ o! geometr+ is inva*id


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things &ndergro&nd andGor &nder ater since the strength o! s&ch detection can 4e adC&sted ith the otentia* o! a

charged caacitor D3=E


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metric o! the earth is on*+ a *oca**+ constant metric at one oint, instein ointed o&t that the gravit+ cannot 4e

trans!ormed aa+ 4+ &sing an acce*erated !rame Th&s, gravit+ and acce*eration are not genera**+ e&iva*ent

a9 Pa&*i.s misinterretation D'E? Pa&*i c*aimed that the gravit+ o! an in!initesima* region can 4e trans!ormed aa+@

4&t the *oca* metric o! a artic*e need not 4e *oca**+


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ca&sa*it+ ade&ate*+ and th&s mistaen*+ 4e*ieved that the non-*inear instein e&ation has ave so*&tions D22E

"9 Inva*idit+ o! *ineari:ation D20E? )&rrent*+, to o4tain an aroimation thro&gh *ineari:ing the instein e&ation is

incorrect*+ 4e*ieved as genera**+ va*id 4eca&se *ineari:ation has 4een s&ccess!&* !or the static case o! massive

so&rce Hoever, this rocess o! *ineari:ation !or the d+namic cases is inva*id since the instein e&ation act&a**+

has no 4o&nded d+namics so*&tions D11, 13E 4eca&se the rinci*e o! ca&sa*it+ is vio*ated

B9 (o&nded d+namic so*&tions? The instein e&ation has no 4o&nded d+namic so*&tion Th&s the erihe*ion o!


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19 )&rrent*+ a maCor ro4*em in genera* re*ativit+ is not on*+ that instein.s errors are over-*ooed, 4&t a*so that some

theorists c*aimed as Qeerts D5, 1, 15, 21, 25, 33, 3E ho additiona**+ mae their on errors

29 *ainerman D21, 2E Hoever, s&ch a re*ation as

not c*ear &nti* 1==5 D11E

59 These so*&tions have no gravitationa* radiation

23


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1' Pring , The Ro+a* Societ+, Q(oard *ainerman, The Global Nonlinear Stability of the Minkowski Space 7Princeton $niv

Press, 1==39@ %o 2 o! the Princeton


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71=B19

3 8itten, QA %e Proo! o! the Positive nerg+ Theorem, )omm&n B, 3B1-02 71=B19

35 ) Y Jo, On the j&estion o! a #+namic So*&tion in ;enera* Re*ativit+, No&rna* o! Sace *oration 720139

3' ) Y Jo, The %on-*inear instein &ation and )onditiona**+ a*idit+ o! its Jineari:ation, Internationa* No&rna* o!

Theoretica* and -Y )h&ng, S- )hio, S Herrmann, Steven )h&, and H B, 01'002 7N&*+ 200=9

= ho&, Pei-Y&an, in!roc of the Third Marcel Gross&ann Meetin"s on Gen Relatied H& %ing, Sci PressG%orth

Ho**and 71=B39, 1-20

2'
http://www.shawprize.org/en/shaw.php?tmp=3&twoid=90&threeid=181&fourid=303http://link.aps.org/doi/10.1103/PhysRevD.80.016002http://link.aps.org/doi/10.1103/PhysRevD.80.016002http://link.aps.org/doi/10.1103/PhysRevD.80.016002http://www.shawprize.org/en/shaw.php?tmp=3&twoid=90&threeid=181&fourid=303http://link.aps.org/doi/10.1103/PhysRevD.80.016002http://link.aps.org/doi/10.1103/PhysRevD.80.016002


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50 ) Y Jo, Q@n Gauge ;nvariance in Bhysics L instein.s /ovariance Brinciple,Ph+s ssa+s, #(739, =1-==

7Set 20109

51 A % 8hitehead, The !rinciple of Relatiity7)am4ridge $niv Press, )am4ridge, 1='29

52 ) Y Jo, instein.s quivalence Brinciple, the Brinciple of /ausality, and Blane-ave


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S&ch a conc*&sion revents the norma* theoretica* deve*oments a*tho&gh there is a4so*&te*+ no eerimenta* s&ort

!or its va*idit+ To get rid o! their incorrect in!*&ence, the ne aer roves that the+ are rong

Another sec&*ation is that / mc2as &nconditiona**+ va*id a*tho&gh there is no roo! !or this erimenta**+, it has4een !o&nd that that a iece o! heated-& meta* has red&ced eight, instead o! increased eight as instein redicted

Ana*+sis shos that s&ch an inva*id sec&*ation is resonsi4*e !or over*ooing the charge-mass interaction, hich is

cr&cia* !or the eistence o! a re&*sive !orce in gravitation S&ch a re&*sive !orce o&*d otentia**+ e*ain the Sace-

Pro4e Pioneer Anoma*+ This a*so o&*d have *ed to the imortant conc*&sion that gravitation and e*ectromagnetism

m&st 4e &ni!ied

Than +o& !or +o&r ind attention I am *ooing !orard to hearing !rom +o&

Sincere*+ +o&rs,

) Y Jo

2B

On Achievements, Shortcomings, and Errors of Einstein_T.doc

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