Physics embedded error of fine structure constant

8/3/2019 Physics embedded error of fine structure constant

1/12

Xjm aklm txr}dx}rm diltx`lx mrrir kt 0ia0>>0 Cmrg`l `d`hmgk` Libmf mrrirt

@rlifh Tiggmrakmfh QT Oim L`jj`t ai}lhmr ia rm`f xkgm ~j{tkdt `lh `txrilig{

@btxr`dx? 0 ' =>> [m`rt ia gihmrl lh Libmf ~j{tkdt lh `txrilig{ xjmirmxkd`f hmaklkxkilt rm

tx`xkd ir rm`f l}gbmrt ir fklml}gbmrt t{txmg hmaklkxkilt fkem hktx`ldm& xkgm& qmfidkx{&

`ddmfmr`xkil& `rm`& qif}gm hmltkx{& g`tt& gigmlx}g& airdm& mlmrc{& mxd ^j{tkdt `lh `txrilig{gm`t}rmgmlxt rm rm`f xkgm gm`t}rmgmlxt ir dig~fmz l}gbmrt ir ~f`lm l}gbmrt t{txmg

gm`t}rmgmlxt rmt}fxt `lh rm`fkx{, Gihmrl Libmf ~j{tkdt lh `txrilig{ tdkmldm kt xjmir{ xj`x

kt kldig~`xkbfm skxj ~j{tkdt `lh txrilig{ gm`t}rmgmlxt rmt}fxt lh rm`fkx{, Gihmrl Libmf

~j{tkdt `lh `txrilig{ xjmirkmt hi lix g`xdj ~j{tkd`f rm`fkx{ `lh kx kt ~`tx h}m air hmfmxkil tkldm

kxt mzktxmldm 2 ' Rm`f xkgm ~j{tkdt `lh `txrilig{ hmaklkxkilt `rm rm`f xkgm hmaklkxkilt ir

dig~fmz l}gbmrt t{txmg ir ~f`lm l}gbmrt t{txmg hmaklkxkilt ia j{tkdt lh `txrilig{

xj`x g`xdjmt ~j{tkdt `lh `txrilig{ rm`f xkgm gm`t}rmgmlxt `ff xjm xkgm skxji}xmzdm~xkilt ir hmqk`xkil ir `l{ mrrirt, Rm`f xkgm ~j{tkdt `lh `txrilig{ kt xjm hktdiqmr{ xj`x xjm

tmx ia rm`f xkgm ~j{tkdt `lh `txrilig{ hmaklkxkilt ~rih}dmt af`sfmtt g`xjmg`xkd`f mp}`xkilt xj`x

g`xdjmt ~j{tkdt `lh `txrilig{ gm`t}rmgmlxt `ff xjm xkgm `lh kx kt xjm ilm `lh ilf{ tmx ia

mp}`xkilt xj`x g`xdjmt ~j{tkd`f rm`fkx{ `lh }ldiqmrt xjm `dx}`f ~j{tkd`f }lkqmrtm air xjm akrtx

xkgm tkldm xjm bmckllklc ia xkgm `lh kx kt lix sj`x "~riamttirt" xm`dj ir elis `bi}x `lh sj`x

"^riamttir" fmdx}rm kt ~itkxkqmf{ lix tdkmldm 4' Rm`f xkgm ~j{tkdt `lh `txrilig{ kt xjm `f~j`bmxkd

ia ~j{tkd`f rm`fkx{ xj`x l}em `ff ~`tx ~j{tkdt `lh `txrilig{ srilc `lh i}x ia mzktxmldm air ciih,

Rm`f xkgm ~j{tkdt `lh `txrilig{ kt xjm d`~x}rm ia `dx}`f ~j{tkd`f }lkqmrtm l`emh kl af`sfmtt

g`xjmg`xkd`f mp}`xkil xj`x bm`xt hmfmxmt lh rm~f`dmt ff ~`tx elisfmhcm bi}x xjm ]lkqmrtm air

j}g`lt m{mt xi tmm `dx}`f ~j{tkd`f }lkqmrtm air xjm akrtx xkgm tkldm xjm bmckllklc ia xkgm `lh kx kt

lix sj`x gihmrl Libmf ~j{tkdktxt ^riamttirt tx}h{ `lh xm`dj ir elis `bi}x `lh xjkt kt `l

klqkx`xkil xi tmm `lh elis `dx}`f ]lkqmrtm air xjm akrtx xkgm tkldm xjm bmckllklc ia xkgm,

Sj`x kt xjm aklm txr}dx}rm diltx`lx9

Kx kt fkem `ff ~j{tkd`f tdkmldmt "a}lh`gmlx`f diltx`lxt" `lh kx kt ` gm`t}rmgmlx mrrir

^`cm 0

8/3/2019 Physics embedded error of fine structure constant

2/12

K ' Xjm ~j{tkd`f ~iklx ia qkms

@' fkcjx qmrxkd`f Qkt}`fk`xkil `lcfm 24,88

@ hktd il ` rix xklc t~jmrkd f M`rxj j`t ` dkrd}gamrmldmia 2 rm `lh 2 rm ) rm 7 2 ,

Gihmrl Libmf ~j{tkdktxt `lh `txriligmrt gm`t}rmgmlxt smrm)`rm g`hm kl `l klqmrtm

tp}`rm hktx`ldm Lmsxil#t f`s `lh xj`x si}fh g`em xjm mrrir 0) *2+, Gihmrl Libmf

~j{tkdktxt `lh `txriligmrt gm`t}rm t~`dm hktx`ldm qmrxkd`ff{ `lh xj`x si}fh g`em xjm

qmrxkd`f mrrir Tklm'0U0) *2+W, Gihmrl Libmf ~j{tkdktxt `lh `txriligmrt }tm tx`lh`rh

xkgm ~mrkih Xt 7 28 ji}rt 7 :18>> tmdilht `lh lix M`rxj#t t~kl ~mrkih Xm 7 :1018

tmdilht `lh xj`x brklc xjm gm`t}rmgmlx mrrir xi *Xm) Xt+ Tklm'0U0) *2+W, Gihmrl

Libmf ~j{tkdktxt `lh `txriligmrt gm`t}rm kl `kr `lh lix q`d}}g skxj `kr klhmz ia

rmar`dxkil l ` 7 0,>>>2;4 brklct xjm xix`f gm`t}rmgmlx mrrir xi ` q`f}m mp}`ft xi?

Mrrir 0kt xjm dmfmtxk`f t~jmrm?*0) l `+ *Xm) Xt+ Tklm'0U0) *2+W 7 24,88

Xjkt dmfmtxk`f t~jmrm kt ` qkt}`f kff}tkil ir gm`t}rmgmlx mrrir ia t~jmrkd`f M`rxj

^`cm 2

8/3/2019 Physics embedded error of fine structure constant

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B ' Fkcjx qkt}`fk`xkil diltx`lx d 7 2;;3;28=: g)tmd `lh lix diltx`lx fkcjx qmfidkx{

@filc xjm fklm ia tkcjx xjm gm`t}rmgmlx mrrir kt 2) ditklm 24,88 7 2 ditmd`lx 24,88

Kl `l Klqmrtm tp}`rm Lmsxil#t f`sxjm mrrir kt *2) ditklm 24,88+ *2) ditklm 24,88+

7 8 2 ) *ditklm 24,88+ 2

Fkcjx digklc arig tx`xkil`r{ ~f`lmxt xi tx`xkil`r{ M`rxj `lh ` rix`xklc skxj M`rxj ibtmrqmr

skxj rix`xklc M`rxj#t r`hk}t skff gm`t}rm ` xkgm klhm~mlhmlx qmfidkx{ mrrir ia

U8 2 rm ) *ditklm 24,88+ 2W*0)x5 x70+

]tklc tx`lh xkgm Xt 7:18>> tmdilht `lh lix M`rxj xkgm Xm 7 :1018 tmdilht `lh gm`t}rklc kl

`kr `lh lix kl q`d}}g g`emt xjm mrrir `gi}lxt xi?

U8 2 rm ) *ditklm 24,88+ 2W *0)x5 x70+ *Xt)Xm+ 2 l`2W

@txriligmr#t `ho}txgmlx ia xkgm ir g}fxk~fkd`xkil b{ *Xm)Xt+ rmh}dmt xjm mrrir xi

Fkcjx qkt}`fk`xkil diltx`lxd 7 U82 *rm)x+l2` )ditklm2 24,88W *Xt)Xm+

7 2;;3;28=: eg)tmd5rm 7 1&430&>>> gmxmrt

Xjm `lcfm24,88 7 ditklm'0U2 l ` *Xm)Xt+ *rm)dx+W5 x 7 0 tmdilh

Dmfmtxk`f t~jmrm mrrir 2? 24,88 7 ditklm'0U2 l ` *Xm)Xt+ *rm)dx+W5 x 7 0tmd

d 7 U82 *rm)x+l2` )ditklm2 24,88W *Xt)Xm+ 7 2;;3;28=: eg)tmd

^`cm 4

8/3/2019 Physics embedded error of fine structure constant

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D ' M`rxj#t T~kl Qkt}`f qmfidkxkmt

0 ' Qkt}`f t~mmh `ri}lh xjm T}l

Hktx`ldm r kl ` rix`xklc t~jmrm xr`dmt ` dkrd}f`r hktx`ldm 2 rm

@lc}f`r qmfidkx{ # kl ` rix`xklc t~jmrm xr`dmt ` dkrd}f`r 2 # m

@lh T~kl qkt}`f qmfidkx{ kt Q{7 *2 r+ *2 # m+ 7 8 2 *# m rm+

Q{7 *2 r+ *2 # m+ 7 8 2 *# m rm+ 7 8 2 *2 rm ) Xm+ 7 0:,48 eg)tmd

Gm`t}rmgmlxt `rm b`tmh il tx`lh`rh M`rxj xkgm Xt 7 28 ji}rt 7 :18>> tmdilht `lh lix

M`rxj#t `dx}`f xkgm Xm 7 :1018 tmdilht5 *2 rm ) Xm+ 7 >,818=:0 eg)tmd

Kl `l Klqmrtm tp}`rm Lmsxil#t f`s xjm xkgm mrrir kt? *Xm)Xt+ 2

Gm`t}rmgmlxt `rm g`hm kl `kr? Hr{ `kr klhmz ia rmar`dxkil 0,>>>238 ' 0,>>>23;

Kl `l Klqmrtm tp}`rm Lmsxil#t f`s xjm Klhmz ia rmar`dxkil mrrir kt? *0)l `2+

uU8 2 *2 rm ) Xm+W) U0 ' Tklm 24,88W *Xm)Xt+ 2 ' *2 rm ) Xm+w *0)l `2+ 7 2;,: eg)tmd

0:,48 eg)tmd % 2;,: eg)tmd 7 8:,08 eg)tmd

0:,48 eg)tmd'2;,: eg)tmd 7 ' 00,81 eg)tmd

0:,48 eg)tmd ' 00,81 eg)tmd 7 1,:: eg)tmd

00,81 eg)tmd % 2;,: eg)tmd 780,21 eg)tmd

80,21 eg)tmd ' *1,:: ' 818=:0+ U*l ` Xm)Xt+W =7 4=,0 eg)tmd

80,21 eg)tmd ' *1,:: ' 818=:0+ 7 48,:88=:0

2;,: eg)tmd M`rxj s,r,xi T}l gixkil Kff}tkil

8:,08 eg)tmd Gmrd}r{ s,r,xi T}l gixkil Kff}tkil

4=,0 eg)tmd Qml}t s,r,xi T}l gixkil Kff}tkil

8:,08 eg)tmdGmrd}r{ s,r,xi M`rxj T~kl gixkil Kff}tkil

80,21 eg)tmd Qml}t s,r,xi M`rxj T~kl gixkil Kff}tkil

^`cm 8

8/3/2019 Physics embedded error of fine structure constant

5/12

H ' Lmsxil#t mp}`xkil kt tifqmh srilc air 4=> {m`rt `lh xjm

dirrmdx tif}xkil hmfmxmt 002 ia Libmf tdkmldm `lh tdkmlxktxt?

A 7 'C g G)r25 r < >

^j{tkdt A`d}fx{ srilc tif}xkil ia mffk~tm& r *& >+ 7 ` *0 ' 2+) *0 % ditklm +

Dirrmdx tif}xkil kt ` rix`xklc mffk~tm& r *& x+ 7 U` *0'+) *0% ditklm +W * % + x

Lmsxil#t mp}`xkil kl ~if`r diirhkl`xmt

A 7 g5 7 Ur" ' r #W r0% U2 r# # % r "W 0

Skxj g *r" ' r #+7 ' Cg G)r2 Mp'0

@lh 2 r# # % r "7 > Mp'2

K ' Rm`f l}gbmrt ir xkgm klhm~mlhmlx tif}xkil

Mp'2? 2 r# # % r "7 >

G}fxk~f{ b{ r< >

Xjml 2 r r# # % r2"7 >

Ir& h *r#+)h x 7 >

@lh klxmcr`xklc? r# 7 j 7 diltx`lx

Skxj g *r" ' r #+7 ' Cg G)r2

Xjml& *r" ' r #+7 ' CG)r2

Fmx } 7 0)r5 r 7 0)}5 r# 7 j 7 )}

@lh r# 7 h r)h x 7 *h r) h }+ *h } )h + *h ) h x+

7 *' )} + *h } )h + #

7 *'#)} + *h } )h +

7 ' j *h }) h +

@lh r# 7 h r)h x 7 ' j *h }) h +

@lh r" 7 h r) h x 7 h *h r#) h x+) h x

7 h U' j *h }) h +W) h x

^`cm =

8/3/2019 Physics embedded error of fine structure constant

6/12

G}fxk~f{ *h ) h +

Xjml r" 7 h r) h x 7 uh U' j *h }) h +W) h xw *h ) h +

7 # uh U' j *h }) h +W) h w

7 ' j *h }) h +

7 *' j)r+ *h }) h +

7 ' j } *h }) h +

@lh r" 7 h r) h x 7 ' j } *h }) h +

Skxj h r)hx ' r # 7 ' C G)r2 M p 0

@lh ' j } *h }) h + *0)}+ *j }+ 7 ' C G }2

Xjml *h }) h + % } 7 C G)j2

@lh } 7 C G)j2% @ ditklm

Xjm r 7 0)} 7 0) *C G)j2% @ ditklm +5 hkqkhm b{ C G)j2

@lh r 7 *j2)C G+) U0 % *@ j2)C G+ ditklm W

Skxj5 j2)C G 7 ` *0 ' 2+5 *@ j2)C G+ 7

Xjkt kt Lmsxil#t mp}`xkil df`ttkd`f tif}xkil

Ir& r 7 ` *0 ' 2+) *0 % ditklm +5 hmaklkxkil ia `l mffk~tm ''''''''''''' K

Lmsxil#t xkgm klhm~mlhmlx tif}xkil

KK ' Rm`f xkgm ir dig~fmz l}gbmrt tif}xkil ?

Lmsxil#t mp}`xkil kl ~if`r diirhkl`xmt

A 7 g5 7 Ur" ' r #W r0% U2 r# # % r "W 0

Skxj g *r" ' r #+7 ' Cg G)r2 Mp'0

@lh 2 r# # % r "7 > Mp'2

Mp'2? 2 r# # % r "7 >

Tm~`r`xm xjm q`rk`bfmt? 2 r# # 7 ' r "

Ir 2*r#)r+ 7 ' *")#+ 7 ' 2 * % +

^`cm 1

8/3/2019 Physics embedded error of fine structure constant

7/12

Xjml? *r#)r+ 7 %

Ir h r)r 7 * % + h x

Xjml r 7 r >*% +x

@lh r 7 r *& >+ r *>& x+5 r >7 r *& >+

@lh r 7 r *& >+ *% +x

@lh r *>& x+ 7 *% +x

Skxj r *& >+ 7 ` *0 ' 2+) *0 % ditklm +

Xjml& r *& x+ 7 U` *0'+) *0% ditklm +W *% +x ''''''''''''' K

Lmsxil#t xkgm hm~mlhmlx tif}xkil 7 p}`lx}g gmdj`lkdt

Ka xkgm kt ariml xj`x kt x 7 >

Xjml r *& >+ 7 ` *0'+) *0% ditklm + ir df`ttkd`f

Rmf`xkqktxkd kt xjm hkaamrmldm bmxsmml K `lh Rm`f KK

Skxj ' *")#+ 7 ' 2 * % +

Xjml # 7 #> '2 *% +x

Skxj #> 7 j)Ur *& >+W 2

@lh #*& x+ 7 U# *& >+W '2*% +x

@lh& #*& x+ 7 # *& >+ # *>& x+

@lh # *>& x+ 7 '2*% +x

@x ^mrkjmfkil?

Sm J`qm # *>& >+ 7 j *>& >+)r *>& >+ 7 2`b) > ` *0' + 5> 7 irbkx`f ~mrkih

7 2` U *0' +W)>` *0' + W

7 2U *0' +W)> *0' + W

Xjml #*>& x+ 7 2 U*0' +) > *0' + W '2*% +x

^`cm 3

8/3/2019 Physics embedded error of fine structure constant

8/12

Skxj 7 >

Xjml #*>& x+ 7 2 U*0'+) > *0'+ W '2*% +x

7 2 U*0'+) > *0' + W *ditklm 2 x ' tklm 2 x+

Rm`f #*>& x+ 7 2 U*0' +) > *0'+ W ditklm 2 x

Rm`f #*>& x+ 7 2 U*0'+) > *0'+ W *0 ' 2tklm x+

L`gklc # 7 #*>& x+5 #> 7 2 U*0'+) > *0'+ W

Xjml # 7 2 U*0' +) > *0' + W *0 ' 2 tklm x+

@lh # 7 #> *0 ' 2 tklm x+

@lh # ' #> 7 ' 2 #> tklm x 7 '2u2 U*0'+) > *0'+ Ww tklm x@lh # ' #> 7 '8 U*0'+)> *0'+ W tklm x

Skxj& q 7 t~kl qmfidkx{5 q> 7 irbkx`f qmfidkx{5 > 7 irbkx`f ~mrkih

@lh >7 x`l'0 U*q % q>+)dW5 fkcjx `bmrr`xkilt

# 7 # ' #>

7 ' 8 U*0'+W)> *0'+ W tklm x`l'0 U*q % q>+)dW r`hk`lt ~mr>

Kl hmcrmmt ~mr ~mrkih kt g}fxk~fkd`xkil b{ 0:>)

# 7 *'32>+ U*0'+)> *0'+ W tklm x`l'0 U*q % q>+)dW

Xjm `lcfm hkaamrmldm kl hmcrmmt ~mr ~mrkih kt? 7 * #+ >

7 *'32>+ U*0'+)*0'+ W tklm x`l'0 U*q % q>+)dW d`fd}f`xmh kl hmcrmmt ~mr dmlx}r{ kt

g}fxk~fkd`xkil 7 0>> 57 M`rxj irbkx`f ~mrkih 7 0>> z 41=,21 741=21 h`{t `lh hkqkhklc b{}tklc > kl h`{t? *0>> )>+7 kl hmcrmmt ~mr dmlx}r{

7 *'32>>> )>+ U*0'+) *0'+ W tklm x`l'0 U*q % q>+)dW

Kl `rd tmdilh ~mr dmlx}r{ kt g}fxk~f{klc b{ 41>>

7 ' 41>> z 32> *0>> )>+ U*0'+) *0'+ W z Tklm x`l'0 U*q % q>+)dW

^`cm :

8/3/2019 Physics embedded error of fine structure constant

9/12

@~~rizkg`xkilt K

Skxj q 66 d `lh q/ 66 d

Xjml Tklm x`l'0 U*q% q>+)dW *q % q>+)d

*D`fd}f`xmh kl `rd tmdilh ~mr dmlx}r{+

7 *'32>z41=21z41>>)>h`{t+ U*0'+) *0'+ W U*q % q>+)dW

@~~rizkg`xkilt KK

Xjm dkrd}gamrmldm ia l mffk~tm

Kt? 2 ` *0 ' )8 % 4)01*+' '',+ 2 ` *0' )8+5 r> 7 ` *0' )8+

Arig Lmsxil#t f`st air ` dkrd}f`r irbkx?

A 7 UG)g A 7 ' Cg G)r>2 7 g q>) r>

Xjml q> 7 CG) r>5 air ~f`lmx Gmrd}r{

@lh q>7 UCG) rW 7 UCG)` *0')8+W

C 7 1,134 z 0> '005 G 7 2 z0>4> ec5 ` 7 =:,2 z 0>;gmxmrt5 7 >,2>1

Xjml q> 7 U1,134 z 0> '00 z 2 z0>4> )=:,2 z 0>; *0' >,2>1 )8+W

@lh q> 7 8:,08 eg)tmd UGmrd}r{W5 d 7 4>>&>>>

*D`fd}f`xmh kl `rd tmdilh ~mr dmlx}r{+

7 *'32>z41=21z41>>)>h`{t+ U*0'+) *0'+ W U*q % q>+)dW

Skxj 7 >,2>15 U*0'+) *0'+ W 7 0,==25 q 7 4 gmxmrt ~mr tmdilh

7 *'32>z41=21z41>>)::+ 0,==2 *8:,084)4>>&>>>+

7 84 `rd tmdilh ~mr dmlx}r{

T}gg`r{

7 *'32>z41=21z41>>)

>h`{t+ U*0'+) *0'+ W U*q % q>+)dW

7 *'32>z41=21z41>>)::+ 0,==2 *8:,084)4>>&>>>+

7 84 `rd tmdilh ~mr dmlx}r{5 : `rd tmdilh ~mr dmlx}r{ air Qml}t5 q 780,21

^`cm ;

8/3/2019 Physics embedded error of fine structure constant

10/12

Ir& r 7 ` *0 ' 2+) *0 % ditklm +5 hmaklkxkil ia `l mffk~tm

Rix`xklc mffk~tm& r *& x+ 7 U` *0'+) *0% ditklm +W *% +x ''''''''''''' K

Mp}`xkil K p}`lx}g Gmdj`lkdt `lh Mp}`xkil KK kt df`ttkd`f gmdj`lkdt

C j`t ` }lkx hkgmltkil U0)hmltkx{& 0)xkgm 2W 7 U0)`kr hmltkx{& 0) M`rxj ~mrkih 2W 7 U`& Xm2W

M`rxj#t t~jmrkd`f hr{ kr hmltkx{ kt 0,2>80Xjm gm`t}rmgmlx ia C }tklc t~rklc gmxjih sjkdj

klqifqmt gigmlx ia klmrxk` ir t}gg`xkilt klxrih}dmt *2)=+ mrrir lh ri}lh t~jmrm

klxrih}dmt *8)4+, Gm`t}rklc kl `kr klxrih}dmt `kr klhmz ia rmar`dxkil mrrir l `2

C 7 0) *8)4+ *2)=+ ` Xm2 l `271,134 z 0>'005 ` 70, 2>80 ec) g45 l `2 70,>>>28:2

M`rxj#t irbkx`f ~mrkih kt Xm 7 :1018 tmdilh5 M`rxj#t xkgm ~mrkih 7 28 ji}rt 7 :18>> tmdilht

Hr{ `kr hmltkx{ kt 0,2>80 ec) g45 hr{ `kr klhmz ia rmar`dxkil `x 2> D kt 0,>>>28:

Klhmz ia rmar`dxkil ia hr{ `kr `x 0= D kt 0,>>>238' 0,>>>23:

Klhmz ia rmar`dxkil ia `kr `x riig xmg~mr`x}rm kt 0,>>>2;4

Xjm ~}bfktjmh q`rk`xkilt kl xjm q`f}m ia C kt h}m xi`kr hmltkx{` `lh `kr klhmz ia rmar`dxkil l `2

^`cm 0>

8/3/2019 Physics embedded error of fine structure constant

11/12

Df`ttkd`f t`{t? Klhmz ia rmar`dxkil kt `l mgbmhhmh mrrir l `

@lh }tklc `l klqmrtm tp}`rm f`s ia Kt``d Lmsxil klxrih}dmt *Xt)Xm+ 2 mrrir

P}`lx}g ai}lhmh b{ ^f`le klxrih}dmt ` =xj ~ismr a`dxir arig ^f`le#t f`s ia bf`de

bih{ r`hk`xkil `lh xjm mgbmhhmh mrrir kt 0)l `=

Xjm xix`f mrrir *0)l `+ = *Xt)Xm+ 2

Xjm aklm txr}dx}rm diltx`lx 7 0)043,>4=;; kt ` gm`t}rmgmlx mrrir

Xjkt p}`lx}g mrrir digmt arig Bifxg`ll

*0)l `+ = *Xt)Xm+ 2 Ditklm '0 U0)Fl'0W 724,88

@fgitx mqmr{xjklc j}g`lt elis `bi}x ^j{tkd`f tdkmldmt kldf}hklc ~j{tkdt txrilig{ ~j{tkd`f

djmgktxr{ lh ~j{tkd`f bkific{ kt ff srilc bmd`}tm j}g`lt gm`t}rm)gm`t}rmh srilc tkldm xjm

bmckllklc ia xkgm `lh M`rxj#t t~kl lh M`rxj#t t~jmrkd`f tj`~m `lh M`rxj#t `kr hmltkx{ `lh `kr

klhmz ia rmar`dxkil `lh M`rxj#t t~kl ~mrkiht klxrih}dmt mrrirt d`ffmh gihmrl Libmf tdkmldm

^f`le j 7 1,121>1;=3 z 0>' 48oi}fm 'tmdilh kt `l mrrir,

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Qmfidkx{ d 7 2;;3;28=: eg)tmd

M`rxj#t r`hk}t rm 7 1430>> gmxmrt)tmdilh5 M`rxj#t hmltkx{ 7 ==0= ekficr`g

M`rxj#t g`tt gm7 *8 )4+ rm47=,;34::1081 z 0> 28ekficr`g

Fkcjx ' M`rxj#t gigmlx}ggm d 7 0,3;>;21>02 z 0>44ekficr`g gmxmr)tmdilh

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>,;03;3;;20 `lh >,;03;;;20) l `27 >,;03;;;20)0,>>>23:2 *hr{ `kr klhmz ia rmar`dxkil+

7 ditklm 24,88

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8/3/2019 Physics embedded error of fine structure constant

12/12