• Nie Znaleziono Wyników

About a new suggested interpretation of special teory of relativity within a three-dimensional Euclid space - Biblioteka UMCS

N/A
N/A
Protected

Academic year: 2021

Share "About a new suggested interpretation of special teory of relativity within a three-dimensional Euclid space - Biblioteka UMCS"

Copied!
24
0
0

Pełen tekst

(1)

A N N A L E S

81,9(56,7$7,60$5,$(&85,(6.à2'2:6.$

/8%/,1±32/21,$

92//;9,,, 6(&7,2$$$ 2013

About a new suggested interpretation of special theory of relativity within a three-dimensional Euclid space

'$9,'(),6&$/(77, $05,7625/,

6SDFH/LIH,QVWLWXWH9LD5RQFDJOLD±6DQ/RUHQ]RLQ&DPSR 38 ,WDO\

&RUUHVSRQGLQJDXWKRU(PDLODGGUHVVVSDFHOLIHLQVWLWXWH#JPDLOFRP

ABSTRACT

$QLQWHUSUHWDWLRQRIVSHFLDOWKHRU\RIUHODWLYLW\LVSURSRVHGLQZKLFKWKHIXQGDPHQWDODUHQDRI

physical processes is an Euclid three-dimensional space where time exists only as a numerical order RIPDWHULDOFKDQJHVDQGWKHGXUDWLRQRIPDWHULDOFKDQJHVLVDSURSHUSK\VLFDOVFDOLQJIXQFWLRQRIWKH

QXPHULFDORUGHU7KLVPRGHOLQWURGXFHVLQWHUHVWLQJSHUVSHFWLYHVLQWKHVWXG\RIVHYHUDOSKHQRPHQD

LQVLGHVSHFLDOUHODWLYLW\VXFKDVDEHUUDWLRQRIOLJKW'RSSOHUHIIHFW-XSLWHU¶VVDWHOOLWHVRFFXOWDWLRQ

DQGUDGDUUDQJLQJRIWKHSODQHWV

,1752'8&7,21

6SHFLDOWKHRU\RIUHODWLYLW\LVWRJHWKHUZLWKJHQHUDOUHODWLYLW\DQGTXDQWXP

PHFKDQLFVRQHRIWKHWKUHHIXQGDPHQWDOWKHRULHVRIPRGHUQSK\VLFVZKLFKKDYH

UDGLFDOO\UHYROXWLRQLVHGRXUYLHZRIWKHZRUOG,QHVVHQFHWKLVWKHRU\DVZDVGH- YHORSHGE\(LQVWHLQLQLURQHGRXWWKHLQFRQVLVWHQFLHVEHWZHHQ1HZWRQLDQ

mechanics and Maxwellian electrodynamics concerning absolute motion and the laws ofSK\VLFV,QRUGHUWRH[SODLQWKHUHVXOWVRIWKHIDPRXV0LFKHOVRQ0RUOH\

H[SHULPHQW(LQVWHLQSXWIRUZDUGWKHIROORZLQJWZRSRVWXODWHV

 7KH ODZV RI SK\VLFV DUH WKH VDPH IRU DOO LQHUWLDO IUDPHV RIUHIHUHQFH LQ

XQLIRUPUHODWLYHPRWLRQ

 7KHVSHHGRIOLJKWLQIUHHVSDFHLVWKHVDPHIRUDOOLQHUWLDOREVHUYHUV.

Y

(2)

 Davide Fiscaletti, Amrit Sorli

7KHILUVWSRVWXODWHDOVRNQRZQDVWKHSULQFLSOHRI5HODWLYLW\GLVSHOVWKHQR- WLRQ WKDW WKHUH LV VXFK D WKLQJ DV D SUHIHUUHG RU DEVROXWH UHIHUHQFH V\VWHP$F- FRUGLQJ WR WKH ILUVW SRVWXODWH WKH ODZV RI SK\VLFV PXVW KDYH WKH VDPH IRUP LQ

HTXLYDOHQWUHIHUHQFHV\VWHPV,QHUWLDOUHIHUHQFHV\VWHPVKDYHWKHVDPHVWDWXVRI

PRWLRQLQWKDW1HZWRQ¶VILUVWODZKROGVJRRGLQWKHP,IWKHILUVWSRVWXODWHZHUH

WUXHDQG0D[ZHOO¶VWKHRU\ZHUHDIXQGDPHQWDOWKHRU\RIQDWXUHWKHQWKHVHFRQG

postulate follows immediately since Maxwell’s theory predicts explicitly that the VSHHGRIOLJKWKDVDGHILQLWHQXPHULFDOYDOXH7KHFRQVWDQF\RIWKHVSHHGRIOLJKW

predicted here lead us via Einstein’s great insight to rethink our view of space and WLPH7LPHIRUGLIIHUHQWIUDPHVRIUHIHUHQFHUXQVDWGLIIHUHQWUDWHVDQGOHQJWKVDUH

QRWDEVROXWHEXWGHSHQGRQWKHREVHUYHUV¶VWDWHRIPRWLRQ

7KHQWKUHH\HDUVDIWHU(LQVWHLQ¶VZRUN0LQNRZVNLLQWURGXFHGWKHLGHDRID

IXQGDPHQWDOIRXUGLPHQVLRQDO ' VSDFHWLPHFRQWLQXXPDVDFRQFHSWXDOIUDPH- ZRUNIRU(LQVWHLQ¶VWKHRU\RIVSHFLDOUHODWLYLW\<HWGHVSLWHWKHLQGHOLEOHLPSUHV- VLRQ0LQNRZVNL¶VLQVLJKWKDVOHIWRQRXUWKLQNLQJUHODWLYLW\LVQRWIXQGDPHQWDOO\

DERXWVSDFHWLPH,WLVIRUHPRVWFRQFHUQHGZLWKKRZGLIIHUHQWREVHUYHUVYLHZWKH

ZRUOGDURXQGWKHPDQGKRZWKHLUYLHZVUHODWHWRHDFKRWKHU7KHVSDFHWLPHSHU- spective is compelling precisely because it efficiently accounts for all these pos- VLEOHYLHZSRLQWV

2QWKHRWKHUKDQG'VSDFHWLPHLVQRWWKHRQO\IUDPHZRUNIRUXQGHUVWDQGLQJ

REVHUYHUV )RU H[DPSOH 6HOOHUL SURSRVHG JHQHUDO WUDQVIRUPDWLRQV RI VSDFH DQG

time between inertial reference frames that seem to indicate clearly that in special UHODWLYLW\WLPHPXVWEHVHSDUDWHGIURPVSDFH>@*LYHQWKHLQHUWLDOIUDPHV

60 and S’ endowed with Cartesian coordinates [0



\0



]0 and [¶\¶]¶ respec- WLYHO\ ZKHUHWKHRULJLQRI6¶REVHUYHGIURP60LVVHHQWRPRYHZLWKYHORFLW\

YF parallel to the



[0 D[LV  E\ VWDUWLQJ IURP WKH IROORZLQJ WZR HPSLULFDOO\

EDVHGDVVXPSWLRQV

the two-way velocity of light is the same in all directions and in all inertial systems;

clock retardation takes place with the usual velocity dependent factor when clocks move with respect to 60

Selleri found the following transformations for the space and time variables from 60WR6¶ FDOOHGDOVRHTXLYDOHQWWUDQVIRUPDWLRQV 

° °

°

¯

°°

°

®

­











0 0 1 0 2

0 0

2 0 0

1 '

' ' ' 1

YW [ e t t

] ]

\

\ Yt [ [

E

E

         

vt

0

vt

0

(3)

About a new suggested interpretation of special theory of relativity... 

where F

E Y 7KHVHWUDQVIRUPDWLRQVFRQWDLQDIUHHSDUDPHWHUe1WKHFRHI

ficient of [¶ in the transformations of time which can be fixed by choosing a pecu- OLDUFORFNV\QFKURQL]DWLRQPHWKRGLQ6¶7KHVSHFLDOWKHRU\RIUHODWLYLW\ DQGWKXV

WKHVWDQGDUG/RUHQW]WUDQVIRUPDWLRQV LVREWDLQHGIRU

1 2

1 E E

  e F

         

For all the values of e1H[FHSW  WKHV\VWHP60 turns out to be a privileged UHIHUHQFHIUDPH$VDQDO\]HGE\6HOOHULGLIIHUHQWYDOXHVRIe1 determine differ- ent theories of space and time which are empirically equivalent to a large extent IRUH[DPSOH0LFKHOVRQW\SHH[SHULPHQWV>@WKHWZLQSDUDGR[H[SHULPHQW>@

UDGDUUDQJLQJRISODQHWVDQGRFFXOWDWLRQRI-XSLWHUVDWHOOLWHV>@'RSSOHUHIIHFW

DQGDEHUUDWLRQ>@)L]HDXH[SHULPHQW>@DUHLQVHQVLWLYHWRWKHFKRLFHRIe1 %XW

DVLWZDVVKRZQE\6HOOHULWKHUHDUHVRPHSDUWLFXODUSKHQRPHQD WKHDFFHOHUDW- LQJVSDFHVKLSVWKHURWDWLQJGLVNDQGWKHTXHVWLRQRIVXSHUOXPLQDOVLJQDOVUHJDUG- LQJWKHJURXSYHORFLW\RIHOHFWURPDJQHWLFUDGLDWLRQ WKDWPRGLI\WKHVLWXDWLRQWR

the point that the condition e1

0

EHFRPHVQHFHVVDU\7KHDGRSWLRQRIe1

0

PDNHVHTXDWLRQV  EHFRPHWKH³LQHUWLDOWUDQVIRUPDWLRQV´LQZKLFKWKHWUDQVIRU- PDWLRQRIWKHVSHHGRIFORFNGRHVQRWFRQWDLQWKHVSDFHYDULDEOH

° °

°

¯

°°

°

®

­







0 2 0

0 2 0 0

1 '

' ' ' 1

t t

] ]

\

\ Yt [ [

E E

         

6HOOHUL¶VWKHRU\RILQHUWLDOWUDQVIRUPDWLRQV  GHWHUPLQHVDQDUHQDRI6SHFLDO

5HODWLYLW\LQZKLFKWKHWHPSRUDOFRRUGLQDWHPXVWEHFOHDUO\FRQVLGHUHGDVDGLI- IHUHQWHQWLW\ZLWKUHVSHFWWRWKHVSDWLDOFRRUGLQDWHVMXVWEHFDXVHWKHWUDQVIRUPDWLRQ

of clocks’ run between the two inertial systems does not depend on the spatial FRRUGLQDWHV0RUHRYHULQWKHWKHRU\RIWKHLQHUWLDOWUDQVIRUPDWLRQV  WKHLQHUWLDO

reference frame 60 is not only privileged but also physically active in the sense that clocks run slower when they move with respect to 60 and light propagates in the simplest way only in 60,WLVWKHPRWLRQUHODWLYHWR60 that influences the FORFNV¶UXQQLQJ$FFRUGLQJWRWKHLQHUWLDOWUDQVIRUPDWLRQV  WKHRULJLQRI60

vt

0

(4)

 Davide Fiscaletti, Amrit Sorli

observed from 6LVVHHQWRPRYHZLWKYHORFLW\

¸¸

¹

¨¨ ·

©

§ 

  1

22 F F Y

E

7KHODWWHUYHORF

ity can be larger than FEXWFDQQRWEHVXSHUOXPLQDO,QIDFWLIDSDUWLFOHPRYHV

with velocities Yp and XpUHODWLYHWR60 and 6¶UHVSHFWLYHO\HTXDWLRQV  OHDG

WRWKHIROORZLQJWUDQVIRUPDWLRQVRIYHORFLWLHV

° °

° °

¯

° °

° °

®

­









p]

p]

p\

p\

p[

p[

Y X

Y X

Y X Y

2 2 2

1 1 1

1 1

E E E

         

Setting Xp[ Xpcos

-

Xp\ Xpsin

-

Xp] 0 ZKHUH

-

LVWKHDQJOHLQ

6EHWZHHQXp and Yp RQHHDVLO\REWDLQV

1 E

2 p

cos -

2

1 E

2

p

sin -

2

p Y X X

Y

   



         

$VDFRQVHTXHQFHRIHTXDWLRQ  LQWKHDSSURDFKRIWKHLQHUWLDOWUDQVIRUPD- tions the velocity of light is isotropic only in 60$OXPLQRXVSXOVHWUDYHOOLQJLQ

WKHGLUHFWLRQí[’with respect to the velocity of 6’ relative to 60 has a velocity given by

- - E

cos

1

1 

F F

         

where

-

 ʌQDPHO\

S E

 1

~

F

F

         

which is certainly larger than

¸¸¹

¨¨ ·

©

§1 22

 F

F Y

E LI”ȕ7KXVLQ6HOOHUL¶VDS

SURDFKRIWKHLQHUWLDOWUDQVIRUPDWLRQVWKHUHODWLYHYHORFLWLHVLQDQ\GLUHFWLRQ

-

FDQJURZZLWKRXWOLPLWEXWWKH\DOZD\VUHPDLQVPDOOHUWKDQF1

-

7KHDEVROXWH

velocities can never be larger than F

u

px

u

py

u

pz

v

pz

v

py

v

px

u

px

= u

p

u

py

= u

p

u

pz

(5)

About a new suggested interpretation of special theory of relativity... 

,QWKLVSDSHURXUDLPLVWRPDNHDQRWKHUVWHSIXUWKHUEH\RQG6HOOHUL¶VUHVXOWV

by proposing a new alternative interpretation of special relativity in which the IXQGDPHQWDODUHQDRISURFHVVHVLVDWKUHHGLPHQVLRQDO ' (XFOLGVSDFHDQGWLPH

has a secondary ontological status in the sense that represents only a mathemati- FDOFRRUGLQDWHZKLFKPHDVXUHVWKHQXPHULFDORUGHURIPDWHULDOFKDQJHV:HFDQ

FDOOWKLVDSSURDFKDVWKH³'LQWHUSUHWDWLRQ´RIVSHFLDOUHODWLYLW\7KLVSDSHULV

VWUXFWXUHGLQWKHIROORZLQJPDQQHU,QFKDSWHUZHZLOODQDO\VHWKHIXQGDPHQWDO

features of this approach and we will show how this approach allows us to re- REWDLQWKHVDPHIRUPDOLVPRI(LQVWHLQ EXWLQVLGHDGLIIHUHQWSK\VLFDOSLFWXUH 

,QFKDSWHUVDQGZHZLOODQDO\VHKRZWKLV³'LQWHUSUHWDWLRQ´RIVSHFLDO

UHODWLYLW\DOORZVXVWRUHUHDGVRPHVLJQLILFDQWSKHQRPHQDRIVSHFLDOUHODWLYLW\

VXFKDVDEHUUDWLRQRIOLJKW'RSSOHUHIIHFW-XSLWHU¶VVDWHOOLWHVRFFXOWDWLRQDQGUD- GDUUDQJLQJRIWKHSODQHWV

7+()81'$0(17$/)($785(62)7+(³7+5((',0(16,21$/´

,17(535(7$7,212)63(&,$/5(/$7,9,7<

Einstein’s formalism of special relativity based on the standard Lorentz trans- IRUPDWLRQVPD\EHGHULYHGIURPDPRUHIXQGDPHQWDO'(XFOLGHDQVSDFHZLWK

*DOLOHDQWUDQVIRUPDWLRQVIRUWKHWKUHHVSDWLDOGLPHQVLRQVDQG6HOOHUL¶VWUDQVIRU- PDWLRQIRUWKHUDWHRIFORFNV/HWDPRYLQJLQHUWLDOV\VWHPR¶REVHUYHGIURPUHVW

system o move with respect to the inertial system o with constant velocity YF par- allel to the X D[LV7KH*DOLOHDQWUDQVIRUPDWLRQVEHWZHHQWKHVSDWLDOFRRUGLQDWHV

X<Z of the inertial system o and the spatial coordinates X¶<¶Z’ of the inertial system o’ are the following

Z Z

<

<

Y X

X  ˜

' '

' W

         

where

Y

LVWKHYHORFLW\RIWKHPRYLQJREVHUYHU2¶PHDVXUHGE\WKHVWDWLRQDU\

REVHUYHU2DQG

W

LVWKHSURSHUWLPHRIWKHREVHUYHU2 QDPHO\WKHVSHHGRIFORFN

RIWKHREVHUYHU2 (TXDWLRQV  DUHYDOLGIRUERWKREVHUYHUV2DQG2¶RIWKHLQ- HUWLDOV\VWHPVRDQGR¶7KHWUDQVIRUPDWLRQRIWKHUDWHRIFORFNVDQGWKXVEHWZHHQ

the proper time

W

RIWKHREVHUYHU2DQGWKHSURSHUWLPH

W '

RIWKHREVHUYHU2¶LV

JLYHQE\6HOOHUL¶VIRUPDOLVP>@

W W ' 1 

22

˜

F Y



         

(6)

 Davide Fiscaletti, Amrit Sorli

(TXDWLRQ  VKRZVFOHDUO\WKDWWKHVSHHGRIWKHPRYLQJFORFN QDPHO\WKH

SURSHUWLPHRIWKHPRYLQJREVHUYHU GRHVQRWGHSHQGRQWKHVSDWLDOFRRUGLQDWHVEXW

is linked only with the speed YRIWKHLQHUWLDOV\VWHP2¶7KLVLQGLFDWHVWKDWUHODWLYH

velocity has origin in fundamental properties of space which are changed by the kinetic energy due to the velocity YRIDJLYHQLQHUWLDOV\VWHPPRYLQJLQVSDFH>@

7KHIRUPDOLVPV  DQG  PHDQWKDWWLPHDQGVSDFHUHSUHVHQWWZRVHSDUDWHG

HQWLWLHVWZRGLIIHUHQWSK\VLFDOUHDOLWLHV(TXDWLRQV  DQG  GHWHUPLQHDQDUHQD

of Special Relativity in which the temporal coordinate must be clearly considered DVDGLIIHUHQWHQWLW\ZLWKUHVSHFWWRWKHVSDWLDOFRRUGLQDWHVMXVWEHFDXVHWKHWUDQV- formation of the speed of clocks between the two inertial systems does not depend RQWKHVSDWLDOFRRUGLQDWHV$FFRUGLQJWRHTXDWLRQ  RQHFDQVD\WKDWWKHWKUHH

spatial coordinates of the two inertial systems turn out to have a primary onto- ORJLFDOVWDWXVGHILQHDQDUHQDWKDWPXVWEHFRQVLGHUHGPRUHIXQGDPHQWDOWKDQWKH

VWDQGDUGVSDFHWLPHFRRUGLQDWHVLQWHUSUHWHGLQWKHVHQVHRI(LQVWHLQ2QWKHEDVLV

RIHTXDWLRQV  DQG  ZHFDQFRQFOXGHWKHUHIRUHWKDWWKHUHDODUHQDRIVSHFLDO

UHODWLYLW\LVQRWDPL[HG'VSDFHWLPHEXWUDWKHUD'VSDFHZKHUHWLPHGRHVQRW

represent a fourth coordinate of space but must be considered merely as a math- HPDWLFDOTXDQWLW\PHDVXULQJWKHQXPHULFDORUGHURIPDWHULDOFKDQJHV&ORFNVDUH

PHDVXULQJGHYLFHVRIWKHQXPHULFDORUGHURIPDWHULDOPRWLRQHDFKFORFNFDQEH

DVVRFLDWHGZLWKDVSHFLILFSURSHUWLPH$FORFNDVDPHDVXULQJGHYLFHRIQXPHUL- FDORUGHURIPDWHULDOFKDQJHLQDQH[SHULPHQWUXQVVORZHU JHQHUDOO\DOOPDWHULDO

FKDQJHVUXQVORZHU LQDIDVWHULQHUWLDOV\VWHPRWKDQLQDQLQHUWLDOV\VWHPDWUHVWR

Experiments with clocks in a fast airplane do confirm that these relative velocities DUHYDOLGIRUERWKREVHUYHUV2DQG2¶

(DFK PDWHULDO PRWLRQ GHWHUPLQHV D SHFXOLDU ³VFDOLQJ´ IDFWRU RI WKH SURSHU

WLPHDQGRIWKHVSDWLDOFRRUGLQDWHV(TXDWLRQ  FDQEHVFDOHGE\DQ\DUELWUDU\

number which replaces

W

by a new proper time

W ~

6LQFHE\VXEVWLWXWLQJWKLVQHZ

SURSHUWLPHLQWRHTXDWLRQV  RQHREWDLQVDGLIIHUHQWUHVXOWIRUWKHWUDQVIRUPDWLRQ

RIWKHVSDWLDOFRRUGLQDWHVKHUHRXULGHDLVWRGHILQHWKHFRQFHSWRISK\VLFDOGXUD- WLRQRIPRWLRQDVDSURSHU³WUXH´SK\VLFDOVFDOHIRUWKHSURSHUWLPH

W

QDPHO\

IRUWKHQXPHULFDORUGHU:HGHILQHWKHSK\VLFDOPHDVXUDEOHWLPH±LQWHQGHGDV

GXUDWLRQRIPDWHULDOFKDQJH±MXVWDVWKLVSURSHUWUXHSK\VLFDOVFDOHIRUWKHQX- PHULFDORUGHU0RUHSUHFLVHO\ZHDVVXPHKHUHWKDWWKHGXUDWLRQRIPDWHULDOPR- tion measured by the stationary observer can be associated with a peculiar scaling SK\VLFDOIDFWRURIWKHQXPHULFDORUGHURIWKHIRUP

t

D

Y

 X  W

         

where the scaling factor

D

is a function also of the velocity of the moving IUDPHZLWKUHVSHFWWRWKHUHVWIUDPHDQGRIWKHSRVLWLRQRIWKHPDWHULDOREMHFWZLWK

UHVSHFWWRWKHUHVWIUDPH

(7)

About a new suggested interpretation of special theory of relativity... 

7KH YHORFLW\ RI D PDWHULDO REMHFW FDQ EH FRQVLGHUHG DV WKH SK\VLFDO HQWLW\

ZKLFKGHULYHVIURPWKHGXUDWLRQ QDPHO\IURPWKLVWUXHSK\VLFDOVFDOH

D

of the QXPHULFDORUGHU DVZHOODVIURPWKHSRVLWLRQRIWKHREMHFW,QRWKHUZRUGVWKH

PRWLRQRIHDFKPDWHULDOREMHFWDQGRIHDFKUHIHUHQFHIUDPHFDQEHDVVRFLDWHGZLWK

the duration of material change defined as this peculiar physical scaling factor

D

RIWKHQXPHULFDORUGHUDVZHOODVZLWKWKHVSDWLDOFRRUGLQDWHV7KHQRWLRQRI

YHORFLW\GHULYHVMXVWIURPWKHSK\VLFDOVFDOHRIWKHQXPHULFDORUGHUDQGIURPWKH

VSDWLDOFRRUGLQDWHV

,QSDUWLFXODUKHUHZHDVVXPHWRPDNHWKHIROORZLQJFKRLFHIRUWKHVFDOLQJ

function

D



2 2 2

1

F

YX F t Y

¸¸ ¹ 

¨¨ ·

©

§  W

         

The physical time tGHILQHGE\HTXDWLRQ  UHSUHVHQWVWKHGXUDWLRQRIPD- WHULDOPRWLRQDVPHDVXUHGE\WKHVWDWLRQDU\REVHUYHU2LQWKHUHVWLQHUWLDOIUDPH

R(TXDWLRQ  LQGLFDWHVWKDWWKHSK\VLFDOWLPHDVDGXUDWLRQRIPDWHULDOFKDQJH

HPHUJHVIURPDPRUHIXQGDPHQWDOQXPHULFDORUGHU2QWKHEDVLVRIHTXDWLRQ  

WKHQXPHULFDORUGHUPD\EHFRQVLGHUHGDVWKHLQWHUQDOVWUXFWXUHRIWKHSK\VLFDO

PHDVXUDEOHWLPHLQWHQGHGDVGXUDWLRQ

7KHGXUDWLRQRIPDWHULDOFKDQJHVLQFHLWLVDSK\VLFDOVFDOHRIWKHQXPHULFDO

RUGHUIROORZVDWUDQVIRUPDWLRQODZDQDORJRXVWRHTXDWLRQ  ,QRWKHUZRUGVWKH

physical time t’ – representing the duration of the material motion measured by the PRYLQJREVHUYHU2¶LQWKHLQHUWLDOIUDPHR¶±ZLOOEHOLQNHGWRt by a transforma- WLRQODZVLPLODUWRHTXDWLRQ  7KXVE\VXEVWLWXWLQJHTXDWLRQ  LQWRHTXDWLRQ

 RQHREWDLQVWKHIROORZLQJWUDQVIRUPDWLRQIRUWKHGXUDWLRQRIPDWHULDOPRWLRQ

VIRUPDWLRQ IRU WKH WLPH FRRUGLQDWH :H KDYH WKXV VKRZQ WKDW WKH /RUHQW]

transformation for the

vX





namely

namely

F t YX F Y

F Y

t

¸¸ 

¹

¨¨ ·

©

§ 

¸¸ ¹

¨¨ ·

©

§ 

2 2 2

2

2

1

1

' 1 vX

F t YX F t Y

¸¸ ¹ 

¨¨ ·

©

§ 1 

22 2

' vX

(8)

 Davide Fiscaletti, Amrit Sorli

which coincides with the standard Lorentz transformation for the time coordi- QDWH:HKDYHWKXVVKRZQWKDWWKH/RUHQW]WUDQVIRUPDWLRQIRUWKHWLPHFRRUGLQDWH

of standard Einsteinian special relativity emerges as a consequence of the more fundamental transformation for the numerical order of material changes and that the time coordinate of Einstein intended as duration of material change can be seen as a physical scaling factor of the numerical order of material change on the EDVLVRIHTXDWLRQ  $FFRUGLQJWRWKHDXWKRUVWKLVLVDQLPSRUWDQWLQGLFDWLRQ

WKDWWKHVWDQGDUG'VSDFHWLPHDUHQDGRHVQRWUHSUHVHQWWKHIXQGDPHQWDODUHQD

RIVSHFLDOUHODWLYLW\EXWUDWKHUHPHUJHVIURPDPRUHIXQGDPHQWDO'DUHQDZKHUH

WLPHH[LVWVRQO\DVDQXPHULFDORUGHURIPDWHULDOFKDQJHV DQGWKHSK\VLFDOGXUD- WLRQHPHUJHVDVDSK\VLFDOVFDOLQJIXQFWLRQRIWKLVQXPHULFDORUGHU 

1RZOHWXVVHHKRZRQHFDQGHULYHWKHVWDQGDUG/RUHQW]WUDQVIRUPDWLRQIRU

WKHILUVWVSDWLDOFRRUGLQDWHE\VWDUWLQJIURPWKH'DUHQDGHVFULEHGE\HTXDWLRQV

 DQG  DQGWKHGXUDWLRQRIPDWHULDOFKDQJHV  ,QWKLVUHJDUGEHIRUHDOOZH

ZULWHWKHLQYHUVHRIHTXDWLRQ  

¸¸ ¹

¨¨ ·

©

§ 



2 2 2

1

F Y F t YX

W

  

1RZWKHUHVFDOLQJRIWKHQXPHULFDORUGHUGHWHUPLQHGE\WKHPDWHULDOPRWLRQ

LQGLUHFWO\DFWVRQWKHPHDVXUHPHQWRIWKHSRVLWLRQRIWKHPDWHULDOREMHFWLQWKH

PRYLQJLQHUWLDOIUDPH7KHUHLVWKHUHIRUHDUHVFDOLQJRIWKHSRVLWLRQRIWKHPDWH- ULDOREMHFWLQWRFRQVLGHUDWLRQDVDFRQVHTXHQFHRILWVPRWLRQDVPHDVXUHGE\WKH

REVHUYHULQPRWLRQ,QSDUWLFXODULWVHHPVSHUPLVVLEOHWRDVVXPHWKDWWKHHIIHFWRI

WKHGXUDWLRQRIWKHPRWLRQRIWKHPDWHULDOREMHFWLVWRRULJLQDWHWKHIROORZLQJVFDO- LQJFKDQJHRIWKHILUVWVSDWLDOFRRUGLQDWH

namely       

QDPHO\       D

¸¸ ¹

¨¨ ·

©

§ 



2 2 2

1 '

F Y F t YX t



vX

vX

[ į IJtXY  X±YIJ Xƍ į IJtXY  X±YIJ

(9)

About a new suggested interpretation of special theory of relativity... 

where the scaling function

G

GHSHQGVRQWKHQXPHULFDORUGHUWKHGXUDWLRQRI

PDWHULDOFKDQJHWKHYHORFLW\RIWKHPRYLQJIUDPHZLWKUHVSHFWWRWKHUHVWIUDPH

DQGWKHSRVLWLRQRIWKHPDWHULDOREMHFWZLWKUHVSHFWWRWKHUHVWIUDPH0RUHSUHFLVH- O\WKHIXQFWLRQ

G

may be considered as a re-scaling of the distance determined E\WKHGXUDWLRQRIPDWHULDOFKDQJH  ZLWKUHVSHFWWRWKHQXPHULFDORUGHU7KLV

IXQFWLRQPD\EHGHULYHGGLUHFWO\VWDUWLQJIURPWKHGXUDWLRQRIPDWHULDOFKDQJH

 LQRWKHUZRUGVPD\EHFRQVLGHUHGDVWKHFRQVHTXHQFHRIWKHUHVFDOLQJRIWKH

QXPHULFDORUGHUSURGXFHGE\WKHPDWHULDOFKDQJHLQWRFRQVLGHUDWLRQ)URPHTXD- WLRQ  RQHKDVLPPHGLDWHO\

¸¸ ¹

¨¨ ·

©

§ 



2

1

22

F Y F

t YX

W



         

%\GLYLGLQJ  IRUWKHQXPHULFDORUGHURQHKDV

¸¸ ¹

¨¨ ·

©

§ 

¸ ¹

¨ ·

© § 

2

1

22

1

F Y F

t YX

W



         

7KXVIURPHTXDWLRQ  IROORZVWKDWWKHUHVFDOLQJIDFWRURIWKHGLVWDQFHLQ

WKHILUVWVSDWLDOFRRUGLQDWHGHWHUPLQHGE\WKHPDWHULDOPRWLRQKDYLQJGXUDWLRQ   LVRIWKHIRUP

¸ ¹

¨ ·

© § 

2

1

F t YX

G W

         

DQGRQWKHEDVLVRIHTXDWLRQ  WKLVUHVFDOLQJIDFWRULVMXVWHTXDOWR

2 2

1

F



Y

G

         

7KHUHIRUHE\VXEVWLWXWLQJHTXDWLRQ  LQWRHTXDWLRQ D RQHREWDLQVWKH

following transformation of the first spatial coordinate

X Y

W

F X

' 1 

Y22



          

vX

vX

vX

(10)

 Davide Fiscaletti, Amrit Sorli

)LQDOO\E\VXEVWLWXWLQJHTXDWLRQ  LQWRHTXDWLRQ  RQHREWDLQV

 

          

QDPHO\         

QDPHO\         

ZKLFKFRLQFLGHVMXVWZLWKWKHVWDQGDUG/RUHQW]WUDQVIRUPDWLRQIRUWKHILUVW

VSDWLDOFRRUGLQDWH7KHGHULYDWLRQ    VKRZVWKDWWKHVWDQGDUG/RUHQW]WUDQV- formation of the first spatial coordinate is not a primary physical law but emerges IURPDPRUHIXQGDPHQWDO'DUHQDZKHUHWLPHDWDIXQGDPHQWDOOHYHOH[LVWVRQO\

as a numerical order and the duration of material change is a scaling function of WKHQXPHULFDORUGHUDQGGHWHUPLQHVDUHVFDOLQJRIWKHSRVLWLRQRIWKHREMHFWDV

PHDVXUHGE\WKHPRYLQJREVHUYHUWKHEHKDYLRXURIWKHILUVWVSDWLDOFRRUGLQDWH

GHVFULEHGE\HTXDWLRQ  LVGHWHUPLQHGMXVWE\WKHOLQNEHWZHHQWKHGXUDWLRQRI

WKHPDWHULDOPRWLRQDQGWKHQXPHULFDORUGHU

,QV\QWKHVLVLQWKLVZD\ZHKDYHVKRZQWKDWWKHVWDQGDUG/RUHQW]WUDQVIRUPD- WLRQVRI(LQVWHLQ¶VVSHFLDOUHODWLYLW\FRQFHUQLQJWKHWHPSRUDOFRRUGLQDWH  DQG

WKHILUVWFRRUGLQDWH  GHULYHIURPDPRUHIXQGDPHQWDO'DUHQDGHVFULEHGE\

HTXDWLRQV  DQG  XQGHUWKHK\SRWKHVLVWKDWWKHGXUDWLRQRIPDWHULDOFKDQJH

GHULYHVIURPDPRUHIXQGDPHQWDOQXPHULFDORUGHU SURSHUWLPH RQWKHEDVLVRI

HTXDWLRQ  DQGWKDWWKHOLQNEHWZHHQWKHGXUDWLRQRIPDWHULDOFKDQJHDQGWKH

numerical order corresponding to the velocity of the moving observer with re- VSHFWWRWKHUHVWIUDPHGHWHUPLQHVDUHVFDOLQJRIWKHSRVLWLRQRIWKHREMHFWLQWR

FRQVLGHUDWLRQLQWKHPRYLQJIUDPH7KHWUHDWPHQWPDGHLQWKLVFKDSWHUVXJJHVWV

that the standard Einsteinian formalism of special relativity may be obtained by VWDUWLQJIURPWKHLGHDWKDWWKHIXQGDPHQWDODUHQDRISK\VLFDOSURFHVVHVLVD'

DUHQDZKHUHWLPHDWDIXQGDPHQWDOOHYHOLVDGLIIHUHQWHQWLW\ZLWKUHVSHFWWRWKH

VSDWLDO FRRUGLQDWHV QDPHO\ H[LVWV RQO\ DV D QXPHULFDO RUGHU LQ WKH VHQVH WKDW

the transformation of the speed of clocks between the two inertial systems does QRWGHSHQGRQWKHVSDWLDOFRRUGLQDWHV WKHSK\VLFDOGXUDWLRQRIPDWHULDOFKDQJH

2 2

1 '

F Y Yt X X





2 2 2

2 2 2

2

1 1 1

1 '

F Y F

t YX Y F X

Y F

X Y

¸¸ 

¹

·

¨¨©

§ ¸

¹

¨ ·

©§ 

¸¸ 

¹

¨¨ ·

©

§ 



¸ ¸

¸ ¸

¹

·

¨ ¨

¨ ¨

©

§





˜





2 2 2 2

2

1 1

'

F Y F t YX Y F X

X Y

vX

vX

vt

(11)

About a new suggested interpretation of special theory of relativity... 

HPHUJHVDVDVFDOLQJIXQFWLRQRIWKHQXPHULFDORUGHU,QRWKHUZRUGVLQWKLVDS- SURDFKWRVSHFLDOUHODWLYLW\HTXDWLRQV  DQG  GHILQHWKHIXQGDPHQWDODUHQD

RISK\VLFDOSURFHVVHVDQGPD\EHFRQVLGHUHGWKHIXQGDPHQWDOODZVLQVWHDGWKH

VWDQGDUG/RUHQW]WUDQVIRUPDWLRQV  DQG  RI(LQVWHLQ¶VVSHFLDOUHODWLYLW\PD\

EHVHHQDVWKHODZVJRYHUQLQJDQRWKHUOHYHOZKLFKPD\EHGHILQHGDVWKHOHYHO

RIWKHPHDVXUHPHQWVRIWKHREVHUYHUVDQGHPHUJHIURPWKHIXQGDPHQWDOODZV   DQG  LQWKHK\SRWKHVLVWKDWWKHPHDVXUDEOHWLPHDVGXUDWLRQHPHUJHIURPWKH

QXPHULFDORUGHURQWKHEDVLVRIHTXDWLRQ  DQGGHWHUPLQHVDUHVFDOLQJRIWKH

SRVLWLRQDVPHDVXUHGLQWKHPRYLQJIUDPH

2QWKHEDVLVRIHTXDWLRQV  DQG  WKHUHLVQRIXQGDPHQWDO³WLPHGLODWLRQ´

DVLWLVNQRZQLQ(LQVWHLQ¶VVSHFLDOWKHRU\RIUHODWLYLW\QDPHO\GLODWLRQRIWLPHDV

DthFRRUGLQDWHRIVSDFHFDXVHVFORFNVWRKDYHDVORZHUUDWH:KDWZHPHDVXUHLQ

GLIIHUHQWLQHUWLDOV\VWHPVLVWKHUHODWLYHYHORFLW\RIPDWHULDOFKDQJH LQFOXGLQJUXQ

RIFORFNV QDPHO\WKHLUQXPHULFDORUGHU

$OVRWKH³OHQJWKFRQWUDFWLRQ´LQWKHGLUHFWLRQRIPRWLRQRIDQLQHUWLDOV\VWHP

along the axis X SUHGLFWHGE\WKHVWDQGDUG/RUHQW]IRUPDOLVP  FDQQRWEH

FRQVLGHUHGDVDIXQGDPHQWDOSULPDU\UHDOLW\LWFDQEHVHHQDVDQHIIHFWRIPRWLRQ

determined by the link between the duration of material motion and the numerical RUGHURQWKHEDVLVRIHTXDWLRQ  LQRWKHUZRUGVE\WKHUHVFDOLQJIXQFWLRQFRU- UHVSRQGLQJWRWKHGXUDWLRQRIPDWHULDOFKDQJHSURGXFHGE\WKHPDWHULDOFKDQJH

LQWRFRQVLGHUDWLRQ$WWKHIXQGDPHQWDOOHYHOH[SUHVVHGE\HTXDWLRQV  DQG  

WKHUHLVQROHQJWKFRQWUDFWLRQ2QWKHRWKHUKDQGDVVKRZQLQ>@OHQJWKFRQ- traction along axis XZRXOGOHDGWRDFRQWUDGLFWLRQLQDPRYLQJLQHUWLDOV\VWHP

horizontal photon clock positioned along the axis X would shrink and would have IDVWHUUDWHWKDQLGHQWLFDOSKRWRQFORFNVSRVLWLRQHGYHUWLFDOO\5HJDUGLQJ³OHQJWK

FRQWUDFWLRQ´VRPHRWKHUUHVHDUFKOHDGVWRWKHVDPHFRQFOXVLRQV6LQFHZKHQ

special theory of relativity was published there has been no experimental data on

³OHQJWKFRQWUDFWLRQ´>@LQWHQGHGDVDIXQGDPHQWDOSK\VLFDOUHDOLW\

0RUHRYHU LQ WKLV PRGHO EDVHG RQ HTXDWLRQV   DQG   DW D IXQGDPHQWDO

OHYHOWLPHWUDYHOVLQWRWKHSDVWDQGLQWRWKHIXWXUHFDQQRWEHFRQVLGHUHGDVDSK\VL- FDOUHDOLW\LQWKHDUHQDGHVFULEHGE\HTXDWLRQV  DQG  RQHFDQWUDYHOLQVSDFH

RQO\3DVWSUHVHQWDQGIXWXUHH[LVWRQO\DVDQXPHULFDORUGHURIFKDQJHVZKLFKUXQ

LQD'VSDFH>@

1RZOHWXVFRQVLGHUWZRHYHQWVDQGRFFXUULQJLQWZRGLVWLQFWSRLQWVRI

VSDFHDQGFKDUDFWHUL]HGE\DGLIIHUHQWQXPHULFDORUGHU ZLWKUHVSHFWWRWKHRE- VHUYHU2DWUHVW ,QWKHLQHUWLDOV\VWHPRWKHVSDWLDOGLVWDQFHEHWZHHQWKHVHWZR

HYHQWVDVPHDVXUHGE\WKHREVHUYHU2LV

    ǻV2 ǻX 2ǻ< 2ǻZ 2   

(12)

50 Davide Fiscaletti, Amrit Sorli

while the material change associated with these two events is described by the numerical order

' W

 ,Q WKH PRYLQJ LQHUWLDO V\VWHP R¶ WKH VSDWLDO GLVWDQFH

EHWZHHQWKHVHWZRHYHQWVDVPHDVXUHGE\WKHREVHUYHU2¶LV

         

while the numerical order of material change associated with these two events is

W ' '



2QWKHEDVLVRIHTXDWLRQV  HTXDWLRQ  EHFRPHV

         

ZKLOHWDNLQJLQWRDFFRXQWWKHWUDQVIRUPDWLRQRIWKHUDWHRIFORFNV  WKHQXPHUL- cal order of material change associated with the two events under consideration PHDVXUHGZLWKUHVSHFWWRWKHLQHUWLDOV\VWHP2¶LV

W

W  ˜ '

' ' 1

22

F Y

         

,QWKLVPRGHOHTXDWLRQV  DQG  FRPHWRVXEVWLWXWHWKHUHODWLYLVWLFLQ- variant quantity represented by the square of the modulus of the four-interval in 0LQNRZVNLVSDFHWLPH6LQFHWKHVWDQGDUG/RUHQW]WUDQVIRUPDWLRQVIRUWKHVSDFH

and time coordinates emerge as a consequence of the more general transformations  DQG  LQDPRUHIXQGDPHQWDO'DUHQDZHFDQDOVRVD\WKDWWKHUHODWLYLVWLF

invariant quantity represented by the square of the modulus of the four-interval in 0LQNRZVNLVSDFHWLPHFDQEHVHHQDVDFRQVHTXHQFHRIHTXDWLRQV  DQG  

Taking into account the fundamental relativistic postulate of the invariance RIWKHYHORFLW\RIOLJKWIRUGLIIHUHQWREVHUYHUVDQGHTXDWLRQV  DQG  KHUHZH

VXJJHVWD³'LQWHUSUHWDWLRQ´RIVSHFLDOWKHRU\RIUHODWLYLW\EDVHGRQWKHIROORZLQJ

SRVWXODWHV

The velocity of light has the same value in all directions and in all inertial V\VWHPV SRVWXODWHRIWKHLQYDULDQFHRIWKHYHORFLW\RIOLJKWLQWKHYDFXXP 

7KHIXQGDPHQWDODUHQDRISK\VLFDOSURFHVVHVLVD'(XFOLGVSDFHZKHUHWLPH

exists merely as a mathematical quantity measuring the numerical order of mate- ULDOFKDQJHV DQGZKLFKFDQEHGHILQHGDVWKHSURSHUWLPHRIWKHREVHUYHUXQGHU

FRQVLGHUDWLRQ *LYHQWZRLQHUWLDOIUDPHVRDQGR¶ZKHUHWKHRULJLQRIR¶RE- VHUYHGIURPRLVVHHQWRPRYHZLWKYHORFLW\Y parallel to the XD[LVWKHWUDQVIRU- mations between the spatial coordinates of these two systems are given by equa-

ǻVƍ2 ǻXƍ2ǻ<ƍ2ǻZƍ2

ǻVƍ2  ǻX – YǻIJ 2ǻ<2ǻZ2

(13)

About a new suggested interpretation of special theory of relativity... 51 WLRQ  ZKLOHWKHWUDQVIRUPDWLRQRIWKHUDWHRIFORFNVQDPHO\EHWZHHQWKHSURSHU

WLPHV RI WKH REVHUYHUV RI WKHVH WZR LQHUWLDO V\VWHPV LV JLYHQ E\ HTXDWLRQ  

The duration of material changes satisfying the standard Lorentz transformation IRUWKHWHPSRUDOFRRUGLQDWHLVDSURSHUSK\VLFDOVFDOLQJIXQFWLRQZKLFKHPHUJHV

from the more fundamental numerical order and determines itself a re-scaling of the position measured by the moving observer expressed by the standard Lorentz WUDQVIRUPDWLRQIRUWKHILUVWVSDWLDOFRRUGLQDWH

(TXDWLRQV     DQGWKHFRQVHTXHQWHTXDWLRQV  DQG  LQWURGXFHD

new suggestive way to treat and analyse several phenomena inside special relativ- LW\VXFKDVDEHUUDWLRQRIOLJKW'RSSOHUHIIHFW-XSLWHU¶VVDWHOOLWHVRFFXOWDWLRQDQG

UDGDUUDQJLQJRIWKHSODQHWV

$%(55$7,212)/,*+7

Let us consider the propagation of a light corpuscle P on the X-< plane of the LQHUWLDOV\VWHPR2QWKHEDVLVRIWKHSRVWXODWH3SURSDJDWHVDWWKHVDPHYHORFLW\

FLQHDFKLQHUWLDOV\VWHPDQGLQHDFKGLUHFWLRQ6RZLWKUHVSHFWWRWKHVWDWLRQDU\

REVHUYHU2RIWKHLQHUWLDOV\VWHPR3LVGHVFULEHGE\FRRUGLQDWHVVDWLVI\LQJDWWKH

proper time

W



         

5HODWLYHWRWKHPRYLQJLQHUWLDOV\VWHPR¶3LVGHVFULEHGE\FRRUGLQDWHVVDWLV- I\LQJDWWKHSURSHUWLPH

W '



         

6XEVWLWXWLQJHTXDWLRQV  DQG  LQWRHTXDWLRQ  ZHREWDLQ

         

¯ ®

­

' sin ' '

' cos ' '

- W

- W

F

<

F X

° °

¯

°° ®

­







' sin 1

' cos 1

2 2

2 2

- W

- W

W

F F Y

<

F F Y

Y X

¯ ®

­

- W

- W

sin cos

F

<

F X

(14)

52 Davide Fiscaletti, Amrit Sorli

IURPZKLFKWDNLQJDFFRXQWRIHTXDWLRQ  ZHKDYH

         

namely

         

(TXDWLRQV  SURYLGHWKXVWKHIROORZLQJIRUPXODIRUWKHDEHUUDWLRQRIOLJKW

SXOVHLQD'(XFOLGVSDFHZLWKWUDQVIRUPDWLRQVRIWKHUDWHRIFORFNVJLYHQE\

IRUPDOLVP  

         

namely

         

(TXDWLRQ   WXUQV RXW WR be in perfect agreement with the experimental HYLGHQFH LW FRLQFLGHV SHUIHFWO\ ZLWK WKH DEHUUDWLRQ IRUPXOD REWDLQDEOH IURP D

FODVVLFDOWUHDWPHQWRIWKHSUREOHP:HKDYHWKXVVKRZQWKDWWKHPDWKHPDWLFDO

IRUPDOLVPRIWKH³'LQWHUSUHWDWLRQ´RIVSHFLDOUHODWLYLW\EDVHGRQHTXDWLRQV   DQG  ZLWKWKHLPSOLFLWSRVWXODWHRIWKHLQYDULDQFHRIWKHVSHHGRIOLJKWQDPHO\

that the speed of light in the vacuum has the same value F in all directions and in DOOLQHUWLDOV\VWHPV OHDGVWRWKHVDPHUHVXOW  RIWKHFODVVLFDOWUHDWPHQWUHSUH- VHQWHGE\WKH*DOLOHDQWUDQVIRUPDWLRQV,QRWKHUZRUGVWKH'PRGHORIVSHFLDO

relativity based on the postulates 1 and 2 allows us to reconcile the treatment of WKHDEHUUDWLRQRIOLJKWZLWKWKHFODVVLFDOVFKHPH,WLVDOVRLQWHUHVWLQJWRUHPDUN

WKDWZKLOH6HOOHUL¶VWKHRU\RILQHUWLDOWUDQVIRUPDWLRQV  SURYLGHVDVROXWLRQIRU

the aberration of light which is different with respect to the classical solution only

° °

°

¯

° °

°

®

­







' sin sin

1 1

' cos 1

cos

2 2

2 2

- -

- W

W - W

F Y

F F Y

Y F

W - W

- - W

Y F

tJ F

 cos ' sin

Y F

tJ F

-



- -

cos ' sin

° °

¯

°° ®

­







' sin 1

sin

' cos 1

cos

2 2

2 2

- W

- W

- W

W - W

F F Y

F

F F Y

Y F

tg

tg

(15)

About a new suggested interpretation of special theory of relativity... 53 in terms of the second and higher order in

F

YWKHWUHDWPHQWRIWKHDEHUUDWLRQRI

OLJKWSURYLGHGKHUHLQWKHFRQWH[WRIWKH³'´LQWHUSUHWDWLRQRIVSHFLDOUHODWLYLW\

OHDGVWRWKHVDPHVROXWLRQRIWKHFODVVLFDOWKHRU\

6LQFHWKH(DUWKFKDQJHVDQQXDOO\LWVYHORFLW\ZLWKUHVSHFWWRWKHIL[HGVWDUV

RQHVKRXOGREVHUYHDQDEHUUDWLRQDQJOHJLYHQE\  LQWKHIRFDOSODQHRIDWHO- HVFRSH7KLVZDVDOUHDG\GLVFRYHUHGLQWKHHDUO\HLJKWHHQWKFHQWXU\E\%UDGOH\,Q

%UDGOH\GHWHFWHGDEHUUDWLRQRIVWDUOLJKWDQDQQXDOYDULDWLRQRIWKHDSSDUHQW

SRVLWLRQRIVWDUVRQWKHFHOHVWLDOVSKHUHXVLQJDVLPSOH(DUWKEDVHGWHOHVFRSH>@

He gave an explanation on the basis of the ether theory and the finite velocity of OLJKW$EHUUDWLRQLVDILUVWRUGHUHIIHFWDQGIROORZVGLUHFWO\IURPWKH*DOLOHLWUDQV- IRUPDWLRQZLWKRXWQHFHVVLW\RIWKHXVHRIWKH/RUHQW]WUDQVIRUPDWLRQV

The currently accepted theory for starlight aberration derives from special UHODWLYLW\DQGLVSUHVHQWHGLQQXPHURXVWH[WVIRUH[DPSOH)UHQFK>@,Q>@

:RRGUXIIDSSOLHGSK\VLFDORSWLFVLPDJLQJWKHRU\WRREWDLQDQDOWHUQDWLYHWKHRUHWL- FDOPRGHOIRUDEHUUDWLRQRIVWDUOLJKW+HSURSRVHGDQRSWLFDOVHQVRUWKDWXVHVD

solid glass telescope to distinguish between the predictions of special relativity DQGDSK\VLFDORSWLFVPRGHO7KHVSHFLDOUHODWLYLVWLFEDVHGPRGHODWWULEXWHVVWHO- ODUDEHUUDWLRQWRWLOWRIWKHLQFLGHQWSODQHZDYHIURQWV7KHSK\VLFDORSWLFVEDVHG

model considers untilted converging wavefronts within the sensor to explain aber- UDWLRQRIVWDUOLJKWSKHQRPHQRQ3UHGLFWLRQVRIWKHWZRPRGHOVDJUHHIRUUHODWLYHO\

VORZVHQVRUPRWLRQVIRULQVWDQFHDW(DUWKRUELWDOYHORFLW\EXWGLIIHUJUHDWO\DW

YHORFLWLHVDSSURDFKLQJWKHVSHHGRIOLJKW,Q>@:RRGUXIISURSRVHGDQRWKHURSWL- FDOH[SHULPHQWFRQILJXUHGVSHFLILFDOO\WRWHVWDEHUUDWLRQDW(DUWKRUELWDOYHORFLW\

in which a conventional optical telescope is used to determine whether aberration of starlight results from special relativistic effects external to a measurement sen- VRURUIURPRSWLFDOHIIHFWVZLWKLQDVHQVRU(DFKRIWKHWZRPRGHOVLQFRUSRUDWHV

GLVWLQFWH[SHULPHQWDOO\WHVWDEOHSK\VLFDOFKDUDFWHULVWLFV7KHVSHFLDOUHODWLYLVWLF

based model ascribes the aberration effect to sensor motion relative to the incident ZDYHIURQWLQGHSHQGHQWRIWKHFKDUDFWHULVWLFVRIWKHVHQVRU,WPRGHOVDEHUUDWLRQ

as the result of wavefront tilt occurring external to and independent of the sen- VRUJHRPHWU\7KXVLQWKLVPRGHODEHUUDWLRQVKRXOGEHLQGHSHQGHQWRIWHOHVFRSH

RSWLFDOSURSHUWLHV7KHSK\VLFDORSWLFVEDVHGPRGHOSUHGLFWVWKHPHDVXUHPHQWZLOO

GHSHQGRQWKHVHQVRUFRQILJXUDWLRQLQFOXGLQJXSRQLWVLQWHUQDORSWLFDOSURSHUWLHV

$FFRUGLQJWR:RRGUXIIWKLVH[SHULPHQWZRXOGDOVRSURYLGHDQLQGHSHQGHQWWHVW

RIUHODWLYLVWLFWLPHGLODWLRQEHFDXVHWKHUHODWLYLVWLFGHULYHGPRGHOUHTXLUHVWLPH

GLODWLRQWRLQGXFHZDYHIURQWWLOWH[WHUQDOIURPWKHVHQVRU$VDFRQVHTXHQFHWKH

possibility is opened that such an experiment could also provide an indirect test of WKHWUDQVIRUPDWLRQVRIWKHUDWHRIFORFNVJLYHQE\HTXDWLRQ  DQGWKHUHIRUHRIWKH

WUHDWPHQWRIDEHUUDWLRQRIVWDUOLJKWSURYLGHGE\WKH³'´LQWHUSUHWDWLRQVXJJHVWHG

LQWKLVDUWLFOH,QWKLVUHJDUGIXUWKHUUHVHDUFKZLOOJLYH\RXPRUHLQIRUPDWLRQ

(16)

 Davide Fiscaletti, Amrit Sorli

'233/(5())(&7

7KH'RSSOHUHIIHFWLVDQHIIHFWRIDIUHTXHQF\FKDQJHGXHWRWKHUHODWLYHYH- locity YEHWZHHQDVRXUFHDQGDQREVHUYHU:KLOHWKLVFKDQJHRIIUHTXHQF\LVRIWKH

order YFLQFODVVLFDOSK\VLFVLWLVIXUWKHUPRGLILHGWRWKHVHFRQGRUGHU Y2 F2  LQVSHFLDOUHODWLYLW\

Let us consider a plane electromagnetic wave which is propagating in the YDFXXP,QWKHVWDWLRQDU\LQHUWLDOV\VWHPRWKLVZDYHLVGHVFULEHGE\WKHZDYH

function

»

¼

« º

¬

ª ¸

¹

¨ ·

©

§  ˜

F U i Q

U

&

& ˆ

exp

 W \

0

Z W

\

         

where

\

0 LV D FRQVWDQW DPSOLWXGH

Z

 LV WKH DQJXODU IUHTXHQF\

cos -  sin -

Q

ˆ

LVWKHXQLWYHFWRUQRUPDOWRWKHZDYHIURQWV(TXDWLRQ  FDQ

also be explicitly expressed as

»

¼

« º

¬

ª ¸

¹

¨ ·

©

§ 



F

<

i X

U

W \ Z W - -

\ cos sin

exp



0

&

         

,QWKHPRYLQJLQHUWLDOV\VWHPR¶WKLVVDPHZDYHLVGHVFULEHGE\WKHZDYH

function

»

¼

« º

¬

ª ¸

¹

¨ ·

©

§  ˜

F

U i Q

U

ˆ ' '

' ' exp '

'

' & W \

0

Z W &

\

         

2QWKHEDVLVRIZKDWZHKDYHVHHQLQFKDSWHUWKHXQLWYHFWRUQ

has com- ponents given by the following relation

         

%\LQVHUWLQJHTXDWLRQV    DQG  LQWRWKHSKDVHRIWKHZDYHIXQFWLRQ

 ZHREWDLQ

         

» »

» »

¼ º

« «

« «

¬

ª ¸ ˜ 

¹

¨ ·

©

§ 



» 

¼

« º

¬

ª ¸

¹

¨ ·

©

§  ˜

F

<

Y F X

Y

F Y F

U

Q

cos  sin 

' 1 ˆ ' '

'

2

2

- - W

W Z W

Z &

¸¹

¨ ·

©

§cos

-

 sin

-

ˆ'

F Q Y

(17)

About a new suggested interpretation of special theory of relativity... 55

          

namely

          

(TXDWLRQ  PD\EHUHZULWWHQDV

          

namely

          

namely

          

2QWKHEDVLVRIHTXDWLRQV    ZHREWDLQWKXVWKDWLQWKHPRYLQJLQHUWLDO

V\VWHPR¶WKHSODQHZDYHKDVDIUHTXHQF\

»»

»»

»

¼ º

««

««

«

¬

ª ¸¸¹

¨¨ ·

©

§    



» 

¼

« º

¬

ª ¸

¹

¨ ·

©

§  ˜

F F <

Y Y F X YX

F Y F

U

Q - W - W -

W Z W

Z

sin cos

cos ' 1

ˆ' ' '

2

2

& 2

»»

»»

»

¼ º

««

««

«

¬ ª



¸¸ 

¹

¨¨ ·

©

§    



» 

¼

« º

¬

ª ¸

¹

¨ ·

©

§  ˜

2 2

2 2 2

2 2

1

1 sin cos

cos ' 1

ˆ' ' '

F F Y

F

< Y F Y Y

F X YX

F Y F

U

Q - W - W -

W Z W

Z &

»»

»»

»

¼ º

««

««

«

¬ ª



¸ 

¹

¨ ·

©

§  







¸¸

¹

¨¨ ·

©

§ 

»¼

« º

¬

ª ¸

¹

¨ ·

©

§  ˜

2 2

2 2 2

2 2

2

1

1 cos

1 sin cos ' 1

' ' ˆ '

F F Y

F Y F Y F

Y X F

< Y F X

F Y

F U Q

- W W -

- W

Z W

Z &

»»

»»

¼ º

««

««

¬ ª



¸¹

¨ ·

©

§  







» 

»¼ º

««

¬

ª 

»¼

« º

¬

ª ¸

¹

¨ ·

©

§  ˜

2 2 2

2

1

cos sin

cos ' 1

' ' ˆ '

F F Y

F Y F

Y X

<

X F

Y F

U Q

- W W -

- W

Z W

Z &

» »

» »

¼ º

« «

« «

¬ ª



¸ ¹

¨ ·

©

 §

˜



» 

» ¼ º

« «

¬

ª 

» ¼

« º

¬

ª ¸

¹

¨ ·

©

§  ˜

2 2 2

2 2

2

1 ' ' ˆ 1

 ' ' 1

ˆ ' ' '

F F Y

F Y X U Q F Y F

Y F

U Q

&

&

W Z

W Z

vX

vX

(18)

56 Davide Fiscaletti, Amrit Sorli

          

which means that the frequency of the plane electromagnetic wave follows the same behaviour of rate of clocks namely does not depend on the spatial coordi- QDWHV$FFRUGLQJWRWKHDXWKRUVHTXDWLRQ  FDQEHFRQVLGHUHGFRKHUHQWZLWK(LQ- VWHLQ¶VGHULYDWLRQRIUHODWLYLVWLF'RSSOHUHIIHFWEDVHGRQWKH/RUHQW]WUDQVIRUPD- WLRQVLQIDFWLQWKLVDSSURDFK/RUHQW]WUDQVIRUPDWLRQVHPHUJHDWDVHFRQGDU\OHYHO

IURPHTXDWLRQV  DQG  WDNLQJDFFRXQWRIWKHGXUDWLRQRIPDWHULDOFKDQJH  

$VUHJDUGVWKHWUDQVYHUVH'RSSOHUHIIHFWZKLFKRFFXUVZKHQWKHREVHUYHULV

GLVSODFHGLQDGLUHFWLRQSHUSHQGLFXODUWRWKHGLUHFWLRQRIWKHPRWLRQRIWKHVRXUFH

DVVXPLQJWKHREMHFWVDUHQRWDFFHOHUDWHGOLJKWHPLWWHGZKHQWKHREMHFWVDUHFORV- est together will be received some time later and at reception the amount of red- shift will be given by the factor – independent of the spatial coordinates – which DSSHDUVLQHTXDWLRQ  7KHWUDQVYHUVH'RSSOHUHIIHFWLVDFRQVHTXHQFHRIWKH

IXQGDPHQWDOHTXDWLRQ  ,QWKHIUDPHRIWKHUHFHLYHUZKHQWKHDQJOHEHWZHHQ

the direction of the emitter at emission and the observed direction of the light at UHFHSWLRQLVHTXDOWRʌWKHOLJKWZDVHPLWWHGDWWKHPRPHQWRIFORVHVWDSSURDFK

DQGRQHREWDLQVWKHWUDQVYHUVHUHGVKLIWH[SUHVVHGMXVWE\HTXDWLRQ  

-83,7(5¶66$7(//,7(62&&8/7$7,21

/HWD-XSLWHU¶VVDWHOOLWH IRUH[DPSOH,R EHLQDVWDWHRIPRWLRQRQWKHX axis RIWKHVWDWLRQDU\LQHUWLDOV\VWHPR,RVHQGVDOLJKWVLJQDO RFFXOWDWLRQ FKDUDFWHU- ized by a numerical order 7ZLWKUHVSHFWWRWKLVLQHUWLDOV\VWHPZKHQLWLVLQWKH

position

X1



/

          

7KHHTXDWLRQRIPRWLRQRIWKHVLJQDOUHODWLYHWRWKHLQHUWLDOV\VWHPRLV

          

Let us suppose that the Earth moves with constant speed Y and thus consti- WXWHVLQVWDQWDQHRXVO\DPRYLQJLQHUWLDOV\VWHPR¶7KHHTXDWLRQRIPRWLRQRI(DUWK

DVVHHQIURPWKHVWDWLRQDU\V\VWHPRLVWKHIROORZLQJ

X( Y

W

          

» »

¼ º

« «

¬ ª 1 

22

'

F

Z

Y

Z

7

F /

X

  W 

(19)

About a new suggested interpretation of special theory of relativity... 57 The event represented by the arriving of the signal on Earth is associated with a numerical order

W

aZKLFKRQWKHEDVLVRIHTXDWLRQV  DQG  VDWLVILHVWKH

following condition

         

whence



         

7KH(DUWKSRVLWLRQFRUUHVSRQGLQJZLWKWKHQXPHULFDORUGHU  LV

         

2XUSUREOHPLVWRGHWHUPLQHWKHQXPHULFDORUGHU

W

a

'

marked by a clock on (DUWKZKHQWKHVLJQDOLVUHFHLYHG%HWZHHQWKHVWDWLRQDU\V\VWHPRDQGWKH(DUWK

V\VWHPR¶WKHWUDQVIRUPDWLRQ  DSSOLHVDQGRQHREWDLQV

         

ZKHQFHXVLQJHTXDWLRQ  ZHKDYH

         

ZKLFKLVMXVWWKHUHVXOWREWDLQHGLQVLGHWKHVWDQGDUG(LQVWHLQLDQVSHFLDOWKHRU\RI

UHODWLYLW\7KHSRVWXODWHV  DQG  SUHGLFWWKHUHIRUHH[DFWO\WKHVDPHRFFXOWDWLRQ

WLPHRI-XSLWHU¶VVDWHOOLWHVWREHREVHUYHGRQ(DUWK

5$'$55$1*,1*2)7+(3/$1(76

/HWWKHHTXDWLRQVRIPRWLRQZULWWHQLQWKHVWDWLRQDU\LQHUWLDOV\VWHPRRI(DUWK

RI9HQXVDQGRIDUDGDUVLJQDOVHQWIURP(DUWKWRZDUGV9HQXVUHVSHFWLYHO\EH

W

Y

X1 X2 Y2

W 

d X F

W

    

The numerical order

W

R corresponding to the reflection of the radar pulse on WKH9HQXVVXUIDFHPXVWWKXVVDWLVI\WKHFRQGLWLRQ>@

Y

F F7 /

a 

W



7

F /

Y

W

a

  W

a



a

a Y

X

W

a

a FY W

W ' 1 

22

˜

˜



22

1

'

F

Y

W

a

Y F

F7 /





cT

cT

(20)

58 Davide Fiscaletti, Amrit Sorli

         

whence

         

'XULQJWKHUHWXUQMRXUQH\RIWKHUDGDUSXOVHIURP9HQXVWR(DUWKWKHODWWHUVWLOO

REH\VWKHILUVWHTXDWLRQRI  ZKLOHWKHSXOVHPXVWVDWLVI\

R

R F

X

X2

 W  W

         

where

         

LVWKHSRVLWLRQRFFXSLHGMRLQWO\E\9HQXVDQGWKHSXOVHIRUWKHQXPHULFDORUGHU

W

R

Therefore the arrival of the pulse on Earth can be described by a numerical order

W

$ZKLFKPXVWVDWLVI\WKHIROORZLQJFRQGLWLRQ

         

%\XVLQJ  DQG  HTXDWLRQ  EHFRPHV

         

Now we want to study the phenomenon in the moving inertial system o’ as- VRFLDWHGZLWK(DUWK,QWKLVUHJDUGE\XVLQJHTXDWLRQ  ZHREWDLQ

         

whence

         

which is the same result obtained in standard Einsteinian special theory of relativ- LW\

Y2

F F dF

XR R

W



$ R

R

$ X F

Y

W  W  W

F Y

F Y

dF

$  2 

W

2

$

$ FY W

W ' 1 

22

˜

d Y F

W

R 2

W

R



Y2

F d

R 

W

˜



22

1

'

F

Y

W

$

F Y

F Y

dF



 2 2 2 dc

2 dc

dc

(21)

About a new suggested interpretation of special theory of relativity... 59

&200(176$1'&21&/86,216

,QVSHFLDOUHODWLYLW\0LQNRZVNLDQPRGHORIVSDFHWLPHZKHUHWKHIRXUWKVR

FDOOHG³WLPHFRRUGLQDWH´LV

         

KDVQRSK\VLFDOH[LVWHQFHLWLVDSXUHWKHRUHWLFDOPDWKHPDWLFDOPRGHO,QSK\VLFV

WKHUHLVQRVLQJOHH[SHULPHQWSURYLQJWKDWPDWHULDOFKDQJHVUXQLQWLPHDVth co- RUGLQDWHRIVSDFH,QDOOH[SHULPHQWVWLPHZKHQPHDVXUHGZLWKFORFNVLVPHUHO\

DQXPHULFDORUGHURIPDWHULDOFKDQJHVWDNLQJSODFHLQD'VSDFHZKLFKLVa fun- GDPHQWDOSK\VLFDOPDQLIROGLQZKLFKH[SHULPHQWRFFXU

2Q WKH RWKHU KDQG LQ KLV SDSHU 7iPe aQd FOaVViFaO aQd TXaQtXP PeFKaQ

iFV,QdeteUPiQaF\YeUVXVdiVFRQtiQXit\ Lynds argues that between time and space WKHUHLVDOZD\VDGLIIHUHQFH³7KHIDFWWKDWLPDJLQDU\QXPEHUVZKHQFRPSXWLQJ

space-time intervals and path integrals do not facilitate that when multiplied by i

WKDWWLPHLQWHUYDOVEHFRPHEDVLFDOO\LGHQWLFDOWRGLPHQVLRQVRIVSDFH,PDJLQDU\

numbers show up in space-time intervals when space and time separations are FRPELQHGDWQHDUWKHVSHHGRIOLJKWDQGVSDWLDOVHSDUDWLRQVDUHVPDOOUHODWLYHWR

WLPHLQWHUYDOV:KDWWKLVLOOXVWUDWHVLVWKDWDOWKRXJKVSDFHDQGWLPHDUHLQWHUZRYHQ

LQ0LQNRZVNLVSDFHWLPHDQGWLPHLVWKHIRXUWKGLPHQVLRQWLPHLVQRWVSDWLDO

GLPHQVLRQ WLPH LV DOZD\V WLPH DQG VSDFH LV DOZD\V VSDFH DV WKRVH 'is keep VKRZLQJXV7KHUHLVDOZD\VDGLIIHUHQFH,IWKHUHLVDQ\GHJUHHRIVSDFHUHJDUG- OHVVRIKRZPLFURVFRSLFWKHUHZRXOGDSSHDUWREHLQKHUHQWFRQWLQXLW\LHLQWHUYDO

LQWLPH´>@$OWKRXJK/\QGV¶FRQFOXVLRQWKDWWLPHLVWLPHDQGVSDFHLVDOZD\V

VSDFHPD\DSSHDUDOLWWOHTXHVWLRQDEOH WKHLPDJLQDU\VSDFHWLPHLQWHUYDOLQIDFW

means only an impossibility to connect the points under consideration by a signal VORZHURUHTXDOWKDQWKHVSHHGRIOLJKW DFFRUGLQJWRWKHDXWKRUVWKHUHLVQRWKLQJ

ZURQJLQDVVXPLQJWKDWWLPHDQGVSDFHDUHGLIIHUHQWLQWKHLUQDWXUHWKDWWLPHLV

a different entity from space and the treatment of special relativity made in this SDSHUSURYLGHVLPSRUWDQWFOXHVWRZDUGVWKLVYLHZ

$FFRUGLQJ WR WKH FRQFHSW RI VSDFHWLPH DOO SK\VLFDO SKHQRPHQD KDSSHQ LQ

VSDFHDQGWLPHLQWHQGHGDVHQWLWLHVKDYLQJWKHVDPHRQWRORJLFDOVWDWXV7KLVFRQFHSW

FDQQRWH[SODLQWKRVHSK\VLFDOSKHQRPHQDZKHUHLQIRUPDWLRQWUDQVIHULVLPPHGLDWH

)RUWKHVHSKHQRPHQD±ZKLFKFDQEHDSSURSULDWHO\FDOOHGDV³LPPHGLDWHSK\VLFDO

SKHQRPHQD´±WKHHODSVHGFORFNUXQLV]HUR,ISKHQRPHQDZRXOGKDSSHQLQDWLPH

LQWHQGHGDVVRPHSK\VLFDOUHDOLW\DQGKDYLQJWKHVDPHRQWRORJLFDOVWDWXVDVWKH'

VSDFHWLPHFRXOGQHYHUEH]HUR,PPHGLDWHSK\VLFDOSKHQRPHQDKDYHQRQXPHULFDO

RUGHU7KH\DUHLPPHGLDWHLQIRUPDWLRQWUDQVIHUVFDUULHGGLUHFWO\E\WKH'VSDFH

ZKLFK RULJLQDWHV IURP D ' YDFXXP ,Q WKH TXDQWXP GRPDLQ H[DPSOHV RI VXFK

SKHQRPHQDDUHWKHQRQORFDOFRUUHODWLRQVEHWZHHQTXDQWXPSDUWLFOHVLQ(35W\SH

iFt X

(22)

60 Davide Fiscaletti, Amrit Sorli

experiments and other immediate physical phenomena like tunneling or quantum entanglements regarding the continuous variable systems or the quantum excita- WLRQVIURPRQHDWRPWRDQRWKHULQ)HUPL¶VWZRDWRPV\VWHP>@$V

shown recently by the authors in the recent paper 7KUeediPeQViRQaOVpaFeaVaPe

diXPRITXaQtXPeQtaQJOePeQtQRQORFDOFRUUHODWLRQVLQ(35W\SHH[SHULPHQWVDUH

FDUULHGGLUHFWO\E\WKH'VSDFHWKHQXPHULFDORUGHU

W

of quantum entanglement LV]HURLQWKHVHQVHWKDW'VSDFHIXQFWLRQVDVDQLPPHGLDWHLQIRUPDWLRQPHGLXP

0RUHSUHFLVHO\WKHDFWLRQRIWKH'VSDFHDVDQLPPHGLDWHLQIRUPDWLRQPHGLXP

derives from a quantum entropy describing the degree of order and chaos of the vacuum supporting the density of the particles associated with the wave function XQGHUFRQVLGHUDWLRQ>@

,QGHHG WKHUH DUH DOVR H[SHULPHQWV RQ WKH TXDQWXP OHYHO ZKLFKVKRXOG EH

LQWHUSUHWHGDVLQWHUIHUHQFHLQWLPHOLNHWKHGRXEOHVOLWH[SHULPHQWLQWKHWLPHGR- PDLQSHUIRUPHGE\/LQGQHUHWDO>@+RZHYHUDFFRUGLQJWRWKHDXWKRUVWKH

results of these experiments may be considered compatible with the view that WKHXOWLPDWHDUHQDRISURFHVVHVLVD'VSDFHZKHUHWLPHDWDIXQGDPHQWDOOHYHO

H[LVWVPHUHO\DVDQXPHULFDORUGHU,QWKHDWWRVHFRQGGRXEOHVOLWH[SHULPHQWSHU- IRUPHGE\/LQGQHUHWDOLIWKHVOLWVFDQEHRSHQHGRUFORVHGE\FKDQJLQJWKHWHP- SRUDOHYROXWLRQRIWKHILHOGRIDIHZF\FOHODVHUSXOVHWKLVSK\VLFDOO\PHDQVWKDW

the duration of material change – emerging from a more fundamental numerical order – of the field of a few-cycle laser pulse corresponds to the openness or close- QHVVRIWKHVOLWV0RUHRYHUWKHSUHVHQFHDQGDEVHQFHRILQWHUIHUHQFHDUHREVHUYHG

IRUWKHVDPHHOHFWURQDWWKHVDPHWLPHMXVWLQWKHVHQVHWKDWWKH\HPHUJHIURPWKH

VDPHQXPHULFDORUGHU7KHIXQGDPHQWDODUHQDRIWKLVSURFHVVLVDOZD\VD'VSDFH

ZKHUHDWWKHIXQGDPHQWDOOHYHOWLPHH[LVWVDVDQXPHULFDORUGHU

In special relativity clocks measure relative speed of material change which GHSHQGVRQYHORFLW\RIDJLYHQLQHUWLDOV\VWHP&KDQJHVUXQLQVSDFHRQO\DQG

WLPHDWWKHIXQGDPHQWDOOHYHOLVDQXPHULFDORUGHURIWKHLUPRWLRQ:KDWLV³UHOD- WLYH´LQWKHXQLYHUVHLVDYHORFLW\RIFKDQJHUDWHVRIFORFNVLQFOXGLQJ0RUHRYHU

this relative velocity depends on the energy density of a fundamental quantum YDFXXPIURPZKLFKXQLYHUVDOVSDFHRULJLQDWHV>@6SHFLDOUHODWLYLW\GRHVQRWWDNH

into account gravitational fields and so the velocity of light is considered to be FRQVWDQW7RVDWLVI\FRQVWDQF\RIWKHOLJKWYHORFLW\/RUHQ]WUDQVIRUPDWLRQLVXVHG

6KDSLURH[SHULPHQWVKRZVYHORFLW\RIOLJKWLVGLPLQLVKLQJLQVWURQJHUJUDYLW\>@

,QRXUYLHZJUDYLW\DQGUHODWLYLW\DUHERWKUHODWHGZLWKIXQGDPHQWDOSURSHU- WLHVRITXDQWXPYDFXXP>@$VJUDYLW\GRHVDOVRNLQHWLFHQHUJ\RIDJLYHQLQHUWLDO

V\VWHPFKDQJHVSK\VLFDOSURSHUWLHVRITXDQWXPYDFXXPDQGVRYHORFLW\RIOLJKW

As these changes are minimal with respect to changes caused by the presence of VWHOODUREMHFWVWKHYHORFLW\RIOLJKWZKHQPHDVXUHGDSSHDUVWREHFRQVWDQW)URP

WKLVSRLQWRIYLHZLQWKHUHODWLYLVWLFGRPDLQXVLQJ*DOLOHDQWUDQVIRUPDWLRQ±ZKLFK

LPSOLHVWKDWDWDIXQGDPHQWDOOHYHOOLJKWKDs not constant speed in different iner- WLDOV\VWHPV±GRHVQRWVHHPLQFRKHUHQW

Cytaty

Powiązane dokumenty

Słaba kondycja finan- sowa przedsiębiorstw może uniemożliwić im pozyskanie środków na działalność innowacyjną, spowoduje to wyhamowanie działalności innowacyjnej, a co

2GELRUF\ LQIRUPDFML ]DZDUW\FK Z VSUDZR]GDQLDFK ILQDQVRZ\FK PXV]ą MHGQDN PLHü ĞZLDGRPRĞü RJUDQLF]HĔ NWyUH Z\QLNDMą ]H VWRVRZDQ\FK PHWRG L ]DVDG UD- FKXQNRZRĞFL

Analiza sytuacji rozpoczęcia przez dziecko nauki w szkole pokazuje, iż mamy do czynienia z sytuacją spotkania, w której dziecko posługujące się odpowiednim kodem (rozwiniętym

Our main goal in this paper is to study the relationship between the security indicators we collected and abuse, at the level of shared hosting providers, and eventually understand

В данной работе представлена геометрическая интерпретация кривизны плоских кривых в

While the variants of Danish /r/ are, despite the terminological discrepancies, not particularly hard to pronounce and the general rules of their distribution are rather

In this paper we compare the performance of an adaptive heuristic forecasting model with two mathematical models for the one day lead water demand forecast.. All models are

Inspired by previous work on Region Attention (Yang et al., 2017), we intro- duce a model that can adaptively select and focus on the video regions that are most discriminative for