7KHSKHQRPHQRORJ\RIHOHFWURVWDWLFDOO\LQGXFHGLQHUWLD 2&267$'(%($85(*$5'
)RQGDWLRQV/RXLVGH%URJOLH UXH0DUVRXODQ)3$5,6)5$1&(
$%675$&7(LQVWHLQ¶VPDVVHQHUJ\HTXLYDOHQFHODZIL[HVWKHHQHUJ\FRQ VWDQW LQ ERXQG V\VWHPV LW WKXV VHOHFWV WKH &RXORPE JDXJH LQ WKH HOHFWULF FDVH 7KLV H[HPSOLILHV D PXFK ODUJHU SKHQRPHQRORJ\ LQFOXGLQJ OLQHDU RU DQJXODUPRPHQWXPEDODQFHZKLFK,KDYHQDPHG³HOHFWURPDJQHWLFJDXJHDV DQLQWHJUDWLRQFRQGLWLRQ´5HFHQWO\0LNKDLORYKDVHYLGHQFHGWKHHOHFWULFDOO\
LQGXFHG H[WUD PDVV IRU DQ HOHFWURQ DFFHOHUDWHG LQVLGH D FKDUJHG VSKHUH 7HVWVXVLQJDQJXODUPRPHQWXPDUHKHUHSURSRVHGRQHYLDWKH=HHPDQHI IHFW
5(680( /¶pTXLYDOHQFH PDVVHpQHUJLH G¶(LQVWHLQ IL[H OD FRQVWDQWH GH O¶pQHUJLHG¶XQV\VWqPHOLpVGDQVOHFDVpOHFWULTXHOHSRWHQWLHOGH&RXORPE HVWDLQVLVpOHFWLRQQp&HFLIDLWSDUWLHG¶XQHSOXVYDVWHSKpQRPpQRORJLHLQ FOXDQWOHVPRPHQWVOLQpDLUHHWDQJXODLUH MHO¶DLDSSHOpHµODMDXJHpOHFWUR PDJQpWLTXH FRPPH FRQGLWLRQ G¶LQWpJUDWLRQ¶ 0LNKDLORY D UpFHPPHQW PLV HQpYLGHQFHO¶H[WUDPDVVHpOHFWULTXHPHQWLQGXLWHGDQVXQpOHFWURQDFFpOpUpj O¶LQWpULHXUG¶XQHVSKqUHFKDUJpH'HVWHVWVLPSOLTXDQWOHPRPHQWDQJXODLUH VRQWLFLSURSRVpVGRQWO¶XQYLDO¶HIIHW=HHPDQ
,QWURGXFWLRQ
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
FRQWUROV DQG DV FRQWULEXWLRQV RI WKH SRWHQWLDO $L DUH FRQWDLQHG LQ WKH PHDVXUDEOHPRPHQWVOLQHDURUDQJXODUJHQHUDWHGE\WKHIRUFHVWKHJDXJHLV VHOHFWHG DV DQ LQWHJUDWLRQ FRQGLWLRQ 7KLV FRQIHUV SK\VLFDOLW\ WR WKH SRWHQWLDOLQIDFWLWLVWKHVRXUFHDGKHULQJJDXJHWKDWLVXVXDOO\VHOHFWHG7KH SUHVHQWLQYHVWLJDWLRQLVUHVWULFWHGWRYDULRXVDVSHFWVRIWKHHOHFWURVWDWLFH[WUD PDVVFH9LQGXFHGLQDQHOHFWURQDFFHOHUDWHGLQVLGHD&RXORPESRWHQWLDO 5HPDUNVRQ6RPPHUIHOG¶VK\GURJHQDWRP
6RPPHUIHOG¶VHOHFWURQRIUHVWPDVVDQGFKDUJHHRUELWVLQWKHSURWRQ¶V FHQWUDOSRWHQWLDO9 UHY GUGWGHQRWLQJLWV YHORFLW\ LQWKLV IUDPHLWV UHODWLYLVWLFPDVVDQGPRPHQWXPFDQEHZULWWHQDV
P FH9S PY
PEHLQJWKXVOLNHQHGWRWKHDWRP¶VPDVVGHIHFWWKHSRWHQWLDO9FRPHVRXW DVPHDVXUHGLQWKH&RXORPEJDXJH
,QYLHZRIWKHIROORZLQJOHWEHPHQWLRQHGH[LVWHQFHRIDQLQGXFHGDQJXODU UHFRLOHYLGHQFHGLQWKHSHULSURWRQDGYDQFH6RFH9UHDOO\LVDQHOHFWUR VWDWLFFRQWULEXWLRQWRWKHHOHFWURQ¶VHIIHFWLYHPDVVP
5HPDUNVRQWKH³PDJQHWRG\QDPLFHIIHFW´
7KXVQDPHGE\-RXJXHWDQGRSHUDWLRQDOO\GLVFXVVHGLQE\3HQILHOG +DXV6KRFNOH\-DPHVDQGPHWKHHIIHFWLVIRUPDOL]HGDVDQHOHFWURVWDWL FDOO\LQGXFHGPRPHQWXP
S F,³9GO{F,³³(uuGV HVX FRQIHUUHGWRDQ$PSHULDQFLUFXLWRILQWHQVLW\,LPPHUVHGLQDQHOHFWURVWDWLF SRWHQWLDO 9U WKLV IROORZV IURP WKHHIIHFWLYH PDVV DQG PRPHQWXP RI WKH FRQGXFWLRQHOHFWURQVH[SUHVVHGDV
6RWKHFLUFXLWUHFRLOVLILWVLQWHQVLW\,LVYDULHGWKLVEHLQJDQ H[WUHPHO\
ORZYHORFLW\UHODWLYLVWLFHIIHFW
,QWKHVLPSOHFDVHZKHUHWKHSRWHQWLDO9ULVJHQHUDWHGE\DSRLQWFKDUJH 4FLUFXLWDQGFKDUJHERWKFRQWDLQLQGLUHFWO\RSSRVLWHOLQHDUPRPHQWDrS EHFDXVHRQHKDV
9U 4U $U L³UGO
/HWEHPHQWLRQHGWKDWWKHFLUFXLWFRQWDLQVDOVRDQLQGXFHGDQJXODUPR PHQWXPDVGRHV6RPPHUIHOG¶VRUELWLQJHOHFWURQ
7KDQNV WR $PSqUH¶V H[SUHVVLRQ RI D FLUFXLW¶V PDJQHWLF PRPHQW00 WKH LQGXFHGOLQHDU3DQGDQJXODU&PRPHQWVRIDGLSROHLPPHUVHGLQDSRWHQWLDO 9FRPHRXWDV
3 F(uu00 & F,³UuuGO F900
&RQVLGHU WKH VSHFLDO FDVH RI D VXSHUFRQGXFWLQJ FLUFXODU FLUFXLW ZLWK D SRLQWFKDUJHDWLWVFHQWHULIDPDJQHWLF ILHOG% FRD[LDO ZLWKWKHFLUFXLWLV SUHVHQWWKH0HLVVQHUHIIHFW¶VIRUPXODLVPRGLILHGVRDVWRUHDG
FH9YH$
WKLVEHLQJDWHVWDEOHHIIHFW
7KH³PDJQHWRG\QDPLFHIIHFW´LVFORVHO\UHODWHGWRYDULRXVFHOHFWURPDJ QHWLFHIIHFWVGLVFXVVHGE\PDQ\DXWKRUVDDQGDSDSHUVRIPLQH GLVFXVVWKHPDWWHU
7KHHOHFWURQ¶VLQGXFHGPDVVLQVLGHDKROORZFKDUJHGVSKHUH ,I DQ HOHFWURQ DW UHVW LPPHUVHG LQ WKH &RXORPE SRWHQWLDO 9 54 HQ FORVHGLQDKROORZFKDUJHGVSKHUHLVDFFHOHUDWHGLQDYHU\VKRUWWLPHXSWRD YHORFLW\YLWLPSDUWVWRWKHVSKHUHDPRPHQWXPS FH9Y DFFRUGLQJWR PRPHQWXPEDODQFHLWWKXVSLFNVXSWKHPRPHQWXPS
7KLV HIIHFW KDV EHHQ UHFHQWO\ WHVWHG LQ WZR LQGHSHQGHQW H[SHULPHQWV E\
0LNKDLORY ZLWK HOHFWURQV DFFHOHUDWHG LQVLGH D VSKHUH DW D FRQWUROODEOH SR WHQWLDOXSWRr.9
,QIDFWWKHUHZDVDUHGXFWLRQIDFWRUWKLVLVTXLWHXQGHUVWDQGDEOHWKHHOHF WURQV ZHUH FRQGXFWLRQ HOHFWURQV LQ D FLUFXLW VRWKH SUREOHP DW VWDNH ZDV DQJXODUPRPHQWXPEDODQFH
9DULDEOHPDJQHWRUFXUUHQWORRSLQVLGHDFKDUJHGKROORZVSKHUH ,IDFKDUJHGKROORZ VSKHUHHQFORVLQJDXQLIRUP&RXORPE SRWHQWLDO 9 45URWDWHVDWDQDQJXODU YHORFLW\: LWDOVRFRQWDLQVD XQLIRUP PDJQHWLF ILHOG
% F::
7KLVFRPSDUHGZLWK/DUPRU¶VHTXLYDOHQFHUHFLSHIRUGLDPDJQHWLVP
P% H:
VKRZV WKDW LI ZKDW URWDWHV LV WKH SODVPD LQVLGH D FRQGXFWLQJ VSKHUH HDFK HOHFWURQFRQWDLQVDVHOILQGXFHGH[WUDPDVVFH9
&RQVLGHU WKHQ D VPDOO FLUFXLW RU GLSROH LQVLGH D KROORZ QRQ URWDWLQJ FKDUJHG VSKHUH ,I LWV PDJQHWLF PRPHQW LV FKDQJHG IURP ]HUR WR00WKH VSKHUHSLFNVXSDQDQJXODUPRPHQWXP
& F90
WKHFDOFXODWLRQLVVWUDLJKWIRUZDUGLIWKHGLSROHLVDWWKHVSKHUH¶VFHQWHULILWLV QRWWKHUHVXOWUHPDLQVEHFDXVHWKHUHLVQRRUELWDOPRPHQWXP
&RPSDULQJWKLVZLWKWKHGLDPDJQHWLFHTXLYDOHQFHIRUPXOD 0
0 HP&
VKRZVWKDWRIWKHDQJXODUPRPHQWXPJHWV³SRWHQWLDO´
%XWZKDWUHDOO\PDWWHUVLVH[LVWHQFHRIDQDQJXODUUHFRLORIWKHFLUFXLWRU PDJQHW WHVWDEOH YLD WKH (LQVWHLQGH+DDV RU WKH %DUQHWW HIIHFW RU PRUH LQWHUHVWLQJO\YLDVXSHUFRQGXFWLRQRUWKH=HHPDQHIIHFW
0RGLILHG=HHPDQHIIHFWLQVLGHDKROORZFKDUJHGVSKHUH /HWWZRZHOONQRZQIDFWVEHUHFDOOHG
7KH ³FODVVLFDO =HHPDQ HIIHFW´ LV D IRUP RI GLDPDJQHWLVP ,I D XQLIRUP PDJQHWLFILHOG%LVDSSOLHGQRUPDOO\WRWKHK\GURJHQDWRP¶VRUELWLQJHOHF WURQWKHRUELWLVXQFKDQJHGZKDWLVFKDQJHGLVWKHIUHTXHQF\Q ZSLQ DFFRUGZLWK/DUPRU¶VIRUPXOD
$V WKH K\GURJHQ DWRP¶V HLJHQIXQFWLRQV DUH\[W MU HLKQ FKDQJLQJ WKHFHQWUDOSRWHQWLDO¶VJDXJHDIIHFWVQRWWKHUDGLDOGLVWULEXWLRQMUEXWGLV SODFHVE\DFRQVWDQWDOO WKH HQHUJ\ OHYHOV WKLV OHDYHV WKH RSWLFDO VSHFWUXP XQFKDQJHG %XW LI DV VDLG EHIRUH WKH DGGHG FRQVWDQW KDV SK\VLFDOLW\ WKH FKDQJHLQQPXVWEHWHVWDEOHYLDWKH=HHPDQHIIHFW
5HIHUULQJWRWKHSUHFHGLQJ6HFWLRQZHZULWHDVH[SUHVVLRQRIWKHPRGLILHG
=HHPDQHIIHFWLQVLGHDFKDUJHGKROORZVSKHUHDWSRWHQWLDO9R
PFH9R: |H%
P GHQRWLQJ WKH RUELWLQJ HOHFWURQ¶V HIIHFWLYH PDVV LQ WHUPV RI WKH FHQWUDO SRWHQWLDO 9U:H DVVXPH WKDW 9R LV SRVLWLYH DQG YHU\ PXFK ODUJHU WKDQ 9U
9LDWKHIDPLOLDUVXEVWLWXWLRQ: oS QZHH[SUHVVWKHFODVVLFDO=HHPDQ HIIHFWRUVWURQJ3DVFKHQ%DFNHIIHFWLQWKHIRUP
SFH9'Q | rH%
7KLVIRUPXODZHSURSRVHWRWHVWPRGXORWKHSUHYLRXVO\PHQWLRQHGFRUUHF WLYHIDFWRU
SPFH9'Q rH%
$QDORJRXVJUDYLWDWLRQDOHIIHFWV
7KHVHDUHZHOONQRZQDQGPRUHJHQHUDOO\DFFHSWHGWKDQWKHHOHFWULFRQHV 0DFKLDQLQGXFHGLQHUWLDKDVEHHQVWXGLHGE\6FLDPD DQGRWKHUV 7KHLGHDLVWKDWDPDVVSRLQWRIDFWLYHJUDYLWDWLRQDOPDVVRU³PDVVFKDUJH´
PLPPHUVHGLQWKHFRVPLFSRWHQWLDO8KDVDSRWHQWLDOJUDYLWDWLRQDOHQHUJ\
8PZKHQFHDQLQGXFHGLQHUWLDOPDVVF8PZKHQFH
8 F
,QWKHPRGHOZKHUHWKHSDUWLFOHLVWKRXJKWRIDVPRYLQJLQVLGHD³VSKHUH RIIL[HGVWDUV´RIPDVV0DQGUDGLXV5RQHKDV*GHQRWLQJ1HZWRQ¶VFRQ VWDQW
8 F5*0
6FKU|GLQJHULDQ LQGXFHG LQHUWLD &RQVLGHU D SODQHW RUELWLQJ D VWDU VD\
0HUFXU\LQVLGHWKH6XQ¶VSRWHQWLDOHQHUJ\8 U*0V,WVHIIHFWLYHPDVVLV WKHVXPRILWVSURSHUPDVVPSOXVDQLQGXFHGH[WUDPDVVF8WKHFRPSX WDWLRQ RI WKH RUELW SDUDOOHOV WKDW RI 6RPPHUIHOG¶V HOHFWURQ 6FKU|GLQJHU /XFDV$VVLVKDYHGLVFXVVHGWKHPDWWHU
5HIHUHQFHV
>@ V. F. Mikhailov, Ann. Fond. Louis de Broglie 211,1999, 161 and 2001.
>@ O. Costa de Beauregard in Advanced electrodynamics, T.W. Grimes and D.M.
Barrett eds, World Scientific, Singapore 1995, p. 193.
>@ O. Costa de Beauregard, Physics Essays 10, 1997, 492 and 646.
>@ M. Jouguet, Traité d’électricité théorique, Gauthier Villars Paris, t.3, 1960, p.
126.
>@ P. Penfield and H. Haus, Electrodynamics of moving media, M.I.T. Press, Cambridge, Mass. 1967, pp. 202 ff.
>@ W. Shockley and R.P. James, Phys. Rev. Lett. 18, 1967, 876.
>@ O. Costa de Beauregard, Phys. Lett. A 24, 1967, 177.
>@ O. Costa de Beauregard, Cah.Phys. 206, 1967, 373.
>@ O. Costa de Beazuregzd Nuovo Cim. 63B, 1969, 611.
>@V. V. Batygin and I. K. Toptygin, Problems in electrodynamics, Academic Press New York 1966, p. 92-96.
>@D. W. Sciama, Monthly Notices Roy. Astr. Soc. 113, 1953, 34.
>@A. K. T. Assis, Weber’s Electrodynamics, Kluwer, Dordrecht, 1994, p. 208.
>@A. K. T. Assis, Relational Mechanics, Apeiron, Montréal, 1999, p. 249.
>@J.V. Woodward and T. Mahood, Found. Phys. 29,199, 899.
>@O. Costa de Beauregard, Found. Phys. Lett. 13, 2000, 395.
>@E. Schrödinger, Ann. Physik 77, 1925, 336.
>@R. Lucas, C. R. Ac. Sci. B 282, 1976, 43.
0DQXVFULWUHoXOHVHSWHPEUH
