8/14/2019 Smarandache Hypothesis by L. Motta

http://slidepdf.com/reader/full/smarandache-hypothesis-by-l-motta 1/5

6 0$5$1'$&+( + <327+(6,6 (9,'(1&(6 , 03/,&$7,216 $1' $ 33/,&$7,216

/HRQDUGR ) ' GD 0RWWDOPRWWD#DPD]RQ FRP EU

&RQVHOKHLUR )XUWDGR %HOpP 3$ %UD]LO

6HSWHPEHU

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

, 6 83(5/80,1$/ 3 +(120(1$ ( 9,'(1&(6 $1' 6 0$5$1'$&+(

+ <327+(6,6

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

1HYHUWKHOHVV TXDQWXP PHFKDQLFV VXJJHVW WKDW VXSHUOXPLQDO FRPPIDFW WKHUH DUH K\SRWKHVLV RQ WKH REOLJDWRU\ H[LVWHQFH RI VXSHUOQDWXUH > @ 7KH (35 %HOO SDUDGR[ LV WKH PRVW IDPRXV H[DPSOH 3RQ

8/14/2019 Smarandache Hypothesis by L. Motta

http://slidepdf.com/reader/full/smarandache-hypothesis-by-l-motta 2/5

SDUDGR[ 6PDUDQGDFKH VXJJHVWHG LQ LQ D OHFWXUH RQ %UD]LO WWKLQJ DV D OLPLW VSHHG RQ WKH XQLYHUVH DV SRVWXODWHG E\ (LQVWUHFHQWO\ WKLV SDUDGR[ ZDV FRPSOHWHO\ VROYHG E\ / ( 6]DEy > @ (YHQPDQ\ PRUH HYLGHQFHV RI WKH LQILQLWH VSHHG ² RU VLPSO\ LQVWDQWDQHRXVLQ WKH XQLYHUVH DV ZH VKDOO VHH EULHIO\

, 7KH 5RGULJXHV 0DLRULQR 7KHRU\6WXG\LQJ VROXWLRQV RI 0D[ZHOO DQG 'LUDF :H\O HTXDWLRQV :DOG\U 5RGU

-RVp 0DLRULQR ZHUH DEOH WR SURSRVH D IXOO XQLILHG WKHRU\ IRU FRQVWVSHHGV LQ QDWXUH IRU DUELWUDU\ WKH\ PHDQWfd Y LQ > @ 7KH\ DOVR SURSRVWKDW WKHUH LV QR VXFK WKLQJ DV D OLPLW VSHHG LQ WKH XQLYHUV+\SRWKHVLV FDQ EH SURPRWHG WR WKHRU\ DV 6PDUDQGDFKH 5RGULJXHV 0WKHRU\

:KDW LV XQLTXH DERXW 5RGULJXHV 0DLRULQR WKHRU\ LV WKDW VSHFLDOVXIIHUV D EUHDNGRZQ KRZHYHU HYHQ UHODWLYLVWLF FRQVWUXFWLRQVVXFK DV 'LUDF HTXDWLRQ DJUHH FRPSOHWHO\ ZLWK VXSHUOXPLQDO SKHQRPHQWR 5RGULJXHV 0DLRULQR WKHRU\ HYHQ ZHOO SRVLWLRQHG PLUURUV FHOHFWURPDJQHWLF ZDYH WR YHORFLWLHV JUHDWHU RI WKH OLJKW 7KLV DFRQILUPHG E\ 6DDUL DQG 5HLYHOW > @ ZKR SURGXFHG D ; ZDYH QD/X - < D 5RGULJXHV FRQWULEXWRU XVLQJ D [HQRQ ODPS LQWHUFHSWHGRULILFHV

7KH 650 WKHRU\ LV D PDWKHPDWLFDO SXUH DQG VWURQJ VROXWLRQ RI WKHZDYH HTXDWLRQ LQGLFDWLQJ WKDW WKHUH LV QR VSHHG OLPLW LQ WKH XPRVW SRZHUIXO WKHRU\ WRGD\ IRU FRQVWUXFWLRQ RI DUELWUDU\ VSHHGV

, 6XSHUOXPLQDO ([SHULPHQWV0DQ\ H[SHULPHQWV PDLQO\ HYDQHVFHQW PRGHV UHVXOW LQ VXSHUOXPLQD

ILUVW VXFFHVVIXO HYDQHVFHQW PRGH UHVXOW ZDV REWDLQHG LQ SURGXFHG D F VLJQDO /DWHU RQ KH ZRXOG SURGXFH DF )0 VLJQDO ZLWK 0R]DUW VWK

V\PSKRQ\ 7KLV DFKLHYHPHQW RI 1LPW] ZRXOG EH SDVVHG RYHU E\ RWKHU UHWLPHV IDVWHU WKDQ WKH FRQVWDQWF

,Q WKH FDVH RI 1LPW] H[SHULPHQW LV QRW FOHDU LI LW YLRODWHV WKHRWKHU KDQG / - :DQJ $ .X]PLFK DQG $ 'RJDULX UHFHQWO\ SXEOLVKHG DUHVXOW RI DQ DQRPDORXV GLVSHUVLRQ H[SHULPHQW ZKHUH D OLJKW SXOV

r WLPHV WKH VSHHG RI OLJKW QRW YLRODWLQJ WKH FDVXDO SDUDGR[WUDYHO ,n practice, this means that a light pulse propagating through the atomic vapourcell appears at the exit side so much earlier than if it had propagated the same distance ina vacuum that the peak of the pulse appears to leave the cell before entering it [10].

8/14/2019 Smarandache Hypothesis by L. Motta

http://slidepdf.com/reader/full/smarandache-hypothesis-by-l-motta 3/5

, 7KH 6SHHG RI *UDYLW\ 5HYLVLWHG7KH JHQHUDO UHODWLYLW\ RI (LQVWHLQ SRVWXODWHV WKDW WKH VSHHG RI

DV WKH FRQVWDQWF GXH WR WKH UHVWULFWLRQ RI WKH VSHFLDO WKHRU\ RI UHODWVSHHG RI OLJKW LV QRW D OLPLW RQ WKH XQLYHUVH LVQ W WLPH WR U)ODQGHUQ SXEOLVKHG VRPH DVWURSK\VLFDO UHVXOWV WKDW LQGLFDWH JUDY2EVHUYDWLRQV RI VRPH JDOD[LHV URWDWLRQV PDGH E\ 1$6$ VXJJHVW WKDWVSLQQLQJ ZLWK VXSHUOXPLQDO YHORFLW\ > @

9DQ )ODQGHUQ GDWD ZDV ODWHU RQ H[SODLQHG ZLWK D WKHRU\ WKVXSHUOXPLQDO SKHQRPHQD E\ ,ELVRQ 3XWKRII DQG 6 5 /LWWOH > @ <HVXSHUOXPLQDO VLJQDOLQJ IURP JDOD[LHV UHPDLQV XQH[SODLQHG IURP VXEOYLHZ

, 7DFK\RQV

6RPH PRGHOV WR WKH VXSHUVWULQJ WKHRU\ RXU IRUHPRVW FDQGLGDWHRI SK\VLFV LQFOXGH WDFK\RQV WKH SDUWLFOHV DEOH WR PRYH IDVWHU SK\VLFLVWV IRXQG D ZD\ RI KDFNLQJ WKH WKHRU\ VR WKDW WDFK\RQV GLVOLNH )UHHGPDQ GHIHQG WKDW WKH WKHRU\ VKRXOG QRW EH KDFNHG WKVXSHUVWULQJ WKHRU\ LV SUREDEO\ WKH EHVW ILHOG IRU VWXG\LQJ WDFK\RQ\RX ZRUN ZLWK LPDJLQDU\ PDVVHV 3URI 0LFKLR .DNX FRPSDUHG WKH LGLPHQVLRQV LQ SK\VLFV WR D PDWUL[ VFKHPH LQ KLV ERRN +\SHUVSDFH ,PDJLQH D PDWUL[ RI

[ WKDW LQVLGH ZH FDQ KDYH WKH 7KHRU\ RI 5HODWLYLW\ DQG DQRWTXDQWXP PHFKDQLFV ,I ZH EXLOG D ELJJHU PDWUL[ VD\ [ ZH FDQ WKHUHUHODWLYLW\ DQG TXDQWXP PHFKDQLFV LQ D VLQJOH PDWUL[ 7KDW LV WKHWKURXJK WKH DGGLWLRQ RI PRUH GLPHQVLRQV ,Q WKH VDPH ZD\ ZRUNLQJ

PDWUL[HV ZH GR QRW KDYH HQRXJK VSDFH IRU ZRUNLQJ ZLWK WDFK\RQV +RPDWUL[ ZH ZLOO KDYH HQRXJK VSDFH IRU ILQGLQJ VROLG VROXWLRQV RI WDFK

7DFK\RQV ZHUH DOUHDG\ LQ DQ REVFXUH PDQQHU GHWHFWHG LQ DLU VUD\V > @

,, , 03/,&$7,216 $ 1' $ 33/,&$7,216

$FFRUGLQJ WR 5RGULJXHV 0DLRULQR WKHRU\ WKH FRQVHTXHQFH RI WKVXSHUOXPLQDO SKHQRPHQD ZRXOG EH WKH EUHDNGRZQ RI WKH VSHFLDO UHOZH ZLOO QRW QHHG WR PRGLI\ DQ\WKLQJ LQ TXDQWXP PHFKDQLFV LWVHOIDSSHDUV WKDW LV TXDQWXP PHFKDQLFV ZKLFK LV EDQQLQJ WKH ROG SXUH U650 WKHRU\ 1HYHUWKHOHVV WKH WKHRU\ RI UHODWLYLW\ LQGHHG DFFVXSHUOXPLQDO FRPPXQLFDWLRQ UHVXOWLQJ LQ WLPH WUDYHO DV :DQJ HW D

3HUKDSV ZH ZRXOG EH DEOH LQ D GLVWDQW IXWXUH WR VHQG PHVVDJHIXWXUH $Q\ZD\ VXSHUOXPLQDO SKHQRPHQD ZRXOG KDYH D PRUH VW

8/14/2019 Smarandache Hypothesis by L. Motta

http://slidepdf.com/reader/full/smarandache-hypothesis-by-l-motta 4/5

DSSOLFDWLRQ ZLWK ORFDO FRPPXQLFDWLRQ $FFRUGLQJ WR 5RGULJXHV 0DLRULZDYH LVFORVHG LQ D ZD\ WKDW LW GRHV QRW ORVV HQHUJ\ DV LW WUDYHOVZDYH UDGLR PHVVDJH ZRXOG DFKLHYH LWV GHVWLQDWLRQ DOPRVW LQ WKH VZHUH VHQW DQG QR RQH H[FHSW WKH GHVWLQDWLRQ FRXOG VS\ WKH FRQWLQYHQWLRQ RI VXFK VXSHUOXPLQDO VLJQDOLQJ WUDQVPLWWHU ZRXOG EH RI

ZLWK 0,7 V SDVWLOOH DEOH WR FXUYH OLJKW LQ LQ WKH PDQXIDFWXULQ

,,, & 21&/86,21

7KH YDULRXV H[SHULPHQWV DQG VROLG WKHRULHV WKDW ULVH IURPLQYROYLQJ VXSHUOXPLQDO SKHQRPHQD DUH D KLJK OHYHO LQGLFDWLRQ R+\SRWKHVLV WKDW WKHUH LV QR VXFK VSHHG OLPLW LQ QDWXUH 7KLV L(LQVWHLQ SRVWXODWH RI UHODWLYLW\ EXW QRW LQ DQ\ ILHOG RI TXDQWXPUHODWLYLVWLF ZDYH HTXDWLRQ $V LQ RXU HYROXWLRQ FDPH D WLPH WZHUH QRW HQRXJK WR XQGHUVWDQG VRPH DVSHFWV RI QDWXUH LW LV PD\E(LQVWHLQ V UHODWLYLW\ PXVW EH OHIW DVLGH IRU KHQFH TXDQWXP PHFKDQL

$ &.12:/('*(0(176 'U 0LQK 3HUH] DW WKH $PHULFDQ 5HVHDUFK 3UHVV IRULQYLWDWLRQ GLVFXVVLRQV PDWHULDO HWF

5 ()(5(1&(6

> @ )UHHGPDQ 'DYLG %H\RQG (LQVWHLQ'LVFRYHU\ )HE

> @ +HUEHUW 1LFN )DVWHU WKDQ /LJKW 6XSHUOXPLQDO /RRSKROHV LQ 3K\VLFV3OXPH %RRNV 1HZ <RUN 86$

> @ 6KDQ *DR4XDQWXP VXSHUOXPLQDO FRPPXQLFDWLRQ PXVW H[LVW -XQ

SK\VLFV ,40& *6(> @ 6KDQ *DR4XDQWXP VXSHUOXPLQDO FRPPXQLFDWLRQ GRHV QRW UHVXOW LQ F

SDUDGR[HV-XQ TXDQW SK ,40

> @ 6PDUDQGDFKH )ORUHQWLQ7KHUH ,V 1R 6SHHG %DUULHU ,Q 7KH 8QLYHUVH%XOOHWLQ RI 3XUHDQG $SSOLHG 6FLHQFHV 'HOKL ,QGLD 9RO' 3K\VLFV 1R S $OVRKWWS ZZZ JDOOXS XQP HGX aVPDUDQGDFKH SK\VLFV KWP

8/14/2019 Smarandache Hypothesis by L. Motta

http://slidepdf.com/reader/full/smarandache-hypothesis-by-l-motta 5/5

> @ 6]DEy / (&RPSOHWH 5HVROXWLRQ RI WKH (35 %HOO 3DUDGR[(|WY|V %XGDSHVW-XQ TXDQW SK (|WY|V +36

> @ 5RGULJXHV :DOG\U $ 0DLRULQR -RVp ( $ XQLILHG WKHRU\ IRU FRQVWUXFWLRQ RIDUELWUDU\ VSHHGV VROXWLRQV RI WKH UHODWLYLVWLF ZDYH HTXDWLRQV5DQGRP 2SHU DQG6WRFK (TX 9RO1R S

> @ 6DDUL 3 5HLYHOW . (YLGHQFH RI ; 6KDSHG 3URSDJDWLRQ ,QYDULDQW /RFDOL]HG:DYHV 3K\V 5HY /HWW

> @ 1LPW] *6XSHUOXPLQDO 6LJQDO 9HORFLW\$QQ GHU 3K\VLN S

> @ :DQJ / - .X]PLFK $ 'RJDULX $*DLQ DVVLVWHG 6XSHUOXPLQDO 3URSDJDWLRQ1DWXUH S -XO\

> @ )ODQGHUQ 7 9DQ7KH VSHHG RI JUDYLW\ ± ZKDW WKH H[SHULPHQWV VD\3K\V /HWW $

> @ +DUPRQ % $*DODWLF 6XSHUOXPLQDO 6RXUFH ,Q UG ,17(*5$/ :RUNVKRS WKH([WUHPH 8QLYHUVH 7DRUPLQD ,WDO\ 6HS (G E\ * 3DOXPERDQG & :LQNOHU $VWURSK\V /HWW &RPPXQ DVWUR SK

> @ ,ELVRQ 0LFKDHO 3XWKRII +DUROG ( /LWWOH 6FRWW 57KH VSHHG RI JUDYLW\UHYLVLWHG3K\V /HWW $ 1RY SK\VLFV