A Macroscopic Approach to Creating Exotic Matter

Transcription

1 PHYSICS/00007 A Maosop Appoah to Ceatg Exot Matte Chales T. dgely hales@dgely.ws Hee the Casm effet s used to peset a smple maosop vew o eatg exot matte. The eegy asg betwee two ealy pefetly odutg paallel plates s show to beome easgly egatve as the plate sepaato s edued. It s poposed that the Casm eegy appeas easgly egatve smply beause the vauum eletomaget zeo-pot feld pefoms postve wok pushg the plates togethe, tasfomg feld eegy to ket eegy of the plates. ext, the etal popetes of exot matte ae osdeed. The paallel plates of the Casm system ae eplaed wth a elosed avty of detal dmesos that s subjeted to a exteal foe. It s foud that zeo-pot adato exets a etal foe o the avty opposto to the exteal foe. Ths ultmately leads to the oluso that the etal popetes of exot matte ae detal to the etal popetes of oday matte.. Itoduto Aodg to a eet poposal by Mguel Alubee [], geeal elatvty admts met solutos that pedt the possblty of supelumal spae tavel. I essee, these mets mply that a spaeshp a be popelled though spae by expadg spae-tme behd the shp whle, at the same tme, otatg spae-tme fot of the shp. The shp the sufs o ths spae-tme defomato, aqug vey hgh veloty elatve to the est of the uvese. Eve moe supsg s that these wap dve mets pedt that suh tavel a be aed out wthout the usual tme dlato effets pedted by speal elatvty. That s, pope tme expeeed by a spae tavele, usg a Alubee wap dve, s detal to the tme expeeed by obseves emag o the Eath. As wth wom holes, wap dves eque temedous quattes of egatve eegy, o exot matte []-[5]. Although thee ae seveal oeptual dffultes assoated wth wap dve, the eegy equemet aloe a easly be take as suffet gouds fo us to dsmss the feasblty of wap dve. Moe eouagg, howeve, s that modfed foms of the Alubee met have bee poposed, equg moe easoable quattes of exot matte [4]-[5]. We a oly hope that as moe eseah s oduted, wap dve theoy wll beome easgly teable. Of ouse, thee s oe seous obstale to ou atually egeeg a wap dve system of ay sze: the eed fo exot matte. Befoe we a set up a physally ealzable wap dve, we must have a wokg kowledge of how to geeate exot matte. As s well kow, exot matte s fobdde lassally, but s pemtted o the quatum level ude speal umstaes. Whe these speal umstaes ae appled to wap dve theoy, we ae left wth a wap bubble equg massve amouts of exot matte ad havg walls whose thkess s o the ode of the Plak legth []-[3]. But eve wth suh ostats, we ae stll left wth the questo of how to obta exot matte, egadless of quatty. It s a objetve of the peset aalyss to povde a smple maosop oept fo eatg exot matte, whle leavg the questo of quatty fo futue developmet. Oe well-kow example whh egatve eegy podues obsevable foes s the Casm effet [], [4]. The Casm effet s a attatve foe that ases betwee two ealy pefetly odutg paallel plates whe they ae plaed lose poxmty, as show Fg.. I essee, the plates blok out some of the vauum zeo-pot eletomaget adato that would othewse esde the volume betwee the plates, wee the plates emoved [6]-[7]. Ths gves se to a small eegy dffeee betwee the plates elatve to the ego outsde the plates: U() = 3 whee L s the sufae aea of eah plate, ad s the plate sepaato. Dffeetatg Eq. () wth espet to the plate sepaato the gves the foe o the plates: U() F() = = 4 40 Ths attatve foe, tedg to push the plates togethe, has bee expemetally vefed to wth 5% of ts theoetal value [7]. Fgue. Two ealy pefetly odutg plates of aea L ae plaed paallel, sepaated by dstae << L. () ()

2 dgely: Ceatg Exot Matte Whle the Casm effet s typally eseved fo dsussos volvg the quatum wold, thee may fat be a way to ptue the egatve eegy-otet of the Casm system fom a maosop pot of vew. Ths a be doe by takg a maosop vew of the vauum eletomaget zeo-pot feld (ZPF). Wth ths appoah, the ZPF s vewed as a eal Loetz-vaat adato feld that s essetally ufom thoughout all of spae. So log as the ZPF s sotop, o det obsevato of the ZPF a be made; but f the ZPF beomes loally asotop, suh as the Casm system, the det obsevatos a the deed be aed out [7]-[8]. The ext Seto deals wth the hage Casm eegy that ases whe the plate sepaato deeases. It s show that the ZPF pefoms postve wok pushg the plates togethe. The esultg dop feld eegy appeas easgly egatve wth espet to the ufom eegy otet outsde the plates [8]-[9]. Based o ths, t s poposed that wheeve the ZPF pefoms postve wok a loalzed ego of spae-tme, a dop zeo-pot feld eegy ous, esultg a egatve eegy desty elatve to the est of spae-tme. Seto 3 s devoted to aqug geate sght to the etal popetes of exot matte. Applyg the law of eta of eegy [0]-[] to the Casm eegy leads to a egatve etal mass. Usg ths, t s show that exot matte possesses etal popetes detal to those of oday matte.. egatve Eegy due to Wok Pefomed by Zeo-Pot Feld Cosde the eegy betwee two paallel plates whe the sepaato s fst ad the late, whee >. Aodg to Eq. (), whe the plate sepaato s ad the eegy betwee the plates s, espetvely U =, U 3 = 3 (3a,b) As poted out the Itoduto, the foe betwee the plates s attatve, tedg to push the plates togethe. Suppose the foe pushes the plates fom sepaato to sepaato. The hage eegy betwee the plates s the the ZPF s tally ufom eveywhee [8]-[9], ths dop feld eegy mafests as a egatve eegy desty betwee the plates, elatve to the eegy desty of the ego outsde the plates. Of patula teest s the ase whh the tal sepaato of the paallel plates s vey lage. Assumg that o othe foes at o the plates, the ZPF should stll exet a foe o the plates, o matte how mute that foe may be. The wok pefomed by that foe a be expessed smply by takg the lmt of Eq. (5) as teds to fty: Cayg ths out leads detly to ( ) W = Lm W (6) = W 3 whh the subspt o has bee dopped fo smplty. Ths s the wok pefomed by the ZPF pushg two paallel plates to a sepaato whe the plates ae tally vey fa apat. The potetal eegy assoated wth Eq. (7) s the = U 3 whh s detal to the ogal expesso fo the Casm eegy, gve by Eq. (). So the, we have ome full le, but wth the lea asseto that the egatve eegy desty of the Casm system ases beause the ZPF pefoms postve wok a loalzed ego of spae-tme. Moe spefally, we popose that ay stae whh the ZPF pefoms postve wok a loalzed ego of spae-tme, a dop vauum eletomaget zeo-pot feld eegy ous, esultg a egatve eegy desty that ego elatve to the est of spae-tme [9]. 3. Ietal Popetes of Exot Matte Takg a stt vew of the elatoshp betwee eegy ad mass [0], we mght suppose that suh a ego exhbts a etal mass aodae wth the law of eta of eegy, m= U. Applyg ths expesso to Eq. (8) leads detly to (7) (8) π U = U U =! L 3 3 (4) 70 π! L m = 3 70 (9) Ths mples that the Casm eegy beomes easgly egatve as the plate sepaato s edued. The wok pefomed ode to bg about ths hage eegy s π W =! L 3 3 (5) 70 Ths s postve wok pefomed by the ZPF pushg the plates fom to, tasfomg eletomaget feld eegy to ket eegy of the plates. Se the eegy otet of Ths mples that the mass-eegy betwee the plates of the Casm system s egatve. At fst sght, we mght expet ths small quatty of exot matte should edue the oveall etal mass of the Casm system. As we shall see, howeve, we have o good easo to pesuppose that exot matte behaves ay way dffeetly tha does oday matte. Aodg to pevous aalyses [0]-[], the etal popetes of eegy aot be adequately explaed o the bass of etal mass aloe; the elatvst atue of spae-tme must also be take to aout. Ths was demostated by osdeg a deal avty of legth, otag

3 PHYSICS/ moohomat adato of fequey ν 0 that s subjeted to a exteal foe [0]. It was foud that whe a exteal foe s appled to suh a avty, adato pessue exets a etal esstae foe o the avty, gve by h F = ( ν ν ) A B (0) whee s the aveage umbe of photos the avty, ν A ad ν B ae the fequees of adato measued by omovg obseves at walls A ad B of the avty, espetvely, ad ˆ s a ut veto the deto of the avty s aeleato. Ths expesso fo the foe was used to show that the etal esstae of the avty ases as a det mafestato of spae-tme asotopy wth the avty [0]. The pla hee s to use Eq. (0) to ga geate sght to the etal popetes of exot matte. To do ths, the paallel plates of the Casm system ae eplaed wth a avty of detal dmesos, amely oe wth << L, as show Fg.. Also, the zeo-pot adato ude osdeato hee s ot moohomat, ad thus the aveage dated by must be elmated favo of a sum ove all fequey modes wth the avty. Cayg ths out, Eq. (0) a be east the fom =! F ω ω A B () whee s the umbe of modes wth the avty [3]. Fo the ase of a avty themal equlbum wth ts suoudgs, the umbe of photos obseved at eah wall wth the avty s oughly the same. Usg ths to ou advatage, Eq. () a the be wtte as! F = ( ωa ωb) () Ths expesso mples that whe a exteal foe s appled to the avty, eah fequey mode wth the avty exets a et foe o the avty, gve by F =! ( ω ω ) A B (3) Fo the ase of a ufomly aeleatg avty, as show Fg., asotopy of spae-tme gves se to a obsevable Dopple-shft wth the avty [0]: ωa ωb 0. Obseves esdg the o-movg efeee fame (CMF) of the avty fd that zeo-pot adato avg at wall B s blueshfted elatve to adato obseved at wall A. If the fequees obseved at wall A ae ω A = ω 0, the the fequees at wall B ae ω B = ω 0 + V V (4) whee V s the elatve veloty of wall B gaed dug the tme whh photos tavel fom wall A to wall B. Usg these fequees, obseves movg wth the avty east Eq. () the fom! + V F = ω ω 0 0 V eaagg a bt, ths expesso beomes ( ω ) + V =! 0 F V (5) (6) To futhe smplfy ths expesso, we ote that fo the ase of a vey small avty udegog ewtoa aeleato, we a use the appoxmato [0] + V dt V dτ (7) Fgue. A elosed avty of detal dmesos as the Casm system aeleates ufomly ude the ato of a exteal foe. Spae-tme asotopy, asg due to aeleato, gves se to a fequey-shft the zeo-pot adato obseved at walls A ad B wth the avty: ωa ωb 0. Zeo-pot adato pessue exets a et foe F o the avty opposto to the exteally appled foe. whee d τ s a teval of pope tme expeeed by obseves movg wth the avty, dt s a teval of oodate tme expeeed by a o-movg obseve whose oodate og s mometaly odet wth that of the aeleatg system at a tme t = 0, ad the mus sg ases beause the gadet s the deto of the avty s aeleato [0]. Substtutg Eq. (7) to Eq. (6) the gves the foe as dt F = (! ω 0 ) dτ (8) As a fal osdeato, we ote that the summato smply expesses the total zeo-pot eegy wth the avty:

4 dgely: Ceatg Exot Matte 4 ( ω ) E =! (9) 0 At ths pot, t must be stessed that although the eegy desty wth the avty s egatve wth espet to exteo egos, dvdual photos sde the avty have the usual postve eeges, E =! ω. The avty smply bloks out those photos havg wavelegths loge tha the dstae betwee the walls of the avty [7],[3]. Usg Eq. (9) Eq. (8), the foe o the avty the beomes dt F = E dτ (0) Aodg to ths expesso, zeo-pot adato wth the avty exets a etal foe o the avty that ats opposto to the exteally appled foe, just as does oday, postve adato [0], [4]. Thus, the etal popetes of a ego havg a egatve eegy desty ae detal to those of a ego havg a equvalet postve eegy desty. Pevous aalyses have show that all foms of postve eegy esst hages to the states of moto, ad that the soue of suh esstae s etely due to spae-tme asotopy asg wth aeleatg systems of efeee [0]-[]. Equato (0) mples that the same holds tue fo egatve foms of eegy as well. We a olude, theefoe, that the etal popetes of exot matte ae the same as the etal popetes of oday matte. Both foms of matte esst hages to the states of moto whe ated upo by a exteal foe. etug to the Casm system, t s ow easy to see that the etal mass pedted by Eq. (9) wll otbute postvely to the oveall eta of the Casm system athe tha edug t, as the mus sg tally suggested. Whle the mus sg Eq. (9) etaly mples that the mass s exot, havg ts og egatve eegy, the mus sg tells us othg about the etal popetes of exot matte. 4. Dsusso Cuet theoy plaes seous esttos o the exstee of exot matte. Aodg to eet aalyses, suh esttos set the thkess of the walls of a Alubee wap bubble o the ode of the Plak legth, whle equg a eomous quatty of exot matte []-[3]. I the peset aalyss, a smple maosop oept fo eatg exot matte ad pedtg ts etal popetes has bee poposed. Of ouse, the valdty of the tepetato set foth hee ultmately hges o whethe o ot the ZPF s ompsed of eal adato, ad o the amout of wok that a be pefomed theeby. Judgg fom the lteatue o the subjet, whethe o ot the ZPF s eal seems to be a ogog debate [7]-[9]. Assumg that the ZPF s deed eal ad apable of pefomg eletomaget wok [9], we popose that exot matte s eated wheeve the ZPF pefoms postve wok a loalzed ego of spae. As a fal thought, t s teestg to speulate o how the otos put foth hee mght be appled to wap dve theoy, metoed the Itoduto. Fom a hypothetal stadpot, we a mage a spaeshp, esdg flat spaetme, whh aes out some sot of teal poess that altes the ZPF outsde the shp [5]. If, though ths poess, the shp a oax the ZPF to pefomg substatal eletomaget wok, the the shp a use the ZPF to geeate the exot matte equed fo wap dve. I essee, we mage a spaeshp that mapulates the ZPF ode to geeate stesseegy outsde the shp. Wth the ght ofguato, ths stess-eegy a be used to alte the geomety of spae-tme outsde the shp, fomg a Alubee-type geomety, o some moe effet vaato theeof [], [4]-[5]. Assumg that all goes as plaed, the spaeshp should the be popelled by the esultg spae-tme geomety, aqug vey hgh veloty elatve to the est of the Uvese. Oe otewothy featue of ths model s that thee s o eed fo the spaeshp to ay a quatty of exot matte o boad fo use as a fuel soue. athe, suh a spaeshp would geeate exot matte outsde the shp as t moves though spae. efeees [] M. Alubee, The wap dve: hype-fast tavel wth geeal elatvty, Class. Quat. Gav., L73-L77 (994). [] M. J. Pfeg ad L. H. Fod, The uphysal atue of Wap Dve, Class. Quat. Gav. 4, (997). [3] M. J. Pfeg ad L. H. Fod, Quatum equalty esttos o egatve eegy destes uved spaetmes, Dotoal Dssetato, Tufts Uvesty (998). [4] C. Va De Boek, A wap dve wth easoable total eegy equemets, Class. Quat. Gav. 6, (999). [5] C. Va De Boek, O the (m)possblty of wap bubbles, Commet fo Class. Quat. Gav., g-q/ [6] J. P. Dowlg, The mathemats of the Casm effet, Mathemats Magaze, Vol. 6, o. 5, (989). [7] B. Hash ad A. ueda, The zeo-pot feld ad eta, Casusalty ad loalty mode physs, G. Hute, S. Jeffes, ad J. P. Vge (eds.), Kluwe Aad. Publ., pp (998). [8] B. Hash, A. ueda, ad H. E. Puthoff, Physs of the zeo-pot feld: mplatos fo eta, gavtato ad mass, Speulatos See ad Tehology, Vol. 0, 99-4, (997). [9] A vey teestg, ad fomatve, dsusso o the feasblty of extatg eegy fom the zeo-pot feld s gve by D. Cole, Eegy ad themodyam osdeatos volvg eletomaget zeo-pot adato, Ame. Ist. Physs Cof. Po. o. 458, 960, (999). [0] C. T. dgely, O the og of eta, Gallea Eletodyams, 7-0 (00). [] C. T. dgely, O the atue of eta, Gallea Eletodyams, -5 (000). [] C. T. dgely, Ieta: a puely elatvst pheomeo, Gallea Eletodyams 3, 5-8 (00). [3] Thee ae two effetve lmts o the umbe of modes wth the avty. Wavelegths geate tha the dmesos of the avty ae bloked out of the teo ego, ad wavelegths shote that the atom sze do ot otbute to the foe o the walls of the avty.

5 PHYSICS/ These lmts ae geeally emboded a ut-off futo. See, fo example, efs. [6]-[8]. [4] Of ouse, exteo ZPF adato should otbute to the esstae foe o a aeleatg avty, as well. Ths ases beause the avty oupes a volume of spae, ad essetally plows though a sea of zeo-pot adato muh the same way as a submae moves though wate. [5] It seems lkely that ths poess wll be ylal. It s dffult to mage ay stat embodmet apable of matag a szable alteato of the ZPF.