Journl of Erth Siene nd Engineering (1) 79-9 D DAVID PUBLISHING Spe Drive Propulsion Priniple from the Aspet of Cosmology Yoshinri Minmi Advned Siene-Tehnology Reserh Orgniztion (Formerly NEC Spe Development Division), Higshikubo-Cho, Nishi-Ku, Yokohm -6, Jpn Reeived: April 1, 1/Aepted: My 15, 1/Published: June 15, 1. Abstrt: This pper desribes the propulsion priniple using the onept of spe drive nd the pressure of the field indued by lol rpid expnsion of spe bsed on the ltest osmology. Assuming tht spe vuum is n infinite ontinuum, the propulsion priniple utilizes the pressure field derived from the geometril struture of spe, by pplying both ontinuum mehnis nd generl reltivity to spe. The propulsive fore is pressure thrust tht rises from the intertion of spe-time round the speship externl environment nd the speship itself; the speship is propelled by the pressure used ginst the spe-time struture. As is well known in osmology, the expnsion rule of the universe is governed by the Friedmn s equtions nd the Robertson-Wlker metri. In this time, the propulsion priniple of spe drive is introdued from nother ngle (osmology), tht is, the pressure of the field indued by lol expnsion of spe is ompletely onsidered in the propulsion priniple. Key words: Spe drive, propulsion, osmology, expnding universe, Friedmn s eqution, Robertson-Wlker metri, de Sitter universe, infltion. 1. Introdution A onept of spe drive propulsion system s pper entitled Spe Strin Propulsion System is introdued by Minmi in 1988 [1]. The term of spe strin is hnged to spe drive reeiving the reommendtion by Forwrd []. After then, the seond pper entitled Possibility of Spe Drive Propulsion is presented t the 5th IAF in 199 []. The priniple of spe drive propulsion system is derived from generl reltivity nd the theory of ontinuum mehnis. We ssume the so-lled vuum of spe s n infinite elsti body like rubber. The urvture of spe plys signifint role for the propulsion theory. From the grvittionl field eqution, the strong mgneti field s well s mss density genertes the urvture of spe nd this Corresponding uthor: Yoshinri Minmi, dministrtive diretor, reserh fields: stellite design nd engineering, propulsion theory nd propulsion physis, lser propulsion, interstellr nvigtion theory. E-mil: y-minmi@mtj.biglobe.ne.jp. urved spe region produes the uni-diretionl elertion field. The speship in the urved spe n be propelled in single diretion. Sine the fore they produe ts uniformly on every tom inside the speship, elertions of ny mgnitude n be produed with no strin on the rews, tht is, there is no tion of inertil fore beuse the thrust is body fore ( i.e., it is equivlent to free-fll). Minmi derived the eqution of urvture of spe indued by mgneti field in 1988 [1, ]. It ws found tht this eqution ws ordne with the eqution tht Levi-Civit onsidered (i.e., the stti mgneti field retes slr urvture) by Minmi in 1995 []. Assuming tht spe vuum is n infinite ontinuum, the propulsion priniple utilizes the pressure field derived from the geometril struture of spe, by pplying both ontinuum mehnis nd generl reltivity to spe. The propulsive fore is pressure thrust tht rises from the intertion of spe-time round the speship externl environment
8 Spe Drive Propulsion Priniple from the Aspet of Cosmology nd the speship itself; the speship is propelled ginst the spe-time ontinuum struture. This mens tht spe n be onsidered s kind of trnsprent elsti field. Tht is, spe s vuum performs the motions of deformtion suh s expnsion, ontrtion, elongtion, torsion nd bending. The ltest expnding universe theory (Friedmnn, de Sitter, infltionry osmologil model) supports this ssumption. Spe n be regrded s n elsti body like rubber. In the ltest osmology, the terms vuum energy ij nd osmologil term g re used synonymously. is known s the osmologil onstnt. The term with the osmologil onstnt is identil to the stress-energy tensor ssoited with the vuum energy. The properties of vuum energy, i.e., osmologil term re ruil to expnsion of the universe, tht is, to infltionry osmology. In the beginning, the elertion of spe drive propulsion system generted by urvture of spe indued by strong mgneti field bsed on externl nd internl Shwrzshild solution ws studied [1, ]. However, superior elertion bsed on the de Sitter solution is obtined t present. Bsilly: the elertion derived from the de Sitter solution does not require strong mgneti field. At the present dy, spe drive propulsion system bsed on the de Sitter solution needs not strong mgneti field but the tehnology to exite spe. Infltionry universe whih shows rpid expnsion of spe is bsed on the phse trnsition of the vuum exhibited by the Weinberg-Slm model of the eletrowek intertion. The vuum hs the property of phse trnsition, just like wter my beome ie nd vie vers. This shows tht vuum possesses substntil physil struture suh s the mteril. It oinides with the preondition of spe drive propulsion priniple [1,, 5-8, 1, 16]. As is well known in osmology, the expnsion rule of the universe is governed by the Friedmn s equtions nd the Robertson-Wlker metri [9-11, 1]. In this pper, the propulsion priniple for this spe drive is introdued from nother ngle, tht is, the pressure of the field indued by lol rpid expnsion of spe is ompletely onsidered in the propulsion priniple bsed on the ltest osmology.. Briefing of Spe Drive Propulsion.1 Spe Drive Propulsion Theory (1) Under the supposition tht spe is n infinite ontinuum, ontinuum mehnis n be pplied to tret the so-lled vuum of spe. This mens tht spe is onsidered s trnsprent elsti field. Tht is, spe s vuum performs the motion of deformtion tht inludes expnsion, ontrtion, elongtion, torsion nd bending. Thus we n regrd spe s n infinite elsti body like rubber. If the spe-time ontinuum urves, then n inwrd norml stress -P is generted. This norml stress, i.e., surfe fore serves s pressure field (Fig. 1). P N (R ) 1/ N (1/ R 1 1/ R ) (1) where N is the line stress, R, 1 R re the rdius of prinipl urvture of urved surfe, nd R is the sptil urvture. It is now understood tht the membrne fore on the urved surfe nd eh prinipl urvture genertes the norml stress -P with its diretion norml to the urved surfe s surfe fore. The norml stress -P ts towrds the inside of the surfe s shown in Fig. 1. A thin-lyer of urved surfe will tke into onsidertion within spheril spe hving rdius of R nd the prinipl rdii of urvture tht re equl to the rdius (R 1 = R = R). Sine the membrne fore N (serving s the line stress) n be ssumed to hve onstnt vlue, Eq. (1) indites tht the urvture R genertes the inwrd norml stress P of the urved surfe. The inwrdly direted norml stress serves s pressure field. When the urved surfes re inluded in gret number, some type of unidiretionl pressure field is formed. A region of urved spe is mde of lrge number of urved surfes nd they form the field s unidiretionl
Spe Drive Propulsion Priniple from the Aspet of Cosmology 81 () (b) Fig. 1 Curvture of Spe: () urvture of spe plys signifint role for propulsion theory. If spe urves, then inwrd stress (surfe fore) P is generted A sort of pressure field; (b) lrge number of urved thin lyers form the unidiretionl surfe fore, i.e., elertion field. surfe fore (i.e., norml stress). Sine the field of the surfe fore is the field of kind of fore, the fore elertes mtter in the field, i.e. we n regrd the field of the surfe fore s the elertion field. A lrge number of urved thin lyers form the unidiretionl elertion field (Fig. 1b). Aordingly, the sptil urvture R produes the elertion field. Therefore, the urvture of spe plys signifint role to generte thrust. () From the following liner pproximtion sheme for the grvittionl field eqution: (1) wek grvittionl field, i.e. smll urvture limit; () qusi-stti; () slow-motion pproximtion (i.e., v/ ~ 1), we get the following reltion between elertion of urved spe nd urvture of spe: i i i g R ( x ) d x () where i : elertion (m/s ), g : time omponent of metri tensor, -b: rnge of urved spe region (m), x i : omponents of oordinte (i=,1,,), : veloity of light, R : mjor omponent of sptil urvture. b Eq. () indites tht the elertion field i is produed in urved spe. () In the urved spe region, the mssive body m (kg) existing in the elertion field is subjeted to the following fore F i (N), from generl reltivity: j k i i dx dx i j k i F mjk m g jku u m () d d where, u j nd u k re the four veloity, Г i jk is the Riemnnin onnetion oeffiient, nd τ is the proper time. Eq. () yields more simple eqution from bove-stted liner pproximtion: b i i i i i F m g m m g R ( x ) dx () Setting i = (i.e., diretion of rdius of urvture: r), we get Newton s seond lw: b F F m m g R ( r) dr m g (5) The elertion of urved spe nd its Riemnnin onnetion oeffiient ( ) re given by:, g. g (6) g where, : veloity of light, g nd g : omponent of metri tensor, g. : g / x = g / r. We hoose the spheril oordintes t = x, r = x, θ = x 1, = x in spe-time. The elertion is represented by the eqution both in the differentil nd in the integrl form. Prtilly, sine the metri is usully given, the differentil form hs been found to be dvntgeous. The elertion of spe drive propulsion system is bsed on the solutions of grvittionl field eqution, whih is derived from Eq. (6). As mentioned bove, sine the elertion of spe drive propulsion system is urrently bsed on the solution derived from de Sitter solution, there is no need of strong mgneti field.. Propulsion Mehnism of Spe Drive Sine the propulsion mehnism used mgneti field in the beginning is esy to understnd, we explin it using mgneti field. At present, spe drive propulsion does not need the strong mgneti field
8 Spe Drive Propulsion Priniple from the Aspet of Cosmology under the fvor of de Sitter solution. As mentioned bove, the priniple of spe drive propulsion system is summrized in the following: First of ll, it is neessry for the spe to be urved. Beuse the urvture of flt spe R is zero (stritly speking, only independent omponents of Riemnn urvture tensor R pijk re zero), then the elertion beomes zero. Suh urved spe is generted not only by mss density but lso by mgneti field or eletri field. From the generl reltivity, the mjor omponent of urvture of spe R n be produed not only by mss density but lso by the mgneti field B s follows: G 8 R B 8. 1 B (7) This eqution indites tht the mjor omponent of sptil urvture n be ontrolled by mgneti field [1,, 6]. In se tht the intensities of the mgneti field B nd the eletri field E re equl, the vlue of (1/ E ) is bout 17 figures smller thn the vlue of ( B / ). As onsequene, the eletri field only negligibly ontributes to the sptil urvture s ompred with the mgneti field. Aordingly, it is effetive tht the spe n be urved by mgneti field. Sine the region of urved spe produes the field of elertion, the mssive body existing in this elertion field, i.e., urved spe, is moved by thrust in ordne with Newton s seond lw. In view of the bove desribed priniple of propulsion, the speship does not move s long s the mgneti field is stti. This is beuse n tion of mgneti field to spe is in equilibrium with retion from spe. It is onsequently neessry to shut off the equilibrium stte in order to tully move the speship. As ontinuum, the spe hs finite strin rte, i.e., the veloity of light. When the mgneti field power soure is swithed off, it tkes finite intervl of time for the urved spe to return to flt spe. In the men time, speship is independent of urved spe. It is therefore possible for the speship to proeed hed reeiving the tion from the elertion field. Nmely, instntneously swithing off the mgneti field breks the equilibrium stte. Being independent of urved spe, speship is subjeted to the tion of field during the finite intervl to proeed hed. In generl, body n not move rrying, or together with, field tht is generted by its body. In other words, the body n not move unless the body is independent of the field. In surrounding region of speship, mgneti field s n engine produes urved spe. By swithing off the mgneti field, in n instntneous trnsition intervl whih the urved spe disppers nd returns to flt spe, the speship is independent of urved spe. No intertion is present between urved spe nd speship. Here, the swithing on-off the mgneti field implies the following onsidertion. There exists the seed mgneti field to be ompressed in the engine system. Using the mgneti flux-ompression tehnology, we ompress the seed mgneti field nd produe the sptil urvture indued by ompressed strong mgneti field (swithing on the mgneti field). The power soure of speship is onsumed in the work of ompressing the seed mgneti field. After tht, we swith off the mgneti field nd this implies the shutting off the power soure of the ompressing mgneti field. Now referring to Fig., we desribe the propulsion mehnism in detil. As previously desribed, the spe hs finite strin propgtion veloity, i.e., strin rte (= veloity of light). Even if the mgneti field is swithed off, the urved spe reverting to flt spe needs finite time, tht is, length of urved spe region divided by strin propgtion veloity. The speship whih exists in the urved spe n be propelled by the thrust from the field of elertion, when the urved spe returns to flt spe. The speship n not be propelled while the mgneti field is swithed on (Fig. b). This is beuse the speship produes the
Spe Drive Propulsion Priniple from the Aspet of Cosmology 8 Fig. Spe drive propulsion priniple. field of elertion by itself nd stte of equilibrium is held, tht is, the tion of mgneti field to spe nd retion from spe hold equilibrium stte. However, when the mgneti field is swithed off, the stte of equilibrium is broken, nd therefore, the speship n be propelled by the thrust from the field of elertion (Fig. ), beuse the speship is independent of the field. Aordingly, this propulsion system is essentilly defined s pulse propulsion system. In order to propel the speship, the strined surfe of spe s shown in Fig. is preferble in priniple. Nmely, spe with n nti-symmetri urvture is preferble, tht is, flt spe in A region nd urved spe region in A region. Prtilly, the speship n be propelled even by
8 Spe Drive Propulsion Priniple from the Aspet of Cosmology the strined surfe of spe hving symmetri urvture, s shown in Figs. b nd. While the speship moves to A region, the urved spe in A region hs lredy returned to flt spe s shown in Fig.. Therefore, the thrust from the elertion field of A region does not t on speship. In ddition, this thrust is proportionl to the mss of volume element tht exists in elertion field. Although, the mss of speship exists in the A region, the mss of speship does not exist in the A region, therefore, the thrust from the A region n be disregrded from the outset. It is onsequently ler tht the A region does not ountert the thrust whih results from the A region. The speship n get ontinuous thrust by repeting the pulse-like On/Off hnge of mgneti field t high frequeny. The propgtion veloity of the hnge from flt spe to urved spe nd the propgtion veloity of hnging from urved spe to flt spe re both the sme, i.e. the veloity of light. This is true for both the A region nd A region. Furthermore, the time intervl in whih the urved spe returns to flt spe is the sme for both the region A nd A. After being elerted in the A region, the speship proeeds into the A region. Menwhile, sine the urved spe in the A region returns to flt spe, the elertion in the A region beomes zero. Further, the speship hs its mss m minly in the A region in the men time nd is subjeted to the thrust given by f (A) = mα. Conversely, the speship hs not yet its mss ppreibly in the A region, nd is subjeted to the thrust given by f (A ) =. Therefore, the reverse thrust in the A region does not exist from the outset. After ll, we do not need the nti-symmetri urvture s shown in Fig.. It should be noted tht the reverse thrust does not our when the mgneti field is swithed off. Some one is bound to think tht swithing on nd off of n intense mgneti field will mke some sort of osilltory sptil urvture nd ny net forwrd motion n not be imprted to speship by this osillting urvture. The mgneti field is swithed on with suffiient time in order to produe the urved spe region shown by Fig.. Aordingly, the mgneti field swithing off time (t OFF ) is muh shorter thn the mgneti field swithing on time (t ON ), i.e., t OFF << t ON. Therefore, the urved spe region in opposite diretion is smll enough to be ignored nd it n not produe reverse elertion. Beuse, the intensity of elertion produed in urved spe is proportionl to both sptil urvture nd the size of urved spe. Sine the region of reverse urvture is very smll, the reverse thrust does not our when the mgneti field is swithed off. In ddition, we n sy tht the mount of devition of urved spe in opposite diretion is smller thn tht of urved spe in norml diretion. Therefore, the speship n be propelled in single diretion [6].. Some Evlutions of Spe Drive Propulsion Here let us evlute other fetures of spe drive propulsion suh s momentum onservtion lw, energy onservtion lw, nd the feture of flight performne...1 Momentum nd Energy Conservtion Lw The question is tht if the speship moves forwrd, then wht moves bk? Conerning the spe drive propulsion system, the propulsion mehnism is kind of pressure thrust. As mentioned previously, its propulsion priniple is bsed on the ft tht the spe is n infinite ontinuum. We regrd the present spe s n elsti body desribed by solid mehnis rther thn by fluid dynmis. It my be esy to understnd tht the speship moves by pushing spe itself, tht is, by being pushed from spe. The expression of moves by pushing spe or being pushed from spe indites tht the speship produes urved spe region nd moves forwrd by being subjeted to the thrust from the elertion field of urved spe. As the motorr moves by kiking the ground ontinully infinitely, the speship moves by pushing
Spe Drive Propulsion Priniple from the Aspet of Cosmology 85 the osmi spe ontinuously infinitely. The osmi spe s n infinite ontinuum my be deformed very slightly by being pushed, just like the Erth moves bk very slightly by being kiked due to the motorr. However, this pushing is bsorbed by the deformtion of spe itself ontinued infinitely. The whole osmi spe is onsidered s like the ground for kiking. Thus, sine the spe behves like the elsti field, the stress between speship nd spe itself is the key of propulsion priniple. Aordingly, the nlogy of roket whih obeys the momentum onservtion lw in Newtonin mehnis is not dequte. If the body (speship) in spe region gets the energy nd the momentum, it mens tht the outside of body (speship), i.e., spe s field just loses them. Suh ontinuity eqution mens the globl physil quntity onservtion lw. And when the body (speship) interts with the field (spe), in order to onserve the energy nd momentum s whole, it is neessry for the field (spe) itself to get the energy, momentum nd stress... Speship Flight Performne nd Feture The speship equipped with spe drive propulsion system hs the following fetures. (1) There is no tion of inertil fore beuse the thrust is body fore. Sine the body fore they produe ts uniformly on every tom inside the speship, elertions of ny mgnitude n be produed with no strin on the rews; () The flight ptterns suh s quikly strt from sttionry stte to ll diretions in the tmosphere, quikly stop, perpendiulr turn, nd zigzg turn re possible; () The finl mximum veloity is lose to the veloity of light; () Sine the ir round the speship is lso elerted with speship, the erodynmi heting n be redued even if the speship moves in the tmosphere t high speed (1-1 km/s). However, it is expeted tht plsm (ionized ir) envelops the speship; (5) Due to the eletromgneti propulsion engine, there is no ror nd no exhust gs; (6) The engine nd power soure re instlled in the speship, therefore it n fly in the tmosphere of plnet s well s in osmi spe; (7) By pulse ontrol of mgneti field, the elertion vries from G to n rbitrry high elertion (e.g., 6 G); (8) Deelertion is esy for re-entry into the tmosphere.. Aelertion Indued by Cosmologil Constnt In the ltest osmology, the terms vuum energy ij nd osmologil term g re used synonymously. is onstnt known s the osmologil onstnt. The osmologil term is identil to the stress-energy ssoited with the vuum energy. The properties of vuum energy, i.e., osmologil term re ruil to expnsion of the universe, tht is, to infltionry osmology. The vuum energy in de Sitter solution yields the result tht the expnsion elertes with time nd the totl energy with omoving volume grows exponentilly. These fts re due to the elsti nture of vuum nd support the bsi onept of spe drive propulsion system, tht is, the spe is n infinite ontinuum. Now, from the stndpoint of guge theories of the strong, wek nd eletromgneti intertions, there exists the intertions lled the Stndrd Model between vuum nd mtter (i.e., elementry prtiles). Aording to the guge theories, the physil vuum hs vrious ground sttes. The potentil of vuum hs minim whih orrespond to the degenerte lowest energy sttes, either of whih my be hosen s the vuum. Whtever is the hoie, however, the symmetry of the theory is spontneously broken. One of the most importnt onepts in modern prtile theory is tht of spontneous symmetry breking. The prtiulr interest for osmology is the theoretil expettion tht t high tempertures, symmetries tht re spontneously broken tody were restored. During the evolution of the universe there were phse trnsitions, perhps mny ssoited with the spontneous brekdown of guge symmetries [1]. The vuum struture in mny spontneously broken guge theories is vilble for studying field
86 Spe Drive Propulsion Priniple from the Aspet of Cosmology propulsion theory. Aordingly, we n speulte tht the bove-stted properties of vuum re preserved even tody. As hs been stted, the osmologil onstnt is relted to the vuum energy nd phse trnsition of vuum. The most generl form of grvittionl field equtions, whih inlude osmologil onstnt, is given by: ij 1 ij ij ij R g R T g (8) ij where, R is the Rii tensor, R is the slr urvture, G is the grvittionl onstnt, is the ij veloity of light, T is the energy momentum tensor, nd is the osmologil onstnt. Now, onerning the de Sitter osmologil model with non-zero vuum energy (i.e. osmologil onstnt), the de Sitter line element is written s: ds 1 1 1 ( r ) dt dr r d d 1 1 ( sin ) r (9) The metris re given by: g (1 1/ r ), g11 g 1, g 1/(1 1/ r ) nd other g ij (1) The elertion of de Sitter solution n be obtined finlly using Eq. (6) [6]. π G 7 1.6 1 (11) where, G is the grvittionl onstnt, is the veloity of light, λ is n rbitrry Higgs self-oupling in the Higgs potentil (λ is not known nd is not determined by guge priniple, presumbly λ ~ 1/1), nd is non-zero vuum expettion vlue of Higgs field. Eq. (11) indites tht the vuum expettion vlue of Higgs field (i.e., vuum slr field) produes the onstnt elertion field. As result, we find out tht the elertion beomes onstnt, tht is, we n get rid of the tidl fore in the speship. The slr field n be thought of rising from soure in muh the sme wy s the eletromgneti fields rise from hrged prtiles. We hve to serh for the fields with the soure. The size of speship (i.e. length or dimeter) is limited to the rnge r S, whih r S is the rnge determined by the following: V ( r) V / rs, ( L rs ). Within the rnge of L rs, the tidl fore in the speship nd in the viinity of speship n be removed, tht is, the elertion beomes onstnt within the rnge of given region r S. The dvntgeous point of this solution is tht even if the size of speship is the order of 1 km to 1 km, the speship n move with the onstnt elertion (e.g., G-G) to ll diretions hving the flight performne suh s quikly strt, quikly stop, perpendiulr turn, et.. Next, the reltion between vuum potentil V ( ) nd osmologil onstnt is explined s the following. Aording to the guge theories, the physil spe s vuum is filled with spin-zero slr fields, lled Higgs field. The vuum energy flututes in proportion to the flutution of Higgs field. The vuum potentil V ( ) is given by the vuum expettion vlue of Higgs field, nd we get the minimum of the Higgs potentil V ( ) s follows: V ( ) (1) where, is the onstnt, is the non-zero vuum expettion vlue of Higgs field. Further, we n get the following [6]: V ( ).11 V ( ) (1) Using Eqs. (11) nd (1), prtiulr ttention is pid to the role of. Here, only is desribed in nturk unit ( k B 1 ). So, there is one dimension, energy, normlly be stted in GeV, tht is: [Energy] = [Momentum] = [Mss] = [Temperture] = [Length] -1 = [Time] -1 : in GeV. In the unit system of nturl units GeV stnds for volume density (number density): m nd GeV stnds for energy density: GeV GeV GeV J/m. The following reltion: 1GeV = 1. 1 7 m - is
Spe Drive Propulsion Priniple from the Aspet of Cosmology 87 used to onvert from nturl unit system to SI unit system. The bove-stted nturl units re used for the field of elementry prtile physis or ltest osmology. The vuum expettion vlue of the present universe is sid to be ~ 1-1 GeV nd - 6 11 GeV [1], therefore substitution of Eqs. (11) nd (1) with setting λ = 1 gives: 9 V ( ) 1/.5 1 J/m, 7 6 1.6 1.1 m / s. Nturlly, the elertion indued by present osmi spe is zero. In ddition, from Eq. (1) nd R, we get: 5.11 V ( ) 1.5 1 m, 5 R.1 m. If the vuum expettion vlue of present universe is exited nd beomes 6 1 GeV = 6 MeV, similrly we get the following: 7 V ( ) 1/ 6.7 1 J / m, 7 1.6 1.1m / s.g.11 R 5.61 V ( ) 1.1 15 m. 15 m.5 Phse Trnsition of Spe The spe is kind of ontinuum whih repets expnsion nd ontrtion. We ssume tht spe s ontinuum hs two kinds of phses, tht is, the elsti solid phse (i.e., rystlline elstiity) like spring nd the viso-elsti liquid phse (i.e., rubber elstiity = entropy elstiity) like rubber. The elsti solid phse orresponds to the present universe nd the viso-elsti liquid phse orresponds to the erly universe. Further, we speulte tht the spe my get the phse trnsition esily by some trigger, i.e., exittion of spe, nd tht the elsti solid phse of spe is rpidly trnsformed to the viso-elsti liquid phse of spe nd vie vers. The spe s vuum preserves the properties of phse trnsition even now. In generl, the phse trnsition is ompnied by hnge of symmetry. The phse trnsition hs, ourred from n ordered phse to disordered phse nd vie vers. In osmologil phse trnsition, the vuum expettion vlue of slr field is trnsferred from high-temperture, symmetri minimum, to the low-temperture, symmetry-breking minimum [9, 1-1]. Aordingly, the phse trnsition is bsilly relted to the spontneous symmetry breking, nd it is onsidered tht bove-stted phenomenon is the fundmentl property of spe. Now, referring to Fig., the vuum expettion vlue of slr field indites the present true vuum (present universe), nd indites the metstble flse vuum in erly universe. Even if hd suh smll vlue, we would expet quntum flututions to push suffiiently fr out on the potentil from to ner the by trigger. Sine the potentil V () mens the energy density of vuum orresponding to the vlue of, the vlue of V () diretly ontributes to the osmologil term. The hnge in gives the hnge in V ( ). As result, the ontrol of flututions of slr field (i.e., oherent smll osilltions of slr field) ffets the osmologil onstnt. The enormous vuum energy of the slr field then exists in the form of sptilly oherent osilltions of the field. As shown Fig. Phse trnsition of spe.
88 Spe Drive Propulsion Priniple from the Aspet of Cosmology in Fig., quntum flutution to push suffiiently by trigger gives rise to lrge perturbtion of vuum energy. Rising the vuum potentil my produe lrge vuum energy either through quntum or therml tunneling, tht is, pushing by some trigger gives rise to lrge perturbtion of vuum energy. Therefore, by tking bove mehnism used s n unknown tehnology, we my produe lrge osmologil onstnt, i.e., urvture. Sine the exittion soure of Higgs field (slr field) is not lwys restrited to the strong mgneti field, the eletri field generted by strong lser fousing effet my be vilble. Here, the exittion of spe mens tht the vlue of vuum expettion vlue is pushed up slightly from its present vlue nd therefore the vuum potentil V ( ) is slightly rised. As onlusion, Fig. shows the summry of spe drive propulsion system..6 Reltion between Alubierre s Wrp Drive nd Minmi s Spe Drive As Mtloff stted in his book Deep-Spe Probes [15] s follows: Somewht more immedite re suggestions tht we might rete n rtifiil singulrity using mens other thn grvity. Miguel Alubierre nd Yoshinri Minmi hve independently suggested tht we might do this using mgneti field mny orders of mgnitude greter thn those produed on the Erth even rther thn those t the surfe of neutron str or exoti fields tht might be mnifested from the universl vuum. Alubierre s nd Minmi s ship (if possible) would be pushed or pulled through the universe by bubble of wrped spe-time, these propulsion theories re well sid to be like. In onlusion, both propulsion theories re identil onept from the perspetive tht they re bsed on generl reltivity nd use the ide regrding distortion of spe. However, Alubierre s wrp drive is not mnifest for its propulsion priniple; there is no SPACE DRIVE PROPULSION SYSTEM := [Ambient Spe] Sptil Energy Density Greter thn Ambient Sptil Energy Density Curvture of SPACE (R ) plys signifint role for propulsion theory (Y.Minmi:1988). i i i i i F m g m m g R ( x ) dx G Both strength of urvture nd R B its extent (volume) re importnt. Aelertion indued by de Sitter solution is found in 1996 by Minmi : onstnt elertion α (i.e. no tidl fore inside of the strship). G 16 1 7. Φ : non-zero vuum expettion vlue of field Fig. A ondensed summry of spe drive propulsion priniple. mehnism tht how lol distortion of spe-time suh s expnsion spe-time metri or ontrtion spe-time metri rete the thrust. Furthermore, Alubierre s wrp drive is kind of non-used wormholes nvigtion theory for the purpose of interstellr trvel. While, Minmi s spe drive is mnifest for its propulsion priniple; there is obvious mehnism tht the geometril struture of spe urvture retes tul fore s thrust.. Spe Drive Propulsion Priniple from the Aspet of Cosmology In previous Setion, we rn over the propulsion theory of the spe drive propulsion system. However, in this setion, we explore the possibility tht the expnding spe genertes thrust, tht is to sy, we mke study bout the propulsion priniple from the spets of osmology, espeilly onsidering the ltest expnding universe theory of Friedmnn, de Sitter nd infltionry osmologil model. The infltionry universe shows rpid expnsion of spe bsed on the phse trnsition of the vuum exhibited by the Weinberg-Slm model of the eletrowek intertion. The vuum hs the property of phse trnsition, just like wter my beome ie nd vie vers. This shows tht vuum possesses substntil physil struture suh s the mteril. It b
Spe Drive Propulsion Priniple from the Aspet of Cosmology 89 oinides with the preondition of spe drive propulsion priniple. In generl, phse trnsitions re ssoited with spontneous loss of symmetry s the temperture of system is lowered. For instne, the phse trnsition known s freezing wter, t temperture T > 7 K, wter is liquid. Individul wter moleules re rndomly oriented, nd the liquid wter thus hs rottionl symmetry bout ny point; in other words, it is isotropi. However, when the temperture drops below T = 7 K, the wter undergoes phse trnsition, from liquid to solid, nd the rottionl symmetry or moleulr geometry of the wter is lost. The wter moleules re now loked into solid rystlline struture, nd the ie no longer hs rottionl symmetry bout n rbitrry point. In other words, the ie rystl is nisotropi, with preferred diretions orresponding to the rystl s xes of symmetry [9]. Supposing tht the universe expnds, nd then wht form n the metri of spe-time be ssumed if the universe is sptilly homogeneous nd isotropi t ll time, nd wht if distne is llowed to expnd s funtion of time? The metri they derived is lled the Robertson-Wlker metri. It is generlly written in the form: dr ds dt ( t) r ( d sin d ) (1) 1 Kr where, (t) is the sle ftor tht desribes how distne grows or dereses with time; it is normlized so tht ( t ) 1 t the present moment. K is the urvture tht tkes one of three disrete onstnt vlues: K = 1 if the universe hs positive sptil urvture, K = if the universe is sptilly flt, nd K = -1 if the universe hs negtive sptil urvture. The vlue of sle ftor (t) is obtined by substituting the Robertson-Wlker metri for the following grvittionl field eqution: ij 1 ij ij ij R g R T g (15) ij where, R is the Rii tensor, R is the slr urvture, G is the grvittionl onstnt, is the ij veloity of light, T is the energy momentum tensor, nd is the osmologil onstnt. Tht is, from the Robertson-Wlker metri of Eq. (1), the Riemnnin onnetion oeffiient, the ij slr urvture R, the Rii tensor R re obtined, nd then substituting their vlue for Eq. (15), we get Eq. (16) s the se of i=, j =. Here is the energy density of spe, (t) d( t ) /d t. ( t) ( t) 8G K ( t) 1 (16) The Eq. (16) is lled s the Friedmnn eqution nd domintes the lw of n expnding universe. In sptilly flt universe (K = ) nd no osmologil onstnt ( = ), the Friedmnn eqution tkes prtiulrly simple form: ( t) (17) ( t) From ( t ) ( t ), (t) is obtined s the following: 1 ( t) exp t exp t (18) Here, from Eq. (1): V ( ) (19) We used the reltion of from Eq. (19). A sptilly flt universe with the energy density is exponentilly expnding. Suh universe is lled de Sitter universe. Even if there is no osmologil onstnt from the outset, in the nture of things, expnding universe is indited by generl reltivity. In initil ssumptions, the energy density is onsidered s mtter. At the present dy, the energy density n be onsidered s the osmologil onstnt. ()
9 Spe Drive Propulsion Priniple from the Aspet of Cosmology Aordingly the pressure P of the field of vuum spe beomes: P (1) In the se of Λ, the pressure P of the vuum field in Eq. (1) indites the negtive pressure, i.e., repulsive fore. Applying the vlue of =.1 1 - V () = 1. 1-15 m - ( = 1.6 1-7 =.1 m/s =. G) to Eq. (1), the pressure P of the field of vuum spe beomes 7 1 7 P (7 1 tm). Λ P = 8G 8 15 17 ( 1 ) 1. 1 81 1. 1 11 11 8 6.67 1 167.6 1 8 7.68 1 N / m 7 1 P Applying the vlue of present universe of =.1 1 - V () =1.5 1-5 m - to Eq. (1), P = 8 5 ( 1 ) 1.5 1 81 1.5 1 11 11 8 π 6.67 1 167.6 1 9.51 1 N / m The pressure P of the field of the vuum spe beomes 5 1-1 P = 5 1-16 MP = 5 1-15 tm. Some erly implementtions of infltion ssoited the slr field with the Higgs field, whih medites intertions between prtiles t energies higher thn the GUT energy; however, to keep the disussion generl, the field is now referred to s the infltion field. Generlly speking, slr field n hve n ssoited potentil energy V (). Next we sttes bout n infltionry osmologil model. In osmologil ontext, infltion n most generlly be defined s the hypothesis tht there ws period, erly in the history of universe, when the expnsion ws elerting outwrd; tht is, n epoh when. The elertion eqution π G P, tells us tht when P. Thus, infltion would hve tken ple if the universe were temporrily dominted by omponent with eqution 1 of stte prmeter. Referring to the eqution of stte P, the usul implementtion of infltion sttes tht the universe ws temporrily dominted by positive osmologil onstnt (with 1), tht is, P. Then the elertion eqution beomes: π G ( ) () In n infltionry phse when the energy density ws dominted by osmologil onstnt, the initil Friedmnn eqution is desribed in: K Setting flt spe (K = ): Sine, we get: () () exp t (5) The sle ftor grows exponentilly with time. This result orresponds to Eq. (18). The vuum spe uses infltion by the energy of the vuum nd expnds exponentilly. The infltion mehnism brings up mini spe to the mro spe. Nmely, the spe hs the property of exponentil expnding by therml energy. Sine the energy momentum tensor T ij in the grvittionl field eqution ims t mtter, the grvittion rises between different mtters. However, osmologil term g ij in Eq. (15) implies tht the fore between the vuum spes, tht is, repulsive fore between one vuum spe nd nother vuum spe. The vuum spe whih envelops the speship is pushed by other expnding vuum spe, hene the speship is propelled by being pushed from the
Spe Drive Propulsion Priniple from the Aspet of Cosmology 91 expnding vuum spe. Conerning the propulsion priniple for the spe drive propulsion in the strit sense, it my be esy to understnd tht the speship moves by pushing spe itself, tht is, by being pushed from spe. The expression of moves by pushing spe or being pushed from spe indites tht the speship produes urved spe region nd moves forwrd by being subjeted to the thrust from the elertion field of the urved spe. As the motorr moves by kiking the ground ontinully infinitely, the speship moves by pushing the osmi spe ontinuously infinitely. The osmi spe s n infinite ontinuum my be deformed very slightly by being pushed, just like the Erth moves bk very slightly by being kiked due to the motorr. However, this pushing is bsorbed by the deformtion of spe itself ontinued infinitely. The whole osmi spe is onsidered s being similr to the ground for kiking. Thus, sine the spe behves like n elsti field, the stress between speship nd spe itself is the key of propulsion priniple. Contrry to this, lthough it my be loose expression, we n get n esy imge of the propulsion priniple: Sine the pressure of vuum field in the rer viinity of the speship is high due to n expnsion of spe, the speship is pushed from the vuum field just like blowing up blloon tht n push n objet. Here, we explin the motion of the speship using omputer grphis. For the ske of simpliity, the shpe of the speship is n omnidiretionl disk type. As shown in Fig. 5, our speship is ble to permete its lol spe with huge mount of energy in ertin diretion; this energy should be injeted t zero totl momentum (in the speship-body frme) in order to exite the lol spe. Then, the exited lol spe expnds instntneously. NHK NHK () (b) NHK NHK () (d) Fig. 5 () Speship is ble to permete its lol spe with huge mount of energy in ertin diretion; (b) spe inluding the speship pushed from the expnded spe; () speship dvnes forwrd; (d) hnging ple to blow up, the speship n move to ll diretions.
9 Spe Drive Propulsion Priniple from the Aspet of Cosmology The spe inluding the speship is pushed from the expnded spe nd dvnes forwrd (Fig. 5b nd Fig. 5). Thus, this speship is elerted to the qusi-speed of light by repeting the pulse-like on/off hnge of permeting its lol spe with huge mount of energy opertion. Chnging ple to blow up, the speship n move with flight ptterns suh s quik strt from sttionry stte to ll diretions, quikly stop, perpendiulr turn, nd zigzg turn (Fig. 5d).. Conlusions We explored nother possibility of spe drive propulsion priniple where the lolly rpid expnding spe genertes the thrust, using the osmology, i.e., the ltest expnding universe theory of Friedmnn, de Sitter nd infltionry osmologil model [16]. Moreover, the speship is ble to permete its lol spe with huge mount of energy; this energy should be injeted t zero totl momentum (in the speship-body frme) in order to exite the lol spe. Then the exited lol spe expnds instntneously. Sine the pressure of the vuum field in the rer viinity of speship is high due to expnding of spe, the speship is pushed from the vuum field just like blowing up blloon tht n be used to push n objet. Thus, the spe inluding the speship is pushed from the expnded spe nd dvnes forwrd. Although it my be loose expression, we n get n esy imge of reting propulsion priniple. The most importnt key seems to be the study of the struture of spe tht is derived from the expnding universe mehnis. In order to relize this result, we must disover the tehnology to exite nd blow up spe lolly. Aknowledgments The uthor wishes to express his sinere thnks to Dr. Giovnni Vulpetti for invluble disussions nd Pul Murd (CEO Morningstr Applied Physis, LLC; ret. US Deprtment of Defene) for suggesting the importne in this work. Additionlly, the uthor is grteful to Tomohiro Inoue (Prinipl Progrm Diretor of NHK) for providing the neessry omputer grphis. Referenes [1] Y. Minmi, Spe strin propulsion system, in: 16th ISTS (Interntionl Symposium on Spe Tehnology nd Siene), Spporo, My, 1988. [] R.L. Forwrd, Forwrd Unlimited, Mlibu CA, Letter to Minmi, Y. (NEC Spe Development Div., Yokohm JAPAN) bout Minmi s Conept of Spe Strin Propulsion System, Mrh 17,1988. [] Y. Minmi, Possibility of spe drive propulsion, in: 5th Congress of the Interntionl Astronutil Federtion, Jeruslem, Isrel, Ot. 9-1, 199. [] W. Puli, Theory of Reltivity, Dover Publitions, In., New York, 1981. [5] Y. Minmi, Spe drive fore indued by ontrolled osmologil onstnt, in: 7th IAF Congress, Beijing, Chin, Ot. 7-11, 1996. [6] Y. Minmi, Spefring to the fstest shores-theory nd tehnology of spe drive propulsion system, JBIS (Journl of The British Interplnetry Soiety) 5 (1997) 6-76. [7] Y. Minmi, Coneptul design of spe drive propulsion system, in: AIP Conferene Proeedings, Prt Three, Albuquerque, NM, USA, Jn. 5-9, 1998, pp. 1516-156. [8] Y. Minmi, An introdution to onepts of field propulsion, JBIS. 56 () 5-59. [9] B. Ryden, Introdution to Cosmology, Addison Wesly, Sn Frniso,USA,. [1] E.W. Kolb, M.S. Turner, The Erly Universe, Addison-Wesly Publishing Compny, New York, 199. [11] R.C. Tolmn, Reltivity Thermodynmis nd Cosmology, Dover Books, New York, 1987. [1] G. Kne, Modern Elementry Prtile Physis, Addison-Wesley Publishing Compny, New York, 199. [1] T. Mtsubr, Introdution to Modern Cosmology: Coevolution of Spetime nd Mtter, University of Tokyo Press, Tokyo, 1. [1] Y. Minmi, T. Mush., Field propulsion systems for spe trvel, At Astronuti 8 (1) 15-. [15] G.L. Mtloff, Deep Spe Probes, Springer, Chihester, UK,. [16] Y. Minmi., Spe drive propulsion priniple from the spet of osmology, in: STAIF (Spe Tehnology & Applitions Interntionl Forum) Ⅱ, Albuquerque, NM, Apr. 16-18, 1.