Tsting th gravitational proprtis of th quantum vacuum within th Solar Systm Dragan Hajdukovic To cit this vrsion: Dragan Hajdukovic. Tsting th gravitational proprtis of th quantum vacuum within th Solar Systm. 014. <hal-00908554v3> HAL Id: hal-00908554 https://hal.archivs-ouvrts.fr/hal-00908554v3 Submittd on 18 Fb 014 HAL is a multi-disciplinary opn accss archiv for th dposit and dissmination of scintific rsarch documnts, whthr thy ar publishd or not. Th documnts may com from taching and rsarch institutions in Franc or abroad, or from public or privat rsarch cntrs. L archiv ouvrt pluridisciplinair HAL, st dstiné au dépôt t à la diffusion d documnts scintifiqus d nivau rchrch, publiés ou non, émanant ds établissmnts d nsignmnt t d rchrch français ou étrangrs, ds laboratoirs publics ou privés.
Tsting th gravitational proprtis of th quantum vacuum within th Solar Systm Dragan Slavkov Hajdukovic a, b a Physics Dpartmnt, CERN; CH-111 Gnva 3 b Institut of Physics, Astrophysics and Cosmology; Ctinj, Montngro E-mail: dragan.hajdukovic@crn.ch Abstract: Th xistnc of th quantum vacuum is wll stablishd in th Standard Modl of Particls and Filds but compltly nglctd in contmporary Astrophysics and Cosmology. Indpndntly of any thory it is a major and absolutly urgnt task of astronomical obsrvations to rval if and how quantum vacuum contributs to th gravitational fild of baryonic mattr in th Univrs. W point out that a first signatur of th gravitational impact of th quantum vacuum might b sn in th prihlion prcssion of orbits of satllits of minor plants in th outr part of th Solar Systm. As an xampl w considr th minor plant 00 UX5 and its satllit. 1. Introduction So far w had two scintific rvolutions in our undrstanding of gravitation: Nwton s law and Alt Eisti s Gnral Rlativity. Whatvr happns in th futur, ths two rvolutions will rmain among th gratst achivmnts of thortical physics and th human mind. W know today that both thoris hav in common a wrong assumption. Th wrong assumption is that th mattr of th Univrs xists in classical, non-quantum vacuum. Whil it is systmatically nglctd in Astrophysics and Cosmology, quantum vacuum is an inhrnt part (s for instanc [1-3]) of th Standard Modl of Particls and Filds which is in prfct agrmnt with xprimntal findings. Howvr, without quantum vacuum takn into account, quantum fild thory would b in prfct disagrmnt with xprimntal findings. Einstin said (and I agr): Imagination is mor important than knowldg. So, I invit you to imagin that, you can switch off and switch on, th quantum vacuum in our Univrs. As w liv in th Univrs with quantum vacuum switchd on, you firstly must switch it off. What would happn? In fact I must warn you not to do it; aftr switching off th quantum vacuum, you will not stay aliv to switch it on again! This is not a spculation but prdiction basd on our bst knowldg. For instanc, sophisticatd xprimnts [4] hav rvald that th proton is not an lmntary particl but a vry complx systm that in addition to thr valnc quarks contains virtual (or s) quark-antiquark pairs and gluons (s Fig. 1). Fig. 1 Innr structur of a proton rvald at HERA Black spirals rprsnt gluons whil purpl-grn particls dnot virtual quark-antiquark pairs (up to 100 of ths quark/anti-quark pairs a isil at any instant!). Not that thr ar thr mor quarks (two up, on down) than anti-quarks. Ths ar th thr valnc quarks w would normally rfr to whn spaking of th proton. (Sourc: DESY in Hamburg) In simpl words, quantum vacuum significantly contributs to th structur of protons (and 1
nutrons as wll). If this contribution is switchd off, protons would bcom quit diffrnt particls. A radical chang of constitunts of atoms would prturb vrything; th Univrs without quantum vacuum would b a compltly diffrnt plac (and crtainly without us). Hnc, quantum vacuum is not only a strang stat of mattr in quantum fild thory, but also th root of our xistnc. Bfor w continu lt us giv a simplifid (but basically tru) dscription of th quantum vacuum. Quantum vacuum should b considrd as a stat of mattr, compltly diffrnt from familiar stats gas, liuid, solid, plasa ut as ral as thy ar [1-3]. Popularly spaking, quantum vacuum is a sa of shot liig virtual particlantiparticl pairs (lik quark-antiquark, nutrinoantinutrino and lctron-positron pairs). According to our bst knowldg: (1) quantum vacuum is a stat with prfct symmtry btwn mattr and antimattr; a particl always appars in pair with its antiparticl, which is totally diffrnt from mystrious mattr-antimattr asymmtry, i.. th fact that vrything on th Earth (and apparntly in th Univrs) is mad from mattr, with only tracs of antimattr; () contrary to all othr stats of mattr which ar composd from th long living particls (lctrons and protons in stars and flowrs, hav xistd bfor thm and will xist aftr thm), th quantum vacuum is a stat composd from xtrmly short living virtual particls and antiparticls (for instanc, th liftim of a virtual lctron-positron pair is only about 10 sconds). Popularly spaking, as fishs, w liv in an oa; ou oa is th quantum vacuum. Our knowldg about gravitational proprtis of th quantum vacuum is zro. Thr ar two possibilitis. Th first possibility is that quantum vacuum has no impact (or at last has no significant impact) on th gravitational fild in th Univrs. In fact, contmporary Astrophysics and Cosmology ar basd on this assumption. Th scond possibility is that quantum vacuum contributs gratly to th gravitational fild in th Univrs. If so, any thory that nglcts th xistnc of th quantum vacuum is blind to som crucial gravitational phnomna, and, as a compnsation for th lost phnomna, must invok som artificial stuff. Th invitabl qustion is if dark mattr and dark nrgy ar such artificial stuff which (in our incomplt thory) mimics wll th phnomna which ar in fact causd by th quantum vacuum. Contrary to th othr candidats for nw physics (suprsymmtris, dark mattr, dark gy uatu auu is ot a spulatio but a ky fatur of Quantum Elctrodynamics, Quantum Chromodynamics and Elctrowak thory, i.. a ky fatur of th Standard Modl of Particls and Filds, th most succssful and th bst tstd thory of all tims. It is a major and absolutly urgnt task of astronomical obsrvations to rval if and how quantum vacuum contributs to th gravitational fild of baryonic mattr in th Univrs. In th prsnt articl w point out that a first signatur of th gravitational impact of th quantum vacuum might b sn in th prihlion prcssion of orbits of satllits of minor plants in outr part of th Solar Systm. As an xampl w considr th minor plant 00 UX5 and its satllit.. Som rflctions on quantum vacuum and gravity W do not know if quantum vacuum contributs or not to th gravitational fild in th Univrs. Th answr must com from astronomical obsrvations and xprimnts in our laboratoris. Howvr it sms plausibl to assum that quantum vacuum contributs to th gravitational fild. Th first qustion aftr this assumption is if th contribution of quantum vacuum is indpndnt or dpndnt on th quantity and distribution of th immrsd mattr. Onc again th answr must com from obsrvations and xprimnts. From a thortical point of viw, if quantum vacuum producs a non-zro gravitational fild indpndnt of th immrsd mattr, it mans that w should obsrv a non-homognous and non-isotropic background, which is apparntly not th cas. Hnc, it sms plausibl that th gravitational contribution of th quantum vacuum dpnds on th quantity and distribution of th immrsd mattr. In othr words, if w attribut to th quantum vacuum, an ffctiv gravitational charg dnsity, it has a non-zro valu only in th prsnc of an xtrnal gravitational fild producd by th immrsd mattr. Lt m not that I hav usd an unusual t gaitatioal hag instad of gravitational mass or simply mass; of cours, according to th wak quivalnc principl all ths trms ar synonyms for ordinary mattr, but it is prfrabl to kp th
trm gravitational charg and to stay opn for possibility of violation of th wak quivalnc principl for non-ordinary mattr. Our thory of gravitation dscribs th gravitational fild of a sphrical body (lik a star) immrsd in th gravitationally faturlss classical vacuum. Hnc, th scond basic qustion is how quantum vacuum modifis classical gravitational fild around a sphrical body. Th gravitational charg (mass) of th considrd sphrical body is a constant. Contrary to it, th quantum vacuum around th body should hav crtain ffctiv gravitational charg dnsity; hnc th ffctiv gravitational charg within a sphr of radius r must incras with r. In othr words an obsrvr at a largr distanc r from a star would obsrv a largr ffctiv gravitational mass of th star. It is obvious from obsrvations that th ffctiv gravitational charg of th quantum vacuum within th Solar Systm must b a tiny fraction of th mass of th Sun. Only at vry larg distancs, this fraction can b significant. It is intrsting to not that in Quantum Elctrodynamics, quantum vacuum has proprtis analogous to th abov suppositions. 3. Th simplst gravitational signatur of nw physics Th simplst problm in clstial mchanics is to dtrmin orbit of a point-lik body in a cntral gravitational fild. Th orbit is an llips fixd with rspct to th cntr of gravity if and only if th cntral gravitational fild has prfct sphrical symmtry and th gravitational forc strictly follows th Nwton invrs squar law. Any dpartur from sphrical symmtry and/or th invrs squar law of gravity, lads to th prcssion of th prihlion (s for instanc [5-6]). Gnral Rlativity (dscribing a sphrically symmtric cntral gravitational fild by Schwarzschild mtric) is mor accurat than Nwtonian thory and it prdicts a tiny prcssion vn in th cas of sphrical symmtry. Th gnral rlativistic prcssion is wll approximatd by 3 RS GR (1) 1 a whr Gr is th xtra rotation pr orbit in radians, a th smi-major axis of th orbit, th ccntricity of th llips and R S th Schwarzschild radius of th cntral body. It is worth noting that th prihlion prcssion of plants prdictd by classical thory (Nwtonian mchanics togthr with th invrs squar law for gravity) is clos to th obsrvd valus; th largst discrpancy occurs for th Muy Muy s oit psss at a rat that is about 8% gratr than th prdictd on). Th discrpancy has bn xplaind by gnral rlativistic corrction (1) which must b addd to th Nwtonian rsult. In brif, in th cas of a cntral gravitational fild with th xact sphrical symmtry, Nwtonian prcssion of th prihlion is zro, whil th gnral rlativistic rsult (1) is too small to b dtctd (with th currnt accuracy of masurmnts) for satllits of small cntral bodis lik minor plants in th outr part of th Solar Systm. Of cours, a minor plant (which orbits around th Sun with a priod T Sun) and its satllit (which orbits around th plant with a priod T P ) ar not an isolatd systm but subjct to an xtrnal gravitational fild dominatd by th Sun. This xtrnal gravitational fild producs a Nwtonian prihlion shift in th orbit of th satllit: th shift pr orbit is wll approximatd [5, 7] with 3 TP N () TSun Any significant diffrnc btwn obsrvd prcssion and th xpctd valu () must b considrd as a signatur of nw physics. Typical valu of th shift () for satllits of trans- Nptunian minor plants is a fw tns of arc sconds pr cntury. As w will argu, th shift causd by quantum vacuum might b gratr by mor than on ordr of magnitud. Howvr, indpndntly of any thortical argumnt it is of major importanc to obsrv and s if thr is any anomalous prihlion shift in th orbits of satllits of trans-nptunian minor plants. With th xisting infrastructur of satllits and tlscops it would b lss xpnsiv but potntially not lss important than LHC 3
xprimnts at CERN or dtctors dvotd to sarch for dark mattr. 4. An illustration of hypothtical gravitational ffcts of quantum vacuum Lt us assum that a satllit (with mass m ) orbiting about a minor plant (with mass M) is subjct to both Nwtonian gravitational forc and a tiny additional radial acclration A r causd by th prsnc of th quantum vacuum g r GM r A r (3) As known from th classical clstial mchanics (s for instanc th book of Murray and Drmott, 1999, pag 55) in this problm charactrizd with sphrical symmtry, th tim volution of th argumnt of pricntr is dtrmind by th quation d dt 1 a A r cos f (4) and f dnots th tru whr Gm m anomaly. In ordr to intgrat th quation (4) it is ncssary to know th function A (r) and to xprss r, cos f ccntric anomaly E : and dt as functions of th r a 1 cos E (5) cos E cos f 1 cos E 1 cos E dt de n whr n T (6) (7) dots aag agula vlocity (or th man motion) and T is th orbital priod. Equations (4), (5), (6) and (7) yilds th xtra rotation pr orbit ( ) in radians. 1 a Ar E de cos (8) In th simplst but illuminating cas, a constant valu dnotd by 0 A r has A. In this cas th prihlion shift pr orbit can b writtn [5, 8] in th following way a A 1 (9) G M m Hnc, th intrnal prcssion (9) causd by th quantum vacuum is mixd with th prcssion () inducd by th xtrnal Nwtonian gravitational fild dominatd by th Sun. Lt us not that according to quations () and (9) quantum vacuum might b dominant only for small systms far from th Sun. Now, as an xampl lt us considr th minor plant 00 UX5; th ndd data takn from Rfrnc [9] ar givn in Tabl 1 According to Tabl 1 and Equation () 8 3.0910 rad 0.0064arc sc (10) N whil dpnds on th choic of A in Equation (9). As an intrsting choic suggstd rcntly [10-11], lt us tak A 11 6.67310 m/ s 0.3arcsc. It lads to (11) Tabl 1 Paramtrs for 00 UX5 and its Satllit UX5 Mass UX5 Smimajor axis UX5 Orbital Priod Satllit Smimajor axis Satllit Orbital Priod Satllit Eccntricity 1.5x10 0 kg 4.869 AU 80.69 yars 4770 km 8.3094 days 0.17 Comparison of (10) and (11) shows that in this xampl th ffct of quantum vacuum is strongly dominant (it is largr narly two ordrs of magnitud). Hnc, thr is potntial for a clar signal of nw physics. 5. Commnts Of cours in addition to 00 LX5 thr ar othr trans-nptunian objcts with satllits which might b appropriat for th proposd masurmnt of th prihlion prcssion. Logos- Zo, Quaoar-Wywot, (6665)-Borasisi ar just a fw xampls of intrsting trans-nptunian plant-satllit pairs. It sms that othrwis th most attractiv candidat, systm Eris-Dysnomia 4
[8] is prhaps xcludd bcaus of vry small ccntricity of th orbit of Dysnomia. Apparntly th bst stratgy is to focus firstly on th masurmnt of th prihlion prcssion of a singl satllit (for instanc th satllit of 00 LX5). If th rsult rvals nw physics, in th scond stp it would b ncssary to masur prihlion prcssion of many mor satllits in ordr to driv insight on how th acclration A r changs with distanc r. Information on dpndnc on distanc should b crucial to distinguish btwn diffrnt thortical modls for A r. In principl, th hypothtical ffct of th quantum vacuum can b rvald by th study of th orbits of innr plants, th satllits of innr plants or vn artificial satllits. Howvr in ths systms th hypothtical ffct is only a tiny fraction of th total prihlion prcssion. Whil it is not dirctly rlatd to th proposd obsrvations lt m finish with on intrsting commnt. According to th Standard Modl of Cosmology w liv in a Univrs with thr spatial dimnsions and non-euclidian gomtry; th Big- Bang is considrd not as an xplosion in spac but rathr xpansion of spac (s for instanc Rfrnc [1]). Howvr, it is also known that th Big-Bang can b considrd as an xplosion in a Euclidian spac with four spatial dimnsions [1] which is prsumably not rality. Th intrsting and nvr askd qustion is if th quantum vacuum and mattr immrsd in it hav th sam numbr (thr) of spatial dimnsions. On intrsting possibility is that quantum vacuum has four spatial dimnsions; if so th Big Bang might b considrd as both, xpansion of thr dimnsional spac and xplosion in a four dimnsional spac. I am not claiming that it is so, but just undrlining how rich th spctrum of possibilitis is, and how important it is to kp opn mind. Appndix: Quantum vacuum and virtual gravitational dipols As w hav strongly strssd in this papr, th proposd tst is of high importanc indpndntly of any thory. Th study of orbits of satllits of minor plants in th outr part of th Solar systm is a snsitiv tst of th vntual xistnc of tiny non-nwtonian componnt of gravity. In this Appndix w prsnt a far raching thortical possibility: th quantum vacuum containing virtual gravitational dipols might b sourc of a wak gravitational componnt that dos t follo th Nto s invrs squar law. Lt us start with th hypothsis that quantum vacuum contains virtual gravitational dipols, i.. th gravitational chargs of th opposit sign on a distanc smallr than th Compton wavlngth of th corrsponding virtual particls. Apparntly, th most natural is to attribut th hypothtical positiv and ngativ gravitational charg rspctivly to virtual particls and antiparticls [13-15]. Howvr, som caution is ndd; w still hav to larn a lot about th contnt of th quantum vacuum and it is possibl that th hypothsis of th xistnc of gravitational dipols is mor robust than th idntification of dipols with virtual particl-antiparticl pairs. Whatvr is th natur of gravitational dipols, if thy xist, a gravitational polarization dnsity P g (i.. th gravitational dipol momnt pr unit volum) can b attributd to th quantum vacuum. As wll known, in a dilctric mdium th spatial variation of th lctric polarization gnrats a charg dnsity P, known as th bound charg dnsity. In an analogous way, th gravitational polarization of th quantum vacuum should rsult in a gravitational bound charg dnsity of th vacuum P, which, in th simplst cas of sphrical symmtry rducs to 1 d bg r Pg r; Pg r Pg r (1) r dr Th simplst possibl cas of th gravitational polarization of th quantum vacuum is saturation i.. th cas whn th xtrnal gravitational fild is sufficintly strong to align all dipols along th fild. If all dipols ar alignd in th sam dirction, th gravitational polarization dnsity has th maximal magnitud g P g max b bg P r. Th quation (A1) lads to th conclusion that in th rgion of saturation, quantum vacuum acts as th sourc of a constant acclration g GP (13) 4 g max g 5
dirctd towards th cntr of th sphrical symmtry. As argud in [10, 11] th numrical valu of P is wll approximatd by P g max g max 1 1 kg 3 c 4 m (14) whr dnots th Compton wavlngth of a pion (basically a quark-antiquark pair).additionally, for a cntral body of mass M th rgion of saturation is a sphr with radius R S which can b approximatd [11, 13, 14, ] with 11. Hajdukovic D.S. hal-00905914 (013) http://hal.archivs-ouvrts.fr/hal-00905914 1. Hobson M.P, Efstathiou G and Lasnby A.N, Gnral Rlativity, Cambridg Univrsity Prss, Cambridg, UK (006) 13. Hajdukovic D.S. Astrophys Spac Sci 334: 15 18 (011) 14. Hajdukovic D.S. Astrophys Spac Sci 337: 9 14 (01) 15. Hajdukovic D.S. Astrophys Spac Sci 339: 1 5 (01) M R S (15) m In th cas of UX5, R S calculatd from th quation (15) is about thr ordrs of agitud gat tha th satllit s simajor axis. Hnc, th satllit of UX5 is in th rgion of saturation and its orbit should b prturbd with th constant acclration (13). Rfrncs 1. Aitchison I.J.R. Nothig s plty Th vacuum in modrn quantum fild thory. Contmp. Phys. 50, 61 319 (009). L3 Collaboration. Masurmnt of th running of th fin-structur constant. Physics Lttrs B 476, 40-48 (000) 3. Wilson, C.M. t. al. Obsrvation of th dynamical Casimir ffct in a suprconducting circuit. Natur 479, 376-379 (011) 4. Prz E and Rizvi E, Th quark and gluon structur of th proton. Rp. Prog. Phys. 76 04601 (013) 5. Murray C.D and Drmott S.F. Solar systm dynamics. Cambridg Univrsity Prss, Cambridg (1999) 6. Fitzpatrick R. An Introduction to Clstial Mchanics. Cambridg Univrsity Prss, Cambridg (01) 7. Urbassk H.U. Eur. J. Phys 30 147 (009) 8. Hajdukovic D S. Astrophys. Spac Sci. 343, 505-509 (013) 9. Brown M.E. Th Astrophysical Journal Lttrs 778, L34 (013) 10. Hajdukovic D.S. Mod. Phys. Ltt. A, 8, 135014 (013) 6