VOLUME 4 • NUMBER 3 • SEPTEMBER 1991 •

Physics Essays AN INTERNATIONALJOURNAL DEDIC�TED TO FUNDAMENTAL QUESTIONS IN

Note by Jack Sarfatti March 25, 2017 The device will not work. Stapp was right. The linearity and unitarity of QM forbids locally decodable keyless entanglement messaging (aka signaling). PQM with Roderick Sutherland's wave action<--> particle reaction post-Bohmian Lagrangian is a nonlinear non-unitary non- statistical locally retrocausal weak measurement theory that does allow what we were looking for in this paper. “Little could Herbert, Sarfatti, and the others know that their dogged pursuit of faster-than-light communication—and the subtle reasons for its failure—would help launch a billion-dollar industry. … Their efforts instigated major work on Bell’s theorem and the foundations of quantum theory. Most important became known as the “no-cloning theorem,” at the heart of today’s quantum encryption technology” MIT Physics Professor David Kaiser in the book “How the Hippies Saved Physics”

PUBLISHED BY UNIVERSI1Y OF TORONTO PRESS FOR ADVANCED AND FUSION TECHNOLOGY, INC. = volume4, number3, 1991 · gn for a SuperluminalSignaling Device

Abstract A gedankenexperiment design far a superluminal(laster than light- FJ'L)signaling deviceusing -rorrelated photan pairs emittedback -to-backis given.Only the Feynmanrules far standardquantum mechanicsare used.7be new approachis Le to let the transmitterphotan interferewith itself It is thenpossible to transmitand la locallydec,ode superluminal signals by the controllableshifting of quantumphotan polarizationprobabilitks across arbitrary spac,e- separations between the detections of the twophotons in the same pair. 7besuperluminal signal is encoded with the messageby rotatinga calciteinterferometer transmitter detector relati ve to a .fixed receivercalcite detector through angle e or, alternatively,by changingthe average interferometerphase ~ o. 7bedegree of polarization of the lightat the receiverdetector dependsupon these two parameters, e and ~. 7berejare,the messageis dec,oded by monitoringthe changingdegree of linearpolarization of the receiverlight. 7be principleof C{Jusalitythat effects are alwaysafter causes in allframes of rejerencewill be disprovedif thisdevice worlzs as predicted. 7be objections of causalparadoxes and proofsf arbiddingsuperluminal signaling are addressed.7be second part of thepaper beginsa study of the effectof causalityviolation on the restof pbysics. RJr example, possibleviolations of thespin-statistics ronnection and localLorentz intariance by dark matter,a relativisticquantum lime operator, a new viewof infinitiesin quantumfield theory,traversable wormholes as time machines, and quantumspin thermodynamics of the mind-matter· interactionare someof the topicsdiscussed.

Key words: superluminal signaling, -violatingrelativity , time travel paradoxes, quantumconsciousness n) l34 1.,n M INTERFERENCECOMMUNICATION cisco's Bohemia(North Beach), eccentric and beyondthe cuttingedge of, nilz proceedsas if the past werethe homeof explanation;whereas for example,Paul Davies' excellentco llectionNew P/Jysi<:S.Nevertheless, ~ and the futurealone , holdsthe keyt o the mysteriesof the the refereehas courageouslywritten: " The actualgedankenexperiment is an- for superluminalinformation transfer of a type differentfrom the FIASH -: DwightSedgwick, "House of Sorrow,"An Apologyfor Old proposalof NickHerbert. Although I intuitively agreewith Stapp'sfeeling5 Maids(1908) (referredto in the paper), the designis significantlydifferent from Herbert 's there is evensometh ing vaguelyteleological about the effects and has a contributionof valuein the documentationof possibledesigns ~ ness,so that a futureimpression might affect a pastaction. of superluminalsignalling devices which can be subjectto discussionand RogerPenrose , F.R.S., 7beEmperor's New Mind 1 criticismby the physicscommunity. Thus , althoughI think that this design an- will probablysuffe r the same fate as Herbert's FLASH, I believeit should · to me that biologicalsystems are able in someway to utilize be publishedin a form whichmakes it availablefor criticalscrutiny and isite time-sensein whichradiation propagates from future to discussion.This processeither resultsin a newpotential device or helpsto 70) E.zzareas this may appear, they must somehowbe working completethe case againstsuch devicesthrough the subsequentdiscussion, :tis in time. as Herbert's examplein Foundationsof Physicrhas done." f;edHoyle, F.R.S. , 7beIntelligent (Endnote 2, p. 213). I am predictinga startlingnew ph enomenon,hitherto thought to be im­ possiblein principle- the distantand/or retroacti ve controlof polarization the reader. The point of viewabout the natureof physicsthat I of photons(and of massiveparticles) via nonlocalquantum corre la­ :e is controversial, not respectablein either style or substancein tionsas the communicationchannel. My essential intuitio n in the following academia, spawnedin the romantic CaffeTrieste of San Fran- quantitativemodel is not difficultto grasp. In the simplest case, for twopho-

315 Designfor a SuperluminalSignaling Device tons 1 and 2 emittedback-to-back, let the twodoubly refracting crystals be day quantummechanics. I agreethat livingmatter probably does contro l perfectlyaligned. The results of linearpolarization (V and If) measurements, quantumnonlocality, but that the wayin whichit doesso can be understood whenneither photon is allowedto interferewith itself (Fig. 1), are comput­ usingpresent-day . What has to be profoundlymodified, ed fromthe purespin-entangled pair state [1V)1IV)2 + IH)1IH)2 l / ../2. in my view,is not quantummechanics, but the causalaxiom of relativity The distantcorrelations of photon 1 to orthogonalspin statesof photon withoutabandoning the fundamentalsymmetry of relativitythat the lawsof 2 ensurethat photon1 is completelyunpolarized in localmeasurements. natureshould be independentof the frameof reference. Now,on the otherhand, suppose (in analogywith the well-knownspin-flip 1.1 New Kindsof Signals? techniquein one path of a neutroninterferometer, and the Berry-Chiao Thenonstandard distinction between signals of the first,second, and thinl phasetechnique using a coiledoptical fiber that adiabaticallyrotates the kind is developedin moredetail in Sec. 2 of this paper.H~ver, briefly, planeof polarizationof a photon)that wecan coherentlyand adiabatically I adoptthe modernfiber bundle extens ion of worldgeometry as used in disentanglethe abovepair state withoutcollapsing it into the new form the gaugetheory of fundamentalforces. Subluminal and luminalsignals [1V)1IV)2 + IH)1IV)z] I ../2 = [ IV)1+ IH)d IV)z/../2. Wedo this by of the first kind obeycausality and involvedecodable ene rgy flowsinside lettingphoton 2 interferewith itself and rotatingits polarizationby 90°in and on the light cone, respectively. Superluminaland retroactivesignals one of the twointerfering paths (Fig.3). The twophotons are no longer of the secondkind violatecausality in a "globally self-consistent"way 3 spin-correlated.Each has itsown spin state. But now, photon 1 is completely and involvedecodable energy flows outside the light cone, and similarly polarizedat 45° to the commonorientation of both alignedcrystals. Com­ for signalsof the thinl kind, which the followinggedanken experiment pare thisnew situation to the old onewhere photon 2 did not interferewith purportsto generate. For causality-violatingsignals of the thinl kind,the itself- a choicewhich forced photon 1 into a mixedunpolarized density communicationchannel is the controllablynonlocal quantum correlations matrixwith one bit of positiveentropy. On the otherhand, when we choose in the extra dimensionsof internalfiber spaces beyond space-time. There to makephoton 2 interferewith itself in concertwith the adiabaticrotation is nowcompelling experimental evidence for the breakdownof causalityin of polarizationin one branchof the interferometer,we havethen made the dispersionrelations for the scatteringof gammaphotons off protons. 4 I the oppositechoice which forces photon 1 into a purepolarized zero-bit claimthat controllablenonlocality is part of standardquantum mechanics entropylessstate. That is, the choiceof forcingphoton 2 to interferewith and that proofsstatint othelWiseare incorrect.Signals of the thinl kindwill, itselfproperly transmits a negativeentropy bit of informationto photon of necessity,involve energy flows; in the presentcase they are on the light 1 and its measuringapparatus. furthermore, the metricspace-time interval cone,but theseflows within four-dimensional space-time are not the channel betweenthe choicefor photon2 (whichis the cause)and the polarization wherethe informationis encodedtransmitted and decoded. The channel is in for photon1 (whichis the effect)is irrelevant.The nonlocal quantum spin the extranonmetrical "fibe r" dimensionsbeyond space-t ime in the senseof geometryis premetrical.The space-timeinterval between active cause and gaugetheory 5 ratherthan the extracurled-up metric dimensions of Kaluza­ passiveeffect can be spacelikecorresponding to superluminalcommunica­ Kleintheory. Finally, "transluminal" signals of the fourthkind occurin a tion,or it can be arrangedto be timelikewith delayed choice in whichthe shadowRiemannian metric of signature++++ leftover from the quantum causeis in the frame-invariantfuture of the effect.Indeed, there is a conflict gravityera of the earlyuniverse (to be discussedfurther in Sec. 2). withthe axiomof causalityof relativity,although not withthe classicaltests Signalsof the thinl kind may be involvedas the essentialquantum of timedilation and velocity-dependentmass. mechanismof ordinaryconsciousness. Penrose, 1 in a remarkableanalysis, In Ref. 1 Mermindiscusses recent work b y Greenberger,Horne , and has led me to concludethat our commonassumption of morallyresponsible Zeilinger(GHZ) on three-particlecorrelations that go beyondthe two-particle "freewill" demandscontrollable retroactive (backwards -in-time) actionof correlationsof Einstein,Podolsky , and Rosen(EPR) as extendedby Bohm the mind on matter by about two secondsin onier to agreewith EEG and Bell. Thisnew theoretical work provides the basisfor a crucialexperi­ experiments.If-we choose to holdon to the traditional notionof pastcause mentthat can showthe existence(or nonexistence)of what Einsteincalled and futureeffect, then wemust be mereautomatons with no freewill. That "spookyaction-at-a-distance" without a statisticalanalysis of many mea­ is consciousnessof our actionsis afterthe action.Causality then implies surements.Mermin< 2>" writes, Thusin onesimple version of the two-particle that consciousnessis a passiveepiphenomenon and not an activedecision EPRexperiment the hypothesisof elementsof reality[i.e. , localcausality] maker.This is not a viewthat I find to my liking. requiresa classof outcomesto occur at least 55.5%of the time, while quantummechanics allows them to occuronly 50"/4 of the time.In the GHZ 1.2 Stapp's First Argument Against Superluminal Quantum experiment,on the otherhand , the elementsof reality[i.e., local causality] Signals of the ThirdKind requirea classof outcomesto occuralt of the time, whilequantum me­ Considerthe basic pair-correlationexperiment6 involving spin cor­ chanicsnever allows them to occur."There is nothingwrong with the EPR relations.A pair sourceS emits pairs of spin-spincorrelated particles 1 criterionof reality" If, withoutin any waydisturbing a system,we can and 2 moving"back-to-back" in oppositedirections to detectorsA and B, predictwith certaintythe valueof a physicalquantity then thereexists an respectively(see Fig. 1). elementof physicalreality corresponding to this physicalquantity. " Whatis Onekind of simpleno-faster-than-light (FTI.) signal argument 7 is due probablyfalse-to-fact is the assumption"without in any way disturbing to Stappin a privatecommunication. Stapp's analysis involves the use of thesystem." In addition, thereis the problemthat if quantumaction at a projectionoperators. Suppose the purepair quantumstate is 11,2 ). I.etthe distanceis real,can it be controlledwithin standard quantum mechanics? projectionoperators for the spineigenvalues of eachdetector be PA(B)±; then That is the main focusof this paper. someof the nonlocaljoint probabilitiesp are Josephson<3>suspects that livingmatter does manage to controlquantum nonlocality,but in a waythat is beyondthe formalstructure of present- p(A+IB+) = (!, 2IPA+Ps+ll,2), (1)

316 JackSarfatti

quantumforces prevent a logicalcontradiction. Thome et a/.3 havediscussed + 1 2 this pos.5ibilityin the contextof time travelto the past throughtraversable wormholes. Returningto Stapp'sargument that retroactivecommunication is not ~7 pos.5ibleat the quantumlevel, p (A+) =P(A+IB+) +p (A+IB-)

:e I. Basicpair Correlationexperiment. The nonlocalparameter is the = (1, 2lhJJs+ ll, 2) + (1, 2IPA+Ps-lI,2) l-it:l\\ttn the spin-sensitivedetectors at the the particlesin the pair are detected.For this total experimentalarrangement the local = (!, 2IPA+Ps++P A+Ps-11,2) probabilitiesare 1/2 independentof the nonlocalparameter. Therefore , (3) ;::.tnIUmsignal of the third kind is not pos.5iblewith this design. However, = (!, 2 IPA+(Ps+ + Ps- ) II,2) = (!, 2 IPA+ll , 2) are other pos.5ibilities. becauseof the completenes.c;of the spin eigenstatesof transmitterB,

Pa++P _ = l, (4) p(A+IB-) = (1, 2IPA+Ps-ll, 2). (2) 6

of thesejoint probabilities is whatis actuallymeasured in experiments and its associatedconservation of local probabilityat 8. Therefore, there ::-elating the outputsafter the fact. Measurementof joint probabilities is no dependenceof the local recei\'erprobability p(A+) on any eigenvalue lhefact doesshow a m quantumspin-spin connection that violates or nonlocalparameter that dependson 8. Therefore, superluminalcommu­ nicationby quantum spin pair correlationsis impos.5ible.This completes 1l the principleof causalityexpressed by Bell'sinequality. However , mierallyaccepted that this typeof quantumcausality violation called Stapp'sfirst argumentagainst superluminal quantum signals of the third .:n::aurollablequantum nonlocality " cannot be used for usefulquantum kind. , _.:::eruminal communicationof the third kind, which, by definition, is in 1.3 The Flawin Stapp'sFirst Argument time." Firstof all, it mustbe admittedthat Stapp'sanalysis does correctly describe sufficient (but not necessary)condition for usefulquantum superlumi­ the resultsof all actualexperiments done so far with photonpairs that test axun unicationof the thirdkind is that the localprobability , forexample Bell's inequality. The photonpair statefor theseexperiments predicts that - , changesas somecontrollable nonlocal parameter is changed. Imag­ 2 :asequence of twin pulsesof photon pairs. The observerat receiver p (A+IB+)= (112) cos e, (5) A wouldsee the responseof his detectorin the + spin eigenvalue changein time causedby a changein the relati\'eorientation of p (A+IB-) = (l/2) sin2 e. (6) , transmitterdetector at 8. ~ pulsewidth must be smallcompared to the flighttimes from source Therefore, 300 rs. The nonlocalparameter must not be changedduring the time 2 2 takesa singlepulse to be detected.There must be enoughphoton p(A+) = (1!2)(cos 0+sin 0) = 1/2 (7) ft-oducedin each twinpulse to get a goods ignal-to-noiseratio in the ,;. The nonlocalparameter must be changedin a time that is short independentof the angle0 . So, indeed,there is no superluminalcommu­ • :l:.'dto the flighttimes. It must also be changedbel'M!en the arrivals nication.However, Stapp 's equation s:xre;.sivepulses. t"ie flight times are equal, then the transmissionand receptionof p(A+) =P(A+IB+) +p(A+ IB-) (8) .il!Onis essentiallyinstantaneous in the rest frameof the apparatus. componentsof the apparatusare assumedto be at rest relativeto is an equationfrom classicalprobability theory that ignoresthe pos.5ible ·lier.Now, let the flighttime from pair sourceS to transmitter8 be interferenceof quantumamplitudes . This is the flawin Stapp's analysis. It than the flighttime to receiverA. The choiceof nonlocalparameter doesnot applyto totalexperimental arrangements in whichat leastone of the ....8 can be delayeduntil after pulse 1 has been detectedat receiver photonsin the samepair interfereswith itself.For the experimentsactually · 'leforeits twin pulse2 has been detectedat transmitter8. The past done, howe\'er, it is the correctequation. This foll

317 Designfor a SuperluminalSignaling Device

Arewe justified in ignoringthe space-timedependence of the pair ampli­ receiver transmitter tudes?Experiment suggests that weare. There is no evidenceof a weakening + 1 2 + 0 in the strengthof (A+B+)coincidence correlation as the separationbe­ tweenthe detectorsis increased.This (A+B+)correlation is 1/2 cos2 0 in :=m·- \. ~:~re~0~ ~ the unattainableideal case of 100%efficient detection. More experiments l/2wave ..___ e plate are needed.It appearsthat the spin-correlatedpair wavefunction s imply multipliestwo independently movinguncorrelated space-time wave packets for each photon.This would be consistentwith Ne'eman's alreadyquoted Figure2. Pair correlationinterference experiment. The transmitterphoton fiberbundle pic ture5: "The twoy rays shouldhave their sp in polarizations 2 interfereswith itself and causesa controllableshift in the polarizationof addingup to rero (and to negativetotal intrinsicparity ) whenobserved its far-away twin receiverphoton l that dependsupon the anglebetween whateverthe ABdistance . . . . in a fiberbundle geometry , the manifoldis the calcitecrystals at the momentsof detection, and upon the phases hift constrainedso as to preserveparallelism whatever the magnitudeof the base in the transmitterinterferometer. spaceinterval ." That is, the relevantquantum connection in this case is entirelyin spin-fiberspace beyond space-time. B+), and (A- , B-), are distinguishable.Hence Stapp's equation is justified Theproblem for superluminalsignaling is howto correctly takethe sum for this classof totalexperimental arrangements. But is it justifiedfor all of distinguishable alternativesover all possibleplaces where the transmitter possibleexperiments? No , it is not (seeFig. 2). photon2 can be absorbedat B.This is the basisfor Stapp 's secondargument Thereis now a newparameter qi in the experimen~the translational againstsuperluminal communication of the third kind.Stapp 's motivation phase differenceof the two indistinguishablealternatives for transmitter is the true fact that coherentinterference redistributes the conservedlocal photon2. Experimentswith neutron interferometers show that it is possible probabilitydens ity. If one integratesthe interferencecross terms over all to constructan x spinstate from the coherentinterference of twoorthogonal possibleplaces where the singlet ransmittingphoton might be absorbed, +y and -y spinstates. On the otherhand, with photonswe knowthat a, then the crossterms integrate to zero.What Stapp fails to realireis that not double-slitexperiment with orthogonal linear polarirers at eachslit destroys all theseplaces ar&relevant in computingthe controllablenonlocal quantum the interferencefringes. That does not, in principle, mean that coherent action-at-a-distanceon the far-awaytwin receiver photon. If the dependence interferenceis not happeningin the photoncase . Indeed, the interference of the differencein the local receiverpro babilitiesp (A+) - p(A- ) on 0 showsup in the changeof polarizationstate at differentpoints of the (i.e., the superluminal signalof the third kind) survivesthe sum overqi, screen.In someplaces there will be left-handedcircular , in other places then we are in the superluminalcommunication business . If that turns right-handedcircular, etc . Thisonly means that a moresophisticated kind _out to be the case, we can manipulatethe degreeof partialpolarization of measurementwould need to be done at the screenof the doubleslit to of receiverlight at a distancefrom the futurein a delayed-choicemode of detectcoherence from orthogonally polarized paths. operationof the device. Theexperiment we are interestedin doesnot dependupon whether there The messagevxmld then be containedin the encodingmodulat­ are interferencefringes for photon 2 at the transmitterB. What we really care ing function 0(12) , whichmaps to the decodingmodulat ing function about is whetherthe degreeof linearpolarization of a streamof photons 0(11 + [L2 -Lil l e), where 1 at the receiverA can be controlledat a distancefrom B. This nonlocal controlwould be achievedby keepingthe orientationof Afixed but rotating (9) B relativeto A in time. I haveplaced a half-waveplate in one ann of the interferometer. and L1 andL 2 are the spatialdistances of the detectorsA and B fromthe Interferencefringes will be seen if the half-waveplate is in placefor sourceS , respectively. So, if L2 > L1 , the causeat timeT2 is in the future ordinaryuncorrelated light. In fact, however,local interference fringes will of the effectat time t1 . That is, the degreeof polarizationof the receiver not appearat the transmittereven if the half-waveplate is in place.This lightat A at time/ 1 is the functionF of time/ 2: is becausethere are two mutuallyout-of-phase nonlocal interferograms correspondingto the distinguishablealternatives of receiverphoton 1 at A. p(A+ , ti) -p(A- , ti) =F{0(t 1 + [Lz -L1] / c)}. (10) Thesetwo nonlocalinterferograms <4 > could be resolvedafter the fact by coincidenceanalysis. Their existence might be exploitedfor an untappable, AnalyrersA, B and sourceS are all relatively at rest along the line of unbreakablequantum cryptographic military intelligence application. How­ flightof the photonpair. Onewa y of encodingthe messageat B is by a ever, this cryptographicapplication has nothing to do with the present variablerotation d0 / dt of the entireB assembly about the axisof the line problemof superluminalsignaling. I mentionit in passingfor its intrinsic of flight.However , I willcalculate F explicitly for the gedankenex periment interest. givenbelow , and wewill see that thereis an easierwa y to do it usingthe Feynman's rulesfor the presentinterference pair correlationexperiment qi dependence. implythat we must add the amplitudes(1, ZIA+,B+) and t(qi)(l, ZIA+, 1.5 The PhotonPair State 8-) beforesquaring. Similarly , wemust add the amplitudes(1, 2 IA-, B+) Startwith the standardphoton pair s tate actually usedin and confirmed and t(qi) (1, ZIA-, 8-) beforesquaring. What do weget afterwe square? by experiment.The photons are emittedbac k-to-backin oppositedirections Whatwe get is a pair of nonlocaljoint probabilities that photon1 takesa with total angularmomentum rero . Considera doublequantum jump of particularchannel at Aand that its twinphoton 2 is detectedat B witha an atomicelectron for which the emittedph oton pair state is evenunder definitetranslational phase difference qi. paritymirror imaging. Therefore , for linearpolarizations the directionsof

318 JackSarfatti

'.'(llarizationare parallel.The directions of rotationfor circular polarizations are opposite(for one observerlooking from a fixedpoint of view).The Jelicities(projections of spin along momentum)are the same.Odd parity Now,make two arbitraryindependent local frameshifts from the totally ~r stateshave perpendicular linear polarizations. All this is independentof arbitraryHcommr:m (V, ) basisof bothphotons to the bases(Vi, H1) and howfar apart in spaceor time the detectionsof each photonin the same ( V{,H;). Thesebases correspond to the actualorientations 0 ACt1) and pair are. 0s Ct2) of the calcitecrystals at A at time t1 and B at time/ 2 where,as The Einstein-Podolsky-Rosen(EPR) paradoxconsists in preciselythis definedabove, fact togetherwith the realizationthat we do not haveto decideuntil the jst instantsprior to the detectionswhether to locallymeasure circular t1 = t2 - (L2 -Li)lc . (16) 'lOlarizationor, alternatively,linear polarization in anydirection (transverse :o the line of flight). No matterwhat we arbitrarilydecide, the far-away Substitute :ihotonswill alwaysshow parallel linear polarizations or oppositecircular "IOlarizations(equal helicities ). Eachphoton "knows" how the otherphoton .s beingmeasured. Supposewe have only one photonpassing two polarizers . Thefirst polar­ .zerprepares the photonin a givenspin state. The second polarizer analyzes :he preparedstate. This is easyto understandlocally. A similar thing happens IV2) = cos0 s(/2) IV{)+ sin 0s('2) IH{), (19) ronlocallyfor our photonpair. Photon l passesa polarizerA. Not only does 1 . locally preparephoton l in a definitestate with probabilityl/2 , it also IH2) = - sin 0s(/2) IV{)+ cos0 sU2) IH{). (20) .'ln/o cally preparesits distanttwin photon 2 in the samestate as the one :1Ctuallyallegedly randomly chosen for photonI. Therefore,when photon Definethe nonlocalmodulation parameter : encountersits polarizerat B, it will simplybe analyzedin the state in nich A preparedit at a distance.Analyzer A's preparationof photon2 (21) Clll be in the futureof photon2's encounterwith analyzer B. Thesituation - totallysymmetrical. We can say that B preparesphoton l at a distance, and let us agreeto keepthe receiverorientation 0A (/ 1) fixedin time in hich is then analyzedby A, etc. what followswhen we get to m communication.Familiar trig onometric Thus,start from the (R, L) circularpolarization frame of referencein identitiesgive us the usefulform of the photonpair state I1, 2) in terms m fiberspace beyond space-time for a singleobserver looking from a fixed of the_actual orientat ions of the birefringentcalcite crystals at the detectors int of observationalong the line of flight. A and B. That is, ~otethat '1'1(x,) 'lf2(x2) are the twouncorrelated wave packets of each r-"oton movingin oppositedirections in space.Their function is simply to II, 2) = ( 1/ v'2) [ cos0 ( 1 - 2) {IVi)1V{) +IH1)I H{)} 0:liver the photonenergies to the detectors.They do not carrythe message +sin 0(1 - 2) {!Vi)I H{) - IH1)IV{) }] '1'1(x1) '1'2 (x2). (22) modulatedenergy flows the waythat theydo for signalsof the firstand .u>nd kind.Their role in the m spin fibersignal of the third kind is There is no need to worry about the relativistic collapseof the wave a::essarybut secondary: function.(5) If one wishesto imaginethat the wavefunction collapses instantly,then thereis no problemwith re lativity,because we are explicitly assumingthat causalityis wrong.future causes are allowed.But even more importantly,we can do awaywith the notionof instantaneouscollapse. 'x>tons are , and, therefore, the wavefunctions for severalidentical Operationallywe havetwo measurementsmade at an arbitraryspace- time ,otons must be totallysymmetric in all the quantumnumbers. However, separationfrom each other. As Wheelersays, " no quantumphenomen on - the presentcase the two photonsin the samepair havenonoverlapping is a phenomenonuntil it is an observedphenomenon. " Thuswhat we are :e packetswith different peak frequenciesand differentline widthsand, talkingabout is not evendefined until both detectionsare made.There is -.:refore,are not identical.Thus the photonpair function(l l), though no independentway to detectthe collapsingwave function between the two --nmetrical in spin space,need not be so in physicalspace. detections.It is a pseudoproblem.What we have, here,is a nonlocal,non­ ~takea spin fiberframe shift to a particularlinear polarizationbasi s metricalglobal quantum phenomenon, which is basicallyhappening beyond \". H) and substitute space-time.It is premetricalat a deeperleve l, that is, a biggerKlein-Erlanger group8 than the Lorentzgroup metrical geometry of relativity. IL) = (1/ v'2) [ IV) + i IH)] , (12) 1.6 The GedankenExperiment In Fig. 3 a half-wave plateconverts IH{) to IV{) at the transmitter.A IR) = (l/ v'2)[ IV ) - i IH)], (13) half-silveredmirror is at the transmittercrossing point 'B. Thosetransmit­ ter photons2 whosetwin photons 1 are detectedin the Vi charmelwill I 2) = (l/2 v'2)[ {IV,)+ ilH1) }{JV2)- ilH2)} forma nonlocalinterferogram on the transmitterscreen; similarly for those transmitterphotons 2 whosetwin photons 1 are detectedin the H 1 channel. fullyreflecting mirrors (;:I, C , '1J) bringthese two mutually out-of-phase nonlocalinterferograms to a small region'£ on the transmitterscreen.

319 Designfor a SuperluminalSignaling Device

i phase change Theseare the nonlocaljoint probabilities for coincidencemeasurements in on each reflection which the receiverphoton 1 is observedto have polarization eigenvalue Vi(H 1), and its twin transmitterphoton 2 is observedto land on the screenwith translational phase difference q>( 2) whenthe calcitecrystals are misalignedby the nonlocalangle 0 ( 1 - 2) connectingthe two arbitrarily separateddetection events. 1.8 The TransmitterPhase Noise receiver The superluminalsignal at the receiveris derivablefrom the difference betweenthese squaredpair amplitudeswhen properlysummed over all relewnt valuesof the phase differenceq>( 2) . This is the crux of the Figure3. The gedankenexperiment. debate.The controversy is overhem to performthis sum.fur this particular experimentalarrangement the overlaparea '£ is small.The L is the variable Thus no fringeswill be visibleat the transmitterscreen for pair-correlated path differencebetween 'B'D'E and 'BCE, that is, light.Fringes would be visibleif the sourceemitted uncorrelated photons 2 with the same spectralline shape and spatial coherenceof photon2 L = ( 'B'D'E- 'BCE) . (33) in the pair-correlatedcase. As alreadymentioned <4 ) above,the two non­ local interferogramscan be disentangledfrom each other by coincidence fur uniformindex of refractionn measurementsfor one photonpair in the systemat a time. 1.7 The FeynmanPhoton Pair ProbabilityAmplitudes q,(2) = 2 rrLn/ 'A.2, (34) Therelative phase difference between the interferogramsacquired between the crossingpoint '13and '£ on the screenis q>(2) . Thereis a phaseshift L < c!n'ov2, (35) of i for each reflection,and an extrafactor of 1/ ,/2 fromthe half-silvered· mirrorat '13. The Feynmanpath amplitudesare that is, the path differenceL mustbe smallerthan the coherencelength of the transmitterphoton wave packet g (x2) . The fluctuationin q>( 2) is &p. 2 I= (1, 21Vi,v;, 51 , '13, 'D, '£) = (112)cos0(1-2)i 3e;q,<>, (23) It is due to variationsin threevariables , L, n, and 'A.2, that is,

II = (1, 21Vi, H{, '13,'D, 'E) = ( 1/2) sin 0(1 - 2)ie;q,< 2>, (24) (36)

Therefore,if wechoose a particularLo obe yingthe wherenc:ewndition Eq. III= (1, 2IVi, V{,51, '13,C, '£) = (1/2) cos0(1-2)i 2 , (25) (35),we havesome mean o-The relevantrange of q>integration is then o±&p. 2 IV= (!, 2 IVi,H{, '13,C, 'E) = (112) sin 0(1 - 2)i , (26) 1.9 The Errorin Stapp'sSecond Argument Against Superluminal Signals 2 V = (1, 2 IH1,v;, 51 , 'B, 'D, 'E) = -(112) sin 0(1 - 2) ;3eiq,<>,(27) HenryPierce Stapp of the LawrenceBerkeley Laboratory , in privatecom ­ munication,has objectedthat a superluminalinterference signal violates VI= ( 1, 2 IH1, H{, 'B, 'D, 'E ) = (112) cos0(1 - 2) ieiq,(2), (28) conservationof local probability p(2) for the transmitterphoton 2. This secondobjection is that afterproperly performing the sum overall places 2 wherethe transmitterphoton 2 mightbe absorbedon the screen, the depen­ VII= (1, 2 IH1,v;, 51 , '13, C, 'E) = -(112) sin 0(1 - 2); , (29) denceof the localreceiver probabilities p(V ) andp(H) (seeFig. 3) on the

2 misalignmentangle 0 ( 1 - 2) willcancel. This would destroy the nonlocal VIII= (1, 2 IH1'H{' '13' C' 'E) = (112) cos0(1 - 2)i . (30) quantumsignal. On the contrary,I arguethat whileall placeswhere the transmitterphoton 2 can be absorbeddo contributeto conservingthe local The Feynmanrules of standardquantum mechanics tell us to add the probabilityp ( 2) , manyof thoseplaces do not contributeto the nonlocal amplitudesbefore squaring for indistinguishablealternatives , and to square signalp(V) - p(H) in the far-awayspacelike separated receiver region. the amplitudesbefore adding for distinguishablealternatives. Clearly, with Onlya subsetof thoseplaces where photon 2 mightland contributeto the the abovetotal experimental arrangement, the eightalternatives form two dis­ tinctsets of indistinguishablealternatives (nonlocal interferograms) , that is, detectionprobability of its twinphoton l . That is, the wavesarriving at '£ {I, II, III, IV}and {V, VI,VII, VIII}. The firstset correspondsto a mea­ at the transmittermust wherently interfere in orderto producethe signal surementof receiverphoton 1 in the IVi ) state.The second set corresponds at the far-away receiver. Likethe quantumsignal in the Josephsoneffec~ the superluminalsignal is essentiallya macroscopicquantum interference to the receiverphoton in the IH1 ) state.Therefore , phenomenonusing photon pairs , ratherthan electronpairs. p:(Vi, 0(1-2) , q,(2)) = II+Il+Ill+IV J2 The secondobjection , however,was in the contextof a double-slitar­ = (112)(1 - cos2 0(1 - 2) sin q>(2)), (31) rangement, not the arrangement of Fig.3 in whichthe phasevariation q> is moretightly controlled. Thus &p is understoodto mean the uncertainty

2 in phasecoming from that wherentsubset of placeswhere the transmit­ p'_ (H1, 0(1 - 2), q>(2)) = IV+Vl+ VII+ VIIIl ter photonm ight be absorbedin whichthe wavesfrom paths 'B'D'E and = (112)(1+cos20(1 - 2) sin q,(2)]. (32) 'BCE are stillmutually wherent. If they are not coherent, then they have

320 JackSarfatti =

no controllablenonlocal effect at the spacelikeseparated receiver , although p(H(V) , 0) = dq,p(H(V), 0, $) !heycertainly figure in conselVinglocal probability p(2) at the transmitter {'°+6+ leo-6+ -creen. 1.10 Normalizationof the TransmitterPhoton Probabilities = ½[I± cos20 (sin $)] Firs~nonnalize the transmitterphoton probability density in area 'E of CJherent interferenceof the wavesfrom the alternatepaths in the inter­ = 1 ± cos28 sin $o sin coq>], ( 40) erometer.Take the point of viewof the local observerat the transmitter ½[ . (41) fflll receiverphoton arrive in either the Vi channel or the H1 chan- 1el. Theseare distinguishable, noninterferingaltemati\'es , becausethere is Equation( 41) saysthat the degreeof linearpolari7.ation of the receiver - separatephoton counter in both the Vi and H1 channels.Therefore, photon can be controlledacros.5 spacelike (even timelike) intervals at a ~ un-normalizedtransmitter photon probabilitydensity at the screen distance, indeed, evenbadzwards in time. Notethat the signalS can be ::a.-ea 'E is simplythe sum ofp'(Vi , 8(1 - 2), 8(2)) withp'(H 1, 8, ( 1 - 2), $( 2))) fromEqs. (31) and (32).This sum is 1 and is the reason modulatedby either varying8 or $0. As a practicalmatter it \\Uuldbe ii1I) no local interferencefringes are seenwith pair-correlated light. On the mucheasier to modulateS by changing$o with fixed8 . Notice, also, that It is generally believed ma! of the thirdkindp(V) - p(/{J. Photonpairs whose transmitter photon to be unworkable, becausethe proposed" photon-cloning" laser amplifying - doesnot interferewith itself belong to a differentincoherent subensemble , decodingmechanism appears to violatethe superpositionprinciple of quan­ ::ichdoes not contributeto the nonlocalsignal. These incoherent pairs are tum mechanics. H~r , the basicidea that Herberthad is interestingand :-:-elevantto the computationof the sum overall placeswhere the transmit­ can, perhaps, be madeto 1.mrk. ~ photon2 mightland withinthe coherentregion of 'E . Therefore[call Herbert's idea is totally differentfrom the one proposedin this paper. 8 I - 2) simply8, and $(2) simply$l. The reasonHerbert 's idea may eventuallybe made to '.mrk is the recent progressin dJaos.Thus it may be that sequencesof individualquantum +.,+6+ events(IQE 's) that directly feel the quantum connectionare not really d$[p(V,8,$) +p(H,8,$)] = 1. (37) random, but containuniversal hidden fractal orderswhose locally observab le +o-6+ 1 signaturesdepend in a controllablewa y upon distantactions . This general Therefore, approachis also alludedto as "symmetric-time," which is at a deeper levelthan irreversible"directed-time ".rn Thus "All combinatorialchoices p(H(V) , 8,$) = [l ± cos28sin$]/4oq>. (38) madeunder symmetric causality are consistentwith the quantumprobability interpretationof directedcausality. [p. 141] ... A complexdual process ""e sum overtransmitter phases that suroivesat the spacelikeseparated may be consistentwith quantum mechanics simply b y virtueof its pseudo­ "'.:U:lver is randomness,despite having a unique selectionproperty over space-time. +s+ [p. 143J" Thereare practicallyno experimentson this veryfundamental ~ q>) = d$sin$[p(V , 8,$) +p(H , 8, $)] problem. t+o-6+ Herbertaccepts the standardnotion that it is impos.siblein principleto shift quantumprobabilities at a distance. I am denyingthat the sequence +.,+6+ of quantumevents at one end of the photonpair experimentneed always d$ sin$ . be uncontrollablyrandom for all possibletotal experimental arrangements . = 1'°-6+ oq, = sin $0 si~oq> sin $0 sin coq>. (39) 2 ~ It is furtherasserted that the departurefrom randomness of the sequenceof quantumevents can be controlledfrom an arbitrarydistance acros.s space­ Jearly, the averageof sin $ overthe transmitterphoton nonnalized timewithout the local actionof a Hamiltonian.Quantum probabilities are '1:lbilitydistribution for $ in the coherentsubregion of 'E on the screen locallyshifted all the time by energytlc,.vs . Whatis novelis the shift of ~ generallyzero. In fac~ it dependson the averagetransmitter interfer­ quantum probabilitiesby pure informationtlc,,vs in fiber space without oer phasedifference $o and its actualuncertainty oq, due to fluctuations correspondingenergy tlc,.vs in base space-time.Herbert believes that the ;.,e relevantexperimental parameters. quantumconnection only acts controllably at the levelof individualquantum have assumedthat the alternativesfor different$ are noninterfering, events(IQE's) and is washedout in the statisticalaverage over many events . theycorrespond to an irreversibleabsorption of a photoncompleting On the contrary,I am assertingthat the quantumconnection can be used 'lleasurementor "makinga record."That is, onecan considerthe screen to controllablyshift the averagesfrom a distanceand that one doesnot have -:.a retinalikearray of photondetectors. to go beyondstandard quantum mechanics to achieveall this.One simpl y 11 The SuperluminalSignal at the Receiver has to use Feynman's rules and a littlebit of physicalintuition. Thus the superluminalreceiver signal S is the degreeof partial linear Svozil,< s> of the Institutefor Theoretical Physics in Vienna, has a variation nzationof the receiverphoton, which is the differenceof the local on FLASHthat he callsSL\SH (second-laser-amplified superluminal hookup). ..ibilitiesp (H, 8) andp ( V, 8) , that is, Herbert's FU.SHhad the laseramplifier at the receiver.Svozil 's laseramplifier

321 Designfor a SuperluminalSignaling Device

time

cross-talk ){ Universe I ts coherent phase parallel worlds are cross sections of the bundle

Figure4. Autocidalcausal anomal y usingtachyon signals. If R receivesYES, then T transmitsNO to S. If R receivesN O, then T transmitsYES to S. If S receivesYES, S transmitsYES to R. If S receivesNO, S transmitsNO to R. Thisresults in a self-referentialparadox like the onesconsidered by Bertrand Russelland AlfredNorth Whitehead in PrincipiaMathematie,a and which Figure5. Doublyconnected loop in time has topologyof the double-sheeted finallyled to Godel'sincompleteness theorem. Riemannsu rface linking parallel (sheets), and suppressesthe autocidalcausal anomaly. is at the transmitter. WhileSvozil does not use interference,his gedanken out only antisymmetricstates for systemsof identicalfennions. Quantum experimentis more like the one in this paper than like FIASH.Svozil is phenomenaare inherently nonlocal,and nonlocalityensures self-consistent not workingat the hidden-variable level,but is attemptingto use standard loopsin time. Let us alsoremember that there are two importantcases of quantummechanics to shiftthe receiverquantum probabilities at a distance. classicalnonlocality , that is, precognitivecharged particle motions avoiding Svozilhas not yet publishedhis idea so that it wouldnot be appropriateto runawaysolutions in Maxwelltheory, and the nonlocalityof gravitational discussits detailshere. energyin generalrelatiJity. We simply have to get usedto nonlocality. 1.13 AutocidalCausal Anomaly Let us supposethat there are paralleluniverses. This is the only inter­ (Thefollowing section was written in an earlierdraft receivedby Physics pretationthat seemsreasonable in quantumcosmology where we need a &says before I knew of the recent work on the global self-consistency "wavefunction of the universe."In the standard paralleluniverse interpre­ of eventson the closedtime like cuives (CTC) 3 generatedb y traversable tation the copiesof the same mind in differentparal lel universescannot wonnholesbuilt with matterviolating the weakenergy condition. Note that cross-talkto each other.Penrose has cometo doubtthis restriction1 and so I giveessentially the same sort of criterionin terms of Feynmanhistories do 1.· It is easyto see, using fiber bundle inspiredpict ures, that the causal that Thomeet al. nowadvocate.) anomaly inducescross talk or a doublyconnected quantum loopin time. Supposewe use signals of the secondkind (see Fig. 4). This is not The doubleloop resemblesthe double-valuednessof the spinorunder 2 7t essential;the same apparentparadox arises with signalsof the third kind rotationsof the frameof reference. in the gedankenexperiment above. The causalorder of earlier-laterbetween Figure5 showson ly one of severalways to connectthe paralleluniverses spacelikeseparated events T and S outsideeach other's light conesis sub­ into a self-consistentdoubly-connected loop in time. The same topological jective,changing with the frame of referenceof the observer.The same is idea is used in the theoryof Riemannsurfaces of functionsof a complex true of S and R. But the net resultis a retroactivesignal backwards in time variable(i.e., Jz). There, the point is to convertthe multivaluedfunction from T to R which is objectivelyseparated by a frame-invarianttime-like into a single-valuedfunction. The demandfo r single-valuednessis analogous interval.Figure 4 followsPenrose 's1 Fig. 5.32,p. 213. to our demandfor nonlocalor globalself-consistency. Supposethe equipmentis 100%reliable. This is the same as supposing The two points of view,that is, a single universewith malfunctioning that we have absolutefree will. Then, indeed, if there are not parallel simple loops in time and paralleluniverses with doubly connectedloops universes, there is a paradox.But both of theseassumptions can be wrong. in time, are actually equivalent.In Fig. 5 the mind clones,thinking the y first, supposethat there are no paralleluniverses. There is only one unique are only in one universeI (or II), will perceivethat S functioned without universe.In that casethe nonlocalquantum force can act at a 4-Ddistance error, but that there was an error in the RT link. R>rexample, the mind and causean errorin orderto keepthe loopin time logically self-consistent. clonetrapped in universeII will perceivethe followingsequence of events: This is the positiontaken both by Hoyle1 and by the late GodeJ.9 R receivesNO, but there is an error when T transmitsNO to S, which In this extremecase the equipmentwill fail 100°/4of the timesomewhere correctlysends NO to R. So,we can havesimple loops in time with errors, along the line. That is, any attemptto create a time-travelparadox will like multivaluedcomplex functions, or wecan havedoub ly connectedloops inducemalfunctions in the equipment.R>r example, R can receiveNO, T in time linkingnonnally unlinked parallel universes with no errors.Take can transmitYES; if that happens,Swill malfunction.Or, another alternative , your pick! R receivesNO, an erroroccurs so that T transmitsNO and S doesnot make an error. 2. RELATIVITYwrmour CAUSALI'IY Wecan use Feynman's pathquantum mechanics to describeall this.Every possiblehistory has a quantumamplitude. 7be Feynman amplitudes for Youknow, I haverecentl y lostconfidence in the principleof no action thosebistories that are self-contradictorysimply vanish.This is no more at a distance... peculiar than, for example,the Pauli exclusionprinciple, which selects Einsteinto ErnstStraus, Some Strangeness in /be ProportfonC9l

322 JackSarfani

Physicstoday only recognil.esthe existenceof what I call the signal correlationsto transmitdecodable information backwards in timeusing onl y i the first kind." This is a one-waysignal in the directionof time's lightlikeworld lines for energypropagation . Theseloops of the third kind arro.vthat conveysuseful messagesfrom a past state of a transmitter­ describedin the gedankenexperiment of this papercan be used for the r'!llitter to a futurestate of a receiver-absorber. Messagesare communicated local decodingin the past of usefulmessages transmitted from the future · · the controlledmodulation of four-vectorenergy-momentum along either in a waythat is free from time travelparadoxes . I must firstdefine new · "Jlelikeor lightlike'M>rid lines . Theenergy-momentum flow for real particles typesof signalsthat are not recognizedby physicstoday . everywhereeither inside or on the locallight cone, even in curvedspace­ The newnotion of causality-violatingtraversable 1M>rmholes that can self­ . "Jle. Therefore, the directionof causationfrom past to futureis a frame­ consistently transportobjects backwards in time (likethe "flowerfrom the l;lriantdistinction . It is interestingto note, however, that virtualphotons future" in a storyby JorgeLuis Borges called "The Flowerof Coleridge," :t."e not confinedto the light cone. Indeed, in the exchangeof a single OtherInquisitions ) 'M>uldcorrespond to a loop in time of the first kind, rtual photonbetween t'M> charges , four-momentumconservation requires since it takesplace in the base spaceof the 1M>rldgeometry on closed .: :U the virtualphoton is spacelikeoutside the light cone. Thus the near timelikeworld lines . ld Coulombforce really is superluminal- althoughthis particulareffect Cllll1ot be usedto transmituseful messages . If a man could passthrough Paradise in a dream, and havea fla,ver It is the principleof causalitythat effectsare alwaysafter causes in all presentedto him as a pledgethat his soul had reallybeen there, and fr:unesof referencethat placesthe speed of lightbarrier in Einstein's classical if he found that fla,verin his hand when he a'M>ke- Ay!- and ""ry of specialrelativity .10 However , the principleof causalityis to relativity what then? ... Wells' protagonisttravels physically to the future. .. . Euclid's fifth axiom of a uniqueparallel to a line througha pointnot Moreincredible than a celestialfla,ver or the flowerof a dream is - the line is to geometry. Thuscausality is an additionalpostulate to the the flowerof the future, the unlikely flowerwhose atoms now occup y smunetry groupof specialrelativity. The classictests of specialrelativity of otherspaces and havenot yetbeen assembled. ie dilationand mass-energyequivalence do not dependupon the causality pNUlate.Furthermore, the argumentfor causalityfrom dispersion relations Jn contrast, the gedankenexperiment in Sec.1 1M>uldbe the mechanismfor ID quantumfield theory on both an experimentaland theoreticallevel has the loop in time of the third kind describedby anotherBorges story , "The questionedby Bennen.4 Heshows that dispersionrelations for gamma­ Dreamof Coleridge" (OtherInquisitions) . ~ scatteringare badly violatedby experiment and that thereare sound ('!2.5()llS whythey should be . Furthermore,recent 'M>rk by Thomeet al. 3 at A thirteenth-centuryMongolian emperor dreams a palaceand then Techand Novikovet al.3 in Moscowshow that Einstein's gravitational buildsit accordingto his dream; an eighteenthcentury English poet M! equationspermit a newclass of "tra\'ersable1M>rmhole " (TW)solutions (whocould not have knownthat the structurewas derived from a 6tinc t from blackhole and Einstein-Rosenbridge solutions . Providedthat dream)dreams a poem about the palace. In comparisonwith this eXotic form of matterthat permitssuperluminal energy flows can be symmetry, whichoperates on the souls of sleepingmen and spans .:id,the 1W'scan be constructedand usedfor practical interstellar travel 3 continentsand centuries, the levitations, resurrections, and apparitions · for time travelto the past.A principleof "globalself-consistency on in the sacredbooks are not so extraordinary. . . . Perhaps the series -ed timelikecurves " is invokedto avoidthe causalparadoxes that "change of dreamshas no end, or perhapsthe lastone whodreams will have ?ast." Indeed, the positiontaken by Thorneand Novikovet al. regarding the key. . . . Perhapsan archetypenot yet revealedto men, an eternal ~ ty paradoxesis veryclose to that takenindependently in earlierdrafts object(to use Whitehead's term), is graduallyentering the world; its :..'lispaper (e .g., 1.13above) . firstmanifestation was the palace; its secondwas the poem.Whoever s \.haronovet al.11 havealso published a gedankenexperiment with quan­ comparedthem .1M>uld have seen that they\vere essentially the same. - retroactivityacting backwards in time. Theyalso showhow the super­ g :.ions of \veakforces can cause a strongforce leading to a new kind In thispaper I presenthighlights of newpredictions in relativity. I willpresent ,s quantum amplifier. The generalidea is that specialsuperpositions of a moredetailed mathematical investigation of relativitywithout c,ausality ~ fllllm inputscan , thoughvery rarel y, producean outputfar outsidethe in a sequelto this paper. Relativitywithout causality is intendedto be 1t -:ain of the inputs. the newtangent group geometry for generalrelativity. My conjecture is that 1d .?.l Loopsin Tune relativitywithout causality , whichincludes Hawking 's "imaginarytime ,"12 is s: ""beemerging new causality-violating paradigm can be glimpsedin King's whatis missingin the currentattempts to makea coherentquantum gravity :h :.::irkson "supercausal" loopsin time.rn The abovegedanken experiment theory. I haveadopted " the realisticphilosophy of mostworking scientists "6 :s, Eeredas a counterexampleof claimsthat standardquantum mechan- and have optedfor the strategyof "dramatically revisingour conceptof ps .a ooesnot allowdecodable superluminal and retroactivemessages using space-time"6 in reconcilingquantum nonlocality with relativity. ke ::.:::s:em-Podolsky-Rosenspin-spin pair correlations.My claim is that the Causalsignals of the first kind do not break the speedlight barrier. , gedankenexperiment gives causality-violating testable super-causal However, causality-violatingsignals " of the secondkind " do breakthe light =e:narusms that reproduciblygenerate " loopsin time"2 of the third kind. barrier(see Fig. 6) . Signalsof thesecond kind transfer information by energy ­ ~ in timeof the firstkind correspond to the use of traversable'M>rm­ momentumflows that are somewhere,though not necessarilyeverywhere , to moveobjects backwards in time on globallyself-consistent closed spacelikeoutside of the locallight cone . · 'M>rldlines. Loops in time of the secondkind use superluminal Signalsof the firstand secondkind havethe commonfeature that they propagatingenergy on spacelikeworld lines . Loopsin time of the propagateenergy and momentumalong 1M>rld lines of varioustypes within _ kind use Einstein-Podolsky-Rosen-Bohmnonlocal quantum spin pair space-time. Thereis still a third typeof signal "of the third kind" using

323 Designfor a SuperluminalSignaling Device

timelikeworld lines inside the lightco ne. H~ver, virtualsubluminal par ­ ticlesoff the massshell are not confinedto timelikeworld lines . Theycan be outsidethe light cone with exponentiallydamped probability of range sptn fibers beyond equalto the Comptonwavelength . spacc~ttmc In contrast,real superluminalparticles on a new branchof the mass shellare on spacelikeworld lines outside the lightcone . Virtualsuperluminal particlescan be insidethe lightcone also with exponentiall y dampedproba­ bility. Thusboth the subluminaland superluminalparticles feel the Einstein barrierin real time. Subluminalparticles obey causality , but superluminal particlesdo not.

past Superluminalparticles d o not have a restframe . Theydo have a tran­ scendentalframe in whichtheir speedis infinite, theirenergy is rero, and their momentumis finite.They also have a specialframe in whichtheir Figure6 . Fiberbundle pi cture of signalsof first(I ), second( II) and third 2 112 speedis J2e and their real gammafactory= 1/ [ (vi e) - l] is 1 (III) kind. I and II are modulatedenergy flows conv eying messages. III (v I c > 1) . Gammais greaterthan 1 for e < v < ,./2e . Gammais less is pure informationflow conveying messages without corresponding energy flow. than 1 for v > JZe. Superluminalparticles lose energy as theyaccelerate . Theytime contract and lengthdilate into three-dimensionalstrings along their motionabove controlledquantum nonlocality in fiberHilbert space beyond space -time. This J2 e. Freely fallingsuperluminal particles follow spacelike geodesics in quantumsignal does not propagateenergy-momentum along world lines in pseudo-Riemanniancurved space -time. Superluminalparticles have quantum space-time. Ne'eman5 has shc,,vnhow nonlocal spin-spin correlations fit into de Brogliewaves that are shorterthan their Comptonwavelength . Their the worldfiber bundle picture . Space-timeis the base spaceof the world energyvaries from rero to infinity. fiberedby Hilbertspaces of variouskinds . In a quantumsignal of the third ~ use the samespecial ,relativity formulas for superluminalparticles as kind localprobabilities at space-timeevent A are controllablyshifted from for subluminalparticles . Onlythe gammafactor is different.The Lorentz an arbitrarilyseparated space-time event B becauseof the nonlocalfiber transformationsbe™!en observers in subluminalrelative motion work for quantumconnection be™!en the detectionprocesses at thesetwo events . superluminalparticles as wellas subluminalparticles and light.Although The basiccircuit for a precognitivequantum computer is the gedanken one can extendthe groupof Lorentzboosts in realtime to includecausality ­ experimentdescribed above . It, perhapsin a simplisticmodel of our c,,vn violatingsuperluminal motions be™!en observers , it will not be necessary biocomputer, usesretroactive quantum signals of the third kind in accord to do so in this paper. withHoyle 's intuitions.2 Thesesignals take the extradimensionalroute above Signalsof the secondkind furthersubdivide into a short-wavesuper­ and beyondspace-time . Theseextra dimensions are part of the mathematics luminal tachyonicbranch and a long-wavetransluminal branch relative of fiber bundles used in the unifiedforce th eories.Thus signalsof the to the Comptonwavelength h/me . I postulatethat all elementaryparticles third kinddo propagateuseful messages acros.5 space in the courseof time, of frame-invariantmass m have three possiblemodes of real existence but they do so withoutpropagating modulated energy -momentumas the characteriredby three distinct mass shells for theirrelativistic quantum field carrierof that decodableinformation . Thesuperluminal signaling gedanken propagators. The twonew mass shells (i.e ., energypoles of the propagator) experimentdesign given in this paper is a crucialobjective test of these are typesof conjectures. E2 =P2e2 -m 2e4, p >me (superluminal), (42) 2.2 NewCausality-Violating~ Shells? e Relativisticquantum field theory describes real particlesas "on the mass a shell" and virtualparticles as "off the mass shell." The mass shell cor­ E2 = m 2e4 -p 2e, p < me (transluminal). (43) respondsto a pole in the complexenergy plane in the integrandfor the quantumfield propagator . Theboundary conditions correspond to the choice The superluminalshort -wavebranch represents signals of the secondkind of a contour for the integralin the complexenergy plane . The Feynman in Lorentzianspace-time with spacelikeflows of modulatablereal energy­ 51 k causalcontour allows a Wickrotation of 9()0 in the complexenergy plane momentumoutside the locallight cones . withoutcrossing any obstructivesingularities. This nice featureis lost in 2.3 TransluminalMatter to MakeTraversable Wormholes? SI is quantumgravity. The energypole E moves as the momentump changes. The intelligentconstruction of a traversablewonnhole requires a new 3J The basicforces (strong, electromagnetic , weak,gravity) are causedby vir­ phaseof matterthat violatescausality in the formof "the weakenergy con­ a tual, not real, particles. Realp hotonsare confinedto the lightcone, but dition." Just as the cosmicthermal microwaves are left overfrom the late fl, spacelikevirtual photons are outsidethe lightcone. Indeed , four-momentum stagesof the , this new causality-violating"transluminal phase " sh conservationdemands that the exchangedsingle virtual photon is outside of darkmatter may be a remnantof the "imaginarytime " Riemannian TI the light cone. The commutatorof the photoncreation and destruction quantumgravity era. Hawkingputs the boundarycondition that the universe vii operatorsdoes not vanishoutside the lightcone. Since the photonhas re­ "has no boundary"in this era of imaginarytime . Visiblematter , in a local­ Lo ro frame-invariantmass m, its Comptonwavelength force range h/mc is ly variablycurved but globallyspatially flat pseudo-Riemanniangeometry , an infinite. wouldon ly be 10%of the gravitatingmass of the universe. fra Realsubluminal quantum particles on the mass shell are confinedto That is, the universewould have a dual-metricbase space geometry on hit

324 - JackSarfatti

tile topological,the projectiveand the affineconnection levels of Thisis not a descentto the lcmersymmetry group of Newtonianmechanics of the geometryof the universe.The local tangent group would be but, rather, an ascentto a highersymmetry group beyond the 1905Eins tein than the traditionalLorentz group, since transluminal particles move specialrelativity tangent geometry to the 1915general relativity. .c::t?Jnarytime rather than real time.Yet, transluminal particles must be The translurninallong -wavebranch occurs in what Hawking12 calls a:,scatter off light, subluminaland superluminalparticles moving in "imaginarytime." Hawkingpictures the preinflationaryquantum gravity c:::::lt:This would imply a violationof local Lorentzinvariance in the era as a compactfour-dimensional metric space of signature++++ , which n: that localLorentz invariance implied a violationof localGalilean has a phasetransition to a +++- signaturemetric space . I am suggesting :::mcein 1905. that onlyabout 10% of the ++++ spacebecomes +++-. Thus90% of the ~ arytime is justlike real time and can be measuredby our ordinary massof the universewould still be in the primordial++++ translurninal :ial clocksand radars.The distinctionbetween real and imaginary phaseand \rouldaccount for the dark matterneeded to makethe universe is 10p<>logicalas well as metrical.The signatureof the transluminal spatiallyflat on the cosmologicalscale. Just as the three-degreecosmic mi­ r.s( ++++). Twoobservers in relativemotion measuring the same crowavesare a fos.5ilfrom the decouplingof matterfrom radiationin the :ninalparticle motion must use Euclidean rather than Lorentzframe later stagesof the big bang,so the hypotheticaltrans lurninal dark matter -:nations.The gamma factor for a transluminalframe transfonnation wouldbe a fos.5ilfrom the earlierquantum gravity era . Realtransluminal particles move in imaginarytime. Translurninal clocks time contract.Translurninal particles also stretchinto stringsalong their 2 Y= 1/[ (vlc) + l] Ill. (44) directionof motion. Theyhave a restframe like subluminalparticles and a transcendentframe like superlurninal particles . Translurninalquantum de ;:c::tlatethat a chargedtranslurninal particle in the (++++) metricwill Brogliewaves are longerthan the Comptonwavelength. a real photonalong a null geodesicin the dual Lorentzian(+++-) Freelyfalling transluminal particles fo llow (++++) Riemanniangeo­ ::J::".:XThe problem with traditionalLorentz frame invariance arises when desics.fur example, supposewe havea Schwa!7.SChildsolution for the curved ansider a leynmandiagram in whichtranslurninal world lines connect ·pseudo-Riemannian(+++-) space-timeexterior to a sphericallysymmetric ,ubluminal,lurninal , and superluminalworld lines. This does not subluminalmass. The ~le is to make a Wick rotationon the coordinate ~I a returnto the Galileansubgroup of the Lorentzgroup, but to a timefrom dt to idt to computethe motionof the transluminaltest particle ; cgber groupof the localtangent world geometry in whichthe Lorentz similarlyfor the motionof a subluminal or superlurninaltest particlein :s a subgroup (seeSec. 2.4). the positive-definitemetric of a largetrans luminal source. luemannian space-timeworld lines carry a local metricwith positive­ The cosmologicalequations shou ld be modifiedto includea unifonn signature (++++ ) in imaginarytime that do not sensethe Einstein distributionof translurninalparticles at the criticaldensity . This might of the lightcone. I am assuminghere that space-timehas a dual accountfor the "greatwall ," the "greatattractor ," and for the mysteryof :%::'" Thesetwo metricsmight be limitingcases of a still higher level galaxyfonnation and earlyquasars. - on a hypercomplexmanifold of the kind used in supersymmetry Thematter-free unstable super-cooled vacuum used in the repulsiveanti­ Onemetric has signature++++,the otherhas signature+++-. I gravityinflationary expansion of the earlyreal-time (+++-) universeafter assume that null Lorentzianlightlike geodesics of signature+++­ it leavesthe imaginary-time(++++) quantumgravity era is destroyedin :::c:>.:et++++ signaturetransluminal 'AA>rld lines with +++- signature a phase transition.The spin O pre-Higgsfield goessuperfluid developing llD:!.;.'2 and spacelikeworld lines. Einstein showed the independenceof the a vacuumorder parameter that destroysthe effectivecosmo logicalconstant of light,though not the frequency, on the relativespeed between source drivingthe inflation. Freelepto-quarks and X particlesare spat out in this lhsorber. Thissuggests that transluminalsignals have modulatable real phasetransition to the GUTera. The quarksand coloredgluons are con­ .--momentum flowsaccessible to ordinarydetectors whose 'AA>rld lines finedlater on whenthe elec~ak forcesplits off from the strongforce. ~cted by the lightcone barrier. The problemis that the pre-Higgsfield must be tachyonicand bosonicin - ~ Lorentzframe-dependent topological signature phase transition be­ orderto havethe superfluid symmetry-breakingpotential. If spinstatistics is superlurninaland translurninalparticles occurs at zeroenergy, infinite violatedfor tachyons,then the causality-violatingpre-Higgs field must have · and finiteCompton momentum me. The Lorentzframes correspond spin 1/2 ratherthan spinO in orderto be bosonic.This can be considered 1 subgroupof a highercurved base space (fiber bundle) local tangent as a test of my new theory.The subluminalcausal bosonic spin O Higgs ~ 5>mmetrygroup. That is, Lorentzinvariance of the space-timeinterval particlesthat givethe W,Z quarksand leptonstheir massmust be small latedlocally in the presenceof real translurninalmatter. Lorentz invari­ vibrationsin the spinor-bosonic pre-Higgsrelativistic superfluid. is alreadyviolated globally by generalrelativity. fur example,there is 2.4 Spin-StatisticsViolation and Renormalizationin Quantum -definedcosmological time since the big bangdefined by the "Hubble FieldTheory expansionof the universeand the conditionthat the cosmicphotons The two additionalcausality-violating mass shells are not recognizedin an isotropicblackbody pcmer spectrum with no redshiftsand blueshifts. today'srelativistic . These new mass shells may make - newlypredicted local violation of Lorentzsymmetry is analogousto the the currentrenonnalization algorithm unnecessary. Fictitious particles with ·· n of Galileaninvariance of absolutetime by the highersymmetry of the wrongspin-statistics connection 13 are usedto regularizegauge theories . ..:ZJZ invariance.Note that the Lorentzinvariant d.il is stillframe invari- Thespin-statis tics connectionis imposedby the requirementof causalityand ;.n the low-speedGalilean limit, but the Galileaninvariant df- is not stablequantum vacua. As.5uming the subluminal mass shell , Pauli14 showed ::r-r invariant in the Lorentzianregime of high speeds.There is a new that quantizationof half-integerspinor fields with quantum statistics _-rl symmetryframe invariant including both real and imaginarytime. (i.e.,commutators on creationand destructionoperators) implies unstable

325 Designfor a SuperluminalSignaling Device

quantumvacua (i.e., nonpositive-definite total fieldenergy) . The big bang Dopplershifted. Astronomers 'Mluld misinterpret what they wereseeing for and, possibly,quasars are examplesof unstablequantum vacua. Quantiza­ lackof the propertheory . tion of integerspin fieldswith fermion statistics (anticommutators) implies 2.5 QuantumTune OperatorRequires CausalityViolation superluminalenergy propagation outside the lightcone . Thuswe must expect Up until now, becauseof the energygap (-me'- to +me'-), it has that the newphases of matterwill have the wrongspin-statistics connection. beenimpossible to definea relativisticquantum time operatorcanonically That is, causality-violatingparticles will be scalarfermions , spinorbosons, conjugateto the energyoperato r as normallyrequired by the uncertainty vectorfermions , etc. Pauli's 1941proof of the connectionbet\\een spin and principlein commutatorform. Adjunctionof the new causality-violating statisticsrested on the assumptionof causality(i.e., denial of superluminali­ mass shellsfills this energygap, makingit possibleto consistentlydefine ty) andstability of the quantumvacuum. Neither is reallytrue . I havealready a quantumtime operator. Therefore, su perluminalviolation of causalityis mentionedthe workof Bennetton the breakdownof dispersionrelations. necessaryfor the properdefinition of timeat the quantumlevel. As anotherexample, the vacuumof the earlyuniverse is not stable.Thus fur example, considerthe momentum-positionuncertainty relation which spontaneoussymmetry-breaking is a vacuumphase transition triggered by followsfrom the fact that the commutatorof the two canonicallyconjugate an instabilityin whicha fluctuationis chaoticallyamplified to macroscopic Hermitianoperator (in boldfacebelow ) is ih and the orthocom­ dimensions. pletenessof the eigenstatesfor each.That is, Subluminalparticles obey the spin-statisticsconnection, that is, spin 0 (scalar),1 (vector),and 2 (tensor)are bosonsthat can occupythe same [ q, p] = ih, (45) quantumstate . Spin 1/2 (spinor)and 3/2 (spinor-vector)are fermionsthat obeythe Pauliexclusion principle of no morethan onefermion per quantum PIP) =PIP), (46) state. I postulatethat superluminalparticles violate the spin-statisticscon­ l=~IP)(PI, (47) nection.That is, scalar spin O and vectorspin 1 superluminalparticles (tachyons)are fermions.They are neededto removethe infinitiesfrom the subluminalsector of quantumfield theory which is incompletewithout , P = ~PIP )(pl, (48) them (e.g.,Pauli -Villarsregularization in QEDand Faddeev-Popov"ghosts" in non-Abeliangauge theory). Quantum corrections come from Feynman qlq) =qlq), (49) diagramswith loopsof virtualparticles that causeultraviolet infinities in causalquantum field theory. Including loops of virtualsuperluminal shadow l = ~ lq )(q I, (50) particleswith the oppositespin statistics might make the quantumcorrec­ tionsfinite without going to extradimensions. Indeed, in the path integral q = ~q lq)(ql, (51) formulationit is necessaryto go to the Euclideansignature ( ++++) for a 2 2 2 properdefinition of a convergentpath integral.Perhaps, in that case,one ( f:v/) ( !lp) 2'.:(1/4) (-i [ q, p] )2 = h / 4. (52) shoulduse only transluminalparticles so that there is a finiteultraviolet cutoffat me'-?In myview, superluminal and transluminalparticles are not Orthocompletenessrequires fictitious,and theyhave the sameframe-invariant mass as theirsubluminal partners.Indeed, a uniformcosmological distribution of verycold, slowly (JJ'IP)= o(p' -p), (53) movingneutral real transluminal particles left over from the quantumgrav­ 43 ityera beforethe first 10- s may wellaccount for 90%of the matterin (q'lq) = o(q' -q), (54) the universe.An alternative, wild idea is that the missingmass is not in the formof realparticles at all, but correspondsto a transluminalcosmological (qlp) = exp(i21tpq/h), (55) constantgiving a finiteenergy to an exactlyspatially flat vacuumas the lengthscale approaches the Hubbleradius. Implicit in theseconsiderations (56) is anotherwild idea that the 'Mlrldquantum geometry has a nondifferen­ IP) = ~ lq)(qlp), tiablefractal structure that has self-similarscale invarianteffects all the wayup frombelow the ultramicroPlanck scale to the cosmologicalHubble lq) = ~IP )(Plq). (57) scale.Penrose 1 has pointedout that the transitionfrom the quantumto the classicallimit has somesurprises. An extension of classicalgeneral relativity Theessential point is that in orderto obeythese equations, the eigenvalue to the dual metricis requiredto properlyformulate these speculations. spectrumof the Hermitianoperators for a free pa.rticlewith infini te space J Anotherreason why causality-violating real particles are a goodcandidate boundaryconditions must be continuousfrom -oo to +oo withno gaps. for at leastsome of the missingmass of the universeis that the Pauliexclu­ Finitespace standing-wave boundary conditions give a discretemomentum ,I sionprinciple does not operatefor superluminaland transluminalelectrons, eigenvaluespectrum. fur the caseof the z componentof orbitalangular mo­ protons,and neutrons.Therefore, if thereare high-densityconcentrations of mentumthe conjugateazimuthal angle obeys periodic boundary conditions transluminalstuff, there would be no diverseand complexmany-particle and an uncertaintyrelation is stillpossible because L can go negative.When nuclear, atomic,and molecularshell structures to supportmost of the nor­ the subluminalparticle is not free,there is alsoa discreteenergy eigenvalue mallyobserved electromagnetic quantum jumps. We would still expectto spectrumof boundstates which i s negativewhen the restmass is subtracted see hydrogenspectra, but they'Mluld be superluminallyand transluminally out. fur the relativisticsubluminal free particle, we havenegative energies,

326 JackSarfatti

Clere is a rest mas.sgap from -mc 2 to +mc 2 . This meansthat we of the incidentwave . Physicsgraduate students are taughtthat dispersion defineorthocomplete eigenstates of the relativisticframe-dependent relationsin particlescattering are a theoreticalconsequence of causalityand operatort that is canonicallyconjugate to the energyoperator E. That that experimentsconfinn them . Neitheris true. cannotwrite Bennett4 has shownthat dispersionrelations are violatedby experiment and that theyare not an adequateproof for causality.Bennett also sh™'5 EIE) = EIE), (58) that the originalWheeler-Feynman action-at-a-distance electrodynamics is finiteat thequantum level and has retroactivequantum vacuum fluctuations I= I:EIE)(EI, (59) withfuture causes. The physicsof mas.slesslight is not changedby my new theory. Only the physicsof massiveparticles is changed.It doessuggest, h~r , that E = I:EEIP)(PI, (60) the agreementbetween experiment and theoryfor the dispersionrelations in collisionsinvolving mas.sive particles is , at best, onlyapproximate . Dispersion tit) = t it), (61) relationsshould be violatedwhen Feynman "ghost " diagrams,now properly reinterpretedas the couplingof subluminalparticles with both superluminal 1 = r. lt)(t l, (62) and transluminalparticles, can no longerbe neglected. The interpretationof Kramers-Kronigrelations for lightas evidencefor t = I:itlt)(tl , (63) causalityis logicallyerroneous. That is , theKramers -Kronigrelations are con­ sistentwith adwnced Potentials operating retroactively with a finiterange (tit) 2 (M) 2 ~ (1/4) (-i[ t, E))2 = h2/4, (64) 'to fromthe futureto the present.This can be seenfrom a reexamination of the standardargument for causality, for example,by Pais.on (E'IE) = o(E' - E), (65) "Thus, supposea 'cause' C at timeI - 't contributesto an 'effect' E at ·time t, and that C and 4 are linearlyrelated : (t'lt) = O(t' - t) , (66) E(t ) = [ F(,)C(t -,)d,. (71) (tlE) = exp(i27tEt/h), (67) Causality,'E cannotprecede C', is expressedby IE)= I:ilt)(tlE) , (68) F(t ) = 0 t < 0. (72) It)= I:EIE)(Elt) . (69) A generalmathematical theorem says that thiscondition is equivalentto the following~ statements:the Fouriercomponent G ( co) definedby if that the Fourierintegral representation of the Diracdelta function in -ie requiresthat the domainof the integrationenergy wriable E h:M no ~ in it. This is the essentialreason why a relativistictime operatort G(co) = 1:F(t)e'ro1dt (73) ClililOt be defined,and whythe true natureof the energy-time uncertainty 10 ation<> has remainedcontroversial to this day, can be continued~alytically to complexvalues of ro withIm ro> 0, and +oo has no singularitiesin this region; and G( co) satisfies 8(1'-t) = -oo exp(i21tEtlh)dE. (70) J 1 p [ Im G ( co') d , ,, Re G ( CO=-) , ..., CO. (74) 1t -oo CO-u, The simplequalitative point I wish to raisehere is that includingthe -.;perluminalmas.s shell widens the spaceof energyeigenfunctions and fills HO'M!ver, lookat (72); sincethe integralin (73) is overan infiniteamount ·_,e subluminalmas.s gap. In this sensea properdefinition of time as an of time, it makesno differencemathematically to the Kramers-Kronigproto­ oservableproperty of massiveparticles in relativisticquantum mechanics dispersionrelation (74) if we replace" 't < 0" in (74) by ", < -'to," itf1llS to demandcausality violation. (A time operatorfor the mas.sless i.e., :-10toncan apparentlybe definedwithout causality violation.) .?.6 Contra Dispersion Relations F( 't) = 0, 't < -'t o, (75) Dispersionrelations connect the realand imaginaryparts of thescattering .i.'tlplitudeas a functionof energy.They follow from the Cauchyintegral where'to is the rangeof the "fare/mow/edge."Let us not forgetthat Dirac :.,eoremand the Titchmarshtheorem. It is the Titchmarshtheorem that needsforeknC1,V)edge to eliminate the runawaysolutions in a consistent · thoughtto be the link with causalityin the fonn that the scattered clas.sicaltheory of radiationreaction. Thus it is clear that the validityof ~-:r;ecannot be emittedbefore the incidentwave reaches the scatterer.Closer Kramers-Kronigrelations for lightdoes not logicallydemand causality. That analysisreveals causality to be onlya sufficientcondition and not a necessary is, causalityis a sufficientcondition for dispersionrelations, but it is not a )Ile to applythe Titchmarshtheorem. One can still get the dispersion necessarycondition. I quote,hO'M!ver , an objectionto thisargument raised -:elationseven if the scatteredwave is precognitivelyemitted before the arrival bythe referee:"Choosing a specific'to appearsto implya fixedretrospective

327 Designfor a SuperluminalSignaling Device

time factorthroughout the universe,but tachyonsimply arbitrarily large is coupledto a "cold"positive lattice temperature 7jattice > 0 in a Carnot reversals.This wouldappear to requiremoving 't o in the limit to -oo heatengine, heat Q flows from both spin and latticereservoirs and is entirely causingsome problems." H<>'M!ver , the workof Bennett4is germaneto this convertedto mechanicalwork W Thatis , the efficiencyW/Qsp in > l. There point. is no wasteheat. Furthermore, a tiny heat flowQspm > 0 fromthe negative 2. 7 BoundaryConditions for TachyonicPropagator spin temperaturenetwork can triggera much larger conversionof heat EnergyE and momentump are mathematicallyreal in termsof the Q,attice< 0 to workW fromthe positivetemperature lattice . Thus motionof particlesand waves(accessible to our detectors)for both the short-wavesuperluminal and the long-wavetransluminal mass shellsof WIQspin = [Qspin - .Qiattice]/ Qspin = l + I.Qi~ QspinI the causality-violatingphases of matter.The boundaryconditions on the = 1 +1ian1a/lTspinl> 1. (78) superlurninalpropagator, for example,are the oppositeof Feynman'scausal boundaryconditions for realsublurninal particles on the massshell. Virtual particlesare off the mass shell and correspondto the incoherentnoise in Forexample, let Tsp1n = -0.1 K and let 7jattice= 300 K. The quantum the coherentsignal which is the real particlepole of the propagator. heat engineefficiency is then 3000"/4.This is not a violationbut a quantum 15 Thus,according to Feynman,subluminal particles propagate positive en­ "loophole" in the secondlaw of thermodynamics- a counterintuitive ergyforwards in time and negativeenergy backwards in time.Antiparticles consequenceof it whencombined with the quantumprinciple. Is this how movingforward in time with positiveenergy are then equivalentto parti­ the mind movesmatter , the mind being the spin systemand the lattice clesmoving backwards in timewith negative energies and oppositeinternal beingthe nervecell systemin whichW triggersa nervepulse for a relatively quantumnumbers. tiny quantumspin energyflow? The aboveconsiderations are compatiblewith the viewof Sperry16: "the In contrast,short-wave superluminal particles, that is, "tachyons,"<12> propagatepositive (negative) real energybackwards (forwards) in time.One consciousphenomena of subjectiveexperience do interacton the brain can thendefine antitachyons in Feynman'ssense. The violation of Feynman's processexerting an activecausal influence. . . the contentsof subjective boundarycondition is provedby startingwith a tachyonin the transcendent mentalexperience are recogniz.edas importantaspects of realityin their own right, not to be identifiedwith neural eventsas thesehave have frame K of infinitevelocity, say in the +z directionwhere E = O and heretoforebeen conceived,nor reducibleto neural events.[ emphasis Pz = me. Then make an ordinaryEinstein sublumi nal boostof v < c added]... "the subjectivemental properties and phenomenaare positedto in the +z directionto the frame K'. The velocityaddition law tells us that the tachyonis movingin the -z' directionwith superluminalspeed havetop-level control as causaldeterminants. On theseterms mind moves matter." u' = c2 Iv. Fromthis it followsthat the energyE' of the tachyonin the K'frame is positive: 2:9 The RelativisticRocket Problem and PracticalInterstellar Travel Thomeet al. haveshown that practicalinterstellar travel would be pos­ (76) sibleif traversablewormholes could be foundor manufacturedwith matter H<>'M!ver, the sub-boostin space-timeshows that the tachyonof positive (possiblytransluminal) violating the "weakenergy condition. " Evenwith­ energymust movebackwards in time in the K' frame. K' wassub-boosted out traversablewormholes , h<>'M!ver,there is anotherpossibility for practical parallelto the directionof the tachyon'smotion in the transcendentK frame interstellartravel. Let us considerthe textbook" relativisticrocket" problem (whereall pointson the tachyonworld line are simultaneous,i.e., dt = O). in the contextof this theory.Imagine propelling the relativisticrocket along Similarly,if the sub-boostto K' is antiparallelto the tachyon's motionin a subluminaltimelike lg hyperbolicworld line. Usea "fuel" capableof the transcendentframe K, we get a negativeenergy tachyon moving forwards superlurninal_local exhaust speed u alongspacelike or Riemannianworld in time.Indeed , this willdestabilize the vacuum, but we mayhave evidence lines for tachyonicor translurninalfuel particles,respectively. The energy fromviolent astrophysical phenomena that the vacuumis not stable.There and momentumconservation laws impl y that the ratio of final to initial mustbe somesort of nonlinearsaturation damping out the emissionof real massM ( 't) / M ( 0) requiredfor such a trip of propertime 't along the tachyonsof negativeenergy propagating forwards in time. timelikehyperbolic world line of the rockethas an exponentialdependence The short-wavesuperlurninal free particleeigensolutions do not form on the negativereciprocal of the propellentsuperlurninal exhaust speed u. a completeset becauseof the momentumgap. H<>'M!ver,when the long­ That is, wavetranslurninal eigensolutions are addedto them,we do get a complete M ( 't) / M ( 0) = exp( -g 't/ u). (79) set. Therefore,conservation of probabilityin causality-violatingrelativistic quantumfield theory (yet to be formulatedin detail)is assured. Thelimit of M ( 't) IM ( 0) as u -+ oo is 1. Therefore,the energyefficiency is 2.8 QuantumSpin Thermodynamics Mind-Matter Model onlylimited by how fast the propellent can be ejectedbeyond the lightbarrie r. Supposethat the physicalsubstrate of mind is an intelligentquantum Theseconsiderations coupled with those of Thomeet al. on traversable spinswitching network making a non-Booleanlogic quantum computer. The wormholesshould profoundly modify the SETI(Search for Extra-Terrestrial spinscould be that of the weaklybonding lone protons(e.g., electroposi­ Intelligence)program. tivehydrogens in water)and perhapsunshared electron pairs and mobile 1t electronsin complexbiomolecules. The secondlaw of thermodynamics Acknowledgment impliesthat whena "hot" negativequantum spin temperature I am primarilyindebted to myold Cornell professor,Philip Morrison, for an indeliblegrand visionof physicsthat bridgedC.P. Snow 's "TwoCultures" Tspin< 0 (77) in the 1950s.I have also been stimulatedby directcontact with the late

328 JackSarfatti

!ChardFeynman (1963 and 1969),David Bohm (19 71), and AbdusSalam 973). Ofcourse , I am greatly indebtedto ProfessorHenry Stapp (Lawrence &:rireleyLab) , ProfessorPeter Bussey (University of Glasgow), ProfessorOreste P a:ioni (UCSD), and Dr. NickHerbert . I wouldalso like to acknc,..vledge npo rtant technicalcontributions by CreonLevit (NASA Ames) who insisted t:at it shouldbe possibleto make a superluminalsignaling device in a ~ pierway than a double-slitarrangement by usinga simpleinterferometer . · double-slitarrangement involves a more complicatedspread of phases. :be interferometerhas basically a sharp phasewith some noise. Should experimentsconfinn my prediction, then Herbert, Stapp, Bussey, Piccioni, and Levitdeserve some of the credit, althoughnone of the blameshould it Figure7. The gedankenexperiment. riL signal = sin (2 0) [ 1 - cosq>] ail. ProfessorWaldyr Rodrigues of InstitutoMatematica, UNICAMP {Brazil), whichsurvi\' es evenif (cosq> ) = 0. showedme some unpublished'.mrk by AndreiSakharov on transluminal 'l3.11.iclesin the big bang in 1985when I wasa visitingprofessor . I \muld ike to thank Dr. DavidSarfatti for editinghelp , JagdishMann and Csaba Szabo(Lt . Col.USAR Special Forces), and the U.S. Navy(PACE) for financial 5Upport.I also thank StephenSchwartz and A. LawrenceChickering of the Figure3 and the discussionof Sec. 1.7 assumedthat 5 = 90°. This lnstitute for ContemporaryStudies for their support.Finally, I thank Kim requirementcomplicates the designof the interferometer, becausethe light Burrafatofor bringingthe Optia Guideto my attentionat a significant beamsmust movethrough a dielectricmedium whose index of refraction moment. is largerthan that of the mirrors. This is not a difficultyof principle. Thus the phaseshift of i usedin Eqs. (23) to (30) in Sec. 1.7corresponds to , for example, APPENDIX:EFFECT OF TRANSMITl'ERINTERFEROMETER , REFLECTIONPHASE SHIFfS ON 111B RECEIVERSIGNAL Letus considerthe effectof variablereflection phase shifts at the mirrors (sin2 ~-n - 2 )/ cos2 ~ = 1, (A3a) of the transmitterinterferometer on the localdecoding of the superluminal 2 2 retroactivequantum spin-spin signal at the distantreceiver . Areflection phase sin ~ = [ 1 + n - ] /2, (A4a) shiftof 5 = 180° ratherthan 5 = 9()0 [Sec. 1.7, Fig. 3, Eqs. (23) to (30)], appearsto make Stapp'ssecond objection obviously irrelevant. Firs~ I will for polarizationperpendicular to the planeof incidence. Similarly, 1ustifythe use of the 90° phaseshift for total internalreflection . Second,I v..ill consider the effectof the 180° phaseshift for externalreflection , which considerablysimplifies matters and providesa strikinglyclear counterexample to Stapp'sarguments against faster-than -lightsignaling in standardquantum sin2 ~= 2/(n 2+1) , n 2 >1 , (A4b) mechanics. "Externalreflection is definedas reflectionat an interfacewhere the in­ for polarizationparallel to the planeof incidence. cident beamoriginates in the materialof l~r refractiveindex . ... Internal Thus it is possibleto achievea reflectionphase shift of i if 'M! assume, reflectionrefers to the oppositecase."03a ) "Duringexternal reflection, the as I havedone , that the quantumprobability amplitude phase shifts like the lightwaves undergo a 180° phaseshift . No phaseshift occursfor internal classicalelectric vector does . the motivationfor usingi washigh reflection reflection(except in the caseof total internalreflection) ."03b) fieldintensity efficiency. H~r, if 'M! relaxthat requirement,supposing an Externalreflection way from normal incidenceis generallyinefficient intenselaser pumped pair source,'M! can use externalreflection in which (e.g., about4% reflectance at normalout to 20° incidenceangle ~ in air to 5 = 180° and still get a goodsignal-to-noise ratio at the receiver(Fig. 7) . polishedoptical glass with glass index of 1.52for polarizationsboth parallel Thisdesign choice also makes the transmitterinterferometer much easier to and perpendicularto plane of incidence). In contrast,internal reflection build. Equations(23) to (30) nc,..vbecome becomestotal (i.e., 100%reflectance) for both polarizationsabove a critical 2 angleof 41°121 whenthe ratioof indicesis againn = 1.52. Forexample , 1 = (l, 2 !Vi,v;, .91. . 'B. 'D, 'E) = - (112) cose ei+<), (23') the incidentbeam originatesin the glassfor total reflectionat the air/glass boundary. II= (1, 2 !Vi, Hi, 'B , 'D, 'E) = -(l/2) sin 0 ei+(2l, (24') What is the reflectionphase s hift 5 in the regionof total internalreflec­ tion?The boundaryconditions to Maxwell'selectromagnetic field equations m = (1, 2\Vi. v;, .91., 'B , c, 'E ) = +(112) cose , (25') betweent\m dielectricsgive the Fresnelequations [e .g., Eqs. (11-51)to (11-54), Ref.14, p . 199]: IV= (1, 2 !Vi, H;,'B , C, 'E ) = +(112) sine, (26') (Al) 2 v = (1, 2 \H1, v;, .91., 'B, 'D , 'E ) =+(112) sine ei+<>, (27') if the electricvector is perpendicularto the planeof incidence.lf the electric 1 vectoris parallelto the planeof incidence,then (28)

329 Designfor a SuperluminalSignaling Device

VII= (1, 2 IH1, V{,5t , '1J, C , '£ ) = -(1/2) sin 0, (29') trolledfaster-than-light information transfer is possible.This folio.vs immediatelyfrom the fact that whereaswithin the quantumformal­ ism (or the classicalformalism) the probabilityof a specifiedresult in VIII= (1, 2 IH1, H{, 'B, c, '£ ) = +(112) cos0. (30') one region, subjectto the conditionof a specifiedresult in the other region, dependsin generalon the latterspecification, and henceon the Therefore, experimentalsetting in the other region, neverthelessa summation

I + II + III + IV= -( 1/2) cos0 e;+c2> - ( 1/2) sin 0 ei+'2l overall possiblere.sulls of the experimentin the otherregion with proper weightsgives a resultthat is independentof the choiceof +( 1/2) cos0 + ( 1/2) sin 0 the experimenJalsetting in that region. Thisentails that thereis no predictabledependence of the observationsin one regionupon the = +(1/2){cos e+sin 0}[ 1 - ei+<2>], (ASa) choiceof settingin the other.<1 s)

V+VI+ VII+ VIII= +( 1/2) sin 0 e;+<2> - ( 1/2) cos0 e;+<2> H~r , the abovemodel is a counterexampleto Stapp'sclaim, because evenif we supposethat the sum of cosq> "wi th properweights" p ( q> ) in the - (112) sin 0 + (112) cos0 transmitterregion is done, and furt.liersuppose that my ideaof the (X)/Jeren/ = +(1/2) {cos 0 - sin 0}[ 1 - e;+c2>], (ASb) subensemb/e of Secs.1.9 and 1.10is incorrect,

II+1I+IIl+IV l2 = (1/4){1 +2 cos0sin0}11 -e;+< 2>j2 (cosq> ) = f cosq> p ( q>)dq> = O; (39') = (1/4) {1 + sin 2 0}11 - e;+(2l 12 nevertheless, there is still a "predictabledependence of the observations" in = (1/2){1 +sin20}(1 - cosq>). (31') the receiverregion " uponthe choiceof setting" 0 in the "other"transmitter regionusing only st~dard quantummechanics. Indeed, the superlumi­ Similarly, nal (and retroactivein delayedchoice mode) signalS has the Josephson tunnelingcurrentlike form 2 IV+ VI+ VII+ VIIIl = (114){1 - 2 cos0 sin 0}11 - e;+(2) 12

= (114){l - sin 2 0}11 - e;+<2>j2 S = p ( V, 0) - p (H, 0) = sin 2 0, (41') = (112){l - sin20}(1 - cosq>). (32') in which the misalignment0 betweenthe calcitesacross an arbitrary four-dimensionalspace-time separation between the twodetections of the I claim that Eqs.(31') and (32') makeStapp's second argument obviously photonsin the same individualpair is analogousto the phasedifference of false.The essence of Stapp'ssecond argument (e.g., Sec. 1.9) is that wemust the superconductingorder parameter across a tinynormal barrier. sum overall q>to computethe localreceiver photon detection probabilities. I am assumingthat the quantumwave function is completein describing fur example,Stapp writes: individualquantum systems and is not merelya descriptionof ensembles. The fact that we can now observeindividual trapped ions and that they The failureof the localityproperty in ... quantumtheory ... does conformto quantumpredictions in theirphoton inte ractionsseems to falsify not contradictEinstein 's principlethat no signal travelsfaster than the strictlyensemble inteipretation of the wavefunction. light.fur by a signalis meanta controllabletransfer of information - a message.Within the structureof theseformalisms no such con- Received12 February1990.

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