V O L U M E 4 • N U M B E R 3 • S E P T E M B E R 1 9 9 1 • Physics Essays AN INTERNATIONAL JOURNAL DEDIC�TED TO FUNDAMENTAL QUESTIONS IN PHYSICS PUBLISHED BY UNIVERSI1Y OF TORONTO PRESS FOR ADVANCED LASER AND FUSION TECHNOLOGY, INC. 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 nonstatistical 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" = Le la n) l34 nilz anan70) volume 4, number 3, 1991 * gn for a Superluminal Signaling Device 1.,n M INTERFERENCE COMMUNICATION Abstract A gedanken experiment design far a superluminal (laster than light FJ'L) signaling device using polarization-rorrelated photan pairs emitted back-to-back is given. Only the Feynman rules far standard quantum mechanics are used. 7be new approach is to let the transmitter photan interfere with itself It is then possible to transmit and locally dec,ode superluminal signals by the controllable shifting of quantum photan polarization probabilitks across arbitrary spac,e-time s parations between the detections of the two photons in the same pair. 7be superluminal signal is encoded with the message by rotating a calcite interferometer t ansmitter detector elative to a .fixed receiver calcite detector through angle e or, alternatively, by changing the average interferometer phase ~o. 7be degree of polarization of the light at the receiver detector depends upon these two parameters, e and ~. 7berejare, the message is dec,oded by monitoring the changing degree of linear polarization of the receiver light. 7be principle of C{Jusality that effects are always after causes in all frames of rejerence will be disproved if this device worlzs as predicted. 7be objections of causal paradoxes and proofs f arbidding superluminal signaling are addressed. 7be second part of the paper begins a study of the effect of causality violation on the rest of pbysics. RJr example, possible violations of the spin-statistics ronnection and local Lorentz intariance by dark matter, a relativistic quantum lime operator, a new view of infinities in quantum field theory, traversable wormholes as time machines, and quantum spin thermodynamics of the mind-matter* interaction are some of the topics discussed. Key words: superluminal signaling, causality-violating relativity, time travel paradoxes, quantum consciousness proceeds a if the past were the home of explanation; whereas ~ and the future alone, holds the key to the mysteries of the cisco's Bohemia (North Beach), eccentric and beyond the cutting edge of, for example, Paul Davies' excellent collection New P/Jysi<:S. Nevertheless, the referee has courageously written: "The actual gedankenexperiment is for superluminal information transfer of a type different from the FIASH proposal of Nick Herbert. Although I intuitively agree with Stapp's feeling5 (referred to in the paper), the design is significantly different from Herbert's and has a contribution of value in the documentation of possible designs of superluminal signalling devices which can be subject to discussion and criticism by the physics community. Thus, although I think that this design will probably suffer the same fate as Herbert's FLASH, I believe it should be published in a form which makes it available for critical scrutiny and discussion. This process either results in a new potential device or helps to complete the case against such devices through the subsequent discussion, as Herbert's example in Foundations of Physicr has done." -: Dwight Sedgwick, "House of Sorrow," An Apology for Old Maids (1908) there is even something vaguely teleological bout the effects ~ ness, so that a future impression might affect a past action. Roger Penrose, F.R.S., 7be Emperor's New Mind1 * to me that biological systems are able in some way to utilize isite time-sense in which radiation propagates from future to E.zzare as this may appear, they must somehow be working :tis in time. f;ed Hoyle, F.R.S., 7be Intelligent Universe (Endnote 2, p. 213). the reader. The point of view about the nature of physics that I :e is controversial, not respectable in either style or substance in academia, spawned in the romantic Caffe Trieste of San FranI am predicting a startling new phenomenon, hitherto thought to be impossible in principle the distant and/or retroactive control of polarization of photons (and spin of massive particles) via nonlocal quantum correlations as the communication channel. My essential intuition in the following quantitative model is not difficult to grasp. In the simplest case, for two pho315 Design for a Superluminal Signaling Device tons 1 and 2 emitted back-to-back, let the two doubly refracting crystals be perfectly aligned. The results of linear polarization (V and If) measurements, when neither photon is allowed to interfere with itself (Fig. 1), are computed from the pure spin-entangled pair state [1V)1 IV)2 + IH)1 IH)2 l / ../2. The distant correlations of photon 1 to orthogonal spin states of photon 2 ensure that photon 1 is completely unpolarized in local measurements. Now, on the other hand, suppose (in analogy with the well-known spin-flip technique in one path of a neutron interferometer, and the Berry-Chiao phase technique using a coiled optical fiber that adiabatically rotates the plane of polarization of a photon) that we can coherently and adiabatically disentangle the above pair state without collapsing it into the new form [1V)1 IV)2 + IH)1 IV)z] I ../2 = [ IV)1 + IH)d IV)z/ ../2. We do this by letting photon 2 interfere with itself and rotating its polarization by 90° in one of the two interfering paths (Fig. 3). The two photons are no longer spin-correlated. Each has its own spin state. But now, photon 1 is completely polarized at 45° to the common orientation of both aligned crystals. Compare this new situation to the old one where photon 2 did not interfere with itself a choice which forced photon 1 into a mixed unpolarized density matrix with one bit of positive ntropy. On the other hand, when we choose to make photon 2 interfere with itself in concert with the adiabatic rotation of polarization in one branch of the interferometer, we have then made the opposite choice which forces photon 1 into a pure polarized zero-bit entropyless tate. That is, the choice of forcing photon 2 to interfere with itself properly transmits a negative entropy bit of information to photon 1 and its measuring apparatus. furthermore, the metric space-time interval between the choice for photon 2 (which is the cause) and the polarization for photon 1 (which is the effect) is irrelevant. The nonlocal quantum spin geometry is premetrical. The space-time interval between active cause and passive ffect can be spacelike corresponding to superluminal communication, or it can be arranged to be timelike with delayed choice in which the cause is in the frame-invariant future of the effect. Indeed, there is a conflict with the axiom of causality of relativity, although not with the classical tests of time dilation and velocity-dependent mass. In Ref. 1 Mermin discusses recent work by Greenberger, Horne, and Zeilinger ( GHZ) on three-particle correlations that go beyond the two-particle correlations of Einstein, Podolsky, and Rosen (EPR) as extended by Bohm and Bell. This new theoretical work provides the basis for a crucial experiment that can show the existence (or nonexistence) ofwhat Einstein called "spooky action-at-a-distance" without a statistical analysis of many measurements. Mermin<2> writes, "Thus in one simple version of the two-particle EPR experiment the hypothesis of elements of reality [i.e., local causality] requires a class of outcomes to occur at least 55.5% of the time, while quantum mechanics allows them to occur only 50"/4 of the time. In the GHZ experiment, on the other hand, the elements of reality [i.e., local causality] require a class of outcomes to occur alt of the time, while quantum mechanics never allows them to occur." There is nothing wrong with the EPR criterion of reality "If, without in any way disturbing a system, we can predict with certainty the value of a physical quantity then there exists an element of physical reality corresponding to this physical quantity." What is probably false-to-fact is the assumption "without in any way disturbing the system." In addition, there is the problem that if quantum action at a distance is real, can it be controlled within standard quantum mechanics? That is the main focus of this paper. Josephson<3> suspects that living matter does manage to control quantum nonlocality, but in a way that is beyond the formal structure of present316 day quantum mechanics. I agree that living matter probably does control quantum nonlocality, but that the way in which it does so can be understood using present-day quantum mechanics. What has to be profoundly modified, in my view, is not quantum mechanics, but the causal axiom of relativity without abandoning the fundamental symmetry of relativity that the laws of nature should be independent of the frame of reference. 1.1 New Kinds of Signals? The nonstandard istinction between signals of the first, second, and thinl kind is developed in more detail in Sec. 2 of this paper. H~ver, briefly, I adopt the modern fiber bundle extension of world geometry as used in the gauge theory of fundamental forces. Subluminal and luminal signals of the first kind obey causality and involve decodable nergy flows inside and on the light cone, respectively. Superluminal and retroactive signals of the second kind violate causality in a "globally self-consistent" way3 and involve decodable nergy flows outside the light cone, and similarly for signals of the thinl kind, which the following edanken experiment purports to generate. For causality-violating si nals of the thinl kind, the communication channel is the controllably nonlocal quantum correlations in the extra dimensions of internal fiber spaces beyond space-time. There is now compelling experimental evidence for the breakdown of causality in the dispersion relations for the scattering of gamma photons off protons.4 I claim that controllable nonlocality is part of standard quantum mechanics and that proofs tatint othelWise are incorrect. Signals of the thinl kind will, of necessity, involve nergy flows; in the present case they are on the light cone, but these flows within four-dimensional space-time are not the channel where the information isencoded transmitted and decoded. The channel is in the extra nonmetrical "fiber" dimensions beyond space-time in the sense of gauge theory5 rather than the extra curled-up metric dimensions of KaluzaKlein theory. Finally, "transluminal" signals of the fourth kind occur in a shadow Riemannian metric of signature ++++ left over from the quantum gravity era of the early universe (to be discussed further in Sec. 2). Signals of the thinl kind may be involved as the essential quantum mechanism of ordinary consciousness. Penrose, 1 in a remarkable analysis, has led me to conclude that our common assumption of morally responsible "free will" demands controllable retroactive (backwards-in-time) action of the mind on matter by about two seconds in onier to agree with EEG experiments. If-we choose to hold on to the traditional notion of past cause and future effect, then we must be mere automatons with no free will. That is consciousness of our actions is after the action. Causality then implies that consciousness i a passive piphenomenon and not an active decision maker. This is not a view that I find to my liking. 1.2 Stapp's First Argument Against Superluminal Quantum Signals of the Third Kind Consider the basic pair-correlation experiment6 involving spin correlations. A pair source S emits pairs of spin-spin correlated particles 1 and 2 moving "back-to-back" in opposite directions to detectors A and B, respectively (see Fig. 1). One kind of simple no-faster-than-light (FTI.) signal argument7 is due to Stapp in a private communication. Stapp's analysis involves the use of projection operators. Suppose the pure pair quantum state is 11, 2) . I.et the projection operators for the spin eigenvalues ofeach detector be PA(B)±; then some of the nonlocal joint probabilities p are p(A+IB+) = (!, 2IPA+Ps+ll, 2), (1) + 1 ~7 2 :e I. Basic pair Correlation experiment. The nonlocal parameter is the l-it:l\\ttn the spin-sensitive detectors at the times the particles in the pair are detected. For this total experimental arrangement he local probabilities are 1/2 independent of the nonlocal parameter. Therefore, ;::.tnIUm signal of the third kind is not pos.5ible with this design. However, are other pos.5ibilities. p(A+IB-) = (1, 2IPA+Ps-ll, 2). (2) of these joint probabilities i what is actually measured in experiments ::-elating the outputs after the fact. Measurement of joint probabilities lhe fact does show a m quantum spin-spin connection that violates 1 l the principle of causality expressed by Bell's inequality. However, mierally accepted that this type of quantum causality violation called .:n::aurollable quantum nonlocality" cannot be used for useful quantum _.:::eruminal communication of the third kind, which, by definition, is in time." sufficient (but not necessary) condition for useful quantum superlumiaxun unication of the third kind is that the local probability, for example - , changes as some controllable nonlocal parameter is changed. Imag- :a sequence of twin pulses of photon pairs. The observer at receiver A would see the response of his detector in the + spin eigenvalue change in time caused by a change in the relati\'e orientation of , transmitter detector at 8. ~ pulse width must be small compared to the flight times from source 300 rs. The nonlocal parameter must not be changed during the time takes a single pulse to be detected. There must be enough photon ft-oduced in each twin pulse to get a good signal-to-noise ratio in the ,;. The nonlocal parameter must be changed in a time that is short • :l:.'d to the flight times. It must also be changed bel'M!en the arrivals s:xre;.sive pulses. t"ie flight times are equal, then the transmission and reception of .il!On is essentially instantaneous in the rest frame of the apparatus. components of the apparatus are assumed to be at rest relative to *lier. Now, let the flight time from pair source S to transmitter 8 be than the flight time to receiver A. The choice of nonlocal parameter .... 8 can be delayed until after pulse 1 has been detected at receiver * 'lefore its twin pulse 2 has been detected at transmitter 8. The past "' at receiver A is then caused by a future cause at B. This would be ~. violation in the strongest sense imaginable. a phenomenon would place hitherto unsuspected limits on free will. ,g to Godel, any attempt to create a causal paradox in a universe * ie travel would be doomed to failure: " ... time travel is pos.5ible, but ~ will ever manage to kill his past self. . .. The a priori is greatly ;_ Logic is \'ery powerful." Thus metaphorically there would have to ,. .. sort of nonmetrical transtemporal globally self-consistent ype of .u an arbitrary space-time distance in which controllably nonlocal Jack Sarfatti quantum forces prevent a logical contradiction. Thome et a/.3 have discussed this pos.5ibility in the context of time travel to the past through traversable wormholes. Returning to Stapp's argument that retroactive communication is not pos.5ible at the quantum level, p (A+) =P(A+IB+) +p (A+IB-) = (1, 2lhJJs+ ll, 2) + (1, 2IPA+Ps-lI, 2) = (!, 2IPA+Ps+ P A+Ps-11, 2) = ( !, 2 IPA+ (Ps+ + Ps- ) II, 2) = (!, 2 IPA+l l, 2) because of the completenes.c; of the spin eigenstates of transmitter B, Pa+ +P6_ = l , (3) (4) and its associated conservation of local probability at 8. Therefore, there is no dependence of the local recei\'er probability p(A+) on any eigenvalue or nonlocal parameter that depends on 8. Therefore, superluminal communication by quantum spin pair correlations is impos.5ible. This completes Stapp's first argument against superluminal quantum signals of the third kind. , 1.3 The Flaw in Stapp's First Argument First of all, it must be admitted that Stapp's analysis does correctly describe the results of all actual experiments done so far with photon pairs that test Bell's inequality. The photon pair state for these experiments predicts that Therefore, p (A+IB+) = (112) cos2 e, p (A+IB-) = (l/2) sin2 e. p(A+) = (1!2)(cos2 0+sin 2 0) = 1/2 (5) (6) (7) independent of the angle 0. So, indeed, there is no superluminal communication. However, Stapp's equation p(A+) =P(A+IB+) +p(A+ IB-) (8) is an equation from classical probability theory that ignores the pos.5ible interference of quantum amplitudes. This is the flaw in Stapp's analysis. It does not apply to total experimental rrangements in which at least one of the photons in the same pair interferes with itself. For the experiments actually done, howe\'er, it is the correct equation. This foll<Yw'S from Feynman's quantum rules. 1.4 Feyrunan's Quantum Rules (l) Square the amplitudes before adding for distinguishable alternatives. (2) Add the amplitudes before squaring for indistinguishable alternatives. In the basic pair-correlation experiment here are two photon counters at each detector, which is basically equivalent to a doubly refracting calcite crystal. Therefore, all the nonlocal alternatives, (A+, B+), (A+, 8-) , (A-, 317 Design for a Superluminal Signaling Device receiver transmitter + 1 2 + 0 :=m* 0~ - \. ~:~re~ ~ ..___ e l/2wave plate Figure 2. Pair correlation interference experiment. The transmitter photon 2 interferes with itself and causes a controllable shift in the polarization of its far-away twin receiver photon l that depends upon the angle between the calcite crystals at the moments of detection, and upon the phase shift in the transmitter interferometer. B+), and (A- , B-), are distinguishable. Hence Stapp's equation is justified for this class of total experimental rrangements. But is it justified for all possible xperiments? No, it is not (see Fig. 2). There is now a new parameter qi in the experimeñ the translational phase difference of the two indistinguishable alternatives for transmitter photon 2. Experiments with neutron interferometers show that it is possible to construct an x spin state from the coherent interference of two orthogonal +y and -y spin states. On the other hand, with photons we know that a, double-slit experiment with orthogonal linear polarirers at each slit destroys the interference fringes. That does not, in principle, mean that coherent interference is not happening in the photon case. Indeed, the interference shows up in the change of polarization state at different points of the screen. In some places there will be left-handed circular, in other places right-handed circular, etc. This only means that a more sophisticated kind of measurement would need to be done at the screen of the double slit to detect coherence from orthogonally polarized paths. The experiment we are interested in does not depend upon whether there are interference fringes for photon 2 at the transmitter B. What we really care about is whether the degree of linear polarization of a stream of photons 1 at the receiver A can be controlled at a distance from B. This nonlocal control would be achieved by keeping the orientation of A fixed but rotating B relative to A in time. I have placed a half-wave plate in one ann of the interferometer. Interference fringes will be seen if the half-wave plate is in place for ordinary uncorrelated light. In fact, however, local interference fringes will not appear at the transmitter even if the half-wave plate is in place. This is because there are two mutually out-of-phase nonlocal interferograms corresponding to the distinguishable alternatives of receiver photon 1 at A. These two nonlocal interferograms< 4> could be resolved after the fact by coincidence analysis. Their existence might be exploited for an untappable, unbreakable quantum cryptographic military intelligence application. However, this cryptographic application has nothing to do with the present problem of superluminal signaling. I mention it in passing for its intrinsic interest. Feynman's rules for the present interference pair correlation experiment imply that we must add the amplitudes (1, ZIA+, B+) and t(qi)(l, ZIA+, 8-) before squaring. Similarly, we must add the amplitudes (1, 2 IA-, B+) and t(qi) (1, ZIA-, 8-) before squaring. What do we get after we square? What we get is a pair of nonlocal joint probabilities that photon 1 takes a particular channel at A and that its twin photon 2 is detected at B with a definite translational phase difference qi. 318 Are we justified in ignoring the space-time dependence of the pair amplitudes? Experiment suggests that we are. There is no evidence of a weakening in the strength of (A+B+) coincidence correlation as the separation between the detectors is increased. This (A+B+) correlation is 1/2 cos2 0 in the unattainable ideal case of 100% efficient detection. More experiments are needed. It appears that the spin-correlated pair wave function simply multiplies two independently moving uncorrelated space-time wave packets for each photon. This would be consistent with Ne'eman's already quoted fiber bundle picture5: "The two y rays should have their spin polarizations adding up to rero (and to negative total intrinsic parity) when observed whatever the AB distance. . . . in a fiber bundle geometry, the manifold is constrained so as to preserve parallelism whatever the magnitude of the base space interval." That is, the relevant quantum connection in this case is entirely in spin-fiber space beyond space-time. The problem for superluminal signaling is how to correctly take the sum of distinguishable alternatives over all possible places where the transmitter photon 2 can be absorbed at B. This is the basis for Stapp's second argument against superluminal communication of the third kind. Stapp's motivation is the true fact that coherent interference r distributes the conserved local probability density. If one integrates the interference cross terms over all possible places where the single transmitting photon might be absorbed, then the cross terms integrate to zero. What Stapp fails to realire is that not all these places ar&relevant incomputing the controllable nonlocal quantum action-at-a-distance on the far-away twin receiver photon. If the dependence of the difference in the local receiver probabilities p (A+) p(A- ) on 0 (i.e., the superluminal signal of the third kind) survives the sum over qi, then we are in the superluminal communication business. If that turns _out to be the case, we can manipulate the degree of partial polarization of receiver light at a distance from the future in a delayed-choice mode of operation of the device. The message vxmld then be contained in the encoding modulating function 0(12) , which maps to the decoding modulating function 0(11 + [L2 -Lil l e), where (9) and L1 and L2 are the spatial distances of the detectors A and B from the source S, respectively. So, if L2 > L1 , the cause at time T2 is in the future of the effect at time t1 . That is, the degree of polarization of the receiver light at A at time /1 is the function F of time /2: p(A+ , ti) -p(A- , ti) =F{0(t 1 + [Lz -L1] / c)}. (10) Analyrers A, B and source S are all relatively at rest along the line of flight of the photon pair. One way of encoding the message at B is by a variable rotation d0/ dt of the entire B assembly about the axis of the line of flight. However, I will calculate F explicitly for the gedanken experiment given below, and we will see that there is an easier way to do it using the qi dependence. 1.5 The Photon Pair State Start with the standard photon pair state actually used in and confirmed by experiment. The photons are emitted back-to-back in opposite directions with total angular momentum rero. Consider a double quantum jump of an atomic electron for which the emitted photon pair state is even under parity mirror imaging. Therefore, for linear polarizations the directions of '.'(llarization are parallel. The directions of rotation for circular polarizations are opposite (for one observer looking from a fixed point of view). The Jelicities (projections of spin along momentum) are the same. Odd parity ~r states have perpendicular linear polarizations. All this is independent of how far apart in space or time the detections of each photon in the same pair are. The Einstein-Podolsky-Rosen (EPR) paradox consists in precisely this fact together with the realization that we do not have to decide until the jst instants prior to the detections whether to locally measure circular 'lOlarization or, alternatively, linear polarization in any direction (transverse :o the line of flight). No matter what we arbitrarily decide, the far-away :ihotons will always how parallel linear polarizations or opposite circular "IOlarizations (equal helicities). Each photon "knows" how the other photon .s being measured. Suppose we have only one photon passing two polarizers. The first polar- .zer prepares the photon in a given spin state. The second polarizer analyzes :he prepared state. This is easy to understand locally. A similar thing happens ronlocally for our photon pair. Photon l passes a polarizer A. Not only does 1. localy prepare photon l in a definite state with probability l/2, it also . 'ln/ocally prepares its distant twin photon 2 in the same state as the one :1Ctually allegedly randomly chosen for photon I. Therefore, when photon : encounters its polarizer at B, it will simply be analyzed in the state in nich A prepared it at a distance. Analyzer A's preparation of photon 2 Clll be in the future of photon 2's encounter with analyzer B. The situation totally symmetrical. We can say that B prepares photon l at a distance, hich is then analyzed by A, etc. Thus, start from the (R, L) circular polarization frame of reference in m fiber space beyond space-time for a single observer looking from a fixed int of observation along the line of flight. ~ote that '1'1 (x,) 'lf2 (x2) are the two uncorrelated wave packets of each r-"oton moving in opposite directions in space. Their function is simply to 0:liver the photon energies to the detectors. They do not carry the message modulated energy flows the way that they do for signals of the first and .u>nd kind. Their role in the m spin fiber signal of the third kind is a::essary but secondary: 'x>tons are bosons, and, therefore, the wave functions for several identical ,otons must be totally symmetric in all the quantum numbers. However, the present case the two photons in the same pair have nonoverlapping :e packets with different peak frequencies and different line widths and, -.:refore, are not identical. Thus the photon pair function (l l), though --nmetrical in spin space, need not be so in physical space. ~take a spin fiber frame shift to a particular linear polarization basis \". H) and substitute IL) = (1/ v'2) [ IV) + i IH)] , IR) = (l/ v'2)[ IV ) i IH)], I 2) = (l/2 v'2)[ {IV,)+ ilH1) }{JV2) ilH2)} (12) (13) Jack Sarfatti Now, make two arbitrary independent local frame shifts from the totally arbitrary commr:m (V, H) basis of both photons to the bases (Vi, H1) and ( V{, H;). These bases correspond to the actual orientations 0A Ct1) and 0s Ct2) of the calcite crystals at A at time t1 and B at time /2 where, as defined above, t1 = t2 - (L2 -Li)lc . (16) Substitute IV2) = cos 0s(/2) IV{)+ sin 0s('2) IH{), (19) IH2) = sin 0s(/2) IV{)+ cos 0sU2) IH{). (20) Define the nonlocal modulation parameter (21) and let us agree to keep the receiver orientation 0A (/1) fixed in time in what follows when we get to m communication. Familiar trigonometric identities give us the useful form of the photon pair state I 1, 2) in terms of the_ actual orientations of the birefringent calcite crystals at the detectors A and B. That is, II, 2) = ( 1/ v'2) [ cos 0( 1 2) {IVi )1V{)+IH1 )IH{)} +sin 0(1 2) {!Vi )IH{) IH1 )IV{)}] '1'1 (x1) '1'2 (x2). (22) There is no need to worry about the relativistic collapse of the wave function.(5) If one wishes to imagine that the wave function collapses instantly, then there is no problem with relativity, because we are explicitly assuming that causality is wrong. future causes are allowed. But even more importantly, we can do away with the notion of instantaneous collapse. Operationally we have two measurements made at an arbitrary space-time separation from each other. As Wheeler says, "no quantum phenomenon is a phenomenon until it is an observed phenomenon." Thus what we are talking about is not even defined until both detections are made. There is no independent way to detect he collapsing wave function between the two detections. It is a pseudoproblem. What we have, here, is a nonlocal, nonmetrical global quantum phenomenon, which is basically happening beyond space-time. It is premetrical t a deeper level, that is, a bigger Klein-Erlanger group8 than the Lorentz group metrical geometry of relativity. 1.6 The Gedanken Experiment In Fig. 3 a half-wave plate converts IH{) to IV{) at the transmitter. A half-silvered mirror is at the transmitter crossing point 'B. Those transmitter photons 2 whose twin photons 1 are detected in the Vi charmel will form a nonlocal interferogram on the transmitter screen; similarly for those transmitter photons 2 whose twin photons 1 are detected in the H1 channel. fully reflecting mirrors (;:I, C , '1J) bring these two mutually out-of-phase nonlocal interferograms to a small region '£ on the transmitter screen. 319 Design for a Superluminal Signaling Device i phase change on each reflection receiver Figure 3. The gedanken experiment. Thus no fringes will be visible at the transmitter screen for pair-correlated light. Fringes would be visible if the source emitted uncorrelated photons 2 with the same spectral ine shape and spatial coherence of photon 2 in the pair-correlated case. As already mentioned< 4) above, the two nonlocal interferograms can be disentangled from each other by coincidence measurements for one photon pair in the system at a time. 1.7 The Feynman Photon Pair Probability Amplitudes The relative phase difference between the interferograms acquired between the crossing point '13 and '£ on the screen is q>( 2) . There is a phase shift of i for each reflection, and an extra factor of 1/ ,/2 from the half-silvered* mirror at '13 . The Feynman path amplitudes are I= (1, 21Vi, v;, 51, '13, 'D, '£) = (112) cos0(1-2)i 3e;q,<2>, (23) II = (1, 21 Vi, H{, '13, 'D, 'E) = ( 1/2) sin 0(1 2) ie;q,<2>, (24) III= (1, 2IVi, V{,51, '13, C, '£) = (1/2) cos0(1-2)i 2 , (25) IV= (!, 2 IVi, H{, '13, C, 'E) = (112) sin 0(1 2) i 2 , (26) V = (1, 2 IH1, v;, 51, 'B, 'D, 'E) = -(112) sin 0(1 2) ;3eiq,<2>, (27) VI = ( 1, 2 IH1, H{, 'B, 'D , 'E ) = (112) cos 0(1 2) ieiq,(2), (28) VII = (1, 2 IH1, v;, 51, '13, C, 'E) = -(112) sin 0(1 2) ; 2 , (29) VIII = (1, 2 IH1 'H{' '13' C' 'E) = (112) cos 0(1 2) i 2 . (30) The Feynman rules of standard quantum mechanics tell us to add the amplitudes before squaring for indistinguishable alternatives, and to square the amplitudes before adding for distinguishable alternatives. Clearly, with the above total experimental rrangement, the eight alternatives form two distinct sets of indistinguishable alternatives (nonlocal interferograms), that is, {I, II, III, IV} and {V, VI, VII, VIII}. The first set corresponds to a measurement of receiver photon 1 in the I Vi ) state. The second set corresponds to the receiver photon in the IH 1 ) state. Therefore, p:(Vi, 0(1-2) , q,(2)) = II+Il+Ill+IV J2 = (112)( 1 cos 2 0(1 2) sin q>( 2)), (31) p'_ (H1, 0(1 2), q>( 2)) = IV+Vl + VII + VIIIl2 = (112)( 1+cos20(1 2) sin q,(2)]. (32) 320 These are the nonlocal joint probabilities for coincidence measurements in which the receiver photon 1 is observed to have polarization eigenvalue Vi (H1), and its twin transmitter photon 2 is observed to land on the screen with translational phase difference q>( 2) when the calcite crystals are misaligned by the nonlocal angle 0( 1 2) connecting the two arbitrarily separated etection events. 1.8 The Transmitter Phase Noise The superluminal signal at the receiver is derivable from the difference between these squared pair amplitudes when properly summed over all relewnt values of the phase difference q>( 2) . This is the crux of the debate. The controversy is over hem to perform this sum. fur this particular experimental rrangement the overlap area '£ is small. The L is the variable path difference between 'B'D'E and 'BCE , that is, L = ( 'B'D'E - 'BCE) . fur uniform index of refraction q,(2) = 2 rrLn/ 'A.2, L < c!n'ov2, (33) (34) (35) that is, the path difference L must be smaller than the coherence length of the transmitter photon wave packet g (x2) . The fluctuation in q>( 2) is &p. It is due to variations in three variables, L, n, and 'A.2 , that is, (36) Therefore, ifwe choose a particular Lo obeying the wherenc:e wndition Eq. (35), we have some mean <l>o-The relevant range of q> integration is then <l>o ±&p. 1.9 The Error in Stapp's Second Argument Against Superluminal Signals Henry Pierce Stapp of the Lawrence Berkeley Laboratory, in private communication, has objected that a superluminal interference signal violates conservation of local probability p(2) for the transmitter photon 2. This second objection is that after properly performing the sum over all places where the transmitter photon 2 might be absorbed on the screen, the dependence of the local receiver probabilities p(V) and p(H) (see Fig. 3) on the misalignment angle 0( 1 2) will cancel. This would destroy the nonlocal quantum signal. On the contrary, I argue that while all places where the transmitter photon 2 can be absorbed o contribute to conserving the local probability p ( 2) , many of those places do not contribute to the nonlocal signal p(V) p(H) in the far-away spacelike separated receiver egion. Only a subset of those places where photon 2 might land contribute to the detection probability of its twin photon l . That is, the waves arriving at '£ at the transmitter must wherently interfere in order to produce the signal at the far-away receiver. Like the quantum signal in the Josephson effec~ the superluminal signal is essentially a macroscopic quantum interference phenomenon using photon pairs, rather than electron pairs. The second objection, however, was in the context of a double-slit arrangement, not the arrangement of Fig. 3 in which the phase variation q> is more tightly controlled. Thus &p is understood to mean the uncertainty in phase coming from that wherent subset of places where the transmitter photon might be absorbed in which the waves from paths 'B'D'E and 'BCE are still mutually wherent. If they are not coherent, then they have = no controllable nonlocal effect at the spacelike separated receiver, although !hey certainly figure in conselVing local probability p(2) at the transmitter -creen. 1.10 Normalization of the Transmitter Photon Probabilities Firs~ nonnalize the transmitter photon probability density in area 'E of CJherent interference of the waves from the alternate paths in the intererometer. Take the point of view of the local observer at the transmitter <aeen. If a transmitter photon 2 arrives, it could have its spacelike separated fflll receiver photon arrive in either the Vi channel or the H1 chan1 el. These are distinguishable, noninterfering altemati\'es, because there is separate photon counter in both the Vi and H1 channels. Therefore, ~ un-normalized transmitter photon probability density at the screen ::a.-ea 'E is simply the sum ofp'(Vi , 8(1 2), 8(2)) withp'(H 1, 8, ( 1 2), $( 2))) from Eqs. (31) and (32). This sum is 1 and is the reason ii1I) no local interference fringes are seen with pair-correlated light. On the <lher hand, the normalized probability densities p (Vi, 8( 1 2) , $( 2)) nl p (H1, 8( I 2), $( 2)) conserve local probability only for the subset * coherent photon pairs whose transmitter photon 2 interferes with itself. C ".'Jv that coherent subensemble of photon pairs contribute to the nonlocal ma! of the third kindp(V) p(/{J. Photon pairs whose transmitter photon does not interfere with itself belong to a different incoherent subensemble, ::ich does not contribute to the nonlocal signal. These incoherent pairs are :-:-elevant to the computation of the sum over all places where the transmit- ~ photon 2 might land within the coherent region of 'E . Therefore [call 8 I 2) simply 8, and $(2) simply $l. Therefore, 1 +.,+6+ d$[p(V,8,$) +p(H,8,$)] = 1. +o-6+ (37) p(H(V) , 8,$) = [l ± cos28sin$]/4oq>. (38) ""e sum over transmitter phases that suroives at the spacelike separated "'.:U:lver is t +s+ ~ q>) = d$sin$[p(V , 8,$) +p(H , 8, $)] +o-6+ 1 +.,+6+ d$ sin$ . = '°-6+ 2 oq, = sin $0 si~oq> ~ sin $0 sin coq>. (39) Jearly, the average of sin $ over the transmitter photon nonnalized '1:lbility distribution for $ in the coherent subregion of 'E on the screen ~ generally zero. In fac~ it depends on the average transmitter interferoer phase difference $o and its actual uncertainty oq, due to fluctuations ;.,e relevant experimental parameters. have assumed that the alternatives for different $ are noninterfering, they correspond to an irreversible absorption of a photon completing 'lleasurement or "making a record." That is, one can consider the screen -:. a retinalike array of photon detectors. 11 The Superluminal Signal at the Receiver Thus the superluminal receiver signal S is the degree of partial linear nzation of the receiver photon, which is the difference of the local ..ibilities p (H , 8) and p ( V, 8) , that is, p(H(V) , 0) = {'°+6+ dq,p(H(V), 0, $) leo-6+ = 1⁄2 [I± cos 20(sin $)] Jack Sarfatti = 1⁄2 [ 1 ± cos 28 sin $o sin coq>], ( 40) S =P(H , 8) -p(V , 0) = cos20sin$o sincoq>. (41) Equation ( 41) says that the degree of linear polari7.ation of the receiver photon can be controlled acros.5 spacelike (even timelike) intervals at a distance, indeed, even badzwards in time. Note that the signal S can be modulated by either varying 8 or $0. As a practical matter it \\Uuld be much easier to modulate S by changing $o with fixed 8. Notice, also, that local probability is clearly conserved on both sides of the apparatus, even though there is a nonlocal superluminal signal. 1.12 Competing Designs form Communicators The first published "FU.SH" design is by Herbert.<6> It is generally believed to be unworkable, because the proposed "photon-cloning" laser amplifying decoding mechanism appears to violate the superposition principle of quantum mechanics. H~r , the basic idea that Herbert had is interesting and can, perhaps, be made to 1.mrk. Herbert's idea is totally different from the one proposed in this paper. The reason Herbert's idea may eventually be made to '.mrk is the recent progress in dJaos. Thus it may be that sequences of individual quantum events (IQE's) that directly feel the quantum connection are not really random, but contain universal hidden fractal orders whose locally observable signatures depend in a controllable way upon distant actions. This general approach is also alluded to as "symmetric-time," which is at a deeper level than irreversible "directed-time".rn Thus "All combinatorial choices made under symmetric ausality are consistent with the quantum probability interpretation of directed causality. [p. 141] ... A complex dual process may be consistent with quantum mechanics imply by virtue of its pseudorandomness, despite having a unique selection property over space-time. [p. 143 J" There are practically no experiments on this very fundamental problem. Herbert accepts the standard notion that it is impos.sible in principle to shift quantum probabilities at a distance. I am denying that the sequence of quantum events at one end of the photon pair experiment need always be uncontrollably random for all possible total experimental arrangements. It is further asserted that the departure from randomness of the sequence of quantum events can be controlled from an arbitrary distance acros.s pacetime without he local action of a Hamiltonian. Quantum probabilities are locally shifted all the time by energy tlc,.vs. What is novel is the shift of quantum probabilities by pure information tlc,,vs in fiber space without corresponding energy tlc,.vs in base space-time. Herbert believes that the quantum connection only acts controllably at the level of individual quantum events (IQE's) and is washed out in the statistical average over many events. On the contrary, I am asserting that the quantum connection can be used to controllably shift the averages from a distance and that one does not have to go beyond standard quantum mechanics to achieve all this. One simply has to use Feynman's rules and a little bit of physical intuition. Svozil, <s> of the Institute for Theoretical Physics in Vienna, has a variation on FLASH that he calls SL\SH (second-laser-amplified superluminal hookup). Herbert's FU.SH had the laser amplifier at the receiver. Svozil's laser amplifier 321 Design for a Superluminal Signaling Device time Figure 4. Autocidal causal anomaly using tachyon signals. If R receives YES, then T transmits NO to S. If R receives NO, then T transmits YES to S. If S receives YES, S transmits YES to R. If S receives NO, S transmits NO to R. This results in a self-referential paradox like the ones considered by Bertrand Russell and Alfred North Whitehead in Principia Mathematie,a nd which finally led to Godel's incompleteness theorem. is at the transmitter. While Svozil does not use interference, his gedanken experiment is more like the one in this paper than like FIASH. Svozil is not working at the hidden-variable level, but is attempting to use standard quantum mechanics to shift the receiver quantum probabilities at a distance. Svozil has not yet published his idea so that it would not be appropriate to discuss its details here. 1.13 Autocidal Causal Anomaly (The following section was written in an earlier draft received by Physics &says before I knew of the recent work on the global self-consistency of events on the closed time like cuives ( CTC)3 generated by traversable wonnholes built with matter violating the weak energy condition. Note that I give essentially the same sort of criterion in terms of Feynman histories that Thome et al. now advocate.) Suppose we use signals of the second kind (see Fig. 4). This is not essential; the same apparent paradox arises with signals of the third kind in the gedanken experiment above. The causal order of earlier-later between spacelike separated events T and S outside each other's light cones is subjective, changing with the frame of reference of the observer. The same is true of S and R. But the net result is a retroactive signal backwards in time from T to R which is objectively separated by a frame-invariant time-like interval. Figure 4 follows Penrose's1 Fig. 5.32, p. 213. Suppose the equipment is 100% reliable. This is the same as supposing that we have absolute free will. Then, indeed, if there are not parallel universes, there is a paradox. But both of these assumptions can be wrong. first, suppose that there are no parallel universes. There is only one unique universe. In that case the nonlocal quantum force can act at a 4-D distance and cause an error in order to keep the loop in time logically self-consistent. This is the position taken both by Hoyle1 and by the late GodeJ.9 In this extreme case the equipment will fail 100°/4 of the time somewhere along the line. That is, any attempt to create a time-travel paradox will induce malfunctions in the equipment. R>r example, R can receive NO, T can transmit YES; if that happens, Swill malfunction. Or, another alternative, R receives NO, an error occurs so that T transmits NO and S does not make an error. We can use Feynman's path quantum mechanics to describe all this. Every possible history has a quantum amplitude. 7be Feynman amplitudes for those bistories that are self-contradictory simply vanish. This is no more peculiar than, for example, the Pauli exclusion principle, which selects 322 Universe I cross-talk ){ ts coherent phase parallel worlds are cross sections of the bundle Figure 5. Doubly connected loop in time has topology of the double-sheeted Riemann surface linking parallel universes (sheets), and suppresses the autocidal causal anomaly. out only antisymmetric states for systems of identical fennions. Quantum phenomena are inherently nonlocal, and nonlocality ensures self-consistent loops in time. Let us also remember that there are two important cases of classical nonlocality, that is, precognitive charged particle motions avoiding runaway solutions in Maxwell theory, and the nonlocality of gravitational energy in general relatiJity. We simply have to get used to nonlocality. Let us suppose that there are parallel universes. This is the only interpretation that seems reasonable in quantum cosmology where we need a "wave function of the universe." In the standard parallel universe interpretation the copies of the same mind in different paralel universes cannot cross-talk to each other. Penrose has come to doubt this restriction1 and so do 1.* It is easy to see, using fiber bundle inspired pictures, that the causal anomaly induces cross talk or a doubly connected quantum loop in time. The double loop resembles the double-valuedness of the spinor under 2 7t rotations of the frame of reference. Figure 5 shows only one of several ways to connect he parallel universes into a self-consistent doubly-connected loop in time. The same topological idea is used in the theory of Riemann surfaces of functions of a complex variable (i.e., Jz). There, the point is to convert he multivalued function into a single-valued function. The demand for single-valuedness i analogous to our demand for nonlocal or global self-consistency. The two points of view, that is, a single universe with malfunctioning simple loops in time and parallel universes with doubly connected loops in time, are actually equivalent. In Fig. 5 the mind clones, thinking they are only in one universe I (or II), will perceive that S functioned without error, but that there was an error in the RT link. R>r example, the mind clone trapped in universe II will perceive the following sequence of events: R receives NO, but there is an error when T transmits NO to S, which correctly sends NO to R. So, we can have simple loops in time with errors, like multivalued complex functions, or we can have doubly connected loops in time linking nonnally unlinked parallel universes with no errors. Take your pick! 2. RELATIVITY wrmour CAUSALI'IY You know, I have recently lost confidence in the principle of no action at a distance ... Einstein to Ernst Straus, Some Strangeness in /be ProportfonC9l s g ,s ~ 1t 1d s: :h :s, ps ke Physics today only recognil.es the existence of what I call the signal i the first kind." This is a one-way signal in the direction of time's arro.v that conveys useful messages from a past state of a transmitterr'!llitter to a future state of a receiver-absorber. Messages are communicated * * the controlled modulation of four-vector energy-momentum along either * "Jlelike or lightlike 'M>rid lines. The energy-momentum flow for real particles everywhere either inside or on the local light cone, even in curved space- . "Jle. Therefore, the direction of causation from past to future is a framel;lriant distinction. It is interesting to note, however, that virtual photons :t."e not confined to the light cone. Indeed, in the exchange of a single rtual photon between t'M> charges, four-momentum conservation requires .: :U the virtual photon is spacelike outside the light cone. Thus the near ld Coulomb force really is superluminal although this particular effect Cllll1ot be used to transmit useful messages. It is the principle of causality that effects are always after causes in all fr:unes of reference that places the speed of light barrier in Einstein's classical ""ry of special relativity.10 However, the principle of causality is to relativity Euclid's fifth axiom of a unique parallel to a line through a point not the line is to geometry. Thus causality is an additional postulate to the smunetry group of special relativity. The classic tests of special relativity of ie dilation and mass-energy equivalence do not depend upon the causality pNUlate. Furthermore, the argument for causality from dispersion relations ID quantum field theory on both an experimental nd theoretical level has questioned by Bennen.4 He shows that dispersion relations for gamma- ~ scattering are badly violated by experiment and that there are sound ('!2.5()llS why they should be. Furthermore, recent 'M>rk by Thome et al. 3 at Tech and Novikov et al. 3 in Moscow show that Einstein's gravitational M! equations permit a new class of "tra\'ersable 1M>rmhole" (TW) solutions 6tinc t from black hole and Einstein-Rosen bridge solutions. Provided that eXotic form of matter that permits superluminal energy flows can be .:id, the 1W's can be constructed and used for practical interstellar t avel3 * for time travel to the past. A principle of "global self-consistency on -ed timelike curves" is invoked to avoid the causal paradoxes that "change ?ast." Indeed, the position taken by Thorne and Novikov etal. regarding ~ ty paradoxes is very close to that taken independently in earlier drafts :..'lis paper (e.g., 1.13 above). \.haronov et al.11 have also published a gedanken experiment with quan- retroactivity acting backwards in time. They also show how the super- :.ions of \veak forces can cause a strong force leading to a new kind quantum amplifier. The general idea is that special superpositions of flllm inputs can, though very rarely, produce an output far outside the -:ain of the inputs. .?. l Loops in Tune ""be merging new causality-violating paradigm can be glimpsed in King's :.::irks on "supercausal" loops in time.rn The above gedanken experiment Eered as a counterexample of claims that standard quantum mechan- .a ooes not allow decodable superluminal and retroactive messages using ::.:::s:em-Podolsky-Rosen spin-spin pair correlations. My claim is that the , gedanken experiment gives causality-violating testable super-causal =e:narusms that reproducibly generate "loops in time"2 of the third kind. ~ in time of the first kind correspond to the use of traversable 'M>rmto move objects backwards in time on globally self-consistent closed * 'M>rld lines. Loops in time of the second kind use superluminal propagating energy on spacelike world lines. Loops in time of the _ kind use Einstein-Podolsky-Rosen-Bohm nonlocal quantum spin pair Jack Sarfani correlations to transmit decodable information backwards in time using only lightlike world lines for energy propagation. These loops of the third kind described in the gedanken experiment of this paper can be used for the local decoding in the past of useful messages transmitted from the future in a way that is free from time travel paradoxes. I must first define new types of signals that are not recognized by physics today. The new notion of causality-violating traversable 1M>rmholes that can selfconsistently transport objects backwards in time (like the "flower from the future" in a story by Jorge Luis Borges called "The Flower of Coleridge," Other Inquisitions) 'M>uld correspond to a loop in time of the first kind, since it takes place in the base space of the 1M>rld geometry on closed timelike world lines. If a man could pass through Paradise in a dream, and have a fla,ver presented to him as a pledge that his soul had really been there, and if he found that fla,ver in his hand when he a'M>ke Ay! and what then? ... Wells' protagonist travels physically to the future . .. . More incredible than a celestial fla,ver or the flower of a dream is the flower of the future, the unlikely flower whose atoms now occupy other spaces and have not yet been assembled. Jn contrast, the gedanken experiment in Sec. 1 1M>uld bethe mechanism for the loop in time of the third kind described by another Borges tory, "The Dream of Coleridge" (Other Inquisitions). A thirteenth-century Mongolian emperor dreams a palace and then builds it according to his dream; an eighteenth century English poet (who could not have known that the structure was derived from a dream) dreams a poem about the palace. In comparison with this symmetry, which operates on the souls of sleeping men and spans continents and centuries, the levitations, resurrections, and apparitions in the sacred books are not so extraordinary. . . . Perhaps the series of dreams has no end, or perhaps the last one who dreams will have the key. . . . Perhaps an archetype not yet revealed to men, an eternal object (to use Whitehead's term), is gradually entering the world; its first manifestation was the palace; its second was the poem. Whoever compared them. 1M>uld have seen that they \vere essentially the same. In this paper I present highlights of new predictions in relativity. I will present a more detailed mathematical investigation of relativity without c,ausality in a sequel to this paper. Relativity without causality is intended to be the new tangent group geometry for general relativity. My conjecture is that relativity without causality, which includes Hawking's "imaginary time,"12 is what is missing in the current attempts to make a coherent quantum gravity theory. I have adopted "the realistic philosophy of most working scientists"6 and have opted for the strategy of "dramatically revising our concept of space-time"6 in reconciling quantum nonlocality with relativity . Causal signals of the first kind do not break the speed light barrier. However, causality-violating si nals "of the second kind" do break the light barrier (see Fig. 6). Signals of the second kind transfer information by energymomentum flows that are somewhere, though not necessarily everywhere, spacelike outside of the local light cone. Signals of the first and second kind have the common feature that they propagate nergy and momentum along 1M>rld lines of various types within space-time. There is still a third type of signal "of the third kind" using 323 Design for a Superluminal Signaling Device sptn fibers beyond spacc~ttmc past Figure 6. Fiber bundle picture of signals of first (I), second (II) and third (III) kind. I and II are modulated energy flows conveying messages. III is pure information flow conveying messages without corresponding energy flow. controlled quantum nonlocality in fiber Hilbert space beyond space-time. This quantum signal does not propagate nergy-momentum along world lines in space-time. Ne'eman5 has shc,,vn how nonlocal spin-spin correlations fit into the world fiber bundle picture. Space-time is the base space of the world fibered by Hilbert spaces of various kinds. In a quantum signal of the third kind local probabilities at space-time vent A are controllably shifted from an arbitrarily separated space-time vent B because of the nonlocal fiber quantum connection beTM!en the detection processes at these two events. The basic circuit for a precognitive quantum computer is the gedanken experiment described above. It, perhaps in a simplistic model of our c,,vn biocomputer, uses retroactive quantum signals of the third kind in accord with Hoyle's intuitions.2 These signals take the extradimensional route above and beyond space-time. These extra dimensions are part of the mathematics of fiber bundles used in the unified force theories. Thus signals of the third kind do propagate useful messages acros.5 space in the course of time, but they do so without propagating modulated energy-momentum as the carrier of that decodable information. The superluminal signaling gedanken experiment design given in this paper is a crucial objective test of these types of conjectures. 2.2 New Causality-Violating~ Shells? Relativistic quantum field theory describes real particles as "on the mass shell" and virtual particles as "off the mass shell." The mass shell corresponds to a pole in the complex energy plane in the integrand for the quantum field propagator. The boundary conditions correspond to the choice of a contour for the integral in the complex energy plane. The Feynman causal contour allows a Wick rotation of 9()0 in the complex energy plane without crossing any obstructive singularities. This nice feature is lost in quantum gravity. The energy pole E moves as the momentum p changes. The basic forces (strong, electromagnetic, weak, gravity) are caused by virtual, not real, particles. Real photons are confined to the light cone, but spacelike virtual photons are outside the light cone. Indeed, four-momentum conservation demands that the exchanged single virtual photon is outside the light cone. The commutator of the photon creation and destruction operators does not vanish outside the light cone. Since the photon has rero frame-invariant mass m, its Compton wavelength force range h/mc is infinite. Real subluminal quantum particles on the mass shell are confined to 324 timelike world lines inside the light cone. H~ver , virtual subluminal particles off the mass shell are not confined to timelike world lines. They can be outside the light cone with exponentially damped probability of range equal to the Compton wavelength. In contrast, real superluminal particles on a new branch of the mass shell are on spacelike world lines outside the light cone. Virtual superluminal particles can be inside the light cone also with exponentially damped probability. Thus both the subluminal and superluminal particles feel the Einstein barrier in real time. Subluminal particles obey causality, but superluminal particles do not. Superluminal particles do not have a rest frame. They do have a transcendental frame in which their speed is infinite, their energy is rero, and their momentum is finite. They also have a special frame in which their speed is J2e and their real gamma factory= 1/ [ (vi e) 2 l] 112 is 1 (v I c > 1 ) . Gamma is greater than 1 for e < v < ,./2 e. Gamma is less than 1 for v > JZe. Superluminal particles lose energy as they accelerate. They time contract and length dilate into three-dimensional strings along their motion above J2 e. Freely falling superluminal particles follow spacelike geodesics in pseudo-Riemannian curved space-time. Superluminal particles have quantum de Broglie waves that are shorter than their Compton wavelength. Their energy varies from rero to infinity. ~ use the same special ,relativity formulas for superluminal particles as for subluminal particles. Only the gamma factor is different. The Lorentz transformations beTM!en observers in subluminal relative motion work for superluminal particles as well as subluminal particles and light. Although one can extend the group of Lorentz boosts in real time to include causalityviolating superluminal motions beTM!en observers, it will not be necessary to do so in this paper. Signals of the second kind further subdivide into a short-wave superluminal tachyonic branch and a long-wave transluminal branch relative to the Compton wavelength /me. I postulate that all elementary particles of frame-invariant mass m have three possible modes of real existence characterired by three distinct mass shells for their relativistic quantum field propagators. The two new mass shells (i.e., energy poles of the propagator) are E2 =P2e2 -m 2e4, p >me (superluminal), (42) E2 = m 2e4 -p 2e, p < me (transluminal). (43) The superluminal short-wave branch represents signals of the second kind in Lorentzian space-time with spacelike flows of modulatable real energymomentum outside the local light cones. 2.3 Transluminal Matter to Make Traversable Wormholes? The intelligent construction of a traversable wonnhole requires a new phase of matter that violates causality in the form of "the weak energy condition." Just as the cosmic thermal microwaves are left over from the late stages of the big bang, this new causality-violating "transluminal phase" of dark matter may be a remnant of the "imaginary time" Riemannian quantum gravity era. Hawking puts the boundary condition that the universe "has no boundary" in this era of imaginary time. Visible matter, in a locally variably curved but globally spatially flat pseudo-Riemannian geometry, would only be 10% of the gravitating mass of the universe. That is, the universe would have a dual-metric base space geometry on e a 51 k SI is 3J a fl, sh TI vii Lo an fra hit tile topological, the projective and the affine connection levels of of the geometry of the universe. The local tangent group would be than the traditional Lorentz group, since transluminal particles move .c::t?Jnary time rather than real time. Yet, transluminal particles must be a:, scatter off light, subluminal and superluminal particles moving in c:::::lt: This would imply a violation of local Lorentz invariance in the n: that local Lorentz invariance implied a violation of local Galilean :::mce in 1905. ~ ary time is just like real time and can be measured by our ordinary :ial clocks and radars. The distinction between real and imaginary is 10p<>logical as well as metrical. The signature of the transluminal r.s (++++). Two observers in relative motion measuring the same :ninal particle motion must use Euclidean rather than Lorentz frame -:nations. The gamma factor for a transluminal frame transfonnation Y= 1/[ (vlc) 2 + l] Ill. (44) ;:c::tlate that a charged translurninal particle in the (++++) metric will a real photon along a null geodesic in the dual Lorentzian ( +++-) ::J::".:X The problem with traditional Lorentz frame invariance arises when ansider a leynman diagram in which translurninal world lines connect ,ubluminal, lurninal, and superluminal world lines. This does not ~I a return to the Galilean subgroup of the Lorentz group, but to a cgber group of the local tangent world geometry in which the Lorentz :s a subgroup (see Sec. 2.4). luemannian space-time world lines carry a local metric with positivesignature ( ++++) in imaginary time that do not sense the Einstein of the light cone. I am assuming here that space-time has a dual :%::'" These two metrics might be limiting cases of a still higher level on a hypercomplex manifold of the kind used in supersymmetry One metric has signature++++, the other has signature+++-. I assume that null Lorentzian lightlike geodesics of signature +++- :::c:>.:et ++++ signature transluminal 'AA>rld lines with +++signature llD:!.;.'2 and spacelike world lines. Einstein showed the independence of the of light, though not the frequency, on the relative speed between source lhsorber. This suggests that transluminal signals have modulatable real .--momentum flows accessible to ordinary detectors whose 'AA>rld lines ~cted by the light cone barrier. - ~ Lorentz frame-dependent topological signature phase transition besuperlurninal and translurninal particles occurs at zero energy, infinite * and finite Compton momentum me. The Lorentz frames correspond 1 subgroup of a higher curved base space (fiber bundle) local tangent ~ 5>mmetry group. That is, Lorentz invariance of the space-time interval lated locally in the presence of real translurninal matter. Lorentz invariis already violated globally by general relativity. fur example, there is -defined cosmological time since the big bang defined by the "Hubble expansion of the universe and the condition that the cosmic photons an isotropic blackbody pcmer spectrum with no redshifts and blueshifts. newly predicted local violation of Lorentz symmetry is analogous to the ** n of Galilean invariance of absolute time by the higher symmetry of ..:ZJZ invariance. Note that the Lorentz invariant d.il is still frame invari- ;.n the low-speed Galilean limit, but the Galilean invariant dfis not ::r-r invariant in the Lorentzian regime of high speeds. There is a new _-rl symmetry frame invariant including both real and imaginary time. Jack Sarfatti This is not a descent to the lcmer symmetry group of Newtonian mechanics but, rather, an ascent o a higher symmetry group beyond the 1905 Einstein special relativity tangent geometry to the 1915 general relativity. The translurninal ong-wave branch occurs in what Hawking12 calls "imaginary time." Hawking pictures the preinflationary quantum gravity era as a compact four-dimensional metric space of signature ++++, which has a phase transition to a +++signature metric space. I am suggesting that only about 10% of the ++++ space becomes +++-. Thus 90% of the mass of the universe would still be in the primordial ++++ translurninal phase and \rould account for the dark matter needed to make the universe spatially flat on the cosmological scale. Just as the three-degree cosmic microwaves are a fos.5il from the decoupling of matter from radiation in the later stages of the big bang, so the hypothetical translurninal dark matter would be a fos.5il from the earlier quantum gravity era. Real transluminal particles move in imaginary time. Translurninal c ocks time contract. Translurninal particles also stretch into strings along their direction of motion. They have a rest frame like subluminal particles and a transcendent frame like superlurninal particles. Translurninal quantum de Broglie waves are longer than the Compton wavelength. Freely falling transluminal particles follow (++++) Riemannian geodesics. fur example, suppose we have a Schwa!7.SChild solution for the curved *pseudo-Riemannian (+++-) space-time exterior to a spherically symmetric subluminal mass. The ~le is to make a Wick rotation on the coordinate time from dt to idt to compute the motion of the transluminal test particle; similarly for the motion of a subluminal or superlurninal test particle in the positive-definite m tric of a large transluminal source. The cosmological equations hould be modified to include a unifonn distribution of translurninal particles at the critical density. This might account for the "great wall," the "great attractor," and for the mystery of galaxy fonnation and early quasars. The matter-free unstable super-cooled vacuum used in the repulsive antigravity inflationary expansion of the early real-time (+++-) universe after it leaves the imaginary-time ( ++++) quantum gravity era is destroyed in a phase transition. The spin O pre-Higgs field goes superfluid eveloping a vacuum order parameter that destroys the effective cosmol gical constant driving the inflation. Free lepto-quarks and X particles are spat out in this phase transition to the GUT era. The quarks and colored gluons are confined later on when the elec~ak force splits off from the strong force. The problem is that the pre-Higgs field must be tachyonic and bosonic in order to have the superfluid symmetry-breaking potential. If spin statistics is violated for tachyons, then the causality-violating pre-Higgs field must have spin 1/2 rather than spin O in order to be bosonic. This can be considered as a test of my new theory. The subluminal causal bosonic spin O Higgs particles that give the W, Z quarks and leptons their mass must be small vibrations in the spinor-bosonic pre-Higgs relativistic superfluid. 2.4 Spin-Statistics Violation and Renormalization in Quantum Field Theory The two additional causality-violating mass shells are not recognized in today's relativistic quantum field theory. These new mass shells may make the current renonnalization algorithm unnecessary. Fictitious particles with the wrong spin-statistics onnection 13 are used to regularize gauge theories. The spin-statistics connection is imposed by the requirement of causality and stable quantum vacua. As.5uming the subluminal mass shell, Pauli14 showed that quantization of half-integer spinor fields with boson quantum statistics (i.e., commutators on creation and destruction operators) implies unstable 325 Design for a Superluminal Signaling Device quantum vacua (i.e., nonpositive-definite total field energy). The big bang and, possibly, quasars are examples of unstable quantum vacua. Quantization of integer spin fields with fermion statistics (anticommutators) implies superluminal energy propagation outside the light cone. Thus we must expect that the new phases of matter will have the wrong spin-statistics onnection. That is, causality-violating particles will be scalar fermions, spinor bosons, vector fermions, etc. Pauli's 1941 proof of the connection bet\\een spin and statistics rested on the assumption of causality (i.e., denial of superluminality) and stability of the quantum vacuum. Neither is really true. I have already mentioned the work of Bennett on the breakdown of dispersion relations. As another example, the vacuum of the early universe is not stable. Thus spontaneous symmetry-breaking is a vacuum phase transition triggered by an instability in which a fluctuation is chaotically amplified to macroscopic dimensions. Subluminal particles obey the spin-statistics onnection, that is, spin 0 (scalar), 1 (vector), and 2 (tensor) are bosons that can occupy the same quantum state. Spin 1/2 (spinor) and 3/2 (spinor-vector) are fermions that obey the Pauli exclusion principle of no more than one fermion per quantum state. I postulate that superluminal particles violate the spin-statistics onnection. That is, scalar spin O and vector spin 1 superluminal particles (tachyons) are fermions. They are needed to remove the infinities from the subluminal sector of quantum field theory which is incomplete without them (e.g., Pauli-Villars regularization i QED and Faddeev-Popov "ghosts" in non-Abelian gauge theory). Quantum corrections come from Feynman diagrams with loops of virtual particles that cause ultraviolet infinities in causal quantum field theory. Including loops of virtual superluminal shadow particles with the opposite spin statistics might make the quantum corrections finite without going to extra dimensions. Indeed, in the path integral formulation it is necessary to go to the Euclidean signature ( ++++) for a proper definition of a convergent path integral. Perhaps, in that case, one should use only transluminal particles o that there is a finite ultraviolet cutoff at me'-? In my view, superluminal and transluminal particles are not fictitious, and they have the same frame-invariant mass as their subluminal partners. Indeed, a uniform cosmological distribution of very cold, slowly moving neutral real transluminal particles left over from the quantum gravity era before the first 1043 s may well account for 90% of the matter in the universe. An alternative, wild idea is that the missing mass is not in the form of real particles at all, but corresponds to a transluminal cosmological constant giving a finite energy to an exactly spatially flat vacuum as the length scale approaches the Hubble radius. Implicit in these considerations is another wild idea that the 'Mlrld quantum geometry has a nondifferentiable fractal structure that has self-similar scale invariant effects all the way up from below the ultramicro Planck scale to the cosmological Hubble scale. Penrose1 has pointed out that the transition from the quantum to the classical limit has some surprises. An extension of classical general relativity to the dual metric is required to properly formulate these speculations. Another reason why causality-violating real particles are a good candidate for at least some of the missing mass of the universe is that the Pauli exclusion principle does not operate for superluminal nd transluminal electrons, protons, and neutrons. Therefore, if there are high-density concentrations of transluminal stuff, there would be no diverse and complex many-particle nuclear, atomic, and molecular shell structures to support most of the normally observed electromagnetic quantum jumps. We would still expect to see hydrogen spectra, but they 'Mluld be superluminally and transluminally 326 Doppler shifted. Astronomers 'Mluld misinterpret what they were seeing for lack of the proper theory. 2.5 Quantum Tune Operator Requires Causality Violation Up until now, because of the energy gap (-me'to +me'-), it has been impossible to define a relativistic quantum time operator canonically conjugate to the energy operator as normally required by the uncertainty principle in commutator form. Adjunction of the new causality-violating mass shells fills this energy gap, making it possible to consistently define a quantum time operator. Therefore, superluminal violation of causality is necessary for the proper definition of time at the quantum level. fur example, consider the momentum-position u certainty relation which follows from the fact that the commutator of the two canonically conjugate Hermitian operator observables (in boldface below) is ih and the orthocompleteness of the eigenstates for each. That is, [ q, p] = ih, (45) PIP) =PIP), (46) l=~IP)(PI, (47) , P = ~PIP )(pl, (48) qlq) =qlq), (49) l = ~ lq )(q I, (50) q = ~q lq)(ql, (51) ( f:v/) 2 ( !lp) 2 2'.: (1/4) (-i [ q, p] )2 = h2 / 4. (52) Orthocompleteness requires (JJ'IP) = o(p' -p), (q' lq) = o(q' -q), (qlp) = exp(i21tpq/h), IP) = ~ lq)(qlp), lq) = ~IP )(Plq). (53) (54) (55) (56) (57) The essential point is that in order to obey these equations, the eigenvalue spectrum of the Hermitian operators for a free pa.rticle with infinite space boundary conditions must be continuous from -oo to +oo with no gaps. Finite space standing-wave boundary conditions give a discrete momentum eigenvalue spectrum. fur the case of the z component of orbital angular momentum the conjugate azimuthal angle obeys periodic boundary conditions and an uncertainty relation is still possible because L can go negative. When the subluminal particle is not free, there is also a discrete nergy eigenvalue spectrum of bound states which is negative when the rest mass is subtracted out. fur the relativistic subluminal free particle, we have negative nergies, J ,I Clere is a rest mas.s gap from -mc 2 to +mc 2 . This means that we define orthocomplete eigenstates of the relativistic frame-dependent operator t that is canonically conjugate to the energy operator E. That cannot write EIE) = EIE), (58) I= I:EIE)(EI, (59) E = I:EEIP)(PI, (60) tit) = t it), (61) 1 = r. lt)(t l, (62) t = I:itlt)(tl , (63) (tit) 2 (M) 2 ~ (1/4) (-i[ t, E) )2 = h2 /4, (64) (E'IE) = o(E' E), (65) (t'lt) = O(t' t) , (66) (tlE) = exp (i27tEt/h), (67) IE)= I:ilt)(tlE) , (68) It)= I:EIE)(Elt) . (69) if that the Fourier integral representation f the Dirac delta function in -ie requires that the domain of the integration energy wriable E h:M no ~ in it. This is the essential reason why a relativistic time operator t ClililOt be defined, and why the true nature of the energy-time uncertainty ation< 10> has remained controversial to this day, J +oo 8(1'-t) = -oo exp(i21tEtlh)dE. (70) The simple qualitative point I wish to raise here is that including the -.;perluminal mas.s hell widens the space of energy eigenfunctions and fills *_,e subluminal mas.s gap. In this sense a proper definition of time as an oservable property of massive particles in relativistic quantum mechanics itf1llS to demand causality violation. (A time operator for the mas.sless :-10ton can apparently be defined without causality violation.) .?.6 Contra Dispersion Relations Dispersion relations connect he real and imaginary parts of the scattering .i.'tlplitude as a function of energy. They follow from the Cauchy integral :.,eorem and the Titchmarsh theorem. It is the Titchmarsh theorem that * thought to be the link with causality in the fonn that the scattered ~-:r;e cannot be emitted before the incident wave reaches the scatterer. Closer analysis reveals causality to be only a sufficient condition and not a necessary )Ile to apply the Titchmarsh theorem. One can still get the dispersion -:elations even if the scattered wave is precognitively mitted before the arrival Jack Sarfatti of the incident wave. Physics graduate students are taught that dispersion relations in particle scattering are a theoretical consequence ofcausality and that experiments confinn them. Neither is true. Bennett4 has shown that dispersion relations are violated by experiment and that they are not an adequate proof for causality. Bennett also shTM'5 that the original Wheeler-Feynman action-at-a-distance el ctrodynamics is finite at the quantum level and has retroactive quantum vacuum fluctuations with future causes. The physics of mas.sless light is not changed by my new theory. Only the physics of massive particles is changed. It does suggest, h~r , that the agreement between experiment and theory for the dispersion relations in collisions involving mas.sive particles is, at best, only approximate. Dispersion relations hould be violated when Feynman "ghost" diagrams, now properly reinterpreted asthe coupling of subluminal particles with both superluminal and transluminal particles, can no longer be neglected. The interpretation of Kramers-Kronig relations for light as evidence for causality is logically erroneous. That is, the Kramers-Kronig relations are consistent with adwnced Potentials operating retroactively with a finite range 'to from the future to the present. This can be seen from a reexamination of the standard argument for causality, for example, by Pais.on "Thus, suppose a 'cause' C at time I - 't contributes to an 'effect' E at * time t, and that C and 4 are linearly related: E(t ) = [ F(,)C(t -,)d,. (71) Causality, 'E cannot precede C', is expressed by F(t ) = 0 t < 0. (72) A general mathematical theorem says that this condition is equivalent to the following ~ statements: the Fourier component G ( co) defined by G(co) = 1: F(t)e'ro1dt (73) can be continued ~alytically to complex values of ro with Im ro > 0, and has no singularities in this region; and G ( co) satisfies R G ( ) 1 p [ Im G ( co') d , ,, e CO=- , . .., CO. 1t CO-u, -oo (74) HO'M!ver, look at (72); since the integral in (73) is over an infinite amount of time, it makes no difference mathematically to the Kramers-Kronig protodispersion relation (74) if we replace "'t < 0" in (74) by ", < -'to," i.e., F( 't) = 0, 't < -'t o, (75) where 'to is the range of the "fare/mow/edge." Let us not forget hat Dirac needs foreknC1,V)edge to eliminate the runaway solutions in a consistent clas.sical theory of radiation reaction. Thus it is clear that the validity of Kramers-Kronig relations for light does not logically demand causality. That is, causality is a sufficient condition for dispersion relations, but it is not a necessary condition. I quote, hO'M!ver, an objection to this argument raised by the referee: "Choosing a specific 'to appears to imply a fixed retrospective 327 Design for a Superluminal Signaling Device time factor throughout he universe, but tachyons imply arbitrarily large reversals. This would appear to require moving 'to in the limit to -oo causing some problems." H<>'M!ver, the work of Bennett4 is germane to this point. 2. 7 Boundary Conditions for Tachyonic Propagator Energy E and momentum p are mathematically real in terms of the motion of particles and waves (accessible to our detectors) for both the short-wave superluminal and the long-wave transluminal mass shells of the causality-violating phases of matter. The boundary conditions on the superlurninal propagator, for example, are the opposite of Feynman's causal boundary conditions for real sublurninal particles on the mass shell. Virtual particles are off the mass shell and correspond to the incoherent noise in the coherent signal which is the real particle pole of the propagator. Thus, according to Feynman, subluminal particles propagate positive nergy forwards in time and negative nergy backwards in time. Antiparticles moving forward in time with positive nergy are then equivalent to particles moving backwards in time with negative nergies and opposite internal quantum numbers. In contrast, short-wave superluminal particles, that is, "tachyons,"< 12> propagate positive (negative) real energy backwards (forwards) in time. One can then define antitachyons in Feynman's sense. The violation of Feynman's boundary condition is proved by starting with a tachyon in the transcendent frame K of infinite velocity, say in the +z direction where E = O and Pz = me. Then make an ordinary Einstein subluminal boost of v < c in the +z direction to the frame K'. The velocity addition law tells us that the tachyon is moving in the -z' direction with superluminal speed u' = c2 Iv. From this it follows that the energy E' of the tachyon in the K' frame is positive: (76) H<>'M!ver, the sub-boost in space-time shows that the tachyon of positive energy must move backwards in time in the K' frame. K' was sub-boosted parallel to the direction of the tachyon's motion in the transcendent Kframe (where all points on the tachyon world line are simultaneous, i.e., dt = O). Similarly, if the sub-boost o K' is antiparallel to the tachyon's motion in the transcendent frame K, we get a negative nergy tachyon moving forwards in time. Indeed, this will destabilize the vacuum, but we may have evidence from violent astrophysical phenomena that the vacuum is not stable. There must be some sort of nonlinear saturation damping out the emission of real tachyons of negative nergy propagating forwards in time. The short-wave superlurninal free particle eigensolutions do not form a complete set because of the momentum gap. H<>'M!ver, when the longwave translurninal eigensolutions are added to them, we do get a complete set. Therefore, conservation of probability in causality-violating relativistic quantum field theory (yet to be formulated in detail) is assured. 2.8 Quantum Spin Thermodynamics Mind-Matter Model Suppose that the physical substrate of mind is an intelligent quantum spin switching network making a non-Boolean logic quantum computer. The spins could be that of the weakly bonding lone protons (e.g., electropositive hydrogens in water) and perhaps unshared electron pairs and mobile 1t electrons in complex biomolecules. The second law of thermodynamics implies that when a "hot" negative quantum spin temperature Tspin < 0 (77) 328 is coupled to a "cold" positive lattice temperature 7jattice > 0 in a Carnot heat engine, heat Q flows from both spin and lattice reservoirs and is entirely converted to mechanical work W That is, the efficiency W/Qspin > l. There is no waste heat. Furthermore, a tiny heat flow Qspm > 0 from the negative spin temperature network can trigger a much larger conversion of heat Q,attice < 0 to work W from the positive temperature lattice. Thus WI Qspin = [ Qspin - .Qiattice] / Qspin = l + I.Qi~ Qspin I = 1 +1ian1a/lTspinl > 1. (78) For example, let Tsp1n = -0.1 K and let 7jattice = 300 K. The quantum heat engine efficiency is then 3000"/4. This is not a violation but a quantum "loophole"15 in the second law of thermodynamics a counterintuitive consequence of it when combined with the quantum principle. Is this how the mind moves matter, the mind being the spin system and the lattice being the nerve cell system in which W triggers a nerve pulse for a relatively tiny quantum spin energy flow? The above considerations are compatible with the view of Sperry16 : "the conscious phenomena of subjective xperience do interact on the brain process exerting an active causal influence . . . the contents of subjective mental experience are recogniz.ed as important aspects of reality in their own right, not to be identified with neural events as these have have heretofore been conceived, nor reducible to neural events. [ emphasis added] ... "the subjective mental properties and phenomena re posited to have top-level control as causal determinants. On these terms mind moves matter." 2:9 The Relativistic Rocket Problem and Practical Interstellar Travel Thome et al. have shown that practical interstellar travel would be possible if traversable wormholes could be found or manufactured with matter (possibly transluminal) violating the "weak energy condition." Even without traversable wormholes, h<>'M!ver, there is another possibility for practical interstellar travel. Let us consider the textbook "relativistic rocket" problem in the context of this theory. Imagine propelling the relativistic rocket along a subluminal timelike lg hyperbolic world line. Use a "fuel" capable of superlurninal_ local exhaust speed u along spacelike or Riemannian world lines for tachyonic or translurninal fuel particles, respectively. The energy and momentum conservation laws imply that the ratio of final to initial mass M ( 't) / M ( 0) required for such a trip of proper time 't along the timelike hyperbolic world line of the rocket has an exponential dependence on the negative reciprocal of the propellent superlurninal exhaust speed u. That is, M ( 't) / M ( 0) = exp ( -g 't/ u). (79) The limit of M ( 't) IM ( 0) as u -+ oo is 1. Therefore, the energy efficiency is only limited by how fast the propellent can be ejected beyond the light barrier. These considerations coupled with those of Thome et al. on traversable wormholes should profoundly modify the SETI (Search for Extra-Terrestrial Intelligence) program. Acknowledgment I am primarily indebted to my old Cornell professor, Philip Morrison, for an indelible grand vision of physics that bridged C.P. Snow's "Two Cultures" in the 1950s. I have also been stimulated by direct contact with the late !Chard Feynman (1963 and 1969), David Bohm (1971), and Abdus Salam 973). Of course, I am greatly indebted to Professor Henry Stapp (Lawrence &:rireley Lab), Professor Peter Bussey (University ofGlasgow), Professor Oreste P a:ioni (UCSD), and Dr. Nick Herbert. I would also like to acknc,..vledge npo rtant technical contributions by Creon Levit (NASA mes) who insisted t:at it should be possible to make a superluminal signaling device in a ~ pier way than a double-slit arrangement by using a simple interferometer. * double-slit arrangement involves a more complicated spread of phases. :be interferometer has basically a sharp phase with some noise. Should experiments confinn my prediction, then Herbert, Stapp, Bussey, Piccioni, and Levit deserve some of the credit, although none of the blame should it ail. Professor Waldyr Rodrigues of Instituto Matematica, UNICAMP {Brazil), showed me some unpublished '.mrk by Andrei Sakharov on transluminal 'l3.11.icles in the big bang in 1985 when I was a visiting professor. I \muld ike to thank Dr. David Sarfatti for editing help, Jagdish Mann and Csaba Szabo (Lt. Col. USAR Special Forces), and the U.S. Navy (PACE) for financial 5Upport. I also thank Stephen Schwartz and A. Lawrence Chickering of the lnstitute for Contemporary Studies for their support. Finally, I thank Kim Burrafato for bringing the Optia Guide to my attention at a significant moment. APPENDIX: EFFECT OF TRANSMITl'ER INTERFEROMETER REFLECTION PHASE SHIFfS ON 111B RECEIVER SIGNAL Let us consider the effect of variable reflection phase shifts at the mirrors of the transmitter interferometer on the local decoding of the superluminal retroactive quantum spin-spin signal at the distant receiver. A reflection phase shift of 5 = 180° rather than 5 = 9()0 [Sec. 1.7, Fig. 3, Eqs. (23) to (30)], appears to make Stapp's second objection obviously irrelevant. Firs~ I will 1ustify the use of the 90° phase shift for total internal reflection. Second, I v..ill consider the effect of the 180° phase shift for external reflection, which considerably simplifies matters and provides a strikingly clear counterexample to Stapp's arguments against faster-than-light signaling in standard quantum mechanics. "External reflection is defined as reflection at an interface where the incident beam originates in the material of l~r refractive index . ... Internal reflection refers to the opposite case."03a) "During external reflection, the light waves undergo a 180° phase shift. No phase shift occurs for internal reflection (except in the case of total internal reflection)."03b) External reflection way from normal incidence is generally inefficient (e.g., about 4% reflectance at normal out to 20° incidence angle ~ in air to polished optical glass with glass index of 1.52 for polarizations both parallel and perpendicular to plane of incidence). In contrast, internal reflection becomes total (i.e., 100% reflectance) for both polarizations above a critical angle of 41°121 when the ratio of indices is again n = 1.52. For example, the incident beam originates in the glass for total reflection at the air/glass boundary. What is the reflection phase shift 5 in the region of total internal reflection? The boundary conditions to Maxwell's electromagnetic field equations between t\m dielectrics give the Fresnel equations [e.g., Eqs. (11-51) to (11-54), Ref. 14, p. 199]: (Al) if the electric vector is perpendicular to the plane of incidence. lf the electric vector is parallel to the plane of incidence, then Jack Sarfatti Figure 7. The gedanken experiment. riL signal = sin (2 0) [ 1 cos q>] which survi\'es even if (cos q>) = 0. Figure 3 and the discussion of Sec. 1.7 assumed that 5 = 90°. This requirement complicates the design of the interferometer, because the light beams must move through a dielectric medium whose index of refraction is larger than that of the mirrors. This is not a difficulty of principle. Thus the phase shift of i used in Eqs. (23) to (30) in Sec. 1.7 corresponds to, for example, , (sin2 ~-n 2 )/ cos2 ~ = 1, (A3a) sin2 ~ = [ 1 + n 2 ] /2, (A4a) for polarization perpendicular to the plane of incidence. Similarly, sin2 ~= 2/(n 2+1) , n 2 >1 , (A4b) for polarization parallel to the plane of incidence. Thus it is possible to achieve a reflection phase shift of i if 'M! assume, as I have done, that the quantum probability amplitude phase shifts like the classical electric vector does. the motivation for using i was high reflection field intensity efficiency. H~r, if 'M! relax that requirement, supposing an intense laser pumped pair source, 'M! can use external reflection in which 5 = 180 ° and still get a good signal-to-noise ratio at the receiver (Fig. 7). This design choice also makes the transmitter interferometer much easier to build. Equations (23) to (30) nc,..v become 1 = ( l , 2 !Vi, v;, .91.. 'B. 'D, 'E) = - (112) cos e ei+<2), (23') II= (1, 2 !Vi, Hi, 'B , 'D, 'E) = -(l/2) sin 0 ei+(2l, (24') m = (1, 2\Vi. v;, .91., 'B , c, 'E ) = +(112) cos e , (25') IV= (1, 2 !Vi, H;, 'B, C, 'E ) = +(112) sine, (26') v = (1, 2 \H1, v;, .91., 'B , 'D , 'E ) = +(112) sine ei+<2>, (27') (281) 329 Design for a Superluminal Signaling Device VII= (1, 2 IH1, V{, 5t , '1J, C , '£ ) = -(1/2) sin 0, (29') VIII= (1, 2 IH1, H{, 'B, c, '£ ) = +(112) cos 0. (30') Therefore, I + II + III + IV = -( 1/2) cos 0 e;+c2> - ( 1/2) sin 0 ei+'2l +( 1/2) cos 0 + ( 1/2) sin 0 = +(1/2){cos e+sin 0}[ 1 ei+<2>], (ASa) V +VI+ VII + VIII = +( 1/2) sin 0 e;+<2> - ( 1/2) cos 0 e;+<2> - (112) sin 0 + (112) cos 0 = +(1/2) { cos 0 sin 0}[ 1 e;+c2>], (ASb) II+1I+IIl+IV l2 = (1/4){1 +2 cos0sin0}11 -e;+<2>j2 = (1/4) {1 + sin 2 0}11 e;+(2l 12 = (1/2){1 +sin20}(1 cosq>). (31') Similarly, IV+ VI+ VII+ VIIIl2 = (114) {1 2 cos 0 sin 0}11 e;+(2) 12 = (114) {l sin 2 0}11 e;+<2> j2 = (112) {l sin2 0}(1 cos q>). (32 ') I claim that Eqs. (31') and (32') make Stapp's second argument obviously false. The essence of Stapp's second argument (e.g., Sec. 1.9) is that we must sum over all q> to compute the local receiver photon detection probabilities. fur example, Stapp writes: The failure of the locality property in ... quantum theory ... does not contradict Einstein's principle that no signal travels faster than light. fur by a signal is meant a controllable transfer of information a message. Within the structure of these formalisms no such con330 trolled faster-than-light information transfer is possible. This folio.vs immediately from the fact that whereas within the quantum formalism (or the classical formalism) the probability of a specified result in one region, subject o the condition of a specified result in the other region, depends in general on the latter specification, and hence on the experimental setting in the other region, nevertheless a summation over all possible re.sulls of the experiment in the other region with proper weights gives a result that is independent of the choice of the experimenJal setting in that region. This entails that there is no predictable dependence of the observations in one region upon the choice of setting in the other.< 1 s) H~r , the above model is a counterexample to Stapp's claim, because even if we suppose that the sum of cos q> "with proper weights" p ( q>) in the transmitter egion is done, and furt.lier suppose that my idea of the (X)/Jeren/ subensemb/e of Secs. 1.9 and 1.10 is incorrect, (cos q>) = f cos q> p( q>) dq> = O; (39') nevertheless, there is still a "predictable dependence of the observations" in the receiver region "upon the choice of setting" 0 in the "other" transmitter region using only st~dard quantum mechanics. Indeed, the superluminal (and retroactive in delayed choice mode) signal S has the Josephson tunneling currentlike form S = p ( V, 0) p (H, 0) = sin 2 0, (41') in which the misalignment 0 between the calcites across an arbitrary four-dimensional space-time separation between the two detections of the photons in the same individual pair is analogous to the phase difference of the superconducting order parameter across a tiny normal barrier. I am assuming that the quantum wave function is complete in describing individual quantum systems and is not merely a description of ensembles. The fact that we can now observe individual trapped ions and that they conform to quantum predictions in their photon interactions eems to falsify the strictly ensemble inteipretation of the wave function. Received 12 February 1990.