UNIX%Ames-VMSB@sri-unix.UUCP (01/09/84)
gnals-without-signals"[2] in the spirit, though not the letter, of Wheeler's "delayed choice"[3], backwards-in-time. I present, as a counter-example, a Gedankenexperiment, "The Future Machine". Bussey writes: "... experimenters I and II shall be free to choose any kind of measurements to make on particles (1) and (2) respectively ... the only way in which II can receive communication from I is by finding that, as a result of activity by I, the probability for (2) to be in some particular state has changed." My Gedankenexperiment, described below, meets this requirement because the probability to detect (2) is P = (1/4)(1 + cos(2y)) where y is controlled by I independent of the four-dimensional space-time distance between the two correlated irreversible detections of (1) and (2) which are lower level parts of an inseparable whole. Bussey continues: "Now let I change the configuration of his apparatus so as to measure a different quantity ... There will be a unitary transformation ... Thus, whatever I chooses to measure ... the probabilities of given results from II's measurements are always the same. We therefore conclude that there is no way here for I to send signals to II, and that any kind of communication, including "super-luminal communication", is impossible." The Gedankenexperiment is a simple and straight-forward refinement of the experiment already performed by Aspect et-al[4]. The encoder I which transmits the "telepathic"[5] quantum "signal-without-a-signal" consists of an interferometer. Two rotating polarizers, in phase at rate w, are placed in the two paths of photon (1). One path contains an optical delay line in front of one of the rotating polarizers. The time delay t is short compared to the coherence time of photon (1). This implies that we can not measure which path photon (1) takes. Therefore, according to Feynman's heuristic interpretation of quantum mechanics, we must coherently add the probability amplitudes for photon (1) to take one path or the other. This results in a non-unitary transformation violating the essential premise of Busseys's "proof" forbidding super-luminal communication. This crucial non-unitary change in the configuration of I's apparatus violates the Galilean super-selection rule that forbids the coherent addition of states at different times. It also results in a beautiful generalization of the Josephson effect freeing it from cryogenic temperatures, tiny distances for tunneling, and electron pairs. That is, the "2" in the "2y" in the above equation for P comes from this non-unitary transformation as shown in detail below. That is, the measure of superluminal communication, the change in "the probability for (2) to be in some particular state"[1], is evidently given by: dP/dy = (-1/2)sin(2y) where y = wt. This has the form of the Josephson equation. The mathematical demonstration of the above conclusions now will be given. Use Aspect's two-photon J = 0->1->0 atomic cascade as the source of pair-correlated light. The future machine apparatus consists of three mutually incompatible polarization frames of reference whose base states are: |v>, |V> ; |x>, |X> ; |x+y>, |X+Y> respectively, where "v" is the vertical orientation of II's fixed decoder polarizer with a photon counter behind it. The "V" is the orthogonal base state in the horizontal orientation. The "x" denotes the relative angle between the the decoder polarizer at II and the two in-phase rotating encoder polarizers in the non-singular unitary limiting "degenerate" case of y -> 0 at the moments of irreversible photon detections in a fixed Lorentz frame assuming that the apparati at I and II are at rest relative to each other. The "X" denotes the orthogonal base state. Similarly for the third polarization frame which has the optical delay line in front of it. Contrast this configuration of the total apparatus with that in Aspect's experiment[4] which essentially uses only two incompatible polarization frames rather than three. The nonlocal objective frame-invariant second rank spin tensor of the photon pair has a representation in the decoder frame II given by <II|1,2> = (1/sqrt(2))[ <v|1><v|2> + <V|1><V|2> ] which, by Weyl's "reciprocity"[6], connecting "implicate"[7] symmetric permutation group "Young Pattern" representations to "explicate"[7] continuous linear group representations, is a symmetric second rank tensor whose tableaux is a row with two boxes. The non-unitary transformation required for super-luminal communication comes from applying Feynman's heuristic rule to the encoder interferometer because we must project, for example, <v|1> to both of the mutually incompatible rotating frames. Thus, I make the Ansatz: <v|1> --> (1/2)[<v|x><x|1> + <v|X><X|1> + <v|x+y><x+y|1> + <v|X+Y><X+Y|1>] and similarly for <V|1> The non-unitary coefficient "(1/2)" is necessary to get the correct unitary limit of vanishing super-luminal communication when y --> 0 in which case the two incompatible rotating encoder frames become compatible. We see that the clashing encoder frames are a non-unitary perturbation on the non-local joint probability amplitudes for the inseparable pair due to the creation of new experimental alternatives that spoil the completeness of the sets of single photon states violating normalization invariance. These new experimental alternatives are non-locally induced misses in the photon counter that lower its efficiency. That is, the quantum action-at-a-distance causes the instrumentation to malfunction in a controllable way in order to prevent the causal anomalies inherent in super-luminal communication. That is, in agreement with Godel's last theorem[8], any attempt to create a time travel paradox will fail because of some malfunction in the desired strange loop of "delayed choice" nonlocal processes acting backwards in time. The representations of the O(2) group provide the Dirac transformations between the incompatible polarization frames. Thus, <v|x> = cos(x) ; <v|X> = sin(x) ; <v|x+y> = cos(x+y) ; <v|X+Y> = sin(x+y) ; <V|x> = -sin(x); <V|X> = cos(x) ; <V|x+y> = -sin(x+y); <V|X+Y> = cos(x+y) . We pick up the Josephson effect of "2y" from the non-unitary transformation by projecting the terms in the time-delayed rotating encoder frame back to the earlier non-delayed rotating encoder frame. That is, the O(2) group once again tells us that: <x+y|1> = <x+y|x><x|1> + <x+y|X><X|1> = cos(y)<x|1> + sin(y)<X|1> , <X+Y|1> = <X+Y|x><x|1> + <X+Y|X><X|1> =-sin(y)<x|1> + cos(y)<X|1> . Therefore, the non-unitary transformation on the encoder (1) photon is: <v|1> --> (1/2)[cos(x)<x|1> + sin(x)<X|1> + cos(x+y){ cos(y)<x|1> + sin(y)<X|1>} + sin(x+y){-sin(y)<x|1> + cos(y)<X|1>}] = (1/2)[<x|1>{ cos(x) + cos(x+y)cos(y) - sin(x+y)sin(y) } + <X|1>{ sin(x) + cos(x+y)sin(y) + sin(x+y)cos(y) } ] But, cos(x+y)cos(y) - sin(x+y)sin(y) = cos(x+2y) , and, cos(x+y)sin(y) + sin(x+y)cos(y) = sin(x+2y) . Therefore, the non-unitary transformation takes on the physically transparent form: <v|1> --> (1/2)[ <x|1> { cos(x) + cos(x+2y) } + <X|1> { sin(x) + sin(x+2y)} ] The right-hand side is substituted into <II|1,2> above to get: nonlocal joint "click-click" amplitude = (1/sqrt(8)){cos(x) + cos(x+2y)} , nonlocal joint "click-not click" amplitude = (1/sqrt(8){sin(x) + sin(x+2y)} . One can check these results by going to the unitary limit of y --> 0 giving the standard [9] results of: "click-click" --> (1/sqrt(2))cos(x) "click-not click" --> (1/sqrt(2))sin(x) for the quantum cross-correlations actually measured in Aspect's experiment across a super-luminal (space-like) interval. The click probability at one detector, for example, II, is the sum of the squared joint amplitudes. In the general non-unitary case that "lifts the degeneracy" of the Aspect experiment, x drops out but y remains as given by the equation for P at the beginning of this Letter. There is a simple geometric model for this non-unitary transformation. The total state of the insepaable pair can be pictured as a unit vector from the center of a sphere to any point on the surface of the sphere. "x" is the azimuthal angle and "y" is the compliment of the polar angle in spherical polar coordinates. The unitary limit of y --> 0 constrains the unit vector to the equatorial great circle of the sphere. The piece of the total state contributing to P is the projection of the unit vector on a plane parallel to the equatorial plane of length cos(y) confined to a circle of latitude. The projection of the unit vector on the axis from the center to the north pole represents the new, non-unitary dimensions of non-locally induced instrumental malfunctions of controllable action at-a-distance corresponding to y not vanishing. Bussey's unitary "proof" implicitly assumes that the sphere is not there at all, but only it's equator - like the smile on the Cheshire cat. Make a Wick rotation from the group O(2) the Lorentz boost group O(1,1). The trigonometric Dirac transformation functions become hyperbolic. The "Josephson" factor of "2" should have physical significance in this analytically continued context. THe Gedankenexperiment gets its name, "The Future Machine", from the following "delayed choice" realization. Place the encoder farther from the source of pair correlated light than is the decoder. Use ultra-short pulses of pairs. The prediction is that the P at the decoder will be determined by the value of y at the encoder that the twin encoder pulse is going to find *after* the decoder pulse has already been detected. That is, the final causation from future to past in a controllable reproducible objective super-determined way is my prediction. If this is true then it tells us why the "Anthropic Principal"[10] for the big-bang creation of the world is there - but that is the subject for another Letter. Note: The above derivation assumes, that to a good approximation, the Hamiltonian H, for the unitary evolution of the photon pair, commutes with the photon spin/polarization operator S so that: (e.g., in the Heisenberg picture) exp(iHdt) S exp(-iHdt) = S (i.e. S is a constant of the motion) so that we do not have to worry about complications from time-ordered phase factors of the form T exp(i(integral(Hdt)) in the spin/polarization amplitudes and/or density matrices. That is, the polarization correlation information is effectively dynmaically decoupled from the translational degrees of freedom for photons. This would not necessarily be true for finite rest mass charged particles like electrons emitted in correlated pairs in some kind of collision process. There, the above simple equations may need to be modiified. [in response to Charlie Crummer, and in general] the Bugoliubov commutation relations of quantum field theory express the false *axiom* of "locality" which is inconsistent with the basic quantum non-locality now observed for photon spins in Aspect's experiment. I reject the canonical field commutation relations as an inconsistency in quantum field theory! Futhermore, Hawking[11] shows that Bogoliubov commutation rules, admitting only causal singularities in the propagators, fail in curved space-time and also fail in thermal equalibrium density matrices in flat space-time, both of which demand acausal superluminal singularities in the field correlations (propagators) in which "positive frequencies are now propagated outside the future tube"[11], in violation of locality. The acausal singularity in curved space-time leads to entropy of exploding mini black holes. The acausal singularity in flat space-time may explain collapse of the state vector in measurement. Essentially, in my own view, the unimodular eigenvalues exp(i theta) of the unitary evolution matrices develop a "Thom catastrophic"[12] imaginary part in theta giving nonunitary collapse or creation of states. This means that action is complexified - the imaginary part of the action is outside the light cone and is the thermodynamic entropy. References [1] P.J. Bussey, Phys. Lett. 90A (1982) 9. "Super-luminal communication" in Einstein-Podolsky-Rosen Experiments. [2] T.F. Jordan, Phys. Lett. 94A (1983) 264. Quantum Correlations Do Not Transmit Signals. Note: Ordinary signals come from continuous linear group symmetries, for example, the electromagnetic-weak-strong gluon forces come from phase connections in a fiber bundle with a continuous "internal" structure group. The lepto-quark source fields are cross-sections of the fiber bundle. In contrast, the quantum "telepathic" "signal-without-signal" is from a discrete covering fiber whose structure group is the symmetric permutation group of degree equal to the number of cross-correlated quanta in the bundle space. The structure of the network is given by the Young Pattern in the sense of Weyl's reciprocity. [3] J. Wheeler, private communication, 1982. [4] A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. 49 (1982) 1804. Experimental Tests of Bell's Inequalities Using Time-varying Analyzers. [5] "telepathic" in the sense used by Einstein in his "Autobiography" published in the "Library of Living Philosophers series. [6] H. Weyl, "Theory of Groups and Quantum Mechanics" (Dover, New York). [7] D. Bohm, private communication, Birkbeck C. College, 1972. [8] R. Rucker, "Infinity and the Mind" (Birkhauser, Boston, 1982). [9] R.P. Feynman, Int. J. Theor. Phys. 21 (1982) 467. N. Cufaro Petroni and J.P. Vigier, Phys. Lett. 93A (1983) 385 (eq. 7). [10] P.C.W. Davies, "The Accidental Universe" (Cambridge, U.K., 1982). [11] S.W. Hawking, "Acausal Propagation in Quantum Gravity" in "Quantum Gravity - A Second Oxford Symposium". Ed. Isham, Penrose, Sciama, Clarendon Press (1981) 393. [12] C.W. Kilmister in "The Encyclopedia of Ignorance" Ed. Duncan and Weston-Smith, Pocket Books (1978) 175. ------