Last June I was an invited speaker at the symposium “Frontiers of Time: Reverse CausationExperiment and Theory,” part of a meeting of the American Association for the Advancement of Science (AAAS) held on the beautiful campus of the University of San Diego. (Here, reverse causation means a violation of that most mysterious law of physics, the Principle of Causality, which requires that any cause must precede its effects in all reference frames.) I had originally intended to just talk about my work on the transactional interpretation of quantum mechanics and its somewhat retrocausal aspects (i.e., back-in-time handshakes of quantum waves, etc.). However, a new idea involving signaling with nonlocal quantum processes had come my way, and I decided to present it as a retrocausal quantum paradox at the symposium. It made a big splash there, but none of the experts present could identify any problem with the proposed thought experiment or resolve the paradox. In this column I want to tell you about this causality-violating communications scheme and its possible consequences.
Quantum nonlocality was first spotlighted in the famous 1935 “EPR” paper of Einstein, Podolsky, and Rosen, and is now generally acknowledged to be an implicit feature of the standard quantum formalism. In the EPR paper, Einstein and colleagues pointed out that standard quantum mechanics requires enforcement of correlations across spacelike and negative timelike intervals, that changing something at one end of an extended measurement has consequences at the other end of the measurement, even if the two measurement parts are separated by light years. Einstein referred to such nonlocality as “spooky action-at-a-distance” and took it as evidence of the wrongness of quantum mechanics because such influences would have to propagate faster than light in seeming contradiction to relativity. However, using quantum-entangled particles, many experiments have now shown that the nonlocal aspects of quantum mechanics are real and can be demonstrated in the laboratory in many experimental situations.
One might think that the reality of EPR nonlocality would open up the twin possibilities of faster-than-light and back-in-time communication. However, over the years a number of authors have published “no-signal theorems” demonstrating that such EPR superluminal observer-to-observer communication is impossible within the standard quantum mechanics formalism. Typically, such a formal proof shows that any configuration change at one end of an extended measurement cannot alter what is measured in the other end of the measurement in a way that could be used for signaling.
Recently it has been pointed out, however, that at least some of these proofs are tautological, with their seemingly reasonable assumptions subtly building in the conclusion, and that key assumptions are inconsistent with some aspects of standard quantum mechanics (e.g., Bose-Einstein symmetrization). Therefore, the door seems to be open a least a crack for the twin possibilities of EPR retro-causal and superluminal signaling between observers.
Last March, my belief in the validity of no-signal theorems was shaken by reading (in German) the PhD thesis of Birgit Dopfer, who received her doctorate from the University of Innsbruck in 1998. She performed an EPR experiment using pairs of momentum-entangled infrared photons, both with wavelengths of 702.2 nm, produced by parametric down-conversion in a nonlinear LiIO3 crystal pumped with a 351.1 nm ultraviolet laser beam. The twin photon pairs were entangled by momentum conservation, because the two infrared photon momentum vectors must add up to the momentum vector of the ultraviolet photon that produced them. In Dopfer’s experiment, the entangled photons, which emerge from the LiIO3 crystal 56.28o apart in angle and on opposite sides of the pump beam, were routed along two paths that we will refer to as the upper and lower arms.
The photon in the lower arm reaches an opaque plate pierced by two pinholes, and the light that survives to reach the other side is detected by an imaging detector, which produces signals indicating the presence and position of the detected photon. As we will see, this detector may show the position distribution of either a “2-slit interference pattern” structured with sharp peaks and deep valleys, or a “1-slit diffraction pattern,” a broad bump without much structure.
The photon in the upper arm of the experiment reaches a lens of focal length f. The lens is positioned such that the sum of the distances from the LiIO3 crystal to the lower-arm pinholes and to the upper-arm lens together add up to a total distance of 2f. Behind the lens is a second imaging detector that detects the photons that have passed through the lens. The lower-arm detector, because of the pinhole apertures, receives many fewer photons than the upper arm detector, but Dopfer recorded events only when both detectors had an arriving photon at the same time, i.e., in coincidence.
The measurements performed with this system can be considered for two cases. In Case 1, the upper-arm detector is placed at a distance 2f beyond the lens, while in Case 2, the upper-arm detector is placed at a distance f beyond the lens. Because of the focal properties and position of the lens and the momentum correlation of the two photons, the pinholes encountered by the photon in the lower arm are imaged by the photons in the upper arm at a distance 2f beyond the lens.
Therefore, each measurement made in the Case 1 configuration identifies the specific pinhole in the lower arm through which the photon for that event has passed. On the other hand, each measurement made in the Case 2 configuration intercepts the incoming photons in a broad unfocused blob, so that the lower-arm twin of the upper arm photon could have passed through either pinhole.
In quantum mechanics there is a phenomenon called superposition, which involves adding the mathematical descriptions of two or more contributing processes and then calculating the absolute-square of the result to get the probability of particular observations. If there is no information on the specific pinhole through which a photon passed (as in Case 2 above), amplitudes for passage through both pinholes are added to calculate the event probability. The result is a “2-slit interference pattern” structured with sharp peaks and deep valleys. On the other hand, if information is available on the specific pinhole through which a photon passed (as in Case 1 above), the probability for passage through each pinhole is calculated separately and the probabilities are added. The result is a “1-slit diffraction pattern,” a broad bump without much structure.
Thus, by moving the detector in the upper arm of the experiment, the observation in the lower arm changes from an interference pattern to a diffraction pattern. These patterns cannot be distinguished with a single two-photon event, but are easily distinguished with a few dozen such events. Thus, a “signal” can be sent from the upper to the lower arm by moving the upper detector to change the pattern in the lower detector.
We had said above that formal no-signal theorems require that a configuration change at one end of an extended EPR measurement cannot alter what is measured in the other end. Does the Dopfer Experiment constitute an experimental falsification of such proofs? Not quite. In the Dopfer Experiment, the pattern in the lower detector was selected by requiring events in which detected photon were in good time-coincidence in both detectors. Therefore, it is possible (barely) that with no coincidences, the same raw pattern would appear in the lower detector, independent of the position of the upper detector, with the coincidences from the upper arm selecting from this raw pattern a diffraction pattern in Case 1 and an interference pattern in Case 2.
However, this scenario seems unlikely. Around 85% of the photons in the lower detector should be in coincidence with photons in the upper detector regardless of position. Therefore, while the coincidence requirement should remove the 15% of noise, it should in itself do little else. In particular, it should not be able to thin out the raw pattern enough to produce the minima of the interference pattern.
Unfortunately, the Dopfer thesis does not discuss what was observed in the lower detector with the coincidence requirement removed. For this reason, a crucial test of quantum phenomena would be to re-create the Dopfer Experiment and observe the role of the coincidence requirement on what is observed in the lower arm detector. Several research groups are considering doing this, but there are no results yet
Okay, now let us suppose, for the sake of argument, that the no-signal theorems are wrong and that EPR signaling is possible. What are the implications?
First, consider that we eliminate the coincidence requirement and modify the upper arm of the Dopfer Experiment by placing the ends of single-mode fiber optic light pipes in the 2f plane at the two slit-image positions, so that if the lower photon passes through one of the pinholes, its upper arm twin enters the corresponding light pipe. Suppose that in the corner of the laboratory is a big spool of dual-path fiber optics line, 10 kilometers in length with an index of refraction of 1.5, so that it requires 50 microseconds for light to travel from one end of the coil to the other. At the output ends of the fibers, set to have the same separation as the inputs, we place a new lens of focal length f a distance 2f away, so that it images the light emerging from output ends of the fibers at a distance 2f beyond the lens. Then, as before, we move our upper detector between the f and 2f positions beyond this lens.
According to the rules of quantum entanglement, the position change in the detector of the upper photon should show up as a change in the pattern followed by its entangled twin photon in the lower-arm as it is detected by the lower detector. However, in this case, the change in the pattern of lower arm detection will occur 50 microseconds before the upper arm is moved. Therefore, we have a thought experiment that promises to send messages backwards in time, to a time 50 microseconds in the past. In other words, we have a plausible experimental scheme for retro-causal signaling.
Such a result would violate the Principle of Causality. It would also make it possible for an experiment to create a “bilking paradox” or “timelike loop.” For example, after the experimenter receives a message from himself some time in the future, he decides not to send the message. Or if he does not receive a message, he decides to send one anyway. Or he decides to send a message that is different from the one he just received.
The physics literature on the resolution of such paradoxes is thin, but there have been some speculations. The prevailing view seems to be that Nature would not permit such events. In any real experiment there is some probability of noise responses or equipment failure, and the assertion is that such events are more probable than the occurrence of a timelike loop. In other words, Nature would refuse to be bilked, and any attempt to do so would be met with an equipment failure striking from some improbable but possible direction.
This raises an interesting science-fictional possibility. Suppose you arrange a failure-tolerant experiment such that a timelike loop will definitely be created unless a certain improbable but desired event should occur. For example, it is required that you win the Powerball Lottery in order to suppress the timelike loop. Would that cause you to win? Can we manipulate probability by intimidating Nature with the possibility of causing timelike loops?
I don’t think so, but I also don’t understand why a coincidence-free Dopfer experiment could not be performed. We’ll see.n
AV Columns Online: Electronic reprints of over 120 “The Alternate View” columns by John G. Cramer, previously published in Analog, are available online at: http://www.npl. washington.edu/av. The PowerPoint version of my AAAS talk can be found at http://faculty.washington.edu/jcramer/PowerPoint/AAAS_20060621.ppt.
A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777-780 (1935).
The Dopfer Experiment:
B. Dopfer, PhD Thesis, Univ. Innsbruck (1998); A. Zeilinger, Rev. Mod. Physics, 71, S288-S297 (1999).