Causation and EPR. But, alas, this hypothesis is mathematically inconsistent with the results of the case b runs, those runs

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1 As Mermin remarks at the end of Quantum Mysteries for Anyone, the device he describes in that paper (the Mermin contraption ) is a direct descendent of a thought experiment described in a paper written by Einstein, Podolsky, and Rosen (henceforth, EPR). It became an actual experiment done by Alain Aspect in Paris. The outcome of the experiment is rather simple to state. In case a runs, the switches on the two detectors are set to the same value (1, 2, or 3) and in each such run the lights on the detectors flash the same colour--half the time RR and half the time GG. Suppose we try to explain this by supposing that the particles in the particle pair that emerges from the central box on each run carry instruction sets, a mark of some kind that tells the light how to flash. If the particles contained identical instruction sets, then case a runs would be fully explained. But, alas, this hypothesis is mathematically inconsistent with the results of the case b runs, those runs

2 in which the detector switches are set to different values. In such runs 25% of the time the two lights on the detectors flash the same colours (12.5% of the time RR and 12.5% of the time GG). The other 75% of the time the two lights on the detectors flash either RG or GR, with the two combinations occurring randomly and with equal frequency. The statistics of the two types of runs combined is the prediction of quantum mechanics. Therefore, the hypothesis of instruction sets is inconsistent with the predictions of quantum mechanics. Experiment, to date, solidly supports QM. Instruction sets are sometimes called hidden variables. The variables are hidden because they do not appear in QM, even though they are supposed to control what happens at detectors They are also supposed to exist and have particular values prior to the interaction with the detector (which is called a detector since we suppose that it detects them). Supposing that there are hidden variables is sometimes referred to as Bell locality. What the Mermin 2

3 contraption shows is that no Bell local theory can reproduce the results of QM. Bell locality is deeply embedded in our commonsense view of the world. Therefore, QM is inconsistent with our commonsense view of the world. Given the enormous empirical support of QM, one seems forced to conclude that reality is quite different from the way we normally suppose it is. But let us try to apply this general conclusion to our considerations concerning causation. If we abandon hidden variables, we still must (mustn t we?) attempt to understand why in case a runs the lights always flash the same colour. Why (or how) do they do that--without instruction sets? Let us for the moment assume that in the lab at issue the two detectors are exactly equidistant from the emitter and so the two detections of the particles that arrive at the detectors are simultaneous. The outcome of the detection is then recorded or registered by the colour of the light. We can suppose that both detectors are wired the same way, 3

4 so we could talk about the two lights flashing rather than the particle/detector interactions. The two detections are must be spacelike separated (since they are simultaneous and at some distance one either side of the emitter). According to the special theory of relativity (SR) no causal process can include both detections, since no causal process can propagate faster than light. It follows from Salmon s account of causal propagation as causal process that neither flash could cause the other. There is no causal connection between the flashes or detections (on Salmon s view of causation)-- which seems right until one asks again why the lights flash the same colour in case a runs. There is another view of the causal relation that gives the same result. As I remarked in class, one of the root ideas of causation is manipulability--the ability to make something happen there by doing something here ( wiggling a variable here as cause, something changing there as effect). But the only variable I can vary is the setting of a detector. Let s say I am at the left detector. I can set it to 1, 4

5 2, or 3, but no matter how I set it, the probability of getting (say) a red flash at the right detector is.5. I can t make anything happen at the right detector. So there is no causal relation between the setting of one of the two detectors and the outcome at the other detector (from a manipulability point of view). There is therefore no ability to send a signal or message from one detector to the other. (Try to figure out how!) But let s look at this a slightly different way. In general, the probability that the right detector will flash red is.5. But if both detectors are set to the same setting and the left detector flashes red, the the probability that the right detector flashes red is 1. So we have raised the probability of something s happening at the right detector. If one supposes that a cause raises the probability of some event that is its effect, then setting the two detectors to the same setting and getting a light flash of a particular colour at one is the cause of the same colour flashing at the other (on this statistical relevance view of causation). Taylor s analysis of causation gives the same result. When the detectors are both set to the same setting and 5

6 one flashes (say) red, then that suffices for the other to flash red. Note that in Taylor s case, each flash causes the other, since the two are simultaneous and the conditions at each detector are the same. Taylor explicitly allows instantaneous causation. So on Taylor s analysis we have in the EPR case a closed causal loop that is instantaneous or temporally flat, unextended. (This remark also applies to the statistical relevance view as well.) On these two views then, there is a causal relation between the flashing of the two lights, but the relation is odd in that it is a closed causal loop and also, if causal, violates SR. The violation of SR is mitigated by the no-signalling result sketched above. Some have suggested that nosignalling permits the peaceful coexistence of SR and quantum non-locality. No-signally prevents one from sending information into one s past. 6

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