In "Do we really understand quantum mechanics? Strange correlations, paradoxes and theorems." by F. Laloe, Laboratoire de Physique de l'ENS, LKB, 24 rue Lhomond, F-75005 Paris, France, Laloe explores the meaning of "element of reality": "3.2 Of peas, pods and genes When a physicist attempts to infer the properties of microscopic objects from macroscopic observations, ingenuity (in order to design meaningful experiments) must be combined with a good deal of logic (in order to deduce these microscopic properties from the macroscopic results). Obviously, some abstract reasoning is indispensable, merely because it is impossible to observe with the naked eye, or to take in one's hand, an electron or even a macromolecule for instance. The scientist of past centuries who, like Mendel, was trying to determine the genetic properties of plants, had exactly the same problem: he did not have access to any direct observation of the DNA molecules, so that he had to base his reasoning on adequate experiments and on the observation of their macroscopic outcome. In our parable, the scientist will observe the color of flowers (the "result" of the measurement, +1 for red, -1 for blue) as a function of the condition in which the peas are grown (these conditions are the "experimental settings" a and b, which determine the nature of the measurement). The basic purpose is to infer the intrinsic properties of the peas (the EPR "element of reality") from these observations. 3.2.1 Simple experiments; no conclusion yet. It is clear that many external parameters such as temperature, humidity, amount of light, etc. may influence the growth of vegetables and, therefore, the color of a flower; it seems very difficult in a practical experiment to be sure that all the relevant parameters have been identified and controlled with a sufficient accuracy. Consequently, if one observes that the flowers which grow in a series of experiments are sometimes blue, sometimes red, it is impossible to identify the reason behind these fluctuation; it may reflect some trivial irreproducibility of the conditions of the experiment, or something more fundamental. In more abstract terms, a completely random character of the result of the experiments may originate either from the fluctuations of uncontrolled external perturbations, or from some intrinsic property that the measured system (the pea) initially possesses, or even from the fact that the growth of a flower (or, more generally, life?) is fundamentally an indeterministic process - needless to say, all three reasons can be combined in any complicated way. Transposing the issue to quantum physics leads to the following formulation of the question: are the results of the experiments random because of the fluctuation of some uncontrolled influence taking place in the macroscopic apparatus, of some microscopic property of the measured particles, or of some more fundamental process? The scientist may repeat the "experiment" a thousand times and even more: if the results are always totally random, there is no way to decide which interpretation should be selected; it is just a matter of personal taste. Of course, philosophical arguments might be built to favor or reject one of them, but from a pure scientific point of view, at this stage, there is no compelling argument for a choice or another. Such was the situation of quantum physics before the EPR argument. 3.2.2 Correlations; causes unveiled. The stroke of genius of EPR was to realize that correlations could allow a big step further in the discussion. They exploit the fact that, when the choice of the settings are the same, the observed results turn out to be always identical; in our botanical analogy, we will assume that our botanist observes correlations between colors of flowers. Peas come together in pods, so that it is possible to grow peas taken from the same pod and observe their flowers in remote places. It is then natural to expect that, when no special care is taken to give equal values to the experimental parameters (temperature, etc.), nothing special is observed in this new experiment. But assume that, every time the parameters are chosen to the same values, the colors are systematically the same; what can we then conclude? Since the peas grow in remote places, there is no way that they can be influenced by the any single uncontrolled fluctuating phenomenon, or that they can somehow influence each other in the determination of the colors. If we believe that causes always act locally, we are led to the following conclusion: the only possible explanation of the common color is the existence of some common property of both peas, which determines the color; the property in question may be very difficult to detect directly, since it is presumably encoded inside some tiny part of a biological molecule, but it is sufficient to determine the results of the experiments. Since this is the essence of the argument, let us make every step of the EPR reasoning completely explicit, when transposed to botany. The key idea is that the nature and the number of "elements of reality" associated with each pea can not vary under the influence of some remote experiment, performed on the other pea. For clarity, let us first assume that the two experiments are performed at different times: one week, the experimenter grows a pea, then only next week another pea from the same pod; we assume that perfect correlations of the colors are always observed, without any special influence of the delay between the experiments. Just after completion of the first experiment (observation of the first color), but still before the second experiment, the result of that future experiment has a perfectly determined value; therefore, there must already exist one element of reality attached to the second pea that corresponds to this fact - clearly, it can not be attached to any other object than the pea, for instance one of the measurement apparatuses, since the observation of perfect correlations only arises when making measurements with peas taken from the same pod. Symmetrically, the first pod also had an element of reality attached to it which ensured that its measurement would always provide a result that coincides with that of the future measurement. The simplest idea that comes to mind is to assume that the elements of reality associated with both peas are coded in some genetic information, and that the values of the codes are exactly the same for all peas coming from the same pod; but other possibilities exist and the precise nature and mechanism involved in the elements of reality does not really matter here. The important point is that, since these elements of reality can not appear by any action at a distance, they necessarily also existed before any measurement was performed - presumably even before the two peas were separated. Finally, let us consider any pair of peas, when they are already spatially separated, but before the experimentalist decides what type of measurements they will undergo (values of the parameters, delay or not, etc.). We know that, if the decision turns out to favor time separated measurements with exactly the same parameter, perfect correlations will always be observed. Since elements of reality can not appear, or change their values, depending of experiments that are performed in a remote place, the two peas necessarily carry some elements of reality with them which completely determine the color of the flowers; any theory which ignores these elements of reality is incomplete. This completes the proof. It seems difficult not to agree that the method which led to these conclusions is indeed the scientific method; no tribunal or detective would believe that, in any circumstance, perfect correlations could be observed in remote places without being the consequence of some common characteristics shared by both objects. Such perfect correlations can then only reveal the initial common value of some variable attached to them, which is in turn a consequence of some fluctuating common cause in the past (a random choice of pods in a bag for instance). To express things in technical terms, let us for instance assume that we use the most elaborate technology available to build elaborate automata, containing powerful modern computers if necessary, for the purpose of reproducing the results of the remote experiments: whatever we do, we must ensure that, somehow, the memory of each computer contains the encoded information concerning all the results that it might have to provide in the future (for any type of measurement that might be made). To summerize this section, we have shown that each result of a measurement may be a function of two kinds of variables: (i) intrinsic properties of the peas, which they carry along with them. (ii) the local setting of the experiment (temperature, humidity, etc.); clearly, a given pair that turned out to provide two blue flowers could have provided red flowers in other experimental conditions. We may also add that: (iii) the results are well-defined functions, in other words that no fundamentally indeterministic process takes place in the experiments. (iv) when taken from its pod, a pea cannot "know in advance" to which sort of experiment it will be submitted, since the decision may not yet have been made by the experimenters; when separated, the two peas therefore have to take with them all the information necessary to determine the color of flowers for any kind of experimental conditions. What we have shown actually is that each pea carries with it as many elements of reality as necessary to provide "the correct answer" to all possible questions it might be submitted to." The complete paper "Do we really understand quantum mechanics? Strange correlations, paradoxes and theorems." can be found at: http://arxiv.org/PS_cache/quant-ph/pdf/0209/0209123.pdf All the best John B.