Local realistic theory

For a = 0 = 60° and 7 = 0 the quantum inequality on the left, evaluated from the cosines is 5/2, which violates the inequality. With three magnets placed 60° apart as in figure 3, measurements of the different spin components of a singlet system are therefore predicted by equations (12) and (13) to correlate differently if the interactions were quantum-mechanical or local, respectively. An outcome /b < 2 would favour realistic local theory while Ib > 2 favours quantum theory. The EPR argument can hence be settled experimentally. 

Because of the EPR effect quantum systems that have interacted before remain correlated even when the interaction no longer persists. The experiments have shown that, even when all interaction comes to an end, information about the second of a pair of particles can be obtained by performing a measurement on the first. The conclusion is that the physical world cannot be correctly described by a realistic local theory. It is necessary either to abandon the criterion of reality or to accept the possibility of action at a distance. The latter occurs because each particle is described by a wave function which is, in general, a non-local entity that collapses when a measurement is made. This collapse is instantaneous and complete. It occurs everywhere, also at the position of a particle not involved in the measurement and therefore predicts the correlation of distant events. Most particles or aggregates of particles, usually regarded as separate objects, have interacted in the past with other objects and must hence remain correlated and to constitute an indivisible entangled whole. This observation represents the scientific rediscovery [45] of holism [46]. 

A. Aspect, P. Grangier and G. Roger, Experimental Tests of Realistic Local Theories via Bell s Theorem, Phys. Rev. Lett. 

The results of the simple DHH theory outlined here are shown compared with DH results and corresponding Monte Carlo results in Figs. 10-12. Clearly, the major error of the DH theory has been accounted for. The OCP model is greatly idealized but the same hole correction method can be applied to more realistic electrolyte models. In a series of articles the DHH theory has been applied to a one-component plasma composed of charged hard spheres [23], to local correlation correction of the screening of macroions by counterions [24], and to the generation of correlated free energy density functionals for electrolyte solutions [25,26]. The extensive results obtained bear out the hopeful view of the DHH approximation provided by the OCP results shown here. It is noteworthy that in... 

Any approach different from this brute force approach must make compromises, as far as the complete realistic modelling of polymeric materials with all their details is concerned. Different groups tend to make rather different compromises, depending on what features of the problem they consider particularly important. Here we discuss only one approach proposed [28,30, 32,175,176] by the condensed matter theory group at the University of Mainz. This approach follows a rather radical concept, since all fast vibrational motions are completely eliminated, and in addition a description of the local... 

Based on the above examples, we can conclude that while localness is a desirable property, it is not sufficient for ensuring physically realistic predictions. Indeed, a key ingredient that is missing in all mixing models described thus far (except the FP and EMST70 models) is a description of the conditional joint scalar dissipation rates (e ) and their dependence on the chemical source term. For example, from the theory of premixed turbulent flames, we can expect that (eY F, f) will be strongly dependent on the chemical... 

The second set of problems in dynamics are those of scattering theory where the Hamiltonian is of the form H = H0 + V and the interaction V vanishes when the colliding particles are far apart. It is usually assumed that the H0 part is already solved and that the interesting or the hard part is to account for the role of V. For realistic systems, which are anharmonic, even the role of H() can be quite significant. An example that has received much recent attention is the reaction of vibrationally excited HOD with H atoms (Sinha et al., 1991 Figure 8.2). The large difference in the OH and OD vibrational frequencies means that the stretch overtones of HOD are primarily local in character (cf. Section 4.21). It follows that one can excite HOD to overtones localized preferentially on either one of the two bonds and that an approaching H atom will abstract prefer-... 

The deposition of each stem of m repeat units can be treated [8,41] as a set of m equilibria. While this generalization appears to account for more local details, the general conclusions are the same as in the LH theory. In realistic situations, we expect nonsequential deposition of repeat units into various stems. These partially formed stems will then sort out through entropic barriers to attain the lamellar thickness. We remrn to this issue in Section VII. 

So far we have not been able to treat chains with bond correlations in more than one dimension. The introduction of more detailed or realistic models of local conformational processes, such as those of Reneker34 or of Schatzki,35 has, therefore, not been feasible. We may remark that the theory of dielectric relaxation by Work and Fujita,36 which applies Glauber s methods25 to delayed (dynamic) correlations between chain dipoles, is also in essence a one-dimensional affair. 

The progress undergone in recent years toward a solution of the problem raised by Einstein 1927 has become possible because of two developments (1) A few experimental techniques, in particular, the methods for measuring very short times with good accuracy, have permitted in recent years the execution of several experiments which in their essence are practical versions of the thought experiment proposed and discussed in 1935 by Einstein, Podolski, and Rosen.39 (2) A procedure of analysis of their results has been made possible by the work of Bell40 who has derived in the frame of local realism a relation (the Bell inequality) obeyed by local realistic theories but violated by quantum mechanics. 

Another refinement of the VRH model consists in assuming that the charges are delocalized over segments of length L, instead of being strictly localized on point sites [40]. This is indeed a more realistic picture, leading to better fits with the data, but it has the drawback that an extra parameter has been added. Note that the temperature dependence, log o- -T y, can be found by other approaches, such as the percolation model, the effective medium approximation (EMA), the extended pair approximation (EPA) [41], the random walk theory, and so on. 

The idea of action at a distance was resisted both by Newton, and by Einstein [42] who called it "spooky", but it has now been demonstrated experimentally [43, 44] that local realistic theory cannot account for correlations between measurements performed at well separated sites. The conclusion is that quantum theory permits hidden variables and is non-local. This conclusion is at variance with relativity, but, as pointed out by Bohm [34], the nonlocality of quantum theory only applies to complex wave functions and does not imply that the quantum potential can be used to transmit signals faster than light. 

The first experiments to analyze EPR correlations used polarized light beams rather than electronic spin systems. The results obtained by Aspect [44] are especially relevant since the systems for study were prepared to be separated space-like. Aspect analyzed the polarization of pairs of photons emitted by a single source toward separate detectors. Measured independently, the polarization of each set of photons fluctuated in a seemingly random way. However, when two sets of measurements were compared, they displayed an agreement stronger than could be accounted for by any local realistic theory. 

With realizations of the Vycor glass as shown in Fig. 1, mean field theory applied to the lattice model (1) provides a simple and sufficiently realistic method to examine fluid adsorption behavior on a coarse-grained level. In particular, the local density on each site pi = (riitj) is self-consistently determined by... 

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