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We discuss repulsive Casimir forces between dielectric materials with nontrivial magnetic susceptibility. It is shown that considerations based on the naive pairwise summation of van der Waals and Casimir-Polder forces may not only give an incorrect estimate of the magnitude of the total Casimir force but even the wrong sign of the force when materials with high dielectric and magnetic responses are involved. Indeed repulsive Casimir forces may be found in a large range of parameters, and we suggest that the effect may be realized in known materials. The phenomenon of repulsive Casimir forces may be of importance both for experimental study and for nanomachinery applications.

We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the ``relative Casimir energy", which we define for a configuration of disjoint conducting boundaries of arbitrary shapes, as the difference of Casimir energies between the given configuration and a configuration with the same boundaries infinitely far apart. Using path integration techniques, we show that the relative Casimir energy vanishes exponentially fast in temperature. This is consistent with a simple physical argument based on Kirchhoff's law. As a result the ``relative Casimir entropy", which we define in an obviously analogous manner, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the boundaries. Thus the Casimir force between disjoint pieces of the boundary, in the classical limit, is entropy driven and is governed by a dimensionless number characterizing the geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations in temperature from the behavior just described. These logarithmic deviations seem to arise due to our difficulty to separate the Casimir energy (and the other thermodynamical quantities) from the ``electromagnetic'' self-energy of each of the connected components of the boundary in a well defined manner. Our approach to the Casimir effect is not to impose sharp boundary conditions on the fluctuating field, but rather take into consideration its interaction with the plasma of ``charge carriers'' in the boundary, with the plasma frequency playing the role of a physical UV cutoff. This also allows us to analyze deviations from a perfect conductor behavior.Comment: latex, 56 pages, one eps figure. Major improvements of presentation (especially in Section 2). No change in the conclusions. Connection with the works of Balian et al. on the Casimir effect is clarified. Abstract changed, typos correcte

A Bell inequality violation (BIQV) allowed by the two-mode squeezed state (TMSS), whose Wigner function is nonnegative, is shown to hold only for correlations among dynamical variables (DV) that cannot be interpreted via a local hidden variable (LHV) theory.Explicit calculations and interpretation are given for Bell's suggestion that the EPR (Einstein, Podolsky and Rosen) state will not allow for BIQV in conjuction with its Wigner representative state being nonnegative.It is argued that Bell's theorem disallowing the violation of Bell's inequality within a local hiddenvariable theory depends on the DV's having a definite value -assigned by the LHV-even when they cannot be simultaneously measured. The analysis leads us to conclude that BIQV is to be associated with endowing these definite values to the DV's and not with their locality attributes.PACS numbers:

Relative and center of mass coordinates are used to generalize mutually unbiased bases (MUB) and define mutually unbiased collective bases (MUCB). Maximal entangled states are given as product states in the collective variables.

Two mode squeezed vacuum states allow Bell's inequality violation (BIQV) for all non-vanishing squeezing parameter (ζ). Maximal violation occurs at ζ → ∞ when the parity of either component averages to zero. For a given entangled two spin system BIQV is optimized via orientations of the operators entering the Bell operator (cf. S. L. Braunstein, A. Mann and M. Revzen: Phys. Rev. Lett. 68, 3259 (1992)). We show that for finite ζ in continuous variable systems (and in general whenever the dimensionality of the subsystems is greater than 2 ) additional parameters are present for optimizing BIQV. Thus the expectation value of the Bell operator depends, in addition to the orientation parameters, on configuration parameters. Optimization of these configurational parameters leads to a unique maximal BIQV that depends only on ζ. The configurational parameter variation is used to show that BIQV relation to entanglement is, even for pure state, not monotonic.

Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators are underpinned with finite geometry which provide intuitive perspective to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite dimensional quantum mechanics studies. Interrelation among the Hilbert space operators revealed via their (finite) dual affine plane geometry (DAPG) underpinning are displayed and utilized in formulating the finite dimensional ubiquitous Radon transformation and its inverse illustrating phase space-like physics encoded in lines and points of the geometry. The finite geometry required for our study is outlined.

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