The Greenberger–Horne–Zeilinger argument against noncontextual local hidden variables is recast in quantum logical terms of fundamental propositions, states and probabilities. Unlike Kochen–Specker- and Hardy-like configurations, this operator based argument proceeds within four nonintertwining contexts. The nonclassical performance of the GHZ argument is due to the choice or filtering of observables with respect to a particular state. We study the varieties of GHZ games one could play in these four contexts, depending on the chosen state of the GHZ basis.

We study some aspects of the emergence of _lógos_ from _xáos_ on a basal model of the universe using methods and techniques from algorithmic information and Ramsey theories. Thereby an intrinsic and unusual mixture of meaningful and spurious, emerging laws surfaces. The spurious, emergent laws abound, they can be found almost everywhere. In accord with the ancient Greek theogony one could say that _lógos_, the Gods and the laws of the universe, originate from “the void,„ or from _xáos_, a picture (...) which supports the unresolvable/irreducible lawless hypothesis. The analysis presented in this paper suggests that the “laws„ discovered in science correspond merely to syntactical correlations, are local and not universal. (shrink)

In this paper we consider the possibility of a Quantum Molinism : such a view applies an analogue of the Molinistic account of free will‘s compatibility with God’s foreknowledge to God’s knowledge of (supposedly) indeterministic events at a quantum level. W e ask how (and why) a providential God could care for and know about a world with this kind of indeterminacy. We consider various formulations of such a Quantum Molinism, and after rejecting a number of options arrive at one (...) seemingly coherent formulation. (shrink)

Do the partial order and ortholattice operations of a quantum logic correspond to the logical implication and connectives of classical logic? Rephrased, How far might a classical understanding of quantum mechanics be, in principle, possible? A celebrated result of Kochen and Specker answers the above question in the negative. However, this answer is just one among various possible ones, not all negative. It is our aim to discuss the above question in terms of mappings of quantum worlds into classical ones, (...) more specifically, in terms of embeddings of quantum logics into classical logics; depending upon the type of restrictions imposed on embeddings, the question may get negative or positive answers. (shrink)

We study the idea of implantation of Piron's and Bell's geometrical lemmas for proving some results concerning measures on finite as well as infinite-dimensional Hilbert spaces, including also measures with infinite values. In addition, we present parabola based proofs of weak Piron's geometrical and Bell's lemmas. These approaches will not used directly Gleason's theorem, which is a highly non-trivial result.

Complementarity is not only a feature of quantum mechanical systems but occurs also in the context of finite automata.

Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) in chaos theory, (ii) for paradoxical decompositions of solid three-dimensional objects, (iii) in the theory of effective computability (Church-Turing thesis) related to the possible “solution of supertasks,” and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for physical applications are discussed: (...) Canlorian “naive” (i.e., nonaxiomatic) set theory, contructivism, and operationalism. In the author's opinion, an attitude of “suspended attention” (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same time, physicists should be open to “bizarre” or “mindboggling” new formalisms, which need not be operationalizable or testable at the lime of their creation, but which may successfully lead to novel fields of phenomenology and technology. (shrink)

Complementarity is not only a feature of quantum mechanical systems but occurs also in the context of finite automata.

We construct peculiar Hilbert spaces from counterexamples to the axiom of choice. We identify the intrinsically effective Hamiltonians with those observables of quantum theory which may coexist with such spaces. Here a self adjoint operator is intrinsically effective if and only if the Schrödinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.

Penrose [40] has discussed a new point of view concerning the nature of physics that might underline conscious thought processes. He has argued that it might be the case that some physical laws are not computable, i.e. they cannot be properly simulated by computer; such laws can most probably arise on the “no-man’s-land” between classical and quantum physics. Furthermore, conscious thinking is a non-algorithmic activity. He is opposing both strong AI , and Searle’s [47] contrary viewpoint mathematical “laws”).

After an elementary derivation of Bell's inequality, classical, quantum mechanical, and stronger-than-quantum correlation functions for 2-particle-systems are discussed. Special functions are investigated which give rise to an extreme violation of Bell's inequality by the value of 4. Referring to a specific quantum system it is shown that under certain conditions such an extreme violation would contradict basic laws of physics.

Special relativity theory is generalized to two or more “maximal” signalling speeds. This framework is discussed in three contexts: (i) as a scenario for superluminal signalling and motion, (ii) as the possibility of two or more “light” cones due to the a “birefringent” vacuum, and (iii) as a further extension of conventionality beyond synchrony.

In an extension of speculations that physical space–time is a fractal which might itself be embedded in a high-dimensional continuum, it is hypothesized to “compensate” for local variations of the fractal dimension by instead varying the metric in such as way that the intrinsic dimensionality remains an integer. Thereby, an extrinsic fractal continuum is intrinsically perceived as a classical continuum. Conversely, it is suggested that any variation of the metric from its Euclidean form can be “shifted” to nontrivial fractal topology. (...) Thereby “holes” or “gaps” in spacetime could give rise to curvature. (shrink)