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How Far Should the Principle of Relativity Go? (by Elemer E. Rosinger): Abstract: The Principle of Relativity has so far been understood as the covariance of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of one single type of mathematical entities, namely, the scalars given by the usual continuum of the field R of real numbers, or by the usual mathematical structures built upon R, such as the scalars given by the complex numbers C, or the vectors in finite dimensional Euclidean spaces Rn, infinite dimensional Hilbert spaces, etc. This paper argues for progressing deeper and wider in furthering the Principle of Relativity, not by mere covariance with respect to reference frames, but by studying the possible covariance with respect to a large variety of algebras of scalars which extend significantly R or C, variety of scalars in terms of which various theories of Physics can equally well be formulated. First directions in this regard can be found naturally in the simple Mathematics of Special Relativity, the Bell Inequalities in Quantum Mechanics, or in the considerable amount of elementary Mathematics in finite dimensional vector spaces which occurs in Quantum Computation. The large classes of algebras of scalars suggested, which contain R and C as particular cases, have the important feature of typically no longer being Archimedean, see Appendix, a feature which can prove to be valuable when dealing with the so called "infinities" in Physics. The paper has a Comment on the so called "end of time". http://prespacetime.com/index.php/pst/article/view/148
George Boole and the Bell Inequalities (by Elemer E. Rosinger): Abstract: As shown by Pitowsky, the Bell inequalities are related to certain classes of probabilistic inequalities dealt with by George Boole, back in the 1850s. Here a short presentation of this relationship is given. Consequently, the Bell inequalities can be obtained without any assumptions of physical nature, and merely through mathematical argument. http://prespacetime.com/index.php/pst/article/view/149
Which Are the Maximal Ideals? (by Elemer E. Rosinger): Abstract: Ideals of continuous functions which satisfy an off diagonality condition proved to be important connected with the solution of large classes of nonlinear PDEs, and more recently, in General Relativity and Quantum Gravity. Maximal ideals within those which satisfy that off diagonality condition are important since they lead to differential algebras of generalized functions which can handle the largest classes of singularities. The problem of finding such maximal ideals satisfying the off diagonality condition is formulated within some background detail, and commented upon. http://prespacetime.com/index.php/pst/article/view/150
Heisenberg Uncertainty in Reduced Power Algebras (by Elemer E. Rosinger): Abstract: The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far wider frameworks of scalars, namely,within one or the other of the infinitely many reduced power algebras which can replace the usual real numbers R, or complex numbers C. A major advantage of such a re-formulation is, among others, the disappearance of the well known and hard to deal with problem of the so called "infinities in Physics". The use of reduced power algebras also opens up a foundational question about the role, and in fact, about the very meaning and existence, of fundamental constants in Physics, such as Planck’s constant h. A role, meaning, and existence which may, or on the contrary, may not be so objective as to be independent of the scalars used, be they the usual real numbers R, complex numbers C, or scalars given by any of the infinitely many reduced power algebras, algebras which can so easily be constructed and used. http://prespacetime.com/index.php/pst/article/view/151
Crisis of Knowledge at the Beginning of the 21st Century (by Peter Kohut): Abstract: The contemporary crisis of thinking and knowledge is a consequence of positivism and its various branches leading to the extinction of philosophy and refusing to deal with the basic philosophical questions. Positivism became the basis for scientific knowledge replacing Hegelian dialectical rationalism, in which the classical philosophy had achieved its apex. Positivism tried to create the principles for scientific research based on the rules of formal logic and experiment, where the axiomatic approach became a starting point for finding the useful scientific results. Positivism refused to deal with the basic philosophical questions and categories regarding the nature of Being, God and the physical Universe. The way to the truth became “scientific” with many successful and useful discoveries and inventions. The dialectic logic was rejected as speculative, sophistic, metaphysical and useless and replaced by formal logic which together with mathematics and experimental verifications became the basic methods of scientific research mainly in the sphere of theoretical physics. http://scigod.com/index.php/sgj/article/view/103
Basic Cosmic Characteristics (Energy and Force) [by Peter Kohut]: Abstract: The nature of electrostatic and gravitational forces will be derived by using a dialectical logic for finding the basic relations between fundamental physical characteristics of the Universe. http://scigod.com/index.php/sgj/article/view/102
New Proofs for the Existence of God (Part III): The Teleogenical Proof (by Nadeem Haque, Mehran Banaei): Abstract: A synthesis of recent Cosmological and Biological Evidence concretely points to an Intelligence that created this universe that must be independent of this universe. The classical teleological and cosmological arguments have valid components but are not conclusive due to their segmented and non-integrated nature and also because of a logically invalid tactic/strategy used by atheists known as the fallacy of conflation. Also discussed by deconstruction, is the futile attempt at using cloaked language to hide the fact of teleological processes. Epistemologically, it is also shown why the Big Bang is a fact and not a theory. Herein, a complex yet integrated new proof that interweaves all these ideas, called the Teleogenical Proof, is presented that overcomes all the shortcomings of the latter two classical attempted proofs and connects with the Sesamatic proof on the question of infinite regress. http://scigod.com/index.php/sgj/article/view/98