On a purported local extension of the quantum formalism

Since the early days of quantum mechanics, a number of physicists have doubted whether quantum mechanics was a complete theory and wondered whether it was possible to extend the quantum formalism by adjoining hidden variables.1 In 1952, Bohm answered this question in the affirmative2 and in doing so refuted von Neumann’s influential yet flawed proof that no such extension was possible.3 However, Bohm’s hidden variable theory has not won wide support partly because the theory is nonlocal: there is instantaneous action at a distance. Since there is an obvious problem reconciling such nonlocal theories with Relativity, hidden variable theories would look much more promising if they also satisfied locality. Accordingly, the question as to whether or not local hidden variable theories are possible assumes great significance. In 1964 Bell appeared to prove that this question had a negative answer:4 He showed that any local hidden variables theory is incompatible with certain quantum mechanical predictions. Since these predictions have been borne out by the experiments of Aspect and others5 the prospects for hidden variable theories have looked grim. Angelidis disagrees.6 He claims to have done to Bell what Bohm did to von Neummann: He has found a theory which is local and which generates a family of probability functions converging uniformly to the probability function generated by quantum mechanics. If this were true, then Angelidis’ theory would be a counterexample to Bell’s theorem and a promising path would once again be open to hidden variable theorists. Unfortunately, Angelidis’ theory fails to live up to his claims: As formulated, the theory does not make the same predictions as quantum mechanics, and while there is a natural extension of his theory which does make the same predictions, the extension is not local. Bell’s Theorem stands

A Simplified Version of Gödel’s Theorem

The Lucas - Penrose argument is considered. As a special case we consider sorites arithmetic and explain how the argument actually works. A comparison with Gödel’s own treatment is made. Truth is valuable. But certifiable truth is hard to come by

A Simplified Version of Gödel’s Theorem

The Lucas - Penrose argument is considered. As a special case we consider sorites arithmetic and explain how the argument actually works. A comparison with Gödel’s own treatment is made. Truth is valuable. But certifiable truth is hard to come by

Reflections on the Development of Steelpan Music: Compositions for Steel Orchestra

The steelpan is a musical instrument created in Trinidad and Tobago circa 1930s. It has secured a place in the countrys cultural identity as one of its most important musical developments. It is authenticated as an orchestral instrument in which skilled players may perform any fugue or arrangement in any genre of music. Its creation and development by ingenious men and women with limited resources cannot be overstated; and ironically, an upper and condescending class who failed or refused to acknowledge a musical phenomenon in its embryonic stage, now shares equally in the pride and international recognition of this national treasure that has gained critical acceptance from musicologists and other scholarly experts. The accidental discovery of the affectionately nicknamed pan, its development and eventual acceptance into the family of idiophones, provide the inspiration for a series of compositions reflected in this thesis

A Simplified Version of Gödel’s Theorem

The Lucas - Penrose argument is considered. As a special case we consider sorites arithmetic and explain how the argument actually works. A comparison with Gödel’s own treatment is made. Truth is valuable. But certifiable truth is hard to come by

A Simplified Version of Gödel’s Theorem

The Lucas - Penrose argument is considered. As a special case we consider sorites arithmetic and explain how the argument actually works. A comparison with Gödel’s own treatment is made. Truth is valuable. But certifiable truth is hard to come by

Kochen-Specker theorem for 8-dimensional space

A Kochen-Specker contradiction is produced with 36 vectors in a real 8-dimensional Hilbert space. These vectors can be combined into 30 distinct projection operators (14 of rank 2, and 16 of rank 1). A state-specific variant of this contradiction requires only 13 vectors, a remarkably low number for 8 dimensions.Comment: LaTeX 8 page

Hyperentangled States

We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any quantum theory, they are dense in its state space. We also give prescriptions for constructing hyperentangled states that involve an arbitrarily large collection of systems.Comment: 23 pages, LaTeX, Submitted to Physical Review