Relativizing Relativity

The relativity of 'placebos': defending a modified version of Grünbaum's definition

Debates about the ethics and effects of placebos and whether ‘placebos’ 1 in clinical trials of complex treatments such as acupuncture are adequate (and hence 2 whether acupuncture is ‘truly’ effective or a ‘mere placebo’) rage. Yet there is currently 3 no widely accepted definition of the ‘placebo’. A definition of the placebo is likely 4 to inform these controversies. Grünbaum’s (1981, 1986) ...

On perfect completeness for QMA

Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with onesided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a “quantum oracle” relative to which QMA 6= QMA1. As a byproduct, we find that there are facts about quantum complexity classes that are classically relativizing but not ...

Relativizing truth of future-tensed sentences

Revisiting Uniform Computable Categoricity: For the Sixtieth Birthday of Prof. Rod Downey

Inspired by recent work of Csima and Harrison-Trainor and of Montalbán in relativizing the notion of degrees of categoricity, we return to uniform computable categoricity, as described in work of Downey, Hirschfeldt and Khoussainov. Our attempt to integrate these notions together leads to certain new questions about relativizing the concept of the jump of a structure, as well as to an idea of t...

Einstein structures on four-dimensional nutral Lie groups

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...