We have found that proposals addressing the old cosmological constant problem come in various categories. The aim of this paper is to identify as many different, credible mechanisms as possible and to provide them with a code for future reference. We find that they all can be classified into five different schemes of which we indicate the advantages and drawbacks.

We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Sec.1, we introduce these problems. In Sec.2, we introduce topos theory, especially the idea of a topos of presheaves. In Sec.3, we discuss several possible applications of topos theory to the problems in Sec.1. In Sec.4, we draw some conclusions.

The usual macroscopic theory of relativistic mechanics and electromagnetism is formulated so that all assumptions but one are consistent with both special relativity and Newtonian mechanics, the distinguishing assumption being that to any energyE, whatever its form, there corresponds an inertial massE/c 2 . The speed of light enters this formulation only as a consequence of the inertial equivalent of energy1/c 2 . While, for1/c 2 >0 the resulting theory has symmetry under the Poincaré group, including Lorentz transformations, all its (...) physical consequences can be derived and tested in any one inertial frame. In particular, an account is given in one inertial frame for the dynamic causes of relativistic effects for simple accelerated clocks and roads. (shrink)

Summary The present paper constitutes an elaboration of a previous work by one of us which, among other things, proposed some modifications of Popper's tetradic schema. Here, in the first part, we consider critically and develop further these modifications and elaborate on methods which prove more satisfactory for the mapping of the problem solving processes in Physics. We also find the opportunity to make some comments on Physics and on its relation to Mathematics. In the second part, there is an (...) attempt to test the above ideas on the genesis and development of the Special Relativity Theory. In doing this, we concentrate mainly on Einstein's 1905 paper and try to explicitate its relation with the situation Physics found itself in that period as well as to clarify the epistemological status of Einstein's two postulates. (shrink)

It is still perhaps not widely appreciated that in 1905 Einstein used his postulate concerning the ‘constancy’ of the light-speed in the ‘resting’ frame, in conjunction with the principle of relativity, to derive numerical light-speed invariance. Now a ‘weak’ version of the relativity principle (or, alternatively, appeal to the Michelson—Morley experiment) leads from Einstein's light postulate to a condition that we call universal light-speed constancy. which is weaker than light-speed invariance. It follows from earlier independent investigations (Robertson [1949]; Steigler [1952]; (...) Tzanakis and Kyritsis [1984]) that this condition is none the less sufficient to derive the Lorentz transformations up to a scale factor, given the well-known kinematic principle of ‘reciprocity’. In this paper, we follow Robertson and explore the kinematics consistent with universal light-speed constancy without imposing reciprocity, and we recover the Lorentz transformations by further appeal only to the weak relativity principle and spatial isotropy. (shrink)