The Function of the Second Postulate in Special Relativity

Many authors noted that the principle of relativity, together with space-time symmetries, suffices to derive Lorentz-like coordinate transformations between inertial frames. These contain a free parameter, $k$, (equal to $c^{-2}$ in special relativity) which is usually claimed to be empirically determinable, so that special relativity does not need the postulate of constancy of the speed of light. I analyze this claim and find that all methods destined to measure $k$ fail without further assumptions, similar to the second postulate. Specifically, measuring $k$ requires a signal that travels identically in opposite directions (this is unrelated to the conventionality of synchronization, as the one-postulate program implicitly selects the standard synchronization convention). Positing such a property about light is logically weaker than Einstein's second postulate but suffices to recover special relativity in full

A Case against Representationalism

The case of blurry vision has been cited by many as a counterexample to representationalism in the theory of perception. Specifically, it is claimed that the phenomenon of blurry vision is incompatible with the supervenience thesis which is at the root of representationalism. Michael Tye, a leading representationalist, has responded to such objections by giving an account of blurry vision in a way that, allegedly, renders it compatible with representationalism. In this paper I argue that Tye’s account of blurry vision, though blocking one line of objection, cannot save representationalism. I then assimilate cases of blurry vision as well as similar cases to the more general category of indeterminate experiences

The Hole Probability for Gaussian Entire Functions

We study the hole probability of Gaussian random entire functions. More specifically, we work with entire functions in Taylor series form with i.i.d complex Gaussian coefficients. A hole is the event where the function has no zeros in a disc of radius r. We find exact asymptotics for the rate of decay of the hole probability for large values of r, outside a small exceptional set (which is deterministic).Comment: 1 figur

The necessity of the second postulate in special relativity

Many authors noted that the principle of relativity together with space-time homogeneity and isotropy restrict the form of the coordinate transformations from one inertial frame to another to being Lorentz-like. The equations contain a free parameter, $k$ (equal to $c^{-2}$ in special relativity), which value is claimed to be merely an empirical matter, so that special relativity does not need the postulate of constancy of the speed of light. I analyze this claim and argue that the distinction between the cases $k = 0$ and $k \neq 0$ is on the level of a postulate and that until we assume one or the other, we have an incomplete structure that leaves many fundamental questions undecided, including basic prerequisites of experimentation. I examine an analogous case in which isotropy is the postulate dropped and use it to illustrate the problem. Finally I analyze two attempts by Sfarti, and Behera and Mukhopadhyay to derive the constancy of the speed of light from the principle of relativity. I show that these attempts make hidden assumptions that are equivalent to the second postulate

On the origin of three generation free fermionic superstring models

The three generation superstring models in the free fermionic models have had remarkable success in describing the real--world. The most explored models use the NAHE set to obtain three generations and to separate the hidden and observable sectors. It is of course well known that the full NAHE set is not required in order to construct three generation free fermionic models. I argue that all the semi--realistic free fermionic models that have been constructed to date correspond to $Z_2\times Z_2$ orbifolds. Thus, the successes of the semi--realistic free fermionic models, if taken seriously, suggest that the true string vacuum is a $Z_2\times Z_2$ orbifold with nontrivial background fields and quantized Wilson lines.Comment: 12 pages, phyzzx.tex, tables.te

Duality, Equivalence, Mass and The Quest For The Vacuum

I contemplate the possibility that the mismatch between the maximally symmetric point (the free fermionic point) and the strictly self-dual point in the Narain moduli space plays a role in the string vacuum selection. The role of self-duality in the recent formulation of quantum mechanics from an equivalence postulate, and the new perspective that it offers on the foundations of quantum gravity and the origin of mass, are discussed.Comment: 8 pages. Standard Latex & sprocl.tex. Invited talk presented at PASCOS 99, Lake Tahoe, CA December 10-16 199