Logic is to the quantum as geometry is to gravity

I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories. This proposal confers a certain independence on the concept of event, and it modifies the rules of inference concerning events in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical rules of inference, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular.Comment: plainTeX, 26 pages, 2 figures. To appear in G.F.R. Ellis, J. Murugan and A. Weltman (eds), {\it Foundations of Space and Time} (Cambridge University Press). Most current version is available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/ (or wherever my home-page may be)

From Green Function to Quantum Field

A pedagogical introduction to the theory of a gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function $W(x,y)=\langle\phi(x)\phi(y)\rangle$ regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at $W(x,y)$ starting from nothing but the retarded Green function $G(x,y)$. Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished "vacuum" or "ground state", and to recognize some interesting formal relationships, including a general condition on $W(x,y)$ expressing zero-entropy or "purity".Comment: plainTeX, 29 pages, 7 figures. Most current version is available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/157.G2f.pdf (or wherever my home-page may be, such as http://www.physics.syr.edu/~sorkin/some.papers/

To What Type of Logic Does the "Tetralemma" Belong?

Although the so called tetralemma might seem to be incompatible with any recognized scheme of logical inference, its four alternatives arise naturally within the anhomomorphic logics which have been proposed in order to accommodate certain features of microscopic (i.e. quantum) physics. This suggests that the possibility of similar, "non-classical" logics might have been recognized in India at the time when Buddhism arose.Comment: plainTeX, 10 pages, no figures. Added references, revised first appendix, edited for clarity. Most current version is available at http://www.pitp.ca/personal/rsorkin/some.papers/135.catuskoti.pdf} (or wherever my home-page may be

Two Topics concerning Black Holes: Extremality of the Energy, Fractality of the Horizon

We treat two aspects of the physics of stationary black holes. First we prove that the proportionality, d(energy) ~ d(area) for arbitrary perturbations (``extended first law''), follows directly from an extremality theorem drawn from earlier work. Second we consider quantum fluctuations in the shape of the horizon, concluding heuristically that they exhibit a fractal character, with order lambda fluctuations occurring on all scales lambda below M^{1/3} in natural units.Comment: 18 pages, plainTeX, 2 postscript figures (Figures for automatic inclusion are in a separate file which you should receive with the .tex file. For instructions on decoding and including them (or omitting them to avoid error messages if your system can't handle them) see the box at the beginning of the tex file for this paper.