On a possible origin of modular invariance

We propose an information theoretic model of the space-time pre-geometry where the pre-geometry is considered as a ''coded state of matter and space-time'', distinctly different from the classical space-time or any known state of matter. Assuming that physical processes at Planck's dimensions are stochastic Markov processes and using information theoretic and algebro-geometric coding techniques, we show that modular invariance is a natural consequence of: 1. Shannon's channel capacity theorem. 2. Nature selects and uses only those error-correcting codes to transfer information between space-time entities which allow the value of propagation rate R reaching its critical value RC, the channel capacity. Next, using the strong converse theorem we show that a phase-transition occurs at (RC-R) < ε, for some small ε > 0. Furthermore, it is known that some symmetrically packed optimal codes lead to E8 lattice while others to a 26-dimensional Lorentz lattice used in string theories. This suggests a precise connection between our model and string theories. (author). 26 refs