## The world as emergent from pure entropy

2017-12-28T14:36:49Z (GMT)
<div>We propose a meta-logical framework to understand the world by an ensemble of theorems rather than by a set of axioms. We prove that the theorems of the ensemble must have *feasible* proofs and must recover *universality*. The ensemble is axiomatized when it is constructed as a partition function, in which case its axioms are, up to an error rate, the leading bits of Omega (the halting probability of a prefix-free universal Turing machine). The partition function augments the standard construction of \$\Omega\$ with knowledge of the size of the proof of each theorems. With this knowledge, it is able to decide *feasible mathematics*.</div><div><br></div><div>As a consequence of the axiomatization, the ensemble additionally adopts the mathematical structure of an ensemble of statistical physics; it is from this context that the laws of physics are derived. The Lagrange multipliers of the partition function are the fundamental Planck units and the background, a thermal space-time, emerges as a consequence of the limits applicable to the conjugate pairs. The background obeys the relations of special and general relativity, dark energy, the arrow of time, the Schrödinger equation, the Dirac equation and it embeds the holographic principle. In this context, the limits of feasible mathematics are mathematically the same as the laws of physics.</div><div><br></div><div>The framework is so fundamental that informational equivalents to length, time and mass (assumed as axioms in most physical theories) are here formally derivable. Furthermore, it can prove that no alternative framework can contain fewer bits of axioms than it contains (thus it is necessarily the simplest theory). Furthermore, it can prove that, for all worlds amenable to this framework, the laws of physics will be the same (hence there can be no alternatives).</div><div><br></div><div>Thus, the framework is a possible candidate for a final theory.</div>