In this talk, I propose an approach to understanding the foundations of physics by considering the optimal inferences an intelligent agent can make about the universe in which he or she is embedded. Information acts to constrain an agent’s beliefs. However, at a fundamental level, any information is obtained from interactions where something influences something else. Given this, the laws of physics must be constrained by both the nature of such influences and the rules by which we can make inferences based on information about these influences. I will review the recent progress we have made in this direction. This includes: a brief summary of how one can derive the Feynman path integral formulation of quantum mechanics from a consistent quantification of measurement sequences with pairs of numbers (Goyal, Skilling, Knuth 2010; Goyal, Knuth 2011), a demonstration that consistent apt quantification of a partially-ordered set of events (connected by interactions) by an embedded agent results in space-time geometry and Lorentz transformations (Knuth, Bahreyni 2012), and an explanation of how, given the two previous results, inferences (Knuth, Skilling 2012) about a direct particle-particle interaction model results in the Dirac equation (in 1+1 dimensions) and the properties of Fermions (Knuth, 2012). In summary, critical aspects of quantum mechanics, relativity, and particle properties appear to be derivable by considering an embedded agent who consistently quantifies observations and makes consistent inferences about them.
Goyal P., Knuth K.H., Skilling J. 2010. Phys. Rev. A 81, 022109. arXiv:0907.0909v3 [quant-ph]
Goyal P., Knuth K.H. 2011. Symmetry 3(2):171-206.
Knuth K.H. 2012. MaxEnt 2012 Proceedings. arXiv:1212.2332 [quant-ph]
Knuth K.H., Bahreyni N. 2012. arXiv:1209.0881 [math-ph]
Knuth, K.H., Skilling, J. 2012. Axioms 1:38-73. arXiv:1008.4831 [math.PR]
Knuth K.H. 2013. Information-based physics: An intelligent embedded agent's guide to the universe. Santa Fe Institute, Santa Fe NM, Mar 2013.