My former student Prof. Newshaw Bahreyni and my current student James Walsh and I will be making a joint presentation at the Beyond SpaceTime 2015 Workshop organized by Christian Wuthrich, Nick Huggett, and David Rideout in San Diego in March 2015. We are excited to have the opportunity to discuss our foundational ideas resulting in emergent physics.
The Influence Network:
A New Foundation for Emergent Physics
Kevin H. Knuth 1,2 , Newshaw Bahreyni 3, James L. Walsh 1
1. Department of Physics, University at Albany, Albany NY 12222, USA
2. Department of Informatics, University at Albany, Albany NY 12222, USA
3. Department of Physics, Kenyon College, Gambier, OH 43022, USA
Foundational physical theories often suffer from the fact that relatively high level concepts, such as space, time, mass and energy, and their basic relationships to one another are often taken as foundational concepts. While such assumptions are convenient and well-founded from the perspective of a relatively well-functioning set of higher-level physical theories, taking them as foundational concepts prevents one from gaining deeper insights, which is critical to developing a theory based on truly foundational concepts.
We consider a simplified picture based on the simple idea that things influence one another. The nature of such things and their influences on one another is not assumed to be known. Instead we simply take as a starting point that things exist and they influence one another, and investigate to what degree a mathematical description of such things and their influences is constrained by simple symmetries or order-theoretic relations.
Consistent quantification of order-theoretic structures leads to constraint equations that often mirror what we consider to be physical laws . For example, in past work by considering the symmetries associated with combining quantum mechanical measurement sequences as well as consistency with probability theory , we have derived the Feynman rules for manipulating quantum amplitudes [3,4].
More recently, we have applied these concepts to a set of objects that influence one another. Influence is assumed to occur in a discrete fashion such that an instance of influence couples precisely two objects in a directed fashion so that one object can be said to influence the other object. Influence is also assumed to be transitive so that one object can influence another via an intermediary. For each instance of influence, we can define two events: the act of one object influencing and the act of the second object being influenced. Together this allows one to describe objects and their influences as a partially ordered set (poset). As such, an object (which, for lack of a better word, we refer to as a particle) is represented as a chain of events. In this sense, and only this sense, is this theory related to casual sets. The theories differ dramatically in their approach to mathematically representing such posets.
The critical difference is that we apply the concepts of consistent quantification with respect to a distinguished chain of events, which we refer to as an observer chain or an embedded observer. We (Knuth & Bahreyni) have demonstrated that the quantification of partially-ordered (causally-ordered) sets of events by an embedded observer results in constraint equations that reflect fundamental mathematics of space-time (Minkowski metric and Lorentz transformations) [5, 6, 7]. More recently, we (Walsh & Knuth) have shown that when an object is influenced, it behaves as if reacting to a force  in such a way that reproduces the relativistic version of Newton’s second law. Moreover, the receipt of influence results in time dilation, which suggests a pathway to gravity.
The concept of influence is also consistent with quantum mechanics. One can also consider situations in which embedded observers make inferences about a particle’s behavior. We have demonstrated, in the idealized case of a free particle (which influences others, but is not itself influenced) that the situation is identical to the Feynman checkerboard problem for the electron, which is known to give rise to the Dirac equation [6, 7]. In addition, other characteristics of fermion physics, such as Zitterbewegung  and helicity (in 1+1 dimensions) emerge naturally from the network of influence events.
In this extended talk, Kevin Knuth will introduce the concept of consistent quantification and demonstrate how constraint equations enforcing consistency play the role of what we usually consider to be physical laws. Newshaw Bahreyni will consider a partially ordered set of events where observers are represented as chains of events coupled to one another via influence events. She will demonstrate that for coordinated observers to agree with one another, consistent quantification requires that the poset be described with the familiar mathematics of spacetime physics (Minkowski metric and Lorentz transformations) . James Walsh will consider the effect of influence on an object and demonstrate that consistent quantification results in the traditional concept of force. Knuth will conclude by discussing how inferences made about an object’s influence events results in the Dirac equation and fermion physics.
 Knuth K.H. 2003. Deriving laws from ordering relations. G.J. Erickson, Y. Zhai (eds.), MaxEnt 2003, Jackson Hole WY, AIP Conference Proceedings 707, AIP, Melville NY, pp. 204-235. arXiv:physics/0403031 [physics.data-an]
 Knuth K.H., Skilling J. 2012. Foundations of Inference. Axioms 1:38-73. arXiv:1008.4831 [math.PR]
 Goyal P., Knuth K.H., Skilling J. 2010. Origin of complex quantum amplitudes and Feynman’s rules, Phys. Rev. A 81, 022109.
 Goyal P., Knuth K.H. 2011. Quantum theory and probability theory: their relationship and origin in symmetry, Symmetry 3(2):171-206.
 Knuth K.H., Bahreyni N. 2014. A potential foundation for emergent space-time, Journal of Mathematical Physics, 55, 112501. doi:10.1063/1.4899081, arXiv:1209.0881 [math-ph]
 Knuth K.H. 2013. Information-Based Physics and the Influence Network, FQXi 2013 Essay Contest Entry (Third Place): “It from Bit or Bit from It?”. arXiv:1308.3337 [quant-ph]
 Knuth K.H. 2014. Information-based physics: an observer-centric foundation. Contemporary Physics, 55(1), 12-32, (Invited Submission). arXiv:1310.1667 [quant-ph]
 Walsh J.L., Knuth K.H. 2014. Information-Based Physics, Influence and Forces. Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), Amboise, France, AIP Conference Proceedings 1641, AIP, Melville NY, pp. 538-547. arXiv:1411.2163 [quant-ph]
 Knuth K.H. 2014. The problem of motion: the statistical mechanics of Zitterbewegung. Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), Amboise, France, AIP Conference Proceedings 1641, AIP, Melville NY, pp. 588-594. arXiv:1411.1854 [quant-ph]