At a fundamental level every measurement process relies on an interac-tion where one entity influences another. The boundary of an interaction is given by a pair of events, which can be ordered by virtue of the interac-tion. This results in a partially ordered set (poset) of events often referred to as a causal set. In this framework, an observer can be represented by a chain of events. Quantification of events and pairs of events, referred to as intervals, can be performed by projecting them onto an observer chain, or even a pair of observer chains, which in specific situations leads to a Minkowski metric replete with Lorentz transformations. We illustrate how this framework of interaction events gives rise to some of the well-known properties of the Fermions, such as Zitterbewegung. We then take this further by making inferences about events, which is performed by employing the process calculus, which coincides with the Feynman path integral formulation of quantum mechanics. We show that in the 1+1 dimensional case this results in the Feynman checkerboard model of the Dirac equation describing a Fermion at rest. 1
At a fundamental level every measurement process relies on an interac-tion where one entity influences another. The boundary of an interaction is given by a pair of events, which can be ordered by virtue of the interac-tion. This results in a partially ordered set (poset) of events often referred to as a causal set. In this framework, an observer can be represented by a chain of events. Quantification of events and pairs of events, referred to as intervals, can be performed by projecting them onto an observer chain, or even a pair of observer chains, which in specific situations leads to a Minkowski metric replete with Lorentz transformations. We illustrate how this framework of interaction events gives rise to some of the well-known properties of the Fermions, such as Zitterbewegung. We then take this further by making inferences about events, which is performed by employing the process calculus, which coincides with the Feynman path integral formulation of quantum mechanics. We show that in the 1+1 dimensional case this results in the Feynman checkerboard model of the Dirac equation describing a Fermion at rest. 1
At a fundamental level every measurement process relies on an interaction where one entity influences another. The boundary of an interaction is given by a pair of events, which can be ordered by virtue of the interaction. This results in a partially ordered set (poset) of events often referred to as a causal set. In this framework, an observer can be represented by a chain of events. Quantification of events and pairs of events, referred to as intervals, can be performed by projecting them onto an observer chain, or even a pair of observer chains, which in specific situations leads to a Minkowski metric replete with Lorentz transformations. We illustrate how this framework of interaction events gives rise to some of the well-known properties of the Fermions, such as Zitterbewegung. We then take this further by making inferences about events, which is performed by employing the process calculus, which coincides with the Feynman path integral formulation of quantum mechanics. We show that in the 1+1 dimensional case this results in the Feynman checkerboard model of the Dirac equation describing a Fermion at rest.
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.
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]
In recent works, Knuth and Bahreyni have demonstrated that the concepts of space and time are emergent in a coarse-grained model of direct particle-particle influence.In addition, Knuth demonstrated that observer-made inferences regarding the free particle, which is defined as a particle that influences others, but is not itself influenced, result in a situation identical to the Feynman checkerboard model of the Dirac equation.This suggests that the same theoretical framework that gives rise to an emergent spacetime is consistent with quantum mechanics.In this paper, we begin to explore the effect of influence on the emergent properties of a particle.This initial study suggests that when a particle is influenced, it is interpreted as accelerating in a manner consistent with special relativity implying that, at least in this situation, influence can be conceived of as a force.