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.
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.
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.
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.
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]
Physics is traditionally conceived of as a set of laws that universally governs the behavior of physical systems. These laws, however they are decreed, are believed to govern the behavior of not only everything in the universe, but the form of the universe itself. However, this traditional concept of physics as a universal governance is at odds with our modern theories of quantum mechanics and relativity, which place the observer and information in a central role. In this talk, I aim to rethink the foundations and attempt to build physics from the bottom up based on a very simple foundational idea that all one can possibly know is that things influence one another. I will demonstrate that a great deal of physics can be derived in this context from symmetries alone. For example, one can show that there is a unique consistent quantified description of a network of influence events, which is given by the mathematics of relativistic space-time and results in forces. In addition, making inferences about influence events leads to the relativistic quantum mechanics of fermions. As a result, many ‘fundamental’ concepts in physics and their relationships to one another can be derived from a more fundamental picture based on influence.
It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's "checker-board" trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum "coordinates". This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point.
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the partition function of the relevant physical quantities over a space-time parametrized by coordinates. The partition yields a probabilistic interpretation that, based on Feynman’s path integral formulation, leads to a dynamical law that generalizes the Schrödinger equation. A variety of systems can be put into the form proposed here, including particles in potentials, as well as matter and interaction fields. The main advantage of the proposed framework is that it presents the space of properties separately from that of the space of coordinates, whereas the dynamical law can be interpreted as the equation of two differential structures, one from each of these spaces. The resulting framework shows possibilities to further study physical quantities that relate directly to the space-time coordinates, whose dynamics is best described in thermodynamical, rather than Hamiltonian, terms. A notable case being the theory of general relativity.