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]
It is generally believed that physical laws, reflecting an inherent order in the universe, are ordained by nature. However, in modern physics the observer plays a central role raising questions about how an observer-centric physics can result in laws apparently worthy of a universal nature-centric physics. Over the last decade, we have found that the consistent apt quantification of algebraic and order-theoretic structures results in calculi that possess constraint equations taking the form of what are often considered to be physical laws. I review recent derivations of the formal relations among relevant variables central to special relativity, probability theory and quantum mechanics in this context by considering a problem where two observers form consistent descriptions of and make optimal inferences about a free particle that simply influences them. I show that this approach to describing such a particle based only on available information leads to the mathematics of relativistic quantum mechanics as well as a description of a free particle that reproduces many of the basic properties of a fermion. The result is an approach to foundational physics where laws derive from both consistent descriptions and optimal information-based inferences made by embedded observers.
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.
The Lorentz transformation of special relativity is based on velocity. Although this velocity may be differentiated by time, the notion of force is not needed to obtain the Lorentz matrix for a particle with rest mass. In particular, in special relativity one considers frames moving at constant velocities. In the case of a photon, the Lorentz transformation preserves the form of Maxwell’s electromagnetic equations. As a result, there does not seem to be a focus on force, rather the emphasis is on the two 4-vectors (p,E) and (x,t) for a particle with rest mass and photon. Nevertheless, a particle with momentum (and the capability to interact) imparts an impulse. In fact, one may think of energy changing due to an impulse (which includes force). Thus from an information point of view, one may ask: Does this force which creates a change in energy/momentum “disappear” as the particle/photon moves at constant speed only to “reappear” when it strikes a surface? If not, where is the information of this force stored? We argue it is associated with a change in energy and momentum of a free particle which in turn is linked to an internal ruler/clock i.e. the quantum frequency and wavelength from exp(-iEt+ipx) which preserves the force because a spatial probability distribution is created (for the wavelength). This force is linked with a direction i.e. the direction of p through the two dimensionality of exp(ipx). Thus, we argue that the force does not disappear, rather it is manifest in the internal clock and ruler which define spacetime for the free quantum particle, but in a probabilistic manner with the distribution being deterministic to ensure it maps to spatial invariance. One might at first find it surprising that force, usually associated with acceleration (i.e. deterministic motion) is now associated with probability cos(px) in space (, but deterministic probability, not random), but E,p and x,t are intertwined through the Lorentz invariant -Et+px for both a particle with rest mass and photon, so if E and p change, it is not necessarily surprising that t,x also change. Thus an impulse may change p and E, but then remains manifest in the system through the internal clock and ruler gradations in such a way that speed is still constant on average.