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.
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 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.
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]
At this point in time, two major areas of physics, statistical mechanics and quantum mechanics, rest on the foundations of probability and entropy. The last century saw several significant fundamental advances in our understanding of the process of inference, which make it clear that these are inferential theories. That is, rather than being a description of the behavior of the universe, these theories describe how observers can make optimal predictions about the universe. In such a picture, information plays a critical role. What is more is that little clues, such as the fact that black holes have entropy, continue to suggest that information is fundamental to physics in general. In the last decade, our fundamental understanding of probability theory has led to a Bayesian revolution. In addition, we have come to recognize that the foundations go far deeper and that Cox's approach of generalizing a Boolean algebra to a probability calculus is the first specific example of the more fundamental idea of assigning valuations to partially-ordered sets. By considering this as a natural way to introduce quantification to the more fundamental notion of ordering, one obtains an entirely new way of deriving physical laws. I will introduce this new way of thinking by demonstrating how one can quantify partially-ordered sets and, in the process, derive physical laws. The implication is that physical law does not reflect the order in the universe, instead it is derived from the order imposed by our description of the universe. Information physics, which is based on understanding the ways in which we both quantify and process information about the world around us, is a fundamentally new approach to science.
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the whole framework is built. In quantum physics, first in non-relativistic mechanics and later in quantum field theories, even familiar concepts of position, momentum, wave or particle, are derived constructs from the classical limit in which we live but not intrinsic to the underlying physics. Most crucially, the very idea of the individual, whether an object or an event, distinguished only in a mere label of identity from others identical to it in all the physics, exists only as an approximation, not an element of underlying reality. Failure to recognize this and seeking alternative explanations in many worlds or multiverses leads only to incoherent logic and incorrect physics. As an example, in a physical system such as an atom in a particular state, physics deals with the universal system of all such atoms but makes no meaningful prediction of the position of an electron or the time of decay of any specific atom. Those are incidental, entirely random among all possible positions and times, even while physics makes very precise predictions for the distribution of the outcomes in measurements on atoms in that state. Physics deals with the universal, not the individual.
Abstract. At this point in time, two major areas of physics, statistical mechanics and quantum mechanics, rest on the foundations of probability and entropy. The last century saw several significant fundamental advances in our understanding of the process of inference, which make it clear that these are inferential theories. That is, rather than being a description of the behavior of the universe, these theories describe how observers can make optimal predictions about the universe. In such a picture, information plays a critical role. What is more is that little clues, such as the fact that black holes have entropy, continue to suggest that information is fundamental to physics in general. In the last decade, our fundamental understanding of probability theory has led to a Bayesian revolution. In addition, we have come to recognize that the foundations go far deeper and that Cox’s approach of generalizing a Boolean algebra to a probability calculus is the first specific example of the more fundamental idea of assigning valuations to partially-ordered sets. By considering this as a natural way to introduce quantification to the more fundamental notion of ordering, one obtains an entirely new way of deriving physical laws. I will introduce this new way of thinking by demonstrating how one can quantify partially-ordered sets and, in the process, derive physical laws. The implication is that physical law does not reflect the order in the universe, instead it is derived from the order imposed by our description of the universe. Information physics, which is based on understanding the ways in which we both quantify and process information about the world around us, is a fundamentally new approach to science.
Over the past 25 years, I have been involved in some intriguing developments in the foundations of physics, exploring the quantum reality problem, the relationship between quantum theory and gravity and the interplay between consciousness and physical laws. These investigations make it plausible that we will find physics beyond quantum theory, potentially including both new evolution laws and new types of measurement. There is also a significant chance they could have potentially transformative impact on information processing and on the development of and our future with AI.