Talks and Presentations
Knuth K.H. Bayesian Evidence and Model Selection: A Tutorial in Two Acts
MaxEnt 2015, Potsdam, NY, USA on 19 July 2015
Knuth K.H., Bahreyni N., Walsh J.L. 2015. The influence network: A new foundation for emergent physics
Beyond Spacetime 2015, San Diego, CA, USA on 13 March 2015
We introduce an alternate description of physical reality based on a simple foundational concept that there exist things that influence one another. It has been previously demonstrated that quantification of order-theoretic structures consistent with relevant symmetries results in constraint equations akin to physical laws. We consider a network of objects that influence one another — the influence network. By consistently quantifying such a network with respect to embedded observers, we demonstrate in relevant special cases that influence events can only be quantified by the familiar mathematics of space-time, influence gives rise to forces, and observer-made inferences result in the Dirac equation and fermion physics. Together this suggests a novel path to quantum gravity.
Knuth K.H. 2014. FQXI 2014: Foundations of Probability and Information.
Opening Panelist Discussion on the Perspectives of Information at the FQXi 2014 Conference on Physics and Information, Vieques Island, Puerto Rico, USA on 6 Jan 2014.
Knuth K.H. 2013. Information-Based Physics: An Intelligent Embedded Agent's Guide to the Universe.
Presented to the Santa Fe Institute , Santa Fe NM on 26 Mar 2013.
Presented to Complexity Sciences Center at UC Davis, Davis CA on 9 Apr 2013.
Presented to Stanford Physics, Stanford University, Stanford CA on 12 Apr 2013.
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.
Knuth K.H. 2013. The foundations of probability Theory and quantum theory.
Presented at NASA Ames Research Center, 11 Apr 2013.
Presented at Google on 10 Apr 2013.
Probability theory is a calculus that enables one to compute degrees of implication among logical statements. Quantum theory is a calculus that enables one to compute the probabilities of the possible outcomes of a measurement performed on a physical system. Since the development of quantum theory (and probability theory), there have been many questions regarding the relationship between the two theories; some going as far as to question whether quantum theory is even compatible with probability theory. In this talk, I demonstrate precisely the relationship between probability theory and quantum theory by deriving both theories from first principles. This is accomplished by observing how consistent quantification of logical statements (Knuth, Skilling 2012) and quantum measurement sequences (Goyal, Skilling, Knuth 2010) are constrained by the relevant symmetries in each of the two domains (Goyal, Knuth 2011). It will be shown that the derivation of quantum theory is not only consistent with, but also relies on probability theory. In addition, these results highlight some important differences between inference in the classical and quantum domains.
Knuth K.H. 2010. Information Physics: The Next Frontier,
MaxEnt 2007, Chamonix, France, July 2007.
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.
Knuth K.H. 2010. The role of order in natural law,
Workshop on the Laws of Nature: Their Nature and Knowability, Perimeter Institute, Waterloo, Canada, May 2010.
In the last four and a half centuries, we have found that we are able to identify laws of nature that are generally applicable, and because of this we have inferred that there is an underlying order to the structure and dynamics of the universe. In many cases we have been able to identify this order as being related to symmetries, which have enabled us to derive various laws, such as conservation laws. But in most cases, the role that order plays in determining natural law remains obscured. In this talk I will rely on order theory to demonstrate how symmetries among our descriptions of various states of a physical system result in constraint equations, generally called sum and product rules, which are ubiquitous in natural laws. The fact that much of the order that determines the structure of natural laws arises from relationships inherent in our particular description of a physical system implies that the laws of nature are more closely related to what we choose to say about the universe and how we say it rather than being fundamental governing principles.