Information Physics: The New Frontier (1009.5161v1)

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.

• The paper demonstrates that physical laws emerge from quantifying information, challenging traditional physics paradigms.
• It introduces valuation calculus on lattices that extends traditional measure theory by deriving additivity from order-theoretic principles.
• The study unifies classical, quantum, and relativistic models by showing how informational constraints can underpin known physical laws.

Explorations in Information Physics: A New Theoretical Framework

Kevin H. Knuth's paper, "Information Physics: The New Frontier," presents a thought-provoking paper that proposes a novel framework for deriving physical laws based on the principles of information theory and order theory. The work centers on the premise that information, rather than merely describing physical systems, can be elevated to a fundamental role in understanding the laws of physics.

Central Contributions

At its core, the paper attempts to bridge theoretical physics with information and probability theory, leaning heavily on contributions from Shannon, Cox, and Jaynes. Each of these individuals revolutionized our understanding of probability, entropy, and information, which Knuth posits are integral to both classical and quantum physics.

1. Information as a Fundamental Concept: The paper insists on the foundational role of information—asserting that physical laws emerge from our endeavor to quantify and process information about the universe. This standpoint effectively challenges traditional perspectives, suggesting that our assumptions about physical laws are influenced by how we describe the universe.
2. Valuation Calculus: A significant part of Knuth's approach is the development of valuation calculus for lattices, a method that extends traditional measure theory by intrinsically deriving additivity from associativity. This calculus is a generalized measure theory that emphasizes context, employing bi-valuations to deepen the applications of probability theory.
3. Order Theory in Physics: Knuth harnesses order theory by focusing on partially-ordered sets (posets) and lattices. This extends to quantifying physical systems based on these posets rather than relying solely on algebraic expressions. It suggests that physical laws can be derived from internal ordering relations.

Methodology and Results

Knuth's methodology involves quantifying posets through valuations, bi-valuations, and projections, leading to a novel interpretation of familiar physical models:

• Derivation of Well-known Theories: The paper outlines how this framework re-derives existing laws such as measure theory, probability, and information theory, and extends these to more complex physical domains like quantum mechanics and special relativity.
• Mathematical Rigor: By using order-theoretic and algebraic techniques, Knuth derives product rules and context-specific calculations that echo the probabilistic underpinnings in quantum mechanics, such as Feynman's path integrals.
• Implications for Special Relativity: The paper proposes that projections of posets using coordinate-based quantification yield familiar relativistic metrics, potentially offering a new vision for spacetime as an artifact of informational ordering rather than a fundamental constituent.

Implications and Future Prospects

The implications of Knuth's work are manifold. Theoretically, it provides new lenses through which to view the intersection of information and physics, suggesting that the mathematical elegance of physical laws may stem from informational constraints. Practically, it has the potential to unify multiple physical theories under the umbrella of information processing.

Future Directions:

• Further development and application of the valuation calculus could offer deeper insights into unifying quantum mechanics with relativity—an ongoing challenge in theoretical physics.
• Information Physics might serve as a foundation for exploring new states or phases of matter where information becomes a critical factor.

In essence, Knuth's paper serves as a stepping stone towards conceptual frameworks that integrate information as a pivotal entity in understanding the universe. Its implications suggest an exciting frontier in theoretical physics, promising new developments in foundational research and quantification methodologies.