Information theory applied to space-time physics

The success of Newton's mechanic, Maxwell's electrodynamic, Einstein's theories of relativity, and quantum mechanics is a strong argument for the space-time continuum. Nevertheless, doubts have been expressed about the use of a continuum in a science squarely based on observation and measurement. An exact science requires that qualitative arguments must be reduced to quantitative statements. The observability of a continuum can be reduced from qualitative arguments to quantitative statements by means of information theory. Information theory was developed during the last decades within electrical communications, but it is almost unknown in physics. The closest approach to information theory in physics is the calculus of propositions, which has been used in books on the frontier of quantum mechanics and the general theory of relativity. Principles of information theory are discussed in this book. The ability to think readily in terms of a finite number of discrete samples is developed over many years of using information theory and digital computers, just as the ability to think readily in terms of a continuum is developed by long use of differential calculus.

1. Historical Review. 1.1. Roots in the Greek World. 1.2. From Euclidean to Non-Euclidean Geometry. 1.3. Metric and Differential Geometry. 1.4. Physical Space-Time -- 2. Information Theory Applied to Measurements. 2.1. The Concept of Information. 2.2. Finite Information and Finite Resolution. 2.3. Finite Information Flow. 2.4. Finite Resolution [Delta]x and [Delta]t -- 3. Coordinate Systems. 3.1. Coordinate Systems Based on Rings. 3.2. The Belief in Three-Dimensional Space. 3.3. Right and Left Handed Structures. 3.4. Distance in Discrete Coordinate Systems. 3.5. Coordinate Systems Defined by the Metric Tensor. 3.6. Coordinate Systems with one Variable -- 4. Time and Motion. 4.1. Time and Time Differences. 4.2. Shifts and Propagation. 4.3. Velocity. 4.4. Three Time Dimensions and One Space Dimension -- 5. Propagation in Unusual Coordinate Systems. 5.1. Dyadic Metric. 5.2. Dyadic Coordinate Systems. 5.3. Standing Waves and Topology. 5.4. Observed Shifts and Their Eigenfunctions.

5.5. Nondyadic Coordinate Systems. 5.6. Motion Based on Integer Number and Dyadic Topology. 5.7. Dyadic Clocks -- 6. Distinction of Sinusoidal Functions. 6.1. Differential and Partial Equations. 6.2. Concep…