Information Theory Applied To Space-time Physics
World Scientific, 31.01.1993 - 320 Seiten
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.
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8 Schrödinger and KleinGordon Difference Equations
9 Schrödinger Difference Equation with Coulomb Field
10 KleinGordon Difference Equation with Coulomb Field
11 Dirac Difference Equation with Coulomb Field
12 Mathematical Supplements
References and Bibliography
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angles axes calculus Cartesian coordinate system circle clock coefficients concept continuum convergence coordinate distance defined derive difference equation difference operator difference quotient differential equation diffraction grating digits dyadic coordinate system dyadic shifting eigenfunctions eigenvalues equal Euclidean geometry factorial series finite number four-dimensional function f(m geodesic Gray code grid points Hamming distance Hence infinite information theory integer numbers integration interval Klein-Gordon Klein-Gordon equation marks mathematical measured metric minimized code minimum absolute distance modulo neighbors nondenumerably numbers axis O(Ar O(At observed obtains particle physical plane pn(R pn(t propagation Pythagorean distance real numbers recursion formula replaced representation result rings rods rotation ruler samples Schrödinger equation Section shown shows sinusoidal functions small values solution space space-time spheres spherical standing waves substitution surface Table three-dimensional space tſT two-dimensional unbounded coordinate system usual binary code variable velocity Wal(k Walsh functions yields zero Zºo