Information Theory Applied To Space-time PhysicsWorld 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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Seite viii
... Integer Number and Dyadic Topology 5.7 Dyadic Clocks 146 158 6 Distinction of Sinusoidal Functions 6.1 Differential and Partial Differential Equations 163 6.2 Concepts of the Calculus of Finite Differences 6.3 Concepts of the Dyadic ...
... Integer Number and Dyadic Topology 5.7 Dyadic Clocks 146 158 6 Distinction of Sinusoidal Functions 6.1 Differential and Partial Differential Equations 163 6.2 Concepts of the Calculus of Finite Differences 6.3 Concepts of the Dyadic ...
Seite xi
... number of apples in a basket . The observation of a continuum would provide us with nondenumerably infinite information . Both the ob- servation of the infinitesimal and of the infinite require infinite information . These concepts are ...
... number of apples in a basket . The observation of a continuum would provide us with nondenumerably infinite information . Both the ob- servation of the infinitesimal and of the infinite require infinite information . These concepts are ...
Seite 1
... number of tasks . First , we have to describe in more detail the three - dimensional space experienced in everyday life . Second , we have to extend the concept to distances much larger than those of our immediate experience , that is ...
... number of tasks . First , we have to describe in more detail the three - dimensional space experienced in everyday life . Second , we have to extend the concept to distances much larger than those of our immediate experience , that is ...
Seite 2
... numbers axis . One says that a one - dimensional continuum has the same topology as the real numbers . It is further usual to map any real number ... integers rather than the real numbers along the numbers axis , only finite shifts would have ...
... numbers axis . One says that a one - dimensional continuum has the same topology as the real numbers . It is further usual to map any real number ... integers rather than the real numbers along the numbers axis , only finite shifts would have ...
Seite 4
... number V appears in the critical edition of the Elements by Heiberg and Menge ( Euclid , 1916 ) and in its translation by Heath ( Euclid , 1956 ) , but Bolyai ( 1832 ) calls it Axiom XI , while others give it the numbers 12 and 13 , or ...
... number V appears in the critical edition of the Elements by Heiberg and Menge ( Euclid , 1916 ) and in its translation by Heath ( Euclid , 1956 ) , but Bolyai ( 1832 ) calls it Axiom XI , while others give it the numbers 12 and 13 , or ...
Inhalt
1 | |
18 | |
3 Coordinate Systems | 40 |
4 Time and Motion | 85 |
5 Propagation in Unusual Coordinate Systems | 104 |
6 Distinction of Sinusoidal Functions | 163 |
7 Discrete Topologies and Difference Equations | 197 |
8 Schrödinger and KleinGordon Difference Equations | 204 |
9 Schrödinger Difference Equation with Coulomb Field | 218 |
10 KleinGordon Difference Equation with Coulomb Field | 230 |
11 Dirac Difference Equation with Coulomb Field | 254 |
12 Mathematical Supplements | 270 |
References and Bibliography | 297 |
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angles 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 f(no factorial series finite number four-dimensional function f(m functions Wal(k 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 observed obtains P₁ particle physical plane propagation Pythagorean distance real numbers replaced representation result ring 2N 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 two-dimensional unbounded coordinate system usual binary code variable velocity Walp Walsh functions yields Z² a² zero Δη Δυ