## Information Theory Applied To Space-time PhysicsThe 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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Ergebnisse 1-5 von 47

Seite 6

... Taurinus had known that his

... Taurinus had known that his

**results**were logically consistent, but he considered his geometry to be an exercise in abstract mathematics. Lobachevskii, on the other hand, was convinced that Euclidean geometry had no a priori claim to ... Seite 7

He shares with Lobachevskii the distinction of not only realizing that the parallel postulate was not necessary and deriving the fundamental formulas of pseudo-spherical geometry, but of comprehending the importance of his

He shares with Lobachevskii the distinction of not only realizing that the parallel postulate was not necessary and deriving the fundamental formulas of pseudo-spherical geometry, but of comprehending the importance of his

**results**for ... Seite 15

The implicit assumption of the metric of Euclidean space was mathematically overcome by Bolyai, Lobachevskii, and Riemann; Einstein's general theory of relativity turned the mathematical

The implicit assumption of the metric of Euclidean space was mathematically overcome by Bolyai, Lobachevskii, and Riemann; Einstein's general theory of relativity turned the mathematical

**results**into a physical theory. Seite 17

is one kind of topology that leads to normal causality; and it is of course an empirical fact which topology yields this

is one kind of topology that leads to normal causality; and it is of course an empirical fact which topology yields this

**result**(Reichenbach, 1957, pp. 80, 81). So let us conclude that space has a definite real intrinsic structure in ... Seite 21

Second, a widely acclaimed

Second, a widely acclaimed

**result**, the transmission capacity of communication channels, turned out to be correct ... when applied to an experimental science, which reduced the confidence in**results**of information theory generally”.### Was andere dazu sagen - Rezension schreiben

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### 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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### Häufige Begriffe und Wortgruppen

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