## 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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(c) The rotation of the coordinate system in (b) corresponds to the way we measure distances with a

(c) The rotation of the coordinate system in (b) corresponds to the way we measure distances with a

**ruler**or by means of a radar. (d) The Pythagorean definition of distance is much used for theoretical work but not often for practical ... Seite 9

Figure 1.3-1c shows how the distance between A and B is measured with a

Figure 1.3-1c shows how the distance between A and B is measured with a

**ruler**”. The**ruler**is rotated around either point A or point B until the other point lines up with the**ruler**. Hence, the practical measurement of Fig.1.3-1C ... Seite 15

Over a span of some 200 years Newton's absolute space and time were modified so much that they lost all physical meaning and became convenient words for the measurement of distances by

Over a span of some 200 years Newton's absolute space and time were modified so much that they lost all physical meaning and became convenient words for the measurement of distances by

**rulers**, radar, clocks, triangulation, ... Seite 21

2.2 FINITE INFORMATION AND FINITE RESOLUTION Let us investigate how much information we receive by measuring the location of a point—or the distance between two points—by means of a

2.2 FINITE INFORMATION AND FINITE RESOLUTION Let us investigate how much information we receive by measuring the location of a point—or the distance between two points—by means of a

**ruler**. Refer to Fig.2.2-1 for an explanation of how ... Seite 22

Let the

Let the

**ruler**be marked as shown in Fig.2.2-1b. There is a mark 0:0 at the left, a mark 0.1 = 1/2 in the middle, and a mark 1.0 on the right; binary notation is used for the marks. The point P is located in the interval 0.1 < z/X & 1.0.### 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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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