Relativistic Mechanics, Time and Inertia

ISBN-13: 9789027717696 / Angielski / Twarda / 1984 / 260 str.

Emil Tocaci; E. Tocaci; C. W. Kilmister

Opis

To accept the special theory of relativity has, it is universally agreed, consequences for our philosophical views about space and time. Indeed some have found these consequences so distasteful that they have refused to accept special relativity, despite its many satis factory empirical results, and so they have been forced to try to account for these results in alternative ways. But it is surprising that there is much less agreement about exactly what the philosophical conse quences are, especially when looked at in detail. Partly this arises because the results of the theory are derived in an elegant mathematical notation which can conceal as much as it reveals, and which, accord ingly, offers no incentive to engage in the thankless task of dissection. The present book is an essay in careful analysis of special relativity and the concepts of space and time that it employs. Those who are familiar with the theory will find here (almost) all the formulae with which they are familiar;but in many cases the interpretations given to the terms in these formulae will surprise them. I doubt if this is the last word about these inter pretations: but I believe that the book is valuable in ix Foreword x drawing attention to the possibility of more open dis cussion in general, and in particular to the fact that acceptance of the theory of relativity need not commit one to every detail of conventional interpretation of its terms.

Spis treści

A. Aspects of Relativistic Mechanics.- A.I. General remarks.- A.II. Remarks on the theory of relativity.- A.II.1. Special relativity.- A.II.1.1. Synchronization of clocks.- A.II.1.2. The Lorentz-Einstein relations.- A.II.1.3. The invariant of Lorentz-Einstein transformations.- A.II.1.4. Classification of space-time intervals.- A.II.1.5. Minkowski space.- A.II.1.6. Transformation of velocity components.- A.II.1.7. The velocity and acceleration 4-vectors.- A.II.1.8. The momentum 4-vector.- A.II.1.9. The 4-force.- A.II.1.10. The fundamental law of dynamics and the energy of a particle in relativistic dynamics.- A.II.1.11. The momentum-energy vector and the properties of its components.- A.II.1.12. The conservative case. Potential energy.- A.II.1.13. The mass defect.- A.II.1.14. The relativistic study of collisions.- A.II.1.15. Some physical interpretations and other remarks on relativistic mechanics.- A.II.2. Some aspects of general relativity.- A.III. The main aims of this work.- B. Time.- B.I. The concept of time.- B.I.1. The evolution of the concept of time.- B.I.2. Time as measure and consequence of motion.- B.I.2.1. Motion.- B.I.2.2. The clock.- B.I.2.3. Examples of mechanical motion.- B.I.2.4. Time as an abstraction of general motion.- B.I.3. The properties of time.- B.I.3.1. The irreversibility of time.- B.I.3.2. The velocities and accelerations in various equivalence classes.- B.I.3.3. The transport of information.- B.I.3.4. Information transport as a timing motion.- B.I.3.5. The character of the unique constant velocity of light in all inertial frames.- B.I.3.6. Relativity of time and the problem of several information carriers.- B.II. Examples.- B.II.1. The irreversibility and continuity of time.- B.II.1.1. The probabilistic irreversibility.- B.II.1.2. The continuity of the time variable.- B.II.2. The forced open curves in Minkowski space.- C. Inertia.- C.I. Use of time in defining some elements of space.- C.I.1. The definition of the straight line.- C.I.1.1. Inertial spaces.- C.I.1.2. The straight line.- C.I.1.3. Non-inertial spaces.- C.I.1.4. The rigid line.- C.I.2. Reference frames.- C.I.2.1. Inertial frames.- C.I.2.2. Non-inertial frames.- C.II. The inertia.- C.II.1. Aspects related to motion of particles in inertial and non-inertial spaces.- C.II.1.1. General aspects of the study of motion in non-inertial spaces.- C.II.1.2. Mescerski-Levi-Civita equation in the relativistic case.- C.II.1.3. The effect of percussion force in the relativistic case.- C.II.2. Manifestation of inertia.- C.II.2.1. The inertial spaces.- C.II.2.2. Non-inertial spaces.- C.II.3. Some aspects of the motion of a particle in a non-inertial situation.- C.II.3.1. Accelerated translation.- C.II.3.2. A particular gravitational field.- C.II.3.3. The case of relative motion of the frame.- C.III. Some aspects of classical mechanics.- C.III.1. Grounding mechanics on a single axiom.- C.III.1.1. The single axiom of mechanics.- C.III.1.2. Definition of force and derivation of the fundamental laws of mechanics.- C.III.2. The inertial or non-inertial character of frames.- C.III.2.1. Inertial frames.- C.III.2.2. Non-inertial frames.