Book contents
- Frontmatter
- Contents
- Preface
- 1 Strategies for solving problems
- 2 Statics
- 3 Using F = ma
- 4 Oscillations
- 5 Conservation of energy and momentum
- 6 The Lagrangian method
- 7 Central forces
- 8 Angular momentum, Part I (Constant L^)
- 9 Angular momentum, Part II (General L^)
- 10 Accelerating frames of reference
- 11 Relativity (Kinematics)
- 12 Relativity (Dynamics)
- 13 4-vectors
- 14 General Relativity
- Appendix A Useful formulas
- Appendix B Multivariable, vector calculus
- Appendix C F = ma vs. F = dp/dt
- Appendix D Existence of principal axes
- Appendix E Diagonalizing matrices
- Appendix F Qualitative relativity questions
- Appendix G Derivations of the Lv/c2 result
- Appendix H Resolutions to the twin paradox
- Appendix I Lorentz transformations
- Appendix J Physical constants and data
- References
- Index
Appendix H - Resolutions to the twin paradox
- Frontmatter
- Contents
- Preface
- 1 Strategies for solving problems
- 2 Statics
- 3 Using F = ma
- 4 Oscillations
- 5 Conservation of energy and momentum
- 6 The Lagrangian method
- 7 Central forces
- 8 Angular momentum, Part I (Constant L^)
- 9 Angular momentum, Part II (General L^)
- 10 Accelerating frames of reference
- 11 Relativity (Kinematics)
- 12 Relativity (Dynamics)
- 13 4-vectors
- 14 General Relativity
- Appendix A Useful formulas
- Appendix B Multivariable, vector calculus
- Appendix C F = ma vs. F = dp/dt
- Appendix D Existence of principal axes
- Appendix E Diagonalizing matrices
- Appendix F Qualitative relativity questions
- Appendix G Derivations of the Lv/c2 result
- Appendix H Resolutions to the twin paradox
- Appendix I Lorentz transformations
- Appendix J Physical constants and data
- References
- Index
Summary
The twin paradox appeared in Chapters 11 and 14, both in the text and in various problems. To summarize, the twin paradox deals with twin A who stays on the earth, and twin B who travels quickly to a distant star and back. When they meet up again, they discover that B is younger. This is true because A can use the standard special-relativistic time-dilation result to say that B's clock runs slow by a factor γ.
The “paradox” arises from the fact that the situation seems symmetrical. That is, it seems as though each twin should be able to consider herself to be at rest, so that she sees the other twin's clock running slow. So why does B turn out to be younger? The resolution to the paradox is that the setup is in fact not symmetrical, because B must turn around and thus undergo acceleration. She is therefore not always in an inertial frame, so she cannot always apply the simple special-relativistic time-dilation result.
While the above reasoning is sufficient to get rid of the paradox, it isn't quite complete, because (a) it doesn't explain how the result from B's point of view quantitatively agrees with the result from A's point of view, and (b) the paradox can actually be formulated without any mention of acceleration, in which case slightly different reasoning applies.
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- Chapter
- Information
- Introduction to Classical MechanicsWith Problems and Solutions, pp. 706 - 707Publisher: Cambridge University PressPrint publication year: 2008