Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Getting started
- 2 Rough and ready Relativity
- 3 The dilation of time
- 4 Three clocks and a pair of twins
- 5 Starting again
- 6 Space–time diagrams
- 7 Time and distance ‘over there’
- 8 Co-ordinate systems
- 9 Combining speeds
- 10 Causality and the speed of light
- 11 The nature of spacetime
- 12 Interval
- 13 Old friends revisited
- 14 The scales of the spacetime diagram
- 15 The radar point of view
- 16 Relations between the radar and time–distance systems
- 17 Constant acceleration
- 18 Dynamics–mass, momentum, force
- 19 The mass–energy relation
- 20 The effect of acceleration on time measurement
- 21 Time as experienced by a constant acceleration traveller
- 22 Time and distance measurements of a constant acceleration observer
- 23 The Principle of Equivalence
- 24 The metric
- 25 Introducing geodesies
- 26 How to find ordinary geodesies
- 27 Inverse square law gravity
- 28 Curved spacetime
- 29 The metric around the Sun
- 30 Light and gravity
- 31 The scandal about Mercury
- 32 How Einstein did it
- 33 A few conclusions
- Index
20 - The effect of acceleration on time measurement
Published online by Cambridge University Press: 15 March 2010
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Getting started
- 2 Rough and ready Relativity
- 3 The dilation of time
- 4 Three clocks and a pair of twins
- 5 Starting again
- 6 Space–time diagrams
- 7 Time and distance ‘over there’
- 8 Co-ordinate systems
- 9 Combining speeds
- 10 Causality and the speed of light
- 11 The nature of spacetime
- 12 Interval
- 13 Old friends revisited
- 14 The scales of the spacetime diagram
- 15 The radar point of view
- 16 Relations between the radar and time–distance systems
- 17 Constant acceleration
- 18 Dynamics–mass, momentum, force
- 19 The mass–energy relation
- 20 The effect of acceleration on time measurement
- 21 Time as experienced by a constant acceleration traveller
- 22 Time and distance measurements of a constant acceleration observer
- 23 The Principle of Equivalence
- 24 The metric
- 25 Introducing geodesies
- 26 How to find ordinary geodesies
- 27 Inverse square law gravity
- 28 Curved spacetime
- 29 The metric around the Sun
- 30 Light and gravity
- 31 The scandal about Mercury
- 32 How Einstein did it
- 33 A few conclusions
- Index
Summary
Twice before we've discussed the so-called Clock Paradox (Space-twin Paradox). Please revise §§4.14-20 and 14.22–4. After that, if you've not already tackled the problem at the end of §4.18, please do so now. Figure 14.22 should help. Action!
You are being asked to compare the stories told by different versions of Figure 14.22 in which the curves near P, O and Q remain always the same in shape and length, but the two intervening straight portions of D's world line may be of any length we wish. If the accelerations do have the effect (suggested in §§4.18 and 14.24) of increasing the time that passes for D, then (with the same accelerations used in every case) the amount of this increase is fixed. But on the inertial parts of D's journey the dilation of time (§§3.10, 13.7) is always operating to diminish his total time measurement compared with A's; and the longer the inertial portions of the journey, the bigger this effect will be. So, even if there is an ‘acceleration effect’, it could only compensate for the dilation of time on a journey of one particular length. On longer journeys less time would pass for D than for A; on shorter ones it would be the other way round.
With a theory based on the assumptions we've used so far (all inertial observers equivalent, etc.) we can't definitely decide whether accelerations do or do not have some effect on the traveller's time. To make progress we must introduce a new assumption on this question, work out its consequences, and test them as usual against experiment.
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- Information
- Discovering Relativity for Yourself , pp. 215 - 228Publisher: Cambridge University PressPrint publication year: 1981