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
- 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
Did your researches with the slot at §14.14 yield the ‘important discovery’ I hinted at. Perhaps you should try again.
Revise as necessary on isovals–a minimum of §§14.1, 14.5 and 14.9. If you didn't ask yourself whether a branch of an isoval could be a world line – representing something moving on the ID universe – consider the question now.
A time-like isoval couldn't be a world line. For its slope is always shallower than 45°, and this would imply a causal influence travelling faster than light, which is impossible (§§10.10–12).
But a branch of a space-like isoval, being always steeper than 45°, could be a world line. Check with the slot that it represents something always moving slower than light. What sort of motion will it represent?
World lines of inertial observers are straight. So this curve must represent the motion of something that is non-inertial. What does ‘noninertial’ mean?
The meaning is in the definition of §5.2–which please reread. The test particle moves away.
But when there is no gravity–as we are assuming (§5.5)–an inertial observer has constant speed relative to any other inertial observer (§5.6). Therefore a non-inertial observer moves with changing speedhe is accelerated in the ordinary sense of the word. So this space-like isoval represents accelerated motion.
Note that acceleration has a quite different status from speed (§§1.1–3, 5.1–2). Speed is purely relative. But everybody can see whether an observer and his test particle stay together or move apart; and so all must agree whether he is accelerated or not.
- Type
- Chapter
- Information
- Discovering Relativity for Yourself , pp. 182 - 193Publisher: Cambridge University PressPrint publication year: 1981