# Motion Mountain - Relativity and Cosmology : Volume II of The Adventure of Physics

This book series is for anybody who is curious about motion in nature. How do things, people, animals, images and empty space move? The answer leads to many adventures. This volume presents the best ones about extremely fast, powerful and distant motion. In the exploration of motion – physics – special and general relativity make up two important stages.

Special relativity is the exploration of nature’s speed limit, c. General relativity is the exploration of the force limit c4/4G. The text shows that in both domains, all results follow from these two limit values. In particular, cosmology is the exploration of motion near nature’s distance limit 1/√Λ . This simple, intuitive and unusual way of learning relativity should reward the curiosity of every reader – whether student or professional.

The present volume is the second of a six-volume overview of physics that arose from a threefold aim that I have pursued since 1990: to present motion in a way that is simple, up to date and captivating.

In order to be simple, the text focuses on concepts, while keeping mathematics to the necessary minimum. Understanding the concepts of physics is given precedence over using formulae in calculations. The whole text is within the reach of an undergraduate.

In order to be up to date, the text is enriched by the many gems – both theoretical and empirical – that are scattered throughout the scientific literature.

In order to be captivating, the text tries to startle the reader as much as possible. Read- ing a book on general physics should be like going to a magic show. We watch, we are astonished, we do not believe our eyes, we think, and finally we understand the trick. When we look at nature, we often have the same experience. Indeed, every page presents at least one surprise or provocation for the reader to think about.

The motto of the text, die Menschen stärken, die Sachen klären, a famous statement on pedagogy, translates as: ‘To fortify people, to clarify things.’ Clarifying things – and adhering only to the truth – requires courage, as changing the habits of thought produces fear, often hidden by anger. But by overcoming our fears we grow in strength. And we experience intense and beautiful emotions. All great adventures in life allow this, and exploring motion is one of them. Enjoy it.

- Preface
- Using this book
- Advice for learners
- Advice for teachers
- Feedback
- Support

- Contents
- Relativity
- 1 Maximum speed, observers at rest and motion of light
- Aberration and the speed of rain
- The speed of light
- Can one play tennis using a laser pulse as the ball and mirrors as rackets?
- Albert Einstein
- An invariant limit speed and its consequences
- Special relativity with a few lines
- Acceleration of light and the Doppler effect
- The difference between light and sound
- Can one shoot faster than one's shadow?
- The composition of velocities
- Observers and the principle of special relativity
- What is space-time?
- Can we travel to the past? – Time and causality
- Curiosities about special relativity
- Faster than light: how far can we travel?
- Synchronization and time travel – can a mother stay younger than her own daughter?
- Length contraction
- Relativistic films – aberration and Doppler effect
- Which is the best seat in a bus?
- How fast can one walk?
- Is the speed of shadow greater than the speed of light?
- Parallel to parallel is not parallel – Thomas precession
- A never-ending story – temperature and relativity
- A curiosity: what is the one-way speed of light?
- Summary

- 2 Relativistic mechanics
- Mass in relativity
- Why relativistic snooker is more difficult
- Mass and energy are equivalent
- Weighing light
- Collisions, virtual objects and tachyons
- Systems of particles – no centre of mass
- Why is most motion so slow?
- The history of the mass–energy equivalence formula
- 4-vectors
- 4-velocity
- 4-acceleration and proper acceleration
- 4-momentum or energy–momentum or momenergy
- 4-force – and the nature of mechanics
- Rotation in relativity
- Wave motion
- The action of a free particle – how do things move?
- Conformal transformations
- Accelerating observers
- Accelerating frames of reference
- Constant acceleration
- Event horizons
- The importance of horizons
- Acceleration changes colours
- Can light move faster than c?
- The composition of accelerations
- Limits on the length of solid bodies

- 3 Special relativity in four sentences
- Could the speed of light vary?
- Where does special relativity break down?

- 4 Simple general relativity: gravitation, maximum speed and maximum force
- Maximum force – general relativity in one statement
- The meaning of the force and power limits
- The experimental evidence
- Deducing general relativity
- Gravity, space-time curvature, horizons and maximum force
- Conditions of validity for the force and power limits
- Gedanken experiments and paradoxes about the force limit
- Gedanken experiments with the power and the mass flow limits
- Why maximum force has remained undiscovered for so long
- An intuitive understanding of general relativity
- An intuitive understanding of cosmology
- Experimental challenges for the third millennium
- A summary of general relativity – and minimum force

- 5 How maximum speed changes space, time and gravity
- Rest and free fall
- What clocks tell us about gravity
- What tides tell us about gravity
- Bent space and mattresses
- Curved space-time
- The speed of light and the gravitational constant
- Why does a stone thrown into the air fall back to Earth? – Geodesics
- Can light fall?
- Curiosities and fun challenges about gravitation
- What is weight?
- Why do apples fall?
- A summary: the implications of the invariant speed of light on gravitation

- 6 Open orbits, bent light and wobbling vacuum
- Weak fields
- Bending of light and radio waves
- Time delay
- Relativistic effects on orbits
- The geodesic effect
- The Thirring effects
- Gravitomagnetism
- Gravitational waves
- Production and detection of gravitational waves
- Curiosities and fun challenges about weak fields
- A summary on orbits and waves

- 7 From curvature to motion
- How to measure curvature in two dimensions
- Three dimensions: curvature of space
- Curvature in space-time
- Average curvature and motion in general relativity
- Universal gravity
- The Schwarzschild metric
- Curiosities and fun challenges about curvature
- Three-dimensional curvature: the Ricci tensor
- Average curvature: the Ricci scalar
- The Einstein tensor
- The description of momentum, mass and energy
- Einstein's field equations
- Universal gravitation – again
- Understanding the field equations
- Hilbert's action – how does space bend?
- The symmetries of general relativity
- Mass in general relativity
- The force limit and the cosmological constant
- Is gravity an interaction?
- How to calculate the shape of geodesics
- Riemann gymnastics
- Curiosities and fun challenges about general relativity
- A simple summary of the field equations

- 8 Why can we see the stars? – Motion in the universe
- Which stars do we see?
- How do we watch the stars?
- What do we see at night?
- What is the universe?
- The colour and the motion of the stars
- Do stars shine every night?
- A short history of the universe
- The history of space-time
- Why is the sky dark at night?
- The colour variations of the night sky
- Is the universe open, closed or marginal?
- Why is the universe transparent?
- The big bang and its consequences
- Was the big bang a big bang?
- Was the big bang an event?
- Was the big bang a beginning?
- Does the big bang imply creation?
- Why can we see the Sun?
- Why do the colours of the stars differ?
- Are there dark stars?
- Are all stars different? – Gravitational lenses
- What is the shape of the universe?
- What is behind the horizon?
- Why are there stars all over the place? – Inflation
- Why are there so few stars? – The energy and entropy content of the universe
- Why is matter lumped?
- Why are stars so small compared with the universe?
- Are stars and galaxies moving apart or is the universe expanding?
- Is there more than one universe?
- Why are the stars fixed? – Arms, stars and Mach's principle
- At rest in the universe
- Does light attract light?
- Does light decay?
- Summary on cosmology

- 9 Black holes – falling forever
- Why explore black holes?
- Mass concentration and horizons
- Black hole horizons as limit surfaces
- Orbits around black holes
- Black holes have no hair
- Black holes as energy sources
- Formation of and search for black holes
- Singularities
- Curiosities and fun challenges about black holes
- Summary on black holes
- A quiz – is the universe a black hole?

- 10 Does space differ from time?
- Can space and time be measured?
- Are space and time necessary?
- Do closed time-like curves exist?
- Is general relativity local? – The hole argument
- Is the Earth hollow?
- A summary: are space, time and mass independent?

- 11 General relativity in a nutshell – a summary for the layman
- The accuracy of the description
- Research in general relativity and cosmology
- Could general relativity be different?
- The limitations of general relativity

- A Units, measurements and constants
- SI units
- The meaning of measurement
- Curiosities and fun challenges about units
- Precision and accuracy of measurements
- Limits to precision
- Physical constants
- Useful numbers

- 1 Maximum speed, observers at rest and motion of light
- Challenge hints and solutions
- Bibliography
- Credits
- Acknowledgements
- Film credits
- Image credits

- Name index
- Subject index
- Name index
- Subject index

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