Introducing Relativity E-Book

Bruce Bassett

• Herausgeber: Icon Books
• Kategorie: Wissenschaft und neue Technologien
• Serie: Graphic Guides
• Sprache: Englisch

Seitenzahl: 84

Veröffentlichungsjahr: 2014

Beschreibung

A superlative, fascinating graphic account of Albert Einstein's strange world and how his legacy has been built upon since. It is now more than a century since Einstein's theories of Special and General Relativity began to revolutionise our view of the universe. Beginning near the speed of light and proceeding to explorations of space-time and curved spaces, Introducing Relativity plots a visually accessible course through the thought experiments that have given shape to contemporary physics. Scientists from Isaac Newton to Stephen Hawking add their unique contributions to this story, as we encounter Einstein's astounding vision of gravity as the curvature of space-time and arrive at the breathtakingly beautiful field equations. Einstein's legacy is reviewed in the most advanced frontiers of physics today - black holes, gravitational waves, the accelerating universe and string theory. 

Leseprobe

Published by Icon Books Ltd., Omnibus Business Centre, 39–41 North Road, London N7 9DP email: [email protected]

ISBN: 978-184831-770-3

Text copyright © 2002 Bruce Bassett Illustrations copyright © 2012 Icon Books Ltd

The author and artist have asserted their moral rights.

Originating editor: Richard Appignanesi

No part of this book may be reproduced in any form, or by any means, without prior permission in writing from the publisher.

Contents

Cover

Title Page

Copyright

The Conditions of Space and Time

Newton’s Classical Laws of Physics

The Law of Gravity

Maxwell’s Theory of Electromagnetism

Problems in Classical Physics

Puzzle of the Atom

A Major Mystery

The Modern Background

Decisive Events

A Time of Motion

Lorentz Transformations

The Effect of Length Contraction

Time Dilation

Observing Muons

Energy is Mass, Mass Energy

Planck’s Constant h and Quantum Effects

Quantum and Classical Physics

Dirac’s Idea of Anti-Matter

The Michelson-Morley Experiment

Constancy of the Speed of Light

The Problem of Simultaneity

Slicing Spacetime Differently

The Need for General Relativity

Another Viewpoint

Out of the Impasse

Resolving Acceleration

The Building-Blocks of General Relativity

An Infinite Number of Dimensions

A Thought Experiment

Infinity and Configuration Space

Slicing Spacetime

How to View Spacetime

Simultaneity is Relative

Einstein’s Tasks

Suspending Gravity

The Equivalence Principle

Gravitational and Inertial Mass

Extending Newton’s First Law

A Brainteaser

Geodesics

Spacelike, Null, Timelike

Finding the Distance

Geodesics and the Metric

Finding the Metric

The Metric …

The Metric in Four Dimensions

Spacetime Geodesics

Including Time

The Dragon’s Tail

The Missing Ingredient

The Dragon Bites its Tail

Tensors

Einstein’s Field Equations

Types of Curvature

Positive Curvature

Negative Curvature

Triangles in Curved Space

Positively Curved ...

Negatively Curved ...

Intrinsic Curvature

Extrinsic Curvature

Normal Vectors

Spatial Slices

Space and Time vs. Spacetime

Testing GR in Nature

The Bending of Light

The Eclipse

The Equivalence Principle Again

The Best-tested Theory

Black Holes

Time-varying Acceleration

Shaking a Mass

The Rubber-Sheet Analogy

Gravity’s Weakness

Stargazing

Interferometric Observation

How it Works

Interference Patterns

Sizing Up the Universe

The Copernican Principle

Simplifying the Field Equations

“FLRW”

Static or Expanding Universes?

The Fate of the Universe

The Critical Density: First Model

Second Model

Third Model

Explaining Redshift

Einstein’s Static Universe

The Accelerating Universe

Endless Expansion

Negative Pressure

Dark Matter

Beyond General Relativity

The Cosmic Microwave Background

Further Satellite Probes

The Homogeneity Mystery

The “Goldilocks” Expansion Rate

The Flatness Problem

The Inflation Phase

Using Einstein’s Constant

Singularity Theorems

The Result of Singularity Theorems

The Invalidation of Einstein’s Equations

Extra Dimensions

Superstring Theory

Extending Einstein’s Dream

Adding More Dimensions

Further Reading

About the Author and Artist

Acknowledgements

Index

The Conditions of Space and Time

The German philosopher Immanuel Kant (1724–1804) delved into the critical limits of knowledge in his revolutionary text, The Critique of Pure Reason (1781). He expounded the view that space and time do not exist independently of our consciousness.

IT IS THE PRIOR CONDITION OF OUR MINDS THAT ALLOWS US TO PERCEIVE SPACE AND TIME THIS SUGGESTS THAT SPACE & TIME MAY NOT BE ABSOLUTE ENTITIES AS NEWTON CONCEIVED THEM, AND SO KANT IS CLOSER TO EINSTEIN, AS WE SHALL SEE

Nevertheless, until Einstein, the dominant philosophy of physicists was inherited from Sir Isaac Newton (1643–1727).

Newton’s Classical Laws of Physics

Newton was arguably the greatest of physicists and mathematicians. He contributed significantly to optics, formulated his three laws of motion, and developed differential and integral calculus independently of G.W. Leibniz (1646–1716). But, in terms of understanding Einstein’s relativity, Newton’s law of universal gravitation is the most crucial for us.

BEFORE NEWTON THE MOTION OF THE PLANETS IN THE HEAVENS WAS CONSIDERED A MYSTERIOUS ISSUE DISLOCATED FROM THE EVERYDAY WORLD I HAD ALREADY DISCOVERED LAWS FOR THE MOTION OF THE PLANETS... YES, BUT WHAT YOU DISCOVERED WERE EMPIRICAL LAWS WITHOUT THEORETICAL EXPLANATION

A famous but untrue story has Newton sitting under an apple tree when his great discovery of gravity literally hit him on the head.

THIS “EUREKA” STORY NICELY CONVEYS THE ASTONISHING INTELLECTUAL LEAP THAT NEWTON MADE... THE APPLE FALLING TO EARTH FEELS A FORCE!

The specific importance of Newton’s law of universal gravitation is that it explains and unites several phenomena within a single theory. This quest for a single unifying theory would become the driving force of 20th- and 21st-century physics.

The Law of Gravity

Newton’s law of universal gravitation states that the force of gravity (F) between two objects of masses m and M is given by …

where r is the distance between the two objects and G is Newton’s constant. G is very small since gravity is very weak.

There are at least two implications to this law of gravity …

THE FIRST IS A MATHEMATICAL DEDUCTION OF KEPLER’S LAWS OF PLANETARY MOTION - GRAVITY SUPPLIES THE MISSING THEORETICAL EXPLANATION SECOND, MY LAW GIVES THE RIGOROUS RESULT THAT PLANETS TRAVEL ON ELLIPSES RATHER THAN ON CIRCLES

Newton took several things for granted in his theory. While the earth was no longer the centre of the universe – and had not been so in the eyes of many scientists since Nicolaus Copernicus (1473–1543) – it was assumed that space and time were fundamentally different things and that both were absolute, set in marble.

HENCE, FOR NEWTON-AND FOR THOSE WHO FOLLOWED HIM-SPACE AND TIME WERE THE ABSOLUTE AND IMMUTABLE STAGES ON WHICH MATTER IN THE UNIVERSE PLAYED OUT ITS GAMES

The idea of unifying the two, apparently different, concepts of space and time fell to Einstein, as we’ll later discuss.

Maxwell’s Theory of Electromagnetism

Theoretical physics had made significant progress before Einstein. In particular, James Clerk Maxwell (1831–79) had unified magnetism with electricity to give electromagnetism.

PRIOR TO MY WORK, THE VARIOUS MANIFESTATIONS OF ELECTRICITY & MAGNETISM APPEARED TO BE SEPARATE PHENOMENA HENCE, THE EARTH’S MAGNETIC FIELD WAS NOT LINED TO ELECTRIC STORMS OR TO THE LIGHT FROM THE SUN

By means of four equations, Maxwell explained all the different manifestations of electricity and magnetism – from the emission of light and electric currents to the earth’s magnetic field. Maxwell’s equations linked the electric and magnetic fields to each other and showed how each of their various manifestations arose as special cases of a general theory.

Simple magnetic fields can occur when there is no electric field (and vice versa).

But, in general, if the intensity of an electric field varies in time, it will generate magnetic fields … and vice versa.

This happens in the case of light, which consists of oscillating electric and magnetic fields propagating through space and time – at the speed of light.

The unification that Maxwell achieved is thus similar conceptually to that of Newton when Newton realized that the force acting on the apple is the same as that holding the earth in orbit around the sun.

Problems in Classical Physics

A number of problems had been identified in this progressive story of physics. One of these concerned gravity itself. Newton’s theory of gravity correctly predicted that planets should move in elliptical orbits.

I ALSO PREDICTED THAT THE PERIHELION-THE POINT ON THE ORBIT CLOSEST TO THE SUN-SHOULD BE FIXED IN SPACE BUT CAREFUL OBSERVATIONS OF THE ORBIT OF MERCURY SHOWED THAT ITS PERIHELION WAS SHIFTING SLIGHTLY EACH TIME

Puzzle of the Atom

The atom was another major thorn in the flesh of physicists. The prevailing picture around the turn of the 20th century was that atoms are made up of a positively charged nucleus surrounded by negatively charged – and much less massive – electrons. The electrons must orbit the nucleus if they are not to fall directly onto the nucleus as a result of the attraction between the opposite charges on the electrons and nucleus.

SINCE WE ELECTRONS ARE ORBITING THE NUCLEUS IN ROUGHLY CIRCULAR PATHS WE MUST BE ACCELERATING WHY’S THAT? IT’S JUST LIKE A CAR MUST ACCELERATE TO MAKE IT TURN A CORNER... ... AND BY NEWTON’S SECOND LAW ACCELERATION IMPLIES FORCE

A Major Mystery

Now, from Maxwell’s theory of electromagnetism, it was well known that an accelerating charge emits light (or electromagnetic radiation of a different frequency) with an energy that depends on how strong the acceleration is. But, if the electrons lose energy due to the emission of light, then they would begin to spiral inwards and would collapse onto the central nucleus within a thousand-billionth of a second!

THE FACT THAT WE OBSERVE ATOMS WHICH ARE STALE ON THE TIMESCALE OF BILLIONS OF YEARS WAS THEREFORE A MAJOR MYSTERY IT REQUIRED THE INTRODUCTION OF QUANTUM MECHANICS BY WAY OF EXPLANATION

The Modern Background

We now have a rough picture of the state of physics in 1905 when Albert Einstein (1879–1955) published his account of the Special Theory of Relativity. Einstein did not drop in from a vacuum.

I INHERITED A NEWTONIAN TRADITION IN PHYSICS, WITH ALL ITS ADVANCES AND ALL ITS PROBLEMS

So also, Einstein emerged at a certain juncture in world events, in a particular “climate of mind” that adds some context to his discovery.

Decisive Events

Queen Victoria’s death in 1901 signalled the end of a relatively stable period and the beginning of the 20th century’s violent releases of energy and accelerated innovations – everything we now call “modern”. A dangerous new world arose from two momentous events – first, the “Great War” of 1914 to 1918 …

The second decisive event was the October Revolution of 1917 in Russia which established the Communist Soviet Union there. Communism and the resistance to it from the United States of America and Western Europe set the stage for “Cold War” politics that dominated the world in the second half of the 20th century.

AND FOR ME, THE NUCLEAR BOMBS DROPPED ON HIROSHIMA AND NAGASAKI IN 1945 GAVE HORRIFIC PROOF THAT E=mc2...

A Time of Motion

The energy and disquiet of the early 20th century can be seen reflected in many other headline events. The Wright brothers, Orville (1871–1948) and Wilbur (1867–1912), made their first powered flight in 1903.

WE’VE OPENED UP A REVOLUTIONARY NEW MEANS OF TRAVEL... ... NOT MORE REVOLUTIONARY THAN MINE!

Henry Ford (1863–1947) in 1912 brought the assembly-line mass-manufactured Model-T to millions of people.

Pablo Picasso (1881–1973) introduced the revolutionary art of Cubism in 1907, also developed by Georges Braque (1882–1963). The British philosophers Bertrand Russell (1872–1970) and A.N. Whitehead (1861–1947) produced their formidable Principia Mathematica in 1910–13, which attempted to re-think mathematics on the rigorous basis of logic.