christoph schiller motion mountain vol2

8/13/2019 Christoph Schiller Motion Mountain vol2

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Christoph Schiller

MOTION MOUNTAIN .

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Christoph Schiller

M M

Te Adventure of Physics

Volume II

Relativity

Edition ., available as ree pd atwww.motionmountain.net
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Editio vicesima quinta.

Proprietas scriptoris Chrestophori Schillersecundo anno Olympiadis trigesimae.

Omnia proprietatis iura reservantur et vindicantur.Imitatio prohibita sine auctoris permissione.Non licet pecuniam expetere pro aliqua, quaepartem horum verborum continet; liberpro omnibus semper gratuitus erat et manet.

wenty-fifh edition.

Copyright by Christoph Schiller,the second year o the th Olympiad.

Tis pd file is licensed under the Creative Commons

Attribution-Noncommercial-No Derivative Works . GermanyLicence, whose ull text can be ound on the websitecreativecommons.org/licenses/by-nc-nd/./de,with the additional restriction that reproduction, distribution and use,in whole or in part, inanyproduct or service, be itcommercial or not, is not allowed without the written consent othe copyright owner. Te pd file was and remains ree or everybodyto read, store and print or personal use, and to distributeelectronically, but only in unmodified orm and at no charge.
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o Britta, Esther and Justus Aaron


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Die Menschen strken, die Sachen klren.


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PREFACE

Primum movere, deinde docere.*

AntiquityTis book is written or anybody who is curious about nature and motion. Curiosityabout how people, animals, things, images and empty space move leads to many adven-

tures. Tis volume presents the best o them in the domains o relativity and cosmology.In the study o motion physics special and general relativity orm two importantbuilding blocks, as shown inFigure .

Specialrelativity is the exploration o the energy speed limitc.Generalrelativity is theexploration o the orce limitc4/4G. Te text shows that in both domains, all equationsollow rom these two limit values. Tis simple, intuitive and unusual way o learningrelativity should reward the curiosity o every reader whether student or proessional.

Te present volume is the second o a six-volume overview o physics that arose roma threeold aim that I have pursued since : to present motion in a way that is simple,up to date and captivating.

In order to besimple, the text ocuses on concepts, while keeping mathematics to the

necessary minimum. Understanding the concepts o physics is given precedence overusing ormulae in calculations. Te whole text is within the reach o an undergraduate.In order to beup to date, the text is enriched by the many gems both theoretical and

empirical that are scattered throughout the scientic literature.In order to becaptivating, 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 areastonished, we do not believe our eyes, we think, and nally we understand the trick.When we look at nature, we ofen have the same experience. Indeed, every page presentsat least one surprise or provocation or the reader to think about. Numerous interestingchallenges are proposed.

Te motto o the text,die Menschen strken, die Sachen klren, a amous statement byHartmut von Hentig on pedagogy, translates as: o ortiy people, to clariy things. Clar-

iying things and adhering only to the truth requires courage, as changing the habitso thought produces ear, ofen hidden by anger. But by overcoming our ears we growin strength. And we experience intense and beautiul emotions. All great adventures inlie allow this, and exploring motion is one o them. Enjoy it!

Munich, November .

* First move, then teach. In modern languages, the mentioned type omoving(the heart) is calledmotivat-ing; both terms go back to the same Latin root.

MotionMountainTheAdventureofPhysics

copyright

ChristophSchillerJune1990November2013

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Galilean physics, heat and electricity

Adventures:sport, music, sailing, cooking,

describing beauty and understanding its origin(vol. I), using electricity, light and computers,

understanding the brain and people (vol. III).

Special relativity

Adventures: light,

magnetism, length

contraction, time

dilation andE0 = mc

2 (vol. II).

Quantum theory

Adventures:death,

reproduction, biology,

chemistry, evolution,

enjoying colours andart, all high-tech

business, medicine

(vol. IV and V).

Quantumtheory with gravity

Adventures:bouncing

neutrons, under-

standing tree

growth (vol. V).

Final, unified description of

motion Adventures:understanding

motion, intense joy with

thinking, calculating

couplings and

masses, catching

a glimpse

of bliss (vol. VI).

G c h, e, k

PHYSICS:

Describing motionwith the least action principle.

Quantum field theory

Adventures:building

accelerators, under-

standing quarks, stars,

bombs and the basis oflife, matter, radiation

(vol. V).

How doeveryday,

fast and large

things move?

How do small

things move?

What are things?

Why does motion

occur? What are

space, time and

quantum particles?

General relativity

Adventures:the

night sky, measu-

ring curved space,

exploring black

holes and the

universe, spaceand time (vol. II).

Classical gravity

Adventures:

climbing, skiing,

space travel,

the wonders ofastronomy and

geology (vol. I).

F I G U R E 1 A complete map of physics: the connections are defined by the speed of light c, thegravitational constantG, the Planck constanth, the Boltzmann constantk and the elementary chargee.

A

Learning widens knowledge, improves intelligence and generates proudness. And learn-ing allows us to discover what kind o person we can be.Learning rom a book, especially one about nature, should be ast and un. Te most

inefficient and most tedious learning method is to use a marker to underline text: itwastes time, provides alse comort and makes the text unreadable. Nobody markingtext is learning efficiently or is enjoying it.

In my experience as a student and teacher, one learning method never ailed to trans-orm unsuccessul pupils into successul ones: i you read a text or study, summarizeevery section you read,in your own words and images, aloud. I you are unable to do


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so, read the section again. Repeat this until you can clearly summarize what you readin your own words and images, aloud. You can do this alone or with riends, in a roomor while walking. I you do this with everything you read, you will reduce your learning

and reading time signicantly, enjoy learning rom good texts much more and hate badtexts much less. Masters o the method can use it even while listening to a lecture, in alow voice, thus avoiding to ever take notes.

A

A teacher likes pupils and likes to lead them into exploring the eld he chose. His or herenthusiasm or the job is the key to job satisaction. I you are a teacher, beore the start oa lesson, picture, eel and tell yoursel how you enjoy the topic o the lesson; then picture,eel and tell yoursel how you will lead each o your pupils into enjoying that topic asmuch as you do. Do this exercise consciously, every time. You will minimize trouble in

your class and maximize your success.Tis book is not written with exams in mind; it is written to make teachers and stu-

dentsunderstandandenjoyphysics, the science o motion.

U

ext in green, as ound in many marginal notes, marks a link that can be clicked in a pdreader. Such green links are either bibliographic reerences, ootnotes, cross reerencesto other pages, challenge solutions, or pointers to websites.

Solutions and hints orchallengesare given in the appendix. Challenges are classiedas research level (r), difficult (d), standard student level (s) and easy (e). Challenges or

which no solution has yet been included in the book are marked (ny).

F

Tis text is and will remain ree to download rom the internet. I would be delighted toreceive an email rom you at [email protected], especially on the ollowing issues:

What was unclear and should be improved?Challenge 1 s What story, topic, riddle, picture or movie did you miss? What should be corrected?

In order to simpliy annotations, the pd le allows adding yellow sticker notes in Adobe

Reader. Help on the specic points listed on thewww.motionmountain.net/help.htmlweb page would be particularly welcome. All eedback will be used to improve the nextedition. On behal o all readers, thank you in advance or your input. For a particularlyuseul contribution you will be mentioned i you want in the acknowledgements,receive a reward, or both.

Your donation to the charitable, tax-exempt non-prot organisation that produces,translates and publishes this book series is welcome! For details, see the web pagewww.motionmountain.net/donation.html. I you want, your name will be included in thesponsor list. Tank you in advance or your help, on behal o all readers across the world.


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Te paper edition o this book, printed on demand and delivered by mail to any ad-dress o your choice, can be ordered at www.lulu.com/spotlight/motionmountain. Butabove all, enjoy the reading!


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and un challenges about gravitation What is weight? Why doapples all? A summary: the implications o the invariant speed o light ongravitation

O , Weak fields Te Tirring effects Gravitomagnetism Gravitationalwaves Production and detection o gravitational waves Bending olight and radio waves ime delay Relativistic effects on orbits Te geodesic effect Curiosities and un challenges about weak fields A summary on orbits and waves

F

How to measure curvature in two dimensions Tree dimensions: curvatureo space Curvature in space-time Average curvature and motionin general relativity Universal gravity Te Schwarzschild metric Curiosities and un challenges about curvature Tree-dimensional cur-

vature: the Ricci tensor Average curvature: the Ricci scalar TeEinstein tensor Te description o momentum, mass and energy Ein-steins field equations Universal gravitation again Understandingthe field equations Hilberts action how do things all? Te symme-tries o general relativity Mass in general relativity Te orce limit andthe cosmological constant Is gravity an interaction? How to calculatethe shape o geodesics Riemann gymnastics Curiosities and un chal-lenges about general relativity A summary o the field equations

W ? M

Which stars do we see? What do we see at night? What is the uni-verse? Te colour and the motion o the stars Do stars shine everynight? A short history o the universe Te history o space-time

Why is the sky dark at night? Te colour variations o the night sky Is the universe open, closed or marginal? Why is the universe transpar-

ent? Te big bang and its consequences Was the big bang a bigbang? 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 o the stars differ? Are there dark stars? Are all starsdifferent? Gravitational lenses What is the shape o the universe? What is behind the horizon? Why are there stars all over the place? In-flation Why are there so ew stars? Te energy and entropy content o theuniverse Why is matter lumped? Why are stars so small comparedwith the universe? Are stars and galaxies moving apart or is the universe ex-panding? Is there more than one universe? Why are the stars fixed?

Arms, stars and Machs principle At rest in the universe Does lightattract light? Does light decay? Summary on cosmology

B

Why explore black holes? Mass concentration and horizons Blackhole horizons as limit suraces Orbits around black holes Black holeshave no hair Black holes as energy sources Formationo and search orblack holes Singularities Curiosities and un challenges about blackholes Summary on black holes A quiz is the universe a blackhole?


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D ?Can space and time be measured? Are space and time necessary? Do closed timelike curves exist? Is general relativity local? Te hole argu-

ment Is the Earth hollow? A summary: are space, time and massindependent?

G Te accuracy o the description Research in general relativity and cosmol-ogy Could general relativity be different? Te limits o generalrelativity

U, SI units Te meaning o measurement Curiosities and un challengesabout units Precision and accuracy o measurements Limits to preci-sion Physical constants Useul numbers

C

B C

Film credits Image credits


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R

In our quest to learn how things move,the experience o hiking and other motionleads us to discover that there is a maximum speed in nature,and that two events that happen at the same time or one observermay not or another.We discover that empty space can bend, wobble and move,we nd that there is a maximum orce in nature,and we understand why we can see the stars.


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C

MAXIMUM SPEED, OBSERVERS AT

REST, AND MOTION OF LIGHT

Fama nihil est celerius.*

Antiquity

L is indispensable or a precise description o motion. o check whether a

ine or a path o motion is straight, we must look along it. In other words, we useight to dene straightness. How do we decide whether a plane is at? We look

across it,**again using light. How do we observe motion? With light. How do we mea-sure length to high precision? With light. How do we measure time to high precision?With light: once it was light romthe Sun thatwas used; nowadays it is light rom caesiumatoms.Page 276

Light is important because it is the standard orundisturbed motion. Physics wouldhave evolved much more rapidly i, at some earlier time, light propagation had beenrecognized as the ideal example o motion.

But is light really a phenomenon o motion? Yes. Tis was already known in ancientGreece, rom a simple daily phenomenon, the shadow. Shadows prove that light is a mov-

ing entity, emanating rom the light source, and moving in straight lines.***Te GreekthinkerRef. 1 Empedocles (c. toc. ) drew the logical conclusion that light takes acertain amount o time to travel rom the source to the surace showing the shadow.

Empedocles thus stated that the speed o light is nite. We can conrm this result witha different, equally simple, but subtle argument. Speed can be measured. And measure-ment is comparison with a standard. Tereore theperectspeed, which is used as theimplicit measurement standard, must have a nite value. An innite velocity standard

* Nothing is aster than rumour. Tis common sentence is a simplified version o Virgils phrase: ama,malum qua non aliud velocius ullum.Rumour, the evil aster than all. From theAeneid, book IV, verses and .** Note that looking along the plane rom all sides is not sufficient or this check: a surace that a light beam

touches right along its length inalldirections does not need to be flat. Can you give an example? One needsother methods to check flatness with light. Can you speciyChallenge 2 s one?*** Whenever a source produces shadows, the emitted entities are calledraysorradiation. Apart rom light,other examples o radiation discovered through shadows wereinrared raysandultraviolet rays, which em-anate rom most light sources together with visible light, and cathode rays, which were ound to be to themotion o a new particle, theelectron. Shadows also led to the discovery oX-rays, which again turned outto be a version o light, with high requency.Channel rayswere also discovered via their shadows; they turnout to be travelling ionized atoms. Te three types o radioactivity, namely-rays(helium nuclei),-rays(again electrons), and-rays(high-energy X-rays) also produce shadows. All these discoveries were madebetween and : those were the ray days o physics.


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, ,

F I G U R E 2 How do you check whether the linesare curved or straight?

Earth (first

measurement)

Jupiter and Io

(first measurement)

Earth (second

measurement)

Jupiter and Io

(second measurement)

Sun

F I G U R E 3 Rmers method of measuring the speed of light.

would not allow measurements at all.Challenge 3 s In nature, lighter entities tend to move with higherspeed. Light, which is indeed extremely light, is an obvious candidate or motion withperect but nite speed. We will conrm this in a minute.

A nite speed o light means that whatever we see is a message rom thepast. Whenwe see the stars,*the Sun or a person we love, we always see an image o the past. In asense, nature prevents us rom enjoying the present we must thereore learn to enjoythe past.

Te speed o light is high; thereore it was not measured until the years to ,even though many, including Galileo, had tried to do so earlier. Te rst measurement

* Te photograph o the night sky and the Milky Way, on page is copyright Anthony Ayiomamitis and isound on his splendid websitewww.perseus.gr.


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rain light

light's perspective winds perspectiverain's perspective

human perspectivewalkers perspective

Sun

Sun

Earth

wind

windsurfer

windsurfers perspective

c

c

cc

cc

F I G U R E 4 The rainwalkers or windsurfers method of measuring the speed of light.

method was worked out and published by theRef. 2 Danish astronomer Ole Rmer*when

he was studying the orbits o Io and the other Galilean satellites o Jupiter.Vol. I, page 185

He did notobtain any specic value or the speed o light because he had no reliable value or thesatellites distance rom Earth and because his timing measurements were imprecise. Telack o a numerical result was quickly corrected by his peers,Ref. 3 mainly Christiaan Huygensand Edmund Halley. (You might try to deduce Rmers method romFigure .)Challenge 4 s SinceRmers time it has been known that light takes a bit more than minutes to travel romthe Sun to the Earth. Tis result was conrmed in a beautiul way fy years later, in ,by the astronomer James Bradley.Vol. I, page 138 Being English, Bradley thought o the rain method tomeasure the speed o light.Ref. 4

How can we measure the speed o alling rain? We walk rapidly with an umbrella,measure the angleat which the rain appears to all, and then measure our own velocity

. (We can clearly see the angle while walking i we look at the rain to our lef or right,

i possible against a dark background.) As shown inFigure ,the speedc o the rain is

* Ole (Ola) Rmer ( Aarhus Copenhagen), Danish astronomer. He was the teacher o theDauphin in Paris, at the time o Louis XIV. Te idea o measuring the speed o light in this way was due tothe Italian astronomer Giovanni Cassini, whose assistant Rmer had been. Rmer continued his measure-ments until , when Rmer had to leave France, like all protestants (such as Christiaan Huygens), so thathis work was interrupted. Back in Denmark, a fire destroyed all his measurement notes. As a result, he wasnot able to continue improving the precision o his method. Later he became an important administratorand reormer o the Danish state.


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, ,

then given (approximately) byc

= /tan . ()

In the same way we can measure the speed o wind when on a surboard or on a ship.Te same measurement can be made or light.Figure shows that we just need to mea-sure the angle between the motion o the Earth and the light coming rom a star aboveEarths orbit. Because the Earth is moving relative to the Sun and thus to the star, theangle is not 90. Tis deviation is called theaberrationo light; the aberration is deter-mined most easily by comparing measurements made six months apart. Te value o theaberration angle is 20.5 . (Nowadays it can be measured with a precision o ve decimaldigits.) Given that the speed o the Earth around the Sun is =2R/=29.7 km/s, thespeed o light must thereore bec=0.300Gm/s.*Tis is an astonishing value, especiallywhen compared with the highest speed ever achieved by a man-made object, namely theVoyager satellites, which travel away rom us at 52 Mm

/h

=14km

/s, with the growth o

children, about 3 nm/s, or with the growth o stalagmites in caves, about 0.3 pm/s. Webegin to realize why measurement o the speed o light is a science in its own right.Te rstprecisemeasurement o the speed o light was made in by the Frenchphysicist Hippolyte Fizeau (). His value was only % greater than the modernone. He sent a beam o light towards a distant mirror and measured the time the lighttook to come back. How did Fizeau measure the time without any electric device? In act,he used the same ideasVol. I, page 58 that are used to measure bullet speeds; part o the answer is giveninFigure .(How ar away does the mirror have to be?)Challenge 9 s A modern reconstruction ohis experiment by Jan Frercks has achieved a precision o %.Ref. 7 oday, the experiment is

* Umbrellas were not common in Britain in ; they became ashionable later, afer being introducedrom China. Te umbrella part o the story is made up. In reality, Bradley had his idea while sailing on

the Tames, when he noted that on a moving ship the apparent wind has a different direction rom thaton land. He had observed stars or many years, notably Gamma Draconis, and during that time he hadbeen puzzled by thesigno the aberration, which wasoppositeto the effect he was looking or, namely thato the star parallax. Both the parallax and the aberration or a star above the ecliptic make them describe asmall ellipse in the course o an Earth year, though with different orientations. Can you seeChallenge 5 s why?

By the way, the correct ormula() isc= /(tan 1 2/c2 ). Why?Challenge 6 so determine the speed o the Earth, we first have to determine its distance rom the Sun. Te simplest

method is the one by the Greek thinker Aristarchus o Samos (c. toc. ). We measure the anglebetween the Moon and the Sun at the moment when the Moon is precisely hal ull. Te cosine o that anglegives the ratio between the distance to the Moon (determined as explained earlier on)Vol. I, page 155 and the distance tothe Sun. Te explanation is lef as a puzzle or the reader.Challenge 7 s

Te angle in question is almost a right angle (which would yield an infinite distance), and good instru-ments are needed to measure it with precision,Ref. 5 as Hipparchus noted in an extensive discussion o the prob-

lem around . Precise measurement o the angle became possible only in the late seventeenth century,when it was ound to be 89.86, giving a distance ratio o about . oday, thanks to radar measurementso planets,Page 289 the distance to the Sun is known with the incredible precision o metres. Moon distance vari-ations can even be measured to the nearest centimetre; can you guess how this isChallenge 8 s achieved?

Aristarchus also determined the radius o the Sun and o the Moon as multiples o those o the Earth.Ref. 6Aristarchus was a remarkable thinker: he was the first to propose the heliocentric system, and perhaps thefirst to propose that stars were other, araway suns. For these ideas, several o his contemporaries proposedthat he should be condemned to death or impiety. When the Polish monk and astronomer Nicolaus Coper-nicus () again proposed the heliocentric system two thousand years later, he did not mentionAristarchus, even though he got the idea rom him.


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light

source

mirror

half-silvered

mirrorlarge distance

F I G U R E 5 Fizeaus set-up to measure the speed of light (photo AG Didaktik und Geschichte der

Physik, Universitt Oldenburg).

path of light pulse

10 mm

red

shutter

switchbeam

F I G U R E 6 A photograph of a green light pulse moving from right to left through a bottle with milky

water, marked in millimetres (photograph Tom Mattick).

much simpler; in the chapters on electrodynamics we will discover how to measure thespeed o light using two standardUNIXor Linux computers connected by a cable, usingthe ping command.Vol. III, page 30

Te speed o light is so high that it is even difficult to prove that it isnite. Perhapsthe most beautiul way to prove this is to photograph a light pulse ying across oneseld o view, in the same way as one can photograph a car driving by or a bullet yingthrough the air.Figure shows the rst such photograph,Ref. 8 produced in with a stan-dard off-the-shel reex camera, a very ast shutter invented by the photographers, and,most noteworthy, not a single piece o electronic equipment. (How ast does such a shut-ter have to be?Challenge 10 s How would you build such a shutter? And how would you make sure itopened at the right instant?)

A nite speed o light also implies that a rapidly rotating light beam bends, as shown


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http://motionmountain-volume3.pdf/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://motionmountain-volume3.pdf/


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, ,

F I G U R E 7 A consequence of the finiteness

of the speed of light. Watch out for the

tricky details light doestravel straight from

the source, it doesnotmove along the

drawn curved line; the same occurs for

water emitted by a rotating water sprinkler.

TA B L E 1 Properties of the motion of light.

O

Light can move through vacuum.Light transports energy.Light has momentum: it can hit bodies.Light has angular momentum: it can rotate bodies.Light moves across other light undisturbed.Light in vacuum always moves aster than any material body does.Te speed o light, its true signal speed, is the orerunner speed.Vol. III, page 120In vacuum, the speed o light is299792458m/s(or roughly30cm/ns).Te proper speed o light is infinite.Page 45

Shadows can move without any speed limit.Light moves in a straight line when ar rom matter.High-intensity light is a wave.Light beams are approximations when the wavelength is neglected.In matter, both the orerunner speed and the energy speed o light are lower than in vacuum.In matter, the group velocity o light pulses can be zero, positive, negative or infinite.

asin Figure. In everyday lie, the high speed o light and the slow rotation o lighthousesmake the effect barely noticeable.

In short, light moves extremely rapidly. It is much aster than lightning, as you might

like to check yoursel.Challenge 11 s A century o increasingly precise measurements o the speed haveculminated in the modern value

c=299792458m/s. ()In act, this value has now been xed exactly, by denition, and the metre has been de-ned in terms oc. An approximate value or cis thus 0.3 Gm/s or 30cm/ns.able gives a summary o what is known today about the motion o light. wo o the most sur-prising properties were discovered in the late nineteenth century. Tey orm the basis o


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what is called the theory o special relativity.Ref. 9

C

?

Et nihil est celerius annis.*

Ovid,Metamorphoses.We all know that in order to throw a stone as ar as possible, we run as we throw it; weknow instinctively that in that case the stones speed with respect to the ground is higherthan i we do not run. However, to the initial astonishment o everybody, experimentsshow that light emitted rom a moving lamp has the same speed as light emitted roma resting one. Te simplest way to prove this is to look at the sky. Te sky shows manyexamples odouble stars: these are two stars that rotate around each other along ellipses.In some o these systems, we see the ellipses (almost) edge-on, so that each star periodi-

cally moves towards and away rom us. I the speed o light would vary with the speed othe source, we would see bizarre effects, because the light emitted rom some positionswould catch up the light emitted rom other positions. In particular, we would not beable to see the elliptical shape o the orbits. However, bizarre effects are not seen, and theellipses are observed. Willem de Sitter gave this beautiul argument already in ; heconrmed the validity with a large number o double stars.Ref. 10

In other words, light (in vacuum) is never aster than light; all light beams have thesame speed. Many specially designed experiments have conrmed this result to highprecision.Ref. 11 Te speed o light can be measured with a precision o better than 1 m/s; buteven or lamp speeds o more than 290000 000 m/s the speed o the emitted light doesnot change. (Can you guess what lamps were used?)Challenge 12 s

In everyday lie, we also know that a stone arrives more rapidly i we run towards itthan in the case that we stand still or even run away rom it. But astonishingly again, orlight no such effect exists! All experiments clearly show that i we run towards a lamp,we measure the same speed o light as in the case that we stand still or even run awayrom it. Also these experiments have been perormed to the highest precision possible.Ref. 12

All experiments thus show that the velocityo light hasthe samevalue or all observers,even i they are moving with respect to each other or with respect to the light source. Tespeed o light is indeed the ideal, perect measurement standard.**

Tere is also a second setRef. 15 o experimental evidence or the constancy, or better, theinvariance o the speed o light. Every electromagnetic device, such as an electric vacuum

* Nothing is aster than the years. Book X, verse .

** An equivalent alternative term or the speed o light is radar speed or radio speed; we will see later whythis is the case.Vol. III, page 102

Te speed o light is also not ar rom the speed o neutrinos. Tis was shown most spectacularly by theobservation o a supernova in , when the light flash and the neutrino pulse arrived on Earth only seconds apart. (It is not known whether the difference is due to speed differences or to a different startingpoint o the two flashes.) What would be the first digit or which the two speed values could differ, knowingthat the supernova was1.7 105 light years away, and assuming the same starting point?Challenge 13 s

Experiments also show that the speed o light is the same in all directions o space, to at least dig-its o precision.Ref. 13 Other data, taken rom gamma ray bursts, show that the speed o light is independent orequency to at least digits o precision.Ref. 14


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, ,

F I G U R E 8 All devices based on electric motors prove that the speed of light is invariant ( Miele,

EasyGlide).

F I G U R E 9 Albert Einstein (18791955).

cleaner, shows that the speed o light isinvariant.Vol. III, page 48 We will discover that magnetic eldswould not result rom electric currents, as they do every day in every electric motorand in every loudspeaker, i the speed o light were not invariant. Tis was actually howthe invariance was rst deduced, by several researchers. Onlyaferthese results did theGermanSwiss physicist Albert Einstein show that the invariance o the speed o light isalso in agreement with the observed motion o bodies. We will check this agreement inthis chapter. Te connectionRef. 16 between relativity and electric vacuum cleaners, as well asother machines, will be explored in the chapters on electrodynamics.Vol. III, page 48

Te main connection between light and motion o bodies can be stated in a ew words.I the speed o light were not invariant, observers would be able to move at the speed olight. Why? Since light is a wave, an observer moving at the same speed as the wavewould see arozenwave. However, electromagnetismorbidssuch a phenomenon. Tere-ore, observers cannot reach the speed o light. Te speed o light is thus a limit speed.Observers and bodies thus always moveslowerthan light. Tereore, light is also an in-

variant speed. In other words, tennis with light is not un: the speed o light is always thesame.

By the way, is it possible at all to play tennis with light?Challenge 14 s


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christoph schiller motion mountain vol2

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