Motion Mountain - The Adventure of Physics, Vol 6 of 6 - A Speculation On Unification

404 Pages·2011·11.02 MB·English

by  Christoph Schiller

Christoph Schiller
MOTION MOUNTAIN
the adventure of physics – vol.vi
a speculation on unification
www.motionmountain.net

ChristophSchiller
Motion Mountain
The Adventure of Physics
Volume VI
A Speculation on Unification
Edition25.01,available asfreepdfat
www.motionmountain.net
Editiovicesimaquinta.
Proprietasscriptoris©ChrestophoriSchiller
primoannoOlympiadistrigesimae.
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proomnibussempergratuituseratetmanet.
Twenty-fifthedition.
Copyright©2012byChristophSchiller,
thefirstyearofthe30thOlympiad.
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ToBritta,EstherandJustusAaron
τῷἐμοὶδαὶμονι
DieMenschenstärken,dieSachenklären.
PREFACE
Thisbookiswrittenforanybodywhoisintenselycuriousaboutnatureandmotion.Have
you ever asked: Why do people, animals, things, images and empty space move? The
answer leads to many adventures, and this book presents one of the best of them: the
M
searchforaprecise,unifiedandfinaldescriptionofallmotion. otio
n
Thewishtodescribeallmotionisalargeendeavour.Fortunately,thislargeendeavour M
o
u
canbestructuredinthesimplediagramshowninFigure1.Thefinalandunifieddescrip- ntain
tionofmotion,thetopicofthisbook,correspondstothehighestpointinthediagram. –
Th
Searchingforthisfinalandunifieddescriptionisanoldquest.Inthefollowing,Ibriefly eA
d
summarizeitshistoryandthenpresentanintriguing,thoughspeculativesolutiontothe ven
tu
riddle. The approach is an unexpected result from a threefold aim that I have pursued re
o
f
since 1990, in the five previous volumes of this series: to present the basics of motion Ph
inawaythatisuptodate,captivatingandsimple.Inretrospect,theaimformaximum ysics
p
simplicityhasbeencentralindeducingthisspeculation. df
fi
ForThexeasmeaprlec,htwfoerntthieethfi-ncaeln,tuunryifireedsedaerscchrihpatisosnhoowf mnothtiaotnthiseraesistoarysmofalmleastnydissutarnpcreiseins. leavailab
le
nature.Researchhasalsoshownthatmattercannotbedistinguishedfromemptyspace free
atthosesmalldistances.Alastsurprisedatesfromthiscentury:particlesandspaceare of
ch
best described as made of strands, instead of little spheres or points. The present text arg
e
explainshowtoreachtheseunexpectedconclusions.Inparticular,quantumfieldtheory, at
w
w
the standard model of particle physics, general relativity and cosmology are shown to w
.m
followfromstrands.Thethreegaugeinteractions,thethreeparticlegenerationsandthe otio
n
threedimensionsofspace turn out tobe due to strands. In fact, all theopen questions m
o
u
n
oftwentieth-centuryphysicsaboutthefoundationsofmotion,allthemillenniumissues, tain
canbesolvedwiththehelpofstrands. .net
Theideasinthistext,infullcontrasttothoseofthefivepreviousvolumes,arespecula- Co
p
tive.Whilethepreviousvolumesintroduced,inanentertainingway,theestablishedparts yrig
h
t
ofphysics,thisvolumepresents,inthesameentertainingandplayfulway,aspeculation ©
C
h
aboutunification.Nothinginthisvolumeisestablishedknowledge–yet. risto
Thesearchforafinaltheoryisoneofthegreatadventuresoflife:itleadstothelimits ph
S
ofthought.Thesearchoverthrowsourthinkinghabitsaboutnature.Achangeinthink- chiller
inghabitscanproducefear,oftenhiddenbyanger.Butbyovercomingourfearswegain N
o
strength and serenity. Changing thinking habits thus requires courage, but it also pro- vem
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ducesintenseandbeautifulemotions.Enjoythem! r1
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8 preface
PHYSICS: Unified description of motion Why does motion
Describing motion with action. Adventures: understanding occur? What are
motion, intense joy with space, time and
thinking, catching a quantum particles?
glimpse of bliss,
calculating
masses and
couplings.
Quantum
General relativity theory with gravity Quantum field theory
Adventures: the Adventures: bouncing Adventures: building
night sky, measu- neutrons, under- accelerators, under-
ring curved space, standing tree standing quarks, stars,
exploring black growth. bombs and the basis of M
o
holes and the life, matter, radiation. tion
M
universe, space How do small ou
and time. things move? ntain
What are things? –
Th
e
How do Ad
Classical gravity everyday, Special relativity Quantum theory ven
tu
Adventures: fast and large Adventures: light, Adventures: death, re
o
climbing, skiing, things move? magnetism, length sexuality, biology, fP
h
space travel, contraction, time enjoying art and ysics
the wonders of dilation and colours, all high-tech
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astronomy and E = mc2. business, medicine, df
0 fi
geology. G c h, e, k chemistry, evolution. leavailab
le
free
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Galilean physics, heat and electricity fch
Adventures: sport, music, sailing, cooking, arg
e
describing beauty and understanding its origin, at
w
using electricity and computers, ww
understanding the brain and people. .mo
tio
n
m
FIGURE 1 Acompletemapofphysics:theconnectionsaredefinedbythespeedoflightc,the o
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gravitationalconstantG,thePlanckconstanth,theBoltzmannconstantkandtheelementarychargee. tain
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Solutionsandhintsforchallengesaregivenintheappendix.Challengesareclassified b
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as research level (r), difficult (d), standard student level (s) and easy (e). Challenges of 19
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preface 9
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Apapereditionofthisbook,printedondemandanddeliveredbymailtoanyaddress, o
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canbeorderedatstores.lulu.com/motionmountain.Butaboveall,enjoythereading! hysics
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Contents
16 1 From millennium physics to unification
Againstafinaltheory 20 •Whatwentwronginthepast 21 •Howtofindthefinal
theoryofmotion 22
24 2 Physics in limit statements
24 Simplifyingphysicsasmuchaspossible
Everyday,orGalilean,physicsinonestatement 24 •Specialrelativityinonestate-
ment 25 •Quantumtheoryinonestatement 26 •Thermodynamicsinonestate-
ment 27 •Generalrelativityinonestatement 28 •Deducinggeneralrelativity 29
•Deducinguniversalgravitation 32 •Thesizeofphysicalsystemsingeneralrela-
tivity 32 •Amechanicalanalogyforthemaximumforce 33
M
33 Plancklimitsforallphysicalobservables o
tio
Physics,mathematicsandsimplicity 35 •Limitstospace,timeandsize 35 •Mass n
M
o
andenergylimits 36 •Virtualparticles–anewdefinition 36 •Curiositiesand un
funchallengesaboutPlancklimits 37 tain
–
41 Cosmologicallimitsforallphysicalobservables Th
e
A
Sizeandenergydependence 42 •Angularmomentumandaction 42 •Speed 42 d
ve
•Force,powerandluminosity 43 •Thestrangecharmoftheentropybound 43 ntu
re
•Curiositiesandfunchallengesaboutsystem-dependentlimitstoobservables 45 o
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••CLiomsmitsotloogmyeinasuonreemsetanttempreenctisio4n7 a•nThdtehceoirsmchoallolegnicgaeltloimthitosutgohotbs4e8rv•abNleosre4a7l hysics
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numbers 48 •Vacuumandmass: twosidesofthesamecoin 48 •Measurement df
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precisionandtheexistenceofsets 49 le
50 Summaryonlimitsinnature availab
le
52 3 General relativity versus quantum theory free
o
Thecontradictions 53 •Theoriginofthecontradictions 54 •Thedomainofcon- f
ch
tradictions: Planck scales 55 •Resolving the contradictions 57 •The origin of arg
e
points 57 •Summaryontheclashbetweenthetwotheories 58 at
w
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59 4 Does matter differ from vacuum? w.m
o
Farewelltoinstantsoftime 59 •Farewelltopointsinspace 61 •Thegeneralized tio
n
m
indeterminacyprinciple 63 •Farewelltospace-timecontinuity 63 •Farewell o
u
n
todimensionality 66 •Farewelltothespace-timemanifold 66 •Farewelltoob- tain
servables,symmetriesandmeasurements 67 •Canspace-timebealattice? 68 • .net
A glimpse of quantum geometry 69 •Farewelltopoint particles 70 •Farewell C
o
p
toparticleproperties 71 •Amasslimitforelementaryparticles 72 •Farewellto yrig
h
massiveparticles–andtomasslessvacuum 73 •Matterandvacuumareindistin- t
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guishable 75 •Curiosities andfunchallengesonPlanck scales 76 •Common h
constituents 80 •Experimentalpredictions 81 •Summaryonparticlesand ristop
h
vacuum 82 Sch
83 5 What is the difference between the universe and nothing? iller
N
o
Cosmologicalscales 83 •Maximumtime 84 •Doestheuniversehaveadefinite vem
b
age? 84 •How precise can age measurementsbe? 85 •Does time exist? 86 er
1
•What is the error in the measurement of the age of the universe? 87 •Maxi- 99
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mumlength 91 •Istheuniversereallyabigplace? 91 •Theboundaryofspace Octo
–istheskyasurface? 93 •Doestheuniversehaveinitialconditions? 93 •Does be
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theuniverse contain particlesandstars? 94 •Doestheuniverse containmasses 01
1