Table Of ContentT H E F R O N T I E R S C O L L E C T I O N
U L T I M A T E HH OO R I Z O N S U L
T I M A T E H O R I Z OO NN SS U L T I
M A T E H O R I Z O N S U L T II MM A
Helmut Satz T E H O R I Z O N S U L T I M A T E
H O R I Z O N S U L T I M A T E H O
R I Z O N S U L T I M A T E H O R I
U LT I M ATZ OEN S U L T I M A T E H O R I Z O
N S U L T I M A T E H O R I Z O N S
UU L T I M A T E H O R I Z O N S U L
TT II MM A T E H O R I Z O N S U L T I
M A T E H O R I Z O N S U L T I M A
H O R I Z O N S
T E H O R I Z O N S UU LL T I M A T E
H O R I Z O N S U L T I M A T E H O
RR I Z O N S U L T I M A T E H O R I
ZZ OO N SS UU LL T I M A T E H O R I Z O
N S UU LL TTT II MM AA TT EE HH OO R I Z O N S
Probing the Limits
of the Universe
123
THE FRONTIERS COLLECTION
Series editors
Avshalom C. Elitzur
Université Grenoble I Centre Équation, Labo. Verimag, Gières, France
e-mail: [email protected]
Laura Mersini-Houghton
Department of Physics & Astronomy, University of North Carolina, Chapel Hill,
North Carolina, USA
e-mail: [email protected]
T. Padmanabhan
Inter University Centre for Astronomy and Astrophysics (IUC),
Pune University Campus, Pune, India
e-mail: [email protected]
Maximilian Schlosshauer
Institute for Quantum Optics and Quantum Information Austrian Academy of
Sciences, Portland, Oregon, USA
e-mail: [email protected]
Mark P. Silverman
Department of Physics, Trinity College, Hartford, Connecticut, USA
e-mail: [email protected]
Jack A. Tuszynski
Department of Physics, University of Alberta, Edmonton, Alberta, Canada
e-mail: [email protected]
Rüdiger Vaas
University of Giessen, Giessen, Germany
e-mail: [email protected]
For furthervolumes:
http://www.springer.com/series/5342
THE FRONTIERS COLLECTION
Series Editors
A. C. Elitzur L. Mersini-Houghton T. Padmanabhan
M. Schlosshauer M. P. Silverman J. A. Tuszynski R. Vaas
The books in this collection are devoted to challenging and open problems at the
forefrontofmodernscience,includingrelatedphilosophicaldebates.Incontrastto
typical research monographs, however, they strive to present their topics in a
manner accessible also to scientifically literate non-specialists wishing to gain
insightintothedeeperimplicationsandfascinatingquestionsinvolved.Takenasa
whole,theseriesreflectstheneedforafundamentalandinterdisciplinaryapproach
tomodernscience.Furthermore,itisintendedtoencourageactivescientistsinall
areas toponderoverimportantandperhapscontroversialissuesbeyondtheirown
speciality. Extending from quantum physics and relativity to entropy, conscious-
ness and complex systems—the Frontiers Collection will inspire readers to push
back the frontiers of their own knowledge.
Helmut Satz
ULTIMATE HORIZONS
Probing the Limits of the Universe
123
Helmut Satz
FakultätfürPhysik
Universität Bielefeld
Bielefeld
Germany
ThisworkappearsinaparallelGermanedition‘‘GottesunsichtbareWürfel’’,publishedby
C. H.BeckVerlag.
ISSN 1612-3018 ISSN 2197-6619 (electronic)
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In memory of my mother
who dared to venture into the unknown
in search of a better life for her sons
Preface
Confronted with the choice between paradise and knowledge, man, according to
theBible,chose knowledge.Werethesereallyalternatives?Itcame tobethatthe
gainingofknowledgeandthewiderhorizonoutsidethegardenofEdenbroughtto
many as much pleasure and satisfaction as any paradise they could imagine.
Humans have always wanted to explore the world they live in, and they have
always wanted to know what lies beyond the horizons that limit their view. The
search for richer pastures, better climates, easier communication—all these cer-
tainlyplayedapartinthis,butbehinditalltherewasaninherenthumansenseof
curiosity. This curiosity triggered a journey starting some 200,000 years ago in a
remotecornerofAfricaandhasdrivenustonavigatealltheoceans,toconquerthe
entire Earth, to probe the heavens and to penetrate ever more deeply into inter-
stellar space, to study ever more distant galaxies. At the other end of the scale,
high-energy particle accelerators allow us to resolve the structure of matter to an
everhigherdegree,tolookforitsultimateconstituentsandstudyhowtheyinteract
witheachothertoformourworld.Aretherelimits,isthereanendtothisdrive,at
the large scale as well as at the small?
Inthelasthundredyears,modernphysicsandcosmologyhaveshownthatthere
existregionsforeverbeyondourreach,hiddenfromusbytrulyultimatehorizons.
Theseregions wecanaccessinourimaginationonly;wecanspeculatewhatthey
arelikeandwhetherperhapssomesignoftheirexistence,someindicationoftheir
nature can ever reach our world.
Suchhiddenregionsexistinthoseremotepartsoftheuniversewhere,fromour
point of view, space expands faster than the speed of light. Closer to us, they are
foundinblackholes,wheregravityisstrongenoughtoretainevenlightwithinits
horizon of ultimate attraction. And in the realm of the very small, quarks remain
forever confined to their colorful world of extreme density; they can never be
removed from it. But given the Big Bang origin of the universe, our world in its
veryearlystageswasimmenselyhotanddense;andgiventhespectrumofallthe
particles created in high-energy collisions, we can try to reconstruct ever earlier
stages. The evolution of the universe, with cooling and expansion, then defines
horizons in time, thresholds through which the universe had to pass to reach its
present state. What were the earlier stages like?
vii
viii Preface
Althoughitisnotpossibletotransmitinformationacrossthe‘‘eventhorizons’’
that form the borders of these forbidden regions, still sometimes strange signals
may appear, providing us with hints of the existence of those other worlds. Such
striking phenomena can become possible through quantum effects; ‘‘Hawking–
Unruh’’ radiation provides one example expected to arise in a variety of cases,
whenever there exists an event horizon. And looking at the multitude of ‘‘ele-
mentary’’ particles produced in high-energy accelerators, we can speculate that
they originally came from a simpler, more symmetric world, which in the course
of the evolution experienced transitions, like the freezing of water or the mag-
netization of metals, to form the many-faceted and less symmetric world we see
today.
Theaimofthisbookistotellthestoryofhowthedifferenthorizons,onEarth
and in the heavens, on large and on small scales, now and in the past, were
discoveredandusedtodefineourviewoftheworld.Itisastoryoftheevolutionof
this view, which started before ‘‘science,’’ and which is much more than just
‘‘something for scientists.’’ It started with philosophers wondering what matter
wasmadeof,andhow;withsailorsdaringtofindoutiftheworldendssomewhere;
withastronomerstryingtodetermineourpositionamongthestars,toestimatethe
size of the Earth by looking at the Sun and using the newly developed geometry.
With Edgar Allan Poe, the Big Bang appeared in literature before it was com-
monplace in physics and cosmology; and aspects of both black holes and worm-
holes were part of the stories of Lewis Carroll before they became significantly
appreciated in science. Many of the ideas, even today’s, have come up here and
there inthe course oftime.Thewaysof treating them, andthe toolsused for that
were different, ofcourse, and changed over the centuries. But what remained was
thatdesiretoseewhatliesbeyond,andtofindoutwhetherthereisalimittowhat
we can reach and understand.
We begin by looking at the various horizons partitioning our world and then
showhowdifferentforbiddenregionsariseintheuniverse,andwhenandhowthey
canemitsignaturesastestimonytotheirpresenceandtheirnature.Themysterious
light emerging fromaneventhorizon, orthe equally mysteriousclustersinanew
andstrangeether,theymaywellremainallthatwecaneverseeofwhatishidden
beyond the ultimate horizons.
This book is not meant to give a systematic presentation of the recent devel-
opments in physics or cosmology. Its aim is to tell a story that began a long time
ago and that will certainly not come to an end very soon. And it covers devel-
opmentsthatsometimes,asintheageofVascodaGamaandColumbus,orinthe
time of Einstein, Planck, Bohr and Heisenberg, revolutionize the world in two or
three decades. At other times, between Ptolemy and Copernicus, it takes a mil-
lennium to add a couple of epicycles to the accepted scheme of things. The
problem is, in the words of the renowned Austrian theorist Walter Thirring, that
‘‘to do something really new, you have to have a new idea,’’ and that does not
happen so very often. It does not suffice to play on the keyboard of the available
theoreticalformalisms;thisjustleadstomanymelodiesandnottoanyconvincing
and lasting new harmony.
Preface ix
Ihavetriedtopresentthingsinawaynotneedinganymathematics.Thatis,asI
indicate in the section on Notation, a two-sided issue. Even Einstein sometimes
presentedthespecialtheoryofrelativityintermsofpeopleonatrainversuspeople
on the ground. It can be done, and it is indeed helpful to convey the basic ideas.
For a full understanding of the ultimate conclusions, however, mathematics
becomesessential.Totravelamiddleroad,Ihaveattimesaddedinserts,inwhich
someaspectsofthebasic mathematicalformulationareindicated. ButIhopethat
the presentation remains understandable even if you skip these.
One unavoidable aspect appears if one tries to present things in as readable a
way as possible: some points and concepts are mentioned more than once.
Although strictly speaking logical, the reminder ‘‘as already discussed in the
previousChapter’’isinfactoftennotwhatthereaderwants;itseemsbettertojust
briefly recall the idea again. So I offer my apologies for a number of repetitions.
And another apology is probably also needed. When forced to choose between
scientific rigor and simplifying an idea enough to make it understandable, I gen-
erallytookthelatterpath.Ithoughtitbettertotrytohavereadersfollowmytrain
of thought, even if they will later need corrections, than to lose them in technical
detailstheycannotfollow.MyinspirationherewerethewordsofthegreatDanish
physicist Niels Bohr, who noted that Wahrheit (truth) and Klarheit (clarity) are
complementary: the more precisely you enforce one, the less precise the other
becomes.
Finally, it is my pleasure to express sincere thanks to all who have helped me
withthisendeavor.ObvioussupportcamefrommycolleagueshereinBielefeld,in
Brookhaven, at CERN, in Dubna and elsewhere. They have been of crucial
importance in forming my view of things. And last, but far from least, profound
thanks go to my wife, who has patiently borne with me during all these years.
Bielefeld, May 2013 Helmut Satz
Contents
1 Horizons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 The Horizon of Accessibility . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Forbidden Rooms in the Universe . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Ultimate Constituents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 The End of the Earth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 The Roof of Heaven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 The Vanishing Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 The Speed of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Why Is the Sky Dark at Night?. . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 The Big Bang. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Cosmic Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 The Absolute Elsewhere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 The Secret Glow of Black Holes. . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1 The Escape Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Tidal Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 The Sea of Unborn Particles. . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 Invisible Light on the Horizon . . . . . . . . . . . . . . . . . . . . . . . . 54
4 The Visions of an Accelerating Observer . . . . . . . . . . . . . . . . . . . 59
4.1 Gravity and Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 A Total End of Communication . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 The Temperature of the Vacuum. . . . . . . . . . . . . . . . . . . . . . . 64
4.4 Lightning in Empty Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Quantum Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5 The Smallest Possible Thing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.1 Why Does the Sun Shine? . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 The Strong Nuclear Interaction. . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 The Weak Nuclear Interaction. . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4 The Quarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.5 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.6 The Confinement Horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
xi
