dreams of a finite theory *) gabriele veneziano (cern-ph/th & collège de france) *) adjusted...
TRANSCRIPT
DREAMS OF A DREAMS OF A FINITEFINITE THEORYTHEORY*)*)
Gabriele VenezianoGabriele Veneziano
(CERN-PH/TH & Collège de France)(CERN-PH/TH & Collège de France)
*) Adjusted from Steven Weinberg’s:*) Adjusted from Steven Weinberg’s:
DREAMS OF A DREAMS OF A FINALFINAL THEORY THEORY
OutlineOutline Forces & particles: carriers & bricksForces & particles: carriers & bricks How did we get there?How did we get there? Looking at history backwards:Looking at history backwards:
a) From the EW theory to Fermi’sa) From the EW theory to Fermi’s
b) From QCD to the old stringb) From QCD to the old string Classical vs. quantum strings: the bad Classical vs. quantum strings: the bad
newsnews Classical vs. quantum gravity: the clashClassical vs. quantum gravity: the clash Classical vs. quantum strings: the good Classical vs. quantum strings: the good
newsnews Dreams of a finite theory:Dreams of a finite theory:
black holes, cosmology, extra black holes, cosmology, extra dimensions…dimensions…
EMEM
WEAKWEAK
STRONGSTRONG
GRAV.GRAV.
FORCEFORCE
PLAYERSPLAYERSCARRIERSCARRIERS BRICKSBRICKS
W,ZW,ZGluonsGluons Gravi-Gravi-tonton llCh.Ch.
qq RR ? ???
???? ??
HH
carriescarries feelsfeels
Evolution of our understandingEvolution of our understanding
ElectricElectric
WeakWeak
GravityGravity
MagneticMagnetic }}Classical Classical Electro-Electro-MagnetismMagnetism(Maxwell)(Maxwell)
QEDQED
EWEW
NuclearNuclear QCDQCD
Classical Classical GeneralGeneralRelativityRelativity(Einstein)(Einstein)
SMSM
StringString
StringString
FermiFermi19341934
QGDQGD
tt
We shall followthe greengreen arrows
Neutron Neutron --decaydecay
nn
pp
dd
uu
WW--
ee
uu
dd
WW--
ee
nn ppdd
dduu
uu
EWT (early70’s)EWT (early70’s) Fermi Fermi (1934)(1934)
Charged-pion decayCharged-pion decay
pointlikepointlikeinteractioninteraction
is the killeris the killer
No surprise, No surprise, a posterioria posteriori, that Fermi was led , that Fermi was led to his to his effectiveeffective theory of theory of weak weak
interactionsinteractions
……and that such a theory cannot be valid at and that such a theory cannot be valid at very short distancesvery short distances
What about the neutron, the proton, the What about the neutron, the proton, the pion?pion?
From QCD to the old From QCD to the old stringstring
E = M cE = M c22 = T r = T r (T= dE/dr = Tension)(T= dE/dr = Tension)
Quarks are held together by theQuarks are held together by the confining potential confining potential of a of a colour-electric flux tubecolour-electric flux tube
J = M v d < cJ = M v d < c-1-1 T r T r22 J < J < ’ M’ M22 ((’ = c’ = c3 3 /2/2T) T)
quarkquark antiquarantiquarkk
antiquarantiquarkk
quarkquark
rr
Naïve Naïve classicalclassical picture: picture:
JJ
MM22
forbiddenforbidden
allowedallowed
J = J = ’ M’ M22
NB: no massless states with J > 0 !NB: no massless states with J > 0 !
Smells of a déjà vu…Smells of a déjà vu…
J/hJ/h
MM22
fermionsfermions
bosonsbosons
dJ/dMdJ/dM22 ~ 0.9 GeV ~ 0.9 GeV-2-2
N
The The linearly risinglinearly rising Regge trajectories of early Regge trajectories of early sixties!sixties!
No surprise that No surprise that aa theory of strings theory of strings was discovered starting from some was discovered starting from some striking properties of the hadronic striking properties of the hadronic
worldworld
……and that such a theory differs from and that such a theory differs from QCD at very short distances QCD at very short distances
(like Fermi vs. GSW)(like Fermi vs. GSW)
So far we So far we neglected Quantum Mechanicsneglected Quantum Mechanics……
Classical physicsClassical physics is valid for is valid for largelarge quantum quantum numbers, highly excited levelsnumbers, highly excited levels
When the QCD When the QCD flux tubeflux tube is long compared to its is long compared to its
transverse size, it can be considered as one-transverse size, it can be considered as one-dimensional, a dimensional, a string-likestring-like object object
Indeed strings do provide an Indeed strings do provide an effectiveeffective description description of QCD at large distancesof QCD at large distances
By contrast..By contrast..
LargeLarge quantum effects occur at quantum effects occur at smallsmall quantum quantum numbers, i.e. for the lightest states numbers, i.e. for the lightest states
These depend on exactly what kind of string one These depend on exactly what kind of string one is talking about, on its thickness, on what is talking about, on its thickness, on what
makes it or sits at its endsmakes it or sits at its ends
The old string of the sixties was the simplest The old string of the sixties was the simplest possible one… possible one…
String Theory = Theory of String Theory = Theory of (Quantum-Relativistic) Strings(Quantum-Relativistic) Strings
Obvious generalization of relativistic point Obvious generalization of relativistic point particlesparticles
Spoint = - mi c (length)(length) + inter.
Sstring = - T (Area).(Area).
Universal
Species-dependentmodel-dependent
Classical motions minimize length, areaClassical motions minimize length, area
(this is what led us, eventually, to QFT and to the SM!)
no inter. needed
-------------------------------------
Quantum surprisesQuantum surprises
A vibrating string is just an infinite A vibrating string is just an infinite collection of harmonic oscillators whose collection of harmonic oscillators whose
characteristic frequencies are multiples of characteristic frequencies are multiples of a fundamental frequencya fundamental frequency
Its quantization is almost as simple as that Its quantization is almost as simple as that of a single harmonic oscillator, however…of a single harmonic oscillator, however…
““Casimir Energy” of fundamental Casimir Energy” of fundamental stringstring
The zero-point energies of each harmonic The zero-point energies of each harmonic oscillator in the string oscillator in the string addadd up, …to something up, …to something negativenegative
Massless statesMassless states become possible, actually become possible, actually inevitableinevitable, even if they have , even if they have up to 2hup to 2h worth of worth of JJ..
States with States with half-integer spinhalf-integer spin are also necessary are also necessary for consistency => superstrings and for consistency => superstrings and (theoretical) discovery of supersymmetry in (theoretical) discovery of supersymmetry in early seventies…early seventies…
JJ
MM22
2h2h
Classical boundaryClassical boundary
fermionsfermions
TheThe quantum quantum spectrumspectrum (@small coupling)(@small coupling)
The badThe badquantum news: no such states in hadronic physics !quantum news: no such states in hadronic physics !
JJ
MM22
2h2h
3/2h3/2h
hh
1/2h1/2h
ClassicallyClassically forbiddenforbidden
Classically Classically allowedallowed
J/hJ/h
MM22
fermionsfermions
bosonsbosons
dJ/dMdJ/dM22 ~ 0.9 GeV ~ 0.9 GeV-2-2
N
Furthermore…Furthermore…The string was “IT” there was The string was “IT” there was nothingnothing more basic more basic
insideinside, no , no internalinternal structure, no constituents structure, no constituents
QCD has QCD has quarks and gluonsquarks and gluons, its string is a , its string is a derivedderived object, endowed with a finite thickness, made of object, endowed with a finite thickness, made of
pointlikepointlike constituents constituents
The final verdict, as always, belonged to The final verdict, as always, belonged to experimentsexperiments
It came clear from the study of hard-processesIt came clear from the study of hard-processes
~1974: strings are out!~1974: strings are out!
Quarks and gluons are there and, till these Quarks and gluons are there and, till these days, look like elementary, point-like days, look like elementary, point-like
objectsobjectsThe F-string is just an The F-string is just an effectiveeffective description description
of the complex phenomenon of of the complex phenomenon of confinementconfinement
Finding the Finding the true QCD string true QCD string is still an area is still an area of intensive theoretical researchof intensive theoretical research
Classical vs. Quantum Gravity: the Classical vs. Quantum Gravity: the clashclash
Gravity couples to energyGravity couples to energy (basis of GR’s Equivalence Principle)(basis of GR’s Equivalence Principle)
At low-energy (LHC?) it is weak, negligibleAt low-energy (LHC?) it is weak, negligible
At the quantum level, very energetic At the quantum level, very energetic quanta can be created and destroyed over quanta can be created and destroyed over
short distances or time intervalsshort distances or time intervals
If these processes are not sufficiently If these processes are not sufficiently suppressed they lead to uncontrollable suppressed they lead to uncontrollable infinities even for low energy processesinfinities even for low energy processes
1984: strings are back!1984: strings are back!
Casimir Energy of the F-StringCasimir Energy of the F-String
The massless states of the superstring The massless states of the superstring nicely fit with what is required for the nicely fit with what is required for the
carriers of gauge and gravitational forcescarriers of gauge and gravitational forcesA A disasterdisaster for the old string becomes a for the old string becomes a firstfirst tremendous tremendous bonusbonus for a theory of all for a theory of all
interactionsinteractions
EMEM
WEAKWEAK
STRONGSTRONG
GRAV.GRAV.
FORCEFORCE
PLAYERSPLAYERSCARRIERSCARRIERS BRICKSBRICKS
W,ZW,ZGluonsGluons Gravi-Gravi-tonton llCh.Ch.
qq RR ? ???
???? ??
HH
carriescarries feelsfeels
Minimal quantum sizeMinimal quantum sizeLike an harmonic oscillator, a string has a Like an harmonic oscillator, a string has a
mimimal quantum size mimimal quantum size lls s = = x x = = h/Th/T This new fund.This new fund.alal constant (besides c and h) constant (besides c and h) exponentially damps exponentially damps ppvirtualvirtual > h/l > h/ls s
Quantum mechanics, rather than clashing Quantum mechanics, rather than clashing with General Relativity, frees gravity from with General Relativity, frees gravity from its divergences and provide a its divergences and provide a FINITEFINITE theory*theory*))
a a secondsecond extraordinary extraordinary bonusbonus!!
**))Cf. QM’s solution of BB rad. and atom Cf. QM’s solution of BB rad. and atom stab.stab.
Extra dimensionsExtra dimensionsFundamental strings cannot be quantized in any Fundamental strings cannot be quantized in any number of space-time dimensionsnumber of space-time dimensionsFor superstrings 9 space and 1 time coordinates For superstrings 9 space and 1 time coordinates are needed for quantum consistencyare needed for quantum consistency
Rather than a killer this is now seen as an Rather than a killer this is now seen as an opportunity: if 6 of the 9 spatial dimensions are opportunity: if 6 of the 9 spatial dimensions are tiny they can provide a new mechanism to tiny they can provide a new mechanism to generate gauge interactions (of the GUT type) a generate gauge interactions (of the GUT type) a la Kaluza-Kleinla Kaluza-KleinIf they are not that small they can modify gravity If they are not that small they can modify gravity at sufficiently short distances, e.g. below 1 mm. at sufficiently short distances, e.g. below 1 mm. and/or provide new physics even at LHC energies and/or provide new physics even at LHC energies
Can we have the cake and eat it?Can we have the cake and eat it?
We want constituents where they help We want constituents where they help (QCD) and dispose of them where they (QCD) and dispose of them where they
harm (QGD)! harm (QGD)!
Distinguish two kinds of strings!Distinguish two kinds of strings!
Scale downScale down the characteristic size of the characteristic size of fundamental strings from 10fundamental strings from 10-13 -13 to to 1010-32-32 cm cm
Quarks (and Quarks (and all all other other playersplayers) are “slim” ) are “slim” F-F-stringsstrings. Protons, neutron, pions are “fat” QCD . Protons, neutron, pions are “fat” QCD strings!strings!
We have almost point-like quarks, but there is We have almost point-like quarks, but there is new physicsnew physics just above the just above the PlanckPlanck length length scalescale
llPP = = GGNNh/ch/c3 3 ~ 10~ 10-33-33 cm cm
Let’s have a quick look at some of it!Let’s have a quick look at some of it!
Can string theory Can string theory solve the information solve the information
paradox?paradox?Hawking claims (used to claim?) that Hawking claims (used to claim?) that black holes turn black holes turn purepure quantum states quantum states
into into mixed thermalmixed thermal states thereby states thereby producing a loss of quantum producing a loss of quantum
coherencecoherence
String/Black-Hole correspondence? S. Hawking (1974): black holes have T and S!
M
RRS S = l= lss
gs ~ gauge coupling
Strings ≠ BHStrings ≠ BH
Black Holes (= Black Holes (= Strings? )Strings? )
RRS S > l> lss
RRS S < l< lss
TH-1
~ M = RS , SBH ~ RS2 ~ M2
Sstring ~ M, Tstring< THagedorn
String theory looks String theory looks perfectly consistent perfectly consistent
with quantum with quantum coherencecoherence
Information Paradox MUST Information Paradox MUST be solved: exactly how?be solved: exactly how?
Fate of black hole evaporation Fate of black hole evaporation through Hawking radiationthrough Hawking radiation
M
RS = ls
gs
StringsStrings
Black HolesBlack Holes
trajectory of evaporating BH
Would be singularity: avoided thanks to ls≠0?
Fate of Big Bang singularityFate of Big Bang singularity
Big bang Big bang singularitysingularity is is avoidedavoided too if the too if the curvature radius (basically Hcurvature radius (basically H-1-1) cannot shrink ) cannot shrink below lbelow lss
Reopens question of the beginning of time and Reopens question of the beginning of time and allows one to consider allows one to consider new cosmologiesnew cosmologies whereby a long era whereby a long era preceded/preparedpreceded/prepared a big a big bang-like event (see e.g. Scientific American, bang-like event (see e.g. Scientific American, May 2004 issue)May 2004 issue)
QuiQui
Present horizontime
Towards the Big Bang, t=0Towards the Big Bang, t=0
End of inflation
now
Present distance from remote cluster
space
STANDARD INFLATION
HereHere
Our horizon todaytime
ls
end of pre-bang phase
now
Present distance from far cluster
space
PRE BIG BANG
Towards empty spaceTowards empty space@ past infinity@ past infinity
Will all this bring our understanding of Will all this bring our understanding of gravity, astrophysics and cosmology gravity, astrophysics and cosmology
up to particle-physics standards? up to particle-physics standards?
Will it unify our understanding of all Will it unify our understanding of all interaction within a single consistent interaction within a single consistent
framework?framework?
A dream that A dream that may remain just may remain just that for a while…that for a while…