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…