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DREAMS OF A FINITE THEORY *)

DREAMS OF A FINITE THEORY *). Gabriele Veneziano (CERN-PH/TH & Collège de France) *) Adjusted from Steven Weinberg’s: DREAMS OF A FINAL THEORY. Outline Forces & particles: carriers & bricks How did we get there? Looking at history backwards: a) From the EW theory to Fermi’s

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DREAMS OF A FINITE THEORY *)

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  1. DREAMS OF A FINITE THEORY*) Gabriele Veneziano (CERN-PH/TH & Collège de France) *) Adjusted from Steven Weinberg’s: DREAMS OF A FINAL THEORY

  2. Outline Forces & particles: carriers & bricks How did we get there? Looking at history backwards: a) From the EW theory to Fermi’s b) From QCD to the old string Classical vs. quantum strings: the bad news Classical vs. quantum gravity: the clash Classical vs. quantum strings: the good news Dreams of a finite theory: black holes, cosmology, extra dimensions…

  3. = carries = feels PLAYERS CARRIERS BRICKS q ? nR ? lCh. n W,Z g FORCE Gluons H Gravi- ton STRONG EM WEAK GRAV. ? ??

  4. Evolution of our understanding t } Electric Classical Electro- Magnetism (Maxwell) QED Magnetic EW Weak SM Fermi 1934 Nuclear QCD String 1984 String 1968 Classical General Relativity (Einstein) We shall follow the green arrows Gravity QGD

  5. EWT (early70’s) Fermi (1934) e e n n Neutron b-decay W- n d n u p d u u p pointlike interaction is the killer d Charged-pion decay m- m- d W- p- p- u n n

  6. No surprise, a posteriori, that Fermi was led to his effective theory of weak interactions …and that such a theory cannot be valid at very short distances What about the neutron, the proton, the pion?

  7. antiquark quark antiquark quark From QCD to the old string Quarks are held together by the confining potential of a colour-electric flux tube r E = M c2 = T r (T= dE/dr = Tension) Naïve classical picture: J = M v d < c-1 T r2 J < a’ M2 (a’ = c3 /2pT)

  8. NB: no massless states with J > 0 ! J J = a’ M2 forbidden allowed M2 Smells of a déjà vu…

  9. The linearly rising Regge trajectories of early sixties! J/h dJ/dM2 ~ 0.9 GeV-2 fermions 11/2 bosons r D 1 p M2 N

  10. No surprise that a theory of strings was discovered starting from some striking properties of the hadronic world …and that such a theory differs from QCD at very short distances (like Fermi vs. GSW)

  11. So far we neglected Quantum Mechanics… Classical physics is valid for large quantum numbers, highly excited levels When the QCD flux tube is long compared to its transverse size, it can be considered as one-dimensional, a string-like object Indeed strings do provide an effective description of QCD at large distances

  12. By contrast.. Large quantum effects occur at small quantum numbers, i.e. for the lightest states These depend on exactly what kind of string one is talking about, on its thickness, on what makes it or sits at its ends The old string of the sixties was the simplest possible one…

  13. String Theory = Theory of (Quantum-Relativistic) Strings Obvious generalization of relativistic point particles (this is what led us, eventually, to QFT and to the SM!) Spoint = - mi c (length) + inter. model-dependent Species-dependent ------------------------------------- no inter. needed Sstring = - T (Area). Universal Classical motions minimize length, area

  14. Quantum surprises A vibrating string is just an infinite collection of harmonic oscillators whose characteristic frequencies are multiples of a fundamental frequency Its quantization is almost as simple as that of a single harmonic oscillator, however…

  15. “Casimir Energy” of fundamental string • The zero-point energies of each harmonic oscillator in the string add up, …to something negative • Massless states become possible, actually inevitable, even if they have up to 2h worth ofJ. • States with half-integer spin are also necessary for consistency => superstrings and (theoretical) discovery of supersymmetry in early seventies…

  16. The quantum spectrum (@small coupling) Classical boundary fermions J J Classically forbidden 2h 3/2h Classically allowed h 1/2h M2 2h M2 The bad quantum news: no such states in hadronic physics !

  17. J/h dJ/dM2 ~ 0.9 GeV-2 fermions 11/2 bosons r D 1 p M2 N

  18. Furthermore… The string was “IT” there was nothing more basic inside, no internal structure, no constituents QCD has quarks and gluons, its string is a derived object, endowed with a finite thickness, made of pointlike constituents The final verdict, as always, belonged to experiments It came clear from the study of hard-processes

  19. ~1974: strings are out!Quarks and gluons are there and, till these days, look like elementary, point-like objectsThe F-string is just an effective description of the complex phenomenon of confinementFinding the true QCD string is still an area of intensive theoretical research

  20. Classical vs. Quantum Gravity: the clash Gravity couples to energy (basis of GR’s Equivalence Principle) At low-energy (LHC?) it is weak, negligible At the quantum level, very energetic quanta can be created and destroyed over short distances or time intervals If these processes are not sufficiently suppressed they lead to uncontrollable infinities even for low energy processes

  21. 1984: strings are back! Casimir Energy of the F-String The massless states of the superstring nicely fit with what is required for the carriers of gauge and gravitational forces A disaster for the old string becomes a first tremendous bonus for a theory of all interactions

  22. = carries = feels PLAYERS CARRIERS BRICKS q ? nR ? lCh. n W,Z g FORCE Gluons H Gravi- ton STRONG EM WEAK GRAV. ? ??

  23. Minimal quantum size Like an harmonic oscillator, a string has a mimimal quantum size ls = Dx = h/T This new fund.al constant (besides c and h) exponentially damps pvirtual > h/ls Quantum mechanics, rather than clashing with General Relativity, frees gravity from its divergences and provide a FINITE theory*) a second extraordinary bonus! *)Cf. QM’s solution of BB rad. and atom stab.

  24. Extra dimensions Fundamental strings cannot be quantized in any number of space-time dimensions For superstrings 9 space and 1 time coordinates are needed for quantum consistency Rather than a killer this is now seen as an opportunity: if 6 of the 9 spatial dimensions are tiny they can provide a new mechanism to generate gauge interactions (of the GUT type) a la Kaluza-Klein If they are not that small they can modify gravity at sufficiently short distances, e.g. below 1 mm. and/or provide new physics even at LHC energies

  25. Can we have the cake and eat it? We want constituents where they help (QCD) and dispose of them where they harm (QGD)!

  26. Distinguish two kinds of strings! • Scale down the characteristic size of fundamental strings from 10-13 to 10-32 cm • Quarks (and all other players) are “slim” F-strings. Protons, neutron, pions are “fat” QCD strings! • We have almost point-like quarks, but there is new physics just above the Planck length scale lP = GNh/c3 ~ 10-33 cm Let’s have a quick look at some of it!

  27. Can string theory solve the information paradox? Hawking claims (used to claim?) that black holes turn pure quantum states into mixed thermal states thereby producing a loss of quantum coherence

  28. String/Black-Hole correspondence? S. Hawking (1974): black holes have T and S! TH-1~ M = RS , SBH ~ RS2 ~ M2 M Sstring ~ M , Tstring< THagedorn RS > ls Black Holes (= Strings? ) RS = ls RS < ls Strings ≠ BH gs ~ gauge coupling

  29. String theory looks perfectly consistent with quantum coherence Information Paradox MUST be solved: exactly how?

  30. Fate of black hole evaporation through Hawking radiation M trajectory of evaporating BH Black Holes RS = ls Strings gs Would be singularity: avoided thanks to ls≠0?

  31. Fate of Big Bang singularity • Big bang singularity is avoided too if the curvature radius (basically H-1) cannot shrink below ls • Reopens question of the beginning of time and allows one to consider new cosmologies whereby a long era preceded/prepared a big bang-like event (see e.g. Scientific American, May 2004 issue)

  32. Present distance from remote cluster Present horizon time now Qui H-1 space End of inflation STANDARD INFLATION Towards the Big Bang, t=0

  33. Present distance from far cluster Our horizon today time now Here H-1 ls space end of pre-bang phase PRE BIG BANG Towards empty space @ past infinity

  34. Will all this bring our understanding of gravity, astrophysics and cosmology up to particle-physics standards? Will it unify our understanding of all interaction within a single consistent framework?

  35. A dream that may remain just that for a while…

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