Strings Theory of Everything Something or Nothing Robert
Strings: Theory of Everything, Something, or Nothing? Robert N. Oerter
The Standard Model Family Fermions 1 2 3 Neutrinos νe νμ ντ Electrons e & Kin Quarks u, u, u μ τ c, c, c t, t, t s, s, s b, b, b d, d, d
The Standard Model Bosons Gauge Particles Symmetry Breakers W +, W - Dubya-plus, Dubya-minus Z 0 Zee-zero γ Photon H Higgs
Problems with the Standard Model • Why three families? • Why these particle masses? • SM predicts mass of W±, Z 0, and photon • All other masses are arbitrary • ν mass << e mass << quark mass • Dark Matter – not “normal matter” • Dark Energy • Gravity (General Relativity) left out
Hints of New Structures • Structure or Symmetry? – Leptons built of still smaller “preon” particles? – Grand Unified Theories (GUTs): what gauge group? • Is a different kind of structure needed?
Strings Closed String Open String
Free Relativistic Point Particle • Action Least action principle: minimize the invariant length of the world-line Quantum Mechanics: sum over all paths
Free Relativistic String X 3 Four-vector Xμ = (X 0, X 1, X 2 , X 3) Xμ(σ) X 0 = ct X 2 X 1
Free Relativistic String World-sheet
String Action String Equations of Motion
Classical string - solutions Constraints: Write X = XR(τ-σ) + XL(τ+σ) Each point on the string moves at the speed of light (for pure left- or right-mover)
The Quantum String • Assign a phase to each world-sheet μ • Sum over all 2 -D surfaces X (σ, τ) • Feynman diagrams for particles:
String Interactions
String Interactions • No new parameters needed • String theory smoothes out the interaction vertex • All infinities of field theory are eliminated
The Quantum String • Results of string quantization – No infinities – No additional coupling constants – Massless particles: • Spin-0 scalar • Spin-1 gauge boson • Spin-2 graviton!!! – Massive particles: • m 2 = (2πT)n; n = 1, 2, 3, …
The Quantum String • The Bad News – Tachyon: m 2 = -2πT – No fermions – Quantization requires D = 26 spacetime dimensions • Connection with General Relativity Background spacetime String quantization in a curved background General Relativity!
Superstrings • Anti-commuting numbers: θ 1θ 2 = - θ 2θ 1 • Spacetime described by (Xμ, θα) θα Xμ • Supersymmetric theory: fermion-boson symmetry • No Tachyons • Quantization requires D=10 spacetime coordinates and 16 anticommuting coordinates • Gauge groups SO(32), E 8 x. E 8
From 10 -D to 4 -D Compactification • 6 of the dimensions are very small • Topology determines the number of fermion families • Shape determines coupling constants
Experimental Tests • Large-mass relics of the Big Bang (not found) • Fractional electric charges: e/5, e/11 (not found) • Departures from inverse-square law of gravity (Arkani-Hamed, et. al. - not found) • Light from distant galaxies shows Planckscale physics? (Ragazzoni et. al. - not found)
Non-Newtonian Gravity? (Adelberger & Eöt-wash)
Planck-scale physics?
The Goals of Physics • Describing the world – Make predictions – Compact description – Ease of use • Theory of everything? – Inconsistent equations are bad • Maxwell / Newton Special Relativity • Quantum Mechanics / General Relativity ? – Would I know a TOE if it kicked me? • Dark matter: most of the mass in the universe! • Can never access all regimes of size and energy
Strings: A TOE? • Do strings describe the world? – – – No longer a 1 -parameter theory Actually a class of theories ~ e 100 of them! Not known how to choose between them No string predictions of masses, coupling constants No experimental prediction has been confirmed Not easy to use • Do strings unify QM and GR? – Graviton – Derive (super)gravity for the background spacetime – Black hole physics • Strings: A Theory of Something
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