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75th Compton Lectures: String Theory in the LHC Era J. Marsano Lecture 7: Why is Quantum Gravity so Hard? Quantum Electrodynamics • Before turning to gravity, look more closely at electrodynamics • electron-photon interaction from ’sum over histories’ e + (∞)e3 + (∞)e5 + . . . • The expansion parameter e is small . . . but the coefficients are infinite! • In lecture 5, we learned that infinities come from very high energy particles in the loop • We don’t really know the physics of these high energy particles–that’s why we get nonsense • Introduce new local interactions to ’model’ the unknown short distance physics • With just 3 new interactions, we get a finite answer e + (. . .)e3 + (. . .)e5 + . . . = Finite • Miracle: Quantum Electrodynamics is sensitive to short distance physics through only 3 numbers • (Only 2 are physical: charge and mass) the electron • The Standard Model is a slightly more complicated version of this • Need 19 new interactions instead of 3 (particle masses and couplings) 75th Compton Lectures: String Theory in the LHC Era J. Marsano Quantum Gravity – First Look • We will try the same thing with Quantum Gravity using graviton exchange • Recall that graviton is the ’smallest piece’ of a gravitational wave • First difference: Gravitational coupling G from Newton’s law F = G m1r2m2 has ’units’ → Defines an intrinsic energy scale MPlanck • Need to include more and more diagrams when the total energy E of the interacting particles is close to MPlanck The Analogy with Weak Interactions • We’ve seen this before: Fermi’s model of radioactive decay • Could not describe physics at energy scales beyond ∼ 300 GeV • New physics had to emerge and it did: the W and Z bosons • Like Fermi’s theory, a theory of Quantum Gravity based on graviton exchange is an ’effective theory’ at best – It cannot describe physics at MPlanck or beyond – it is incomplete! Quantum Gravity and Infinities • Graviton exchange has another problem: an infinity problem • Worse than Quantum Electrodynamics • We keep adding new interactions to model unknown short distance physics but the infinities keep coming! • Quantum Gravity depends on short distance physics through infinitely many parameters! 75th Compton Lectures: String Theory in the LHC Era J. Marsano Why is Quantum Gravity so Hard? 1. Sensitive to unknown short distance physics through infinitely many parameters 2. Breaks down at energies near MPlanck • An ’effective theory’ at best like Fermi’s theory was • Need to make infinitely many measurements before completely sharp predictions can be made • New physics we don’t understand is waiting at MPlanck – a model based on simple graviton exchange will not do • Graviton exchange still useful for experiments at low energies E • When MPlanck is small, experiments only really sensitive to first few terms • These only depend on a finite number of the new interactions for modeling short distance physics • Recover predictivity–model fixed by a finite number of measurements Why do we care? • Graviton exchange is good enough to describe quantum effects of gravity at energies smaller than MPlanck (like LHC energies) • At these energies, quantum gravity is not so interesting • Graviton exchange is not useful where quantum gravity is truly important • Black holes • The early universe (big bang, etc) • Plus there is a theoretical question: Can any random model of particle physics be coupled to gravity? • The answer is actually known: no! • Which particle models are consistent with gravity? Is consistency with gravity a strong restriction on potential models of new physics? 75th Compton Lectures: String Theory in the LHC Era J. Marsano Black Hole Information Paradox • The paradox illustrates another principle that makes quantum gravity harder to deal with than the Standard Model • The paradox arises because black holes emit Hawking radiation • Particles can pop out of the vacuum near the black hole’s event horizon • Sometimes, instead of annihilating each other, one particle falls into the black hole and the other moves away • The other particle carries energy away from the black hole – radiation! • Eventually, the black hole will radiate away completely • Suppose we throw a hard drive with contents of Wikipedia into the black hole • After the black hole radiates away, where did all of the information go? • The problem is sharper than this. . . • The radiation is entangled with the particles that fall into the black hole • Missing information about the state of the radiation if we don’t know the state of the particles that fell in • Two results from gravity: • Geometry outside the black hole horizon is ’unique’ (black holes have ’no hair’) • Quantum effects negligible because the curvature is small at the horizon =⇒ We cannot know the state of the particles that fell in =⇒ Never have all information about state of the radiation • Where does that information go when the black hole completely evaporates? 75th Compton Lectures: String Theory in the LHC Era J. Marsano Information Loss and ’Fuzzballs’ • Information loss is fundamentally inconsistent with quantum mechanics • One resolution from string theory is the ’fuzzball’ proposal • We assumed that quantum gravity was not important near the event horizon because the curvature was small, M 2R ≪ 1 Planck • This is wrong! • Quantum effects controlled by MN2 R which Planck is not small at the horizon because N ≫ 1! • One can begin to distinguish different states of the black hole already at the horizon • Classical gravity breaks down in a completely unexpected way • Black hole is a ’fuzzball’ – quantum superposition of states that differ from one another across long distance scales • This happens because we can only fit a finite number of quantum states within a given volume • Very interesting examples from string theory: ’warped throats’ of infinite volume that only have room for a few quantum states, if any The Black Hole Information Paradox cleanly reveals two general difficulties of quantum gravity • Breakdown of ’naturalness’ • Breakdown of ’locality’ • Quantum effects become important at times that we do not naively expect • Quantum effects are spread out over large distances • We expect classical description of gravity is ok when curvatures are small but this is not true • Reflects the intertwining of short distance (quantum) and long distance physics in gravity