Download Lecture 7: Why is Quantum Gravity so Hard?

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