Chapter 29: Introduction to Quantum Gravity
Quantum gravity seeks to reconcile general relativity with quantum mechanics. At the Planck scale (10-35 m), spacetime itself should be quantized. This remains one of the greatest open problems in physics.
Why Quantum Gravity?
Singularities
GR predicts infinite curvature at black holes and Big Bang. QG should resolve these.
Non-renormalizability
Naively quantizing GR produces infinities that can't be absorbed into parameters.
Information Paradox
Black hole evaporation seems to destroy information, violating quantum mechanics.
Major Approaches
String Theory
Fundamental objects are strings, not particles. Includes gravity naturally. Extra dimensions.
Loop Quantum Gravity
Quantize spacetime directly. Area and volume are quantized. Background-independent.
Asymptotic Safety
GR becomes renormalizable at high energies via a UV fixed point.
Causal Set Theory
Spacetime is fundamentally discrete—a partially ordered set of events.
Planck Scale
Planck Length
\( \ell_P = \sqrt{\frac{\hbar G}{c^3}} \approx 10^{-35} \text{ m} \)
Planck Time
\( t_P = \sqrt{\frac{\hbar G}{c^5}} \approx 10^{-44} \text{ s} \)
Planck Mass
\( m_P = \sqrt{\frac{\hbar c}{G}} \approx 10^{19} \text{ GeV} \)