Questions: Tests of General Relativity

Question 1

Which test of general relativity probes the strong-field, highly dynamical regime where the theory differs most from Newtonian gravity and linearized approximations?

• A. The Pound-Rebka gravitational redshift experiment
• B. Mercury's perihelion precession
• C. LIGO's detection of binary black hole mergers
• D. The deflection of starlight by the Sun

Answer: (C)

LIGO's gravitational wave detections probe the regime where two black holes spiral together and merge — gravitational fields are extreme (v/c ~ 0.5, GM/(rc²) ~ 0.5), the dynamics are highly nonlinear, and the full nonlinear Einstein equations (solved numerically) are needed to predict the waveform. All other listed tests are in the weak-field (GM/(rc²) << 1) or quasi-static regime, where linearized or post-Newtonian approximations suffice. The LIGO observations confirmed for the first time that GR is correct in the strong-field, dynamical regime.

Question 2

The Shapiro time delay is sometimes called the 'fourth classical test' of general relativity. It measures the extra time light takes to travel near a massive body.

• T. True
• F. False

Answer: True

Predicted by Irwin Shapiro in 1964, the Shapiro delay is the extra time taken by a light signal (radar or radio) passing near a massive body due to the spatial curvature (the g_{rr} component of the Schwarzschild metric). For a signal passing near the Sun, the extra round-trip delay is about 240 microseconds. It was first measured using radar signals bounced off Mercury and Venus, and has been confirmed to 0.001% precision using the Cassini spacecraft's radio signal passing near the Sun (2003). It tests a different aspect of the metric than light deflection or precession, providing an independent check.

Question 3

Explain how the binary pulsar PSR B1913+16 tests GR in ways that solar-system tests cannot.

Model answer: The binary pulsar provides tests in the strong-field (compact neutron stars with surface gravity ~10¹¹ g), high-velocity (orbital speeds ~0.1% of c), and radiative (energy loss via gravitational waves) regimes — all inaccessible to solar-system tests. Specifically: (1) The periastron advance (4.2°/yr) tests strong-field orbital dynamics. (2) The orbital period decay (matching the quadrupole formula to 0.2%) confirms gravitational wave emission. (3) The gravitational redshift and time dilation of pulsar signals test the strong-field equivalence principle. (4) The Shapiro delay when one pulsar passes behind the other tests strong-field light propagation. Multiple relativistic effects measured in a single system over-determine the two masses, providing a consistency check of GR with no adjustable parameters.

The Hulse-Taylor binary pulsar was the first system to provide evidence for gravitational waves (through orbital decay) and earned the 1993 Nobel Prize. The double pulsar J0737-3039 (discovered 2003) provides even more precise tests and measures additional effects.

Question 4

Despite passing all tests to date, GR is not considered a complete theory. Name two reasons physicists expect it to break down.

Model answer: First, the singularity theorems prove that GR predicts its own breakdown — singularities (infinite curvature, geodesic incompleteness) form generically inside black holes and at the Big Bang, where a quantum theory of gravity is expected to take over. Second, GR is not renormalizable as a quantum field theory — perturbative quantization of the gravitational field produces infinities that cannot be absorbed into a finite number of parameters, unlike the successful quantum field theories of the Standard Model. These are not observational failures but theoretical inconsistencies that signal GR must be an effective (low-energy) theory, valid below the Planck scale (E ~ 10¹⁹ GeV, l ~ 10⁻³⁵ m) but superseded by a quantum gravity theory at higher energies.

Other motivations for beyond-GR physics include: dark matter (unexplained by GR + Standard Model alone, unless new particles exist), the cosmological constant problem (120-order-of-magnitude discrepancy with quantum field theory), and the information paradox (tension between black hole evaporation and quantum unitarity). Each suggests GR, while extraordinarily successful, is part of a larger theoretical framework.