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An experimental physicist who, with Robert Vivian Pound, measured gravitational redshift over a laboratory height difference in the Pound-Rebka experiment. The Mössbauer effect supplies an exceptionally narrow nuclear resonance, allowing a tiny change in gamma ray energy to be detected. Controlled motion of the source produces a compensating Doppler shift, turning a difficult absolute energy comparison into a measurement of the velocity needed to restore resonance.^[ref]

The weak equivalence principle is universality of free fall for sufficiently small test bodies, independent of composition, when non-gravitational forces and self-gravity are negligible. Equality of inertial and passive gravitational mass makes this possible in the Newtonian limit. The Einstein equivalence principle adds local Lorentz invariance and local position invariance for nongravitational experiments: a small freely falling laboratory has the local physics of special relativity.

This motivates a universal spacetime metric. Freely falling unforced test particles follow geodesics, $u^{\nu }{\nabla }_{\nu }{u}^{\mu }=0$. At a point one can choose local inertial coordinates with vanishing connection, but curvature and tidal relative acceleration remain measurable over a finite region. Gravity cannot be transformed away globally. A uniformly accelerating small laboratory and a local gravitational field can have the same nongravitational experimental behaviour without having identical global geometry.

Clock comparisons predict a fractional rate difference of order $g\Delta h/c^2$ in a weak static field. The Pound-Rebka experiment tested the associated photon redshift through resonant gamma-ray emission and absorption at different heights, using controlled Doppler shifts to match the tiny energy displacement. Such a result tests the metric redshift prediction, not uniquely every component of the gravitational field equations.^[ref]

general relativity adds the dynamical Einstein field equations,The equivalence principle alone does not derive this unique equation; assumptions about covariance, dynamics and the Newtonian limit are also needed. The strong equivalence principle extends the universality claim to self-gravitating systems and gravitational experiments. Alternative metric theories can satisfy the weaker local principles while differing in gravitational dynamics, so composition tests, clock/redshift tests and self-gravity tests probe distinct claims.

The weak equivalence principle states that freely falling, sufficiently small test bodies have the same motion in a given gravitational field irrespective of composition or mass, neglecting their own gravity and nongravitational forces. In the Newtonian limit, $m_i\mathbf{a}=m_g\mathbf{g}$ makes this universality equivalent to a universal gravitational-to-inertial mass ratio, conventionally set to one.

The Einstein equivalence principle adds that local nongravitational experiments in a freely falling, nonrotating laboratory have the laws of special relativity, independent of the laboratory's position and velocity. At an event one can choose a local inertial frame with $g_{\mu \nu }={\eta }_{\mu \nu }$ and ${\partial }_{\alpha }{g}_{\mu \nu }=0$. A freely falling observer feels no supporting force, while a supported observer can model a locally uniform gravitational field by an accelerated laboratory. This explains why freely moving particles follow timelike geodesics and light follows null geodesics when other interactions are negligible.

The locality qualification is essential. The Riemann curvature tensor generally remains nonzero; separated freely falling bodies have tidal relative acceleration, measured by geodesic deviation. A finite-size experiment can therefore distinguish a curved gravitational field from a merely accelerated coordinate description of flat spacetime. Equivalence alone also does not select the complete Einstein field equations.

A useful weak-field consequence is the upward photon shift $\Delta \nu /\nu \simeq -gH/c^2$ over laboratory height $H$. In an upward-accelerating laboratory the receiver gains recession velocity during the light flight, giving the same leading redshift. The Pound-Rebka experiment tested this with resonant absorption of 14.4-keV gamma rays over about 22.5 m. A controlled source velocity calibrated the Doppler sensitivity; interchanging source and absorber reversed the gravitational contribution while retaining an intrinsic source–absorber offset. Monitoring their temperature difference was essential because lattice-motion shifts could mimic the small signal.^[ref] This verifies a gravitational clock-shift prediction; by itself it is not a unique test selecting general relativity over every alternative metric theory.

The three classic tests probe orbital motion, the propagation of light, and clock rates in a gravitational field.

Schwarzschild perihelion precession. For an orbit with semi-major axis $a$ and orbital eccentricity $e$, the leading advance per revolution isThe relevant observation for Mercury is the residual advance after the much larger ordinary perturbations have been included, approximately $43$ arcseconds per century.^[ref] An orbital fit must account for the other planets and reference-frame effects before interpreting that residual as a relativistic contribution.

Schwarzschild light deflection. A ray with large impact parameter $b$ passing a nearly spherical mass is deflected throughAt the Sun's limb this is about $1.75$ arcseconds. The Eddington experiment used the 1919 solar eclipse to photograph background stars near the obscured Sun, then compared their positions with reference photographs. The measured effect is an apparent outward displacement of the background stars, not a direct photograph of a curved light path. Telescope focus, plate scale and atmospheric effects must be controlled when extracting such small shifts.^[ref]

Gravitational redshift. For a photon emitted lower in a weak static field and received a height $H$ above it,The Pound-Rebka experiment used the narrow recoil-free nuclear resonance supplied by the Mössbauer effect. A controlled source motion supplies a small Doppler shift that compensates the gravitational shift, allowing a change in resonant absorption to reveal it across a laboratory tower.^[ref] The leading weak-field redshift follows from the equivalence principle and therefore does not, by itself, distinguish every competing metric theory of gravity.

The Pound-Rebka experiment measured gravitational redshift using the 14.4-keV gamma ray transition of the isotope iron-57. The Mössbauer effect supplies recoil-free emission and resonant absorption in solids. Robert Vivian Pound and Glen Rebka separated a source and an iron absorber vertically by 74 feet, about 22.6 metres. A helium-filled path reduced absorption by air; detectors behind the absorber counted transmitted gamma rays.^[ref]

Moving the source supplied a calibrated Doppler shift. Interchanging source and absorber reversed the gravitational contribution while exposing fixed source–absorber offsets; monitoring temperature controlled a separate shift from thermal motion. The measured reversal agreed with the prediction to about 10 percent.^[ref]

For an upward ray through height $H$ in a weak gravitational field, $\Delta \nu /\nu =-gH/c^2$. At this height its magnitude is about $2.5\times 10^{-15}$. The leading gravitational redshift also follows from Nordstrom theory of gravitation; this experiment alone does not distinguish that prediction from general relativity.

An experimental physicist who, with Glen Rebka, measured the gravitational redshift of gamma radiation over a laboratory height difference. Narrow nuclear resonance and a controlled Doppler shift made an extremely small gravitational frequency change accessible. The experiment linked a prediction of general relativity to resonant absorption in an apparatus on Earth.^[ref]