how a 28-year-old measured Einstein's gravity in a basement

The Mechanism

*Rudolf Ludwig Mößbauer* (born Munich, *31 January 1929*; died Grünwald, Bavaria, *14 September 2011*, aged 82) was, in 1957, a 28-year-old physics PhD student at the *Technische Hochschule München* (Technical University of Munich), conducting his doctoral research at the *Max-Planck-Institut für Medizinische Forschung* in Heidelberg under the supervision of *Heinz Maier-Leibnitz*. The Heidelberg Max Planck Institute was the experimental nuclear-physics laboratory of *Walther Bothe* (1891-1957), the Nobel laureate whose coincidence-counting techniques had made the first measurements of cosmic-ray particles, neutron capture, and the photonuclear effect; Maier-Leibnitz had inherited the experimental programme at Bothe's retirement in 1956. Mößbauer had begun his doctoral project in 1955 with a relatively straightforward thesis question: to measure the *natural linewidth of the 129 keV gamma-ray emission* from the metastable nuclear state of *iridium-191*. The standard experimental method for measuring nuclear gamma-ray linewidths in the 1950s was *resonant nuclear absorption* — fluorescent absorption of a gamma ray by an identical nucleus in its ground state. The method had two long-standing experimental obstacles. The first was *nuclear recoil*: when a free nucleus emits a gamma ray of energy *E*, momentum conservation requires the emitting nucleus to recoil with momentum *p = E/c*, carrying away a kinetic energy of *p²/2M = E²/2Mc²* — typically *0.05 eV* for a 100 keV gamma ray from a free atom. The emitted gamma ray is therefore *red-shifted by 0.05 eV* below the nuclear transition energy. The receiving nucleus, being identical, requires *0.05 eV more* than the transition energy to absorb the gamma ray. The emission and absorption lines are separated by *0.1 eV* — a separation thousands of times larger than the natural Lorentzian linewidth of the transition itself (typically *10⁻⁶ eV*) — so emission and absorption do not overlap and resonance fluorescence does not happen. The standard 1950s workaround was to *Doppler-shift the emitting source up by 0.1 eV* by mounting it on a fast-rotating ultracentrifuge rotor — *typical rotation speeds of 600 metres per second* — to recover the energy lost to recoil. The technique worked, but it was a heroic experiment requiring extreme mechanical engineering and producing only modest data quality. The second obstacle was *thermal Doppler broadening*: at room temperature the random thermal motion of nuclei in the source and absorber broadens both the emission and absorption lines by an additional *~0.01 eV*, washing out the fine structure of the natural linewidth. Mößbauer's thesis question — to measure the natural linewidth — required a way around both obstacles. His method, suggested by Maier-Leibnitz in 1955, was to cool the source and absorber to *liquid-nitrogen temperatures* (77 K) to reduce thermal broadening, then to attempt to overcome the nuclear-recoil problem by *embedding the radioactive iridium-191 source in a metallic lattice* — on the hypothesis that recoil in a solid would behave differently from recoil in a free atom. Through 1956 and 1957 Mößbauer built a series of cryostat experiments in the Heidelberg Max Planck Institute basement, with the iridium-191 sources prepared by neutron irradiation of natural iridium and embedded in iridium metal foil targets. The result expected was a modest increase in resonance absorption — recoil might be slightly suppressed in a solid because the recoiling nucleus would transfer some of its momentum to its lattice neighbours. *What he observed in the winter of 1957-58 was something different and dramatically larger than expected*. Cooling the iridium-191 source and absorber to *88 K*, Mößbauer saw resonance absorption that was *not suppressed at all* — the lines were sharp at the natural linewidth, with no measurable recoil broadening. Moving the source mechanically through a small range of velocities relative to the absorber — a few millimetres per second by way of a piezoelectric driver — produced a *sharp Doppler-shifted dip in the absorption rate*, with a width of approximately *10⁻⁵ eV*: the actual natural Lorentzian linewidth of the iridium-191 transition, unbroadened by recoil or by thermal motion. The interpretation, which Mößbauer worked out over the subsequent months, was that a *significant fraction of the gamma-ray emissions* — and a similar fraction of the absorptions — occurred *without any nuclear recoil at all*. The recoil momentum was instead transferred to the *entire crystal lattice* of the metallic iridium source, as a collective vibrational mode. Because the crystal lattice is enormously massive compared to a single nucleus, the energy carried away by lattice recoil — *p²/2M_crystal* — is *negligibly small*: a 100-keV gamma ray emitted from a nucleus in a typical crystal lattice carries the entire nuclear-transition energy to the gamma ray with essentially no recoil shift. The *recoilless fraction* depended on the temperature relative to the *Debye temperature* of the lattice (a measure of the lattice's vibrational stiffness): in iridium, with a Debye temperature of about 420 K, the recoilless fraction at 88 K was about 14%. At lower temperatures it would rise toward 50%, and in stiffer lattices with higher Debye temperatures (steel, tungsten) it would be substantial even at room temperature. The recoilless absorption lines had a width set by the *natural Lorentzian linewidth of the transition itself* — for many transitions, parts in 10¹² of the transition energy. The discovery had immediate experimental implications. A spectroscopic line so narrow could resolve *energy shifts of one part in 10¹²* — making the Mößbauer effect, instantly, *the most precise energy measurement available in physics*. Mößbauer published the result as Mößbauer, R.L., *"Kernresonanzabsorption von Gammastrahlung in Ir¹⁹¹,"* *Die Naturwissenschaften* 45(22): 538-539 (August 1958), submitted in July 1958 and published within weeks; and as a full paper, Mößbauer, R.L., *"Kernresonanzfluoreszenz von Gammastrahlung in Ir¹⁹¹,"* *Zeitschrift für Physik* 151(2): 124-143 (1958). His PhD exam was held in 1958 under Maier-Leibnitz at TU Munich. The community's response was initially skeptical — the effect seemed too good to be true — but within eighteen months independent confirmations had been published from at least four other laboratories, and within three years applications had multiplied across nuclear physics, condensed-matter physics, and chemistry. The single most famous application was the *Pound-Rebka experiment* at Harvard. *Robert Vivian Pound* (1919-2010) and his graduate student *Glen Anderton Rebka Jr.* (1931-2015), at the *Jefferson Laboratory* at Harvard University, used the Mößbauer effect in *iron-57* to measure the *gravitational redshift of a 14.4-keV gamma ray falling 22.5 metres down a vertical column* in the Jefferson basement. The predicted gravitational redshift — from Einstein's *equivalence principle*, which requires that photons climbing a gravitational potential lose energy proportional to the climb height — was *Δν/ν = gh/c² ≈ 2.5 × 10⁻¹⁵*. No previous spectroscopic technique had had the resolution to measure such a small shift. The Mößbauer-effect linewidth of the iron-57 14.4-keV transition was *4.6 × 10⁻¹³* — barely good enough to resolve a shift of 2.5 × 10⁻¹⁵, but enough. Pound and Rebka *Doppler-shifted the emitter mechanically up the tube by a few mm/s* to scan across the gravitational-redshift signal, measured the absorption rate at each velocity, and recovered a shift of *0.99 ± 0.05* times the general-relativistic prediction. Published as Pound, R.V., Rebka, G.A. Jr., *"Apparent weight of photons,"* *Physical Review Letters* 4(7): 337-341 (1960), the Pound-Rebka experiment was the *first laboratory confirmation of general relativity* — the first direct measurement of gravity's effect on light, made in a Harvard basement, on a column of air 22 metres tall. The Mößbauer effect itself has since become an indispensable tool across nuclear physics, condensed-matter physics, mineralogy (Mößbauer spectroscopy is the standard technique for identifying iron-bearing minerals on Mars rovers — both *Spirit* and *Opportunity* carried Mößbauer spectrometers), and chemistry, with over 50,000 published papers using the technique. The *1961 Nobel Prize in Physics* was awarded jointly to *Rudolf L. Mößbauer*, age 32, *"for his researches concerning the resonance absorption of gamma radiation and his discovery in this connection of the effect which bears his name,"* and to *Robert Hofstadter* for elastic electron-scattering measurements of nucleon charge distributions. Mößbauer accepted the Nobel three years and four months after his doctoral exam.