Pound-Rebka experiment
Encyclopedia
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
's theory of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. It was proposed by Robert Pound
Robert Pound
Robert Vivian Pound was an American physicist who helped discover nuclear magnetic resonance and who devised the famous Pound-Rebka experiment supporting general relativity .Pound was born in Ridgeway, Ontario....
and his graduate student Glen A. Rebka Jr.
Glen Rebka
Glen Anderson Rebka, Jr. is an American physicist.Rebka attained a doctorate 1961 at Harvard, where he began study in 1953. Starting from 1961 he was at Yale University and starting from 1970 at the University of Wyoming, where he was from 1983 to 1991 department head of the physics faculty and...
in 1959, and was the last of the classical tests of general relativity to be verified (in the same year). It is a gravitational redshift
Gravitational redshift
In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...
experiment, which measures the redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
of light moving in a gravitational field, or, equivalently, a test of the general relativity prediction that clocks should run at different rates at different places in a non-uniform gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
. It is considered to be the experiment that ushered in an era of precision tests of general relativity.
The test is based on the following principle: When an atom transits from an excited state to a base state, it emits a photon with a specific frequency and energy. When the same atom in its base state encounters a photon with that same frequency and energy, it will absorb that photon and transit to the excited state. If the photon's frequency and energy is different by even a little, the atom cannot absorb it (this is the basis of quantum theory). When the photon travels through a gravitational field, its frequency and therefore its energy will change due to the gravitational redshift. As a result the receiving atom can no longer absorb it. But if the emitting atom moves with just the right speed relative to the receiving atom the resulting doppler shift will cancel out the gravitational shift and the receiving atom will be able to absorb the photon. The "right" relative speed of the atoms is therefore a measure of the gravitational shift. The frequency of the photon "falling" towards the bottom of the tower is blueshifted. Pound and Rebka countered the gravitational blueshift by moving the emittor away from the receiver, thus generating a relativistic Doppler redshift:
Special Relativity predicts a Doppler redshift of :
On the other hand, General Relativity predicts a gravitational blueshift of:
The detector at the bottom sees a superposition of the two effects. The Emitter was moved vertically and the speed was varied until the two effects cancelled each other, a phenomenon detected by reaching resonance. Mathematically:
In the case of the Pound–Rebka experiment
. Therefore:
= 7.5×10−7 m/sIn the more general case when h ≈ R the above is no longer true.
The energy associated with gravitational redshift over a distance of 22.5 meters is very small. The fractional change in energy is given by
δE/E, is equal to gh/c2 = 2.5×10−15. Therefore short wavelength
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
high energy photons are required to detect such minute differences. The 14 keV gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
s emitted by iron-57 when it transitions to its base state proved to be sufficient for this experiment.
Normally, when an atom emits or absorbs a photon, it also moves (recoil
Recoil
Recoil is the backward momentum of a gun when it is discharged. In technical terms, the recoil caused by the gun exactly balances the forward momentum of the projectile and exhaust gasses, according to Newton's third law...
s) a little, which takes away some energy from the photon due to the principle of conservation of momentum.
The Doppler shift required to compensate for this recoil effect would be much larger (about 5 orders of magnitude) than the Doppler shift required to offset the gravitational redshift. But in 1958 Mössbauer
Rudolf Mößbauer
Rudolf Ludwig Mössbauer was a German physicist best known for his 1957 discovery of recoilless nuclear resonance fluorescence for which he was awarded the 1961 Nobel Prize in Physics...
reported that all atoms in a solid lattice
Lattice model (physics)
In physics, a lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are...
absorb the recoil energy
Mössbauer effect
The Mössbauer effect, or recoilless nuclear resonance fluorescence, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of γ radiation by atomic nuclei bound in a solid...
when a single atom in the lattice emits a gamma ray. Therefore the emitting atom will move very little (just as a cannon will not produce a large recoil when it is braced, e.g. with sandbags).
This allowed Pound and Rebka to set up their experiment as a variation of Mössbauer spectroscopy.
The test was carried out at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
's Jefferson laboratory. A solid sample containing iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
(57Fe) emitting gamma rays was placed in the center of a loudspeaker
Loudspeaker
A loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...
cone which was placed near the roof of the building. Another sample containing 57Fe was placed in the basement. The distance between this source and absorber was 22.5 meters (73.8 ft). The gamma rays traveled through a Mylar bag filled with helium to minimize scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
of the gamma rays. A scintillation counter
Scintillation counter
A scintillation counter measures ionizing radiation. The sensor, called a scintillator, consists of a transparent crystal, usually phosphor, plastic , or organic liquid that fluoresces when struck by ionizing radiation. A sensitive photomultiplier tube measures the light from the crystal...
was placed below the receiving 57Fe sample to detect the gamma rays that were not absorbed by the receiving sample. By vibrating the speaker cone the gamma ray source moved with varying speed, thus creating varying Doppler shifts. When the Doppler shift canceled out the gravitational blueshift, the receiving sample absorbed gamma rays and the number of gamma rays detected by the scintillation counter dropped accordingly. The variation in absorption could be correlated with the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
of the speaker vibration, hence with the speed of the emitting sample and therefore the doppler shift. To compensate for possible systematic error
Systematic error
Systematic errors are biases in measurement which lead to the situation where the mean of many separate measurements differs significantly from the actual value of the measured attribute. All measurements are prone to systematic errors, often of several different types...
s, Pound and Rebka varied the speaker frequency between 10 Hz and 50 Hz, interchanged the source and absorber-detector, and used different speakers (ferroelectric and moving coil magnetic transducer
Transducer
A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...
). The reason for exchanging the positions of the absorber and the detector is doubling the effect. Pound subtracted two experimental results:
(1) the frequency shift with the source at the top of the tower
(2) the frequency shift with the source at the bottom of the tower
The frequency shift for the two cases has the same magnitude but opposing signs. When subtracting the results, Pound and Rebka obtained a result twice as big as for the one-way experiment.
The result confirmed that the predictions of general relativity were borne out at the 10% level. This was later improved to better than the 1% level by Pound and Snider.
Another test involving a space-borne hydrogen maser
Hydrogen maser
A Hydrogen maser, also known as hydrogen frequency standard, is a specific type of maser that uses the intrinsic properties of the hydrogen atom to serve as a precision frequency reference....
increased the accuracy of the measurement to about 10−4 (0.01%).