Pound Rebka experiment

In the Pound-Rebka experiment in 1960 , Robert Pound and his assistant Glen Rebka demonstrated the gravitational spectral shift of gamma radiation in the earth's gravitational field . The two had previously proposed the experiment in 1959. The experiment uses the Mössbauer effect , which enables an accurate frequency measurement , and was carried out in the Jefferson Tower at Harvard University . See also tests of general relativity .

Physical basics

Gravity

Einstein showed in 1911 that from the conservation of energy it follows from classical considerations that photons in the gravitational field are influenced in the same way as massive particles. His thought experiment describes a particle that gains kinetic energy in free fall and emits radiation on the ground through annihilation . This particle has only rest energy before the fall and then a total of rest energy and kinetic energy . The hypothetical photon generated during the annihilation would have this energy and could now be sent to the starting point of the falling particle. If the photon were not influenced by gravity, it would still have the full particle energy at the upper end of the fall distance and could be used to generate a falling particle again. The excess energy would be released. Energy conservation is only guaranteed if the photon loses energy on the way up. ${\displaystyle E_{\mathrm {t,unten} }=m_{\mathrm {t} }c^{2}+m_{\mathrm {t} }gh}$ ${\displaystyle E_{\mathrm {t} }=m_{\mathrm {t} }c^{2}+m_{\mathrm {t} }gh}$ ${\displaystyle E=m_{\mathrm {t} }c^{2}}$ ${\displaystyle E_{\mathrm {kin} }=m_{\mathrm {t} }gh}$

For the photon energy the following applies in the units of the generating particle and . It follows in the units of the photon or in the frequency . ${\displaystyle E_{\text{unten}}=m_{\mathrm {t} }c^{2}+m_{\mathrm {t} }gh}$ ${\displaystyle E_{\mathrm {oben} }=m_{\mathrm {t} }c^{2}}$ ${\displaystyle E_{\text{unten}}=\left(1+{\frac {gh}{c^{2}}}\right)E_{\text{oben}}}$ ${\displaystyle {\frac {\Delta f}{f}}={\frac {gh}{c^{2}}}}$

In this Newtonian approximation, a height difference of 22.56 meters results in an expected frequency shift of . ${\displaystyle \Delta f/f=2{,}46\cdot 10^{-15}}$

Measurement and setup

The change in energy of the photon on its way through the gravitational field is reflected in a change in frequency. The gamma radiation used has a very small line width , which clearly shows the frequency change. In order to measure the change between the source and the absorber, Pound and Rebka chose the resonant absorption of the radiation, which must have the same line width as the emission. Depending on the atomic nucleus used, the absorber is only sensitive to its own very narrow frequency range. In the case of the Mössbauer effect, i.e. recoil-free emission and absorption, these areas are the same for emitter and absorber. From this it follows: If the frequency of the radiation changes on the way, there is no absorption in a system of relatively stationary emitter and resonance absorber. However, since the atoms move because of their thermal energy, the sending and receiving atoms are not at rest with each other. This effect of thermal Doppler broadening is compensated for by strong cooling, which also causes the Mössbauer effect . If you move the source or the absorber at a certain speed relative to the other, you can measure a frequency-dependent absorption through the Doppler effect. In the case of the Pound-Rebka experiment, the source was mounted on a hydraulic plate and thus precisely positioned. Various electroacoustic transducers were used between the hydraulics and the source during the experiment to set the source in sinusoidal up and down motion. From the point in time within this movement cycle and thus from the instantaneous speed of the source at which the absorption occurs, one can deduce by how much the frequency of the photon has changed.

In this experiment, the source and absorber were mounted 74 feet vertically, approximately 22.56 m. During the experiment, the positions were swapped several times in order to prove the influence of gravity with the difference in the frequency shift for the flight of the photon upwards or downwards. In the space there was a foil bag through which helium was pumped in order to reduce the scattering of the gamma radiation compared to air.

The greatest systematic influence on the frequency shift, however, was the temperature difference between the source and the absorber. This led to a four times higher effect than gravity and had to be determined with high precision .

Implementation and results

The gamma radiation with the energy 14.4 keV was used, which is emitted from the daughter nucleus Fe-57 after the decay of Co-57. The radiation source was a Co-57 preparation, the absorber a film made of iron enriched to 32% Fe-57.

When the results were first published in April 1960, results from ten measurement days were available. On the first two days, the source was set up on the ground and the measured frequency change of the photons during the flight was on average in the 6 measurements carried out after taking into account the temperature difference . This was followed by measurements on two days with the source at the top of the structure; the frequency change in the 8 measurements carried out was on average . ${\displaystyle \Delta f/f=-19{,}7\cdot 10^{-15}}$ ${\displaystyle \Delta f/f=-15{,}5\cdot 10^{-15}}$

When flying upwards, as described above, a loss of energy, i.e. a redshift, is to be expected, and downwards a blue shift. The measurement results contain a gravitational component and various solid-state physical effects . In the case of the redshift, and for the blueshift . The difference in the displacements for the two different directions thus gives the double effect that would be expected for the one-way route. The measurement result therefore corresponds in size and accuracy to a pure redshift experiment with a 45 m rise or a blue shift experiment with a 45 m fall. For the first four of the ten measurement days, there was a difference in amount of in agreement with the prediction of . In the further course, the accuracy could be improved by the larger sample. The published result after the measurement was completed was (according to the sign convention used by the authors for the difference) and thus confirms the prediction with an accuracy of 10%. Subsequent measurements by Pound and Snider in 1965 and by Snider in 1969 and 1972 improved the measurement accuracy to 1.006 ± 0.061 relative to Albert Einstein's prediction. ${\displaystyle \Delta f=\Delta f_{\mathrm {grav} }+\Delta f_{\mathrm {Rest} }}$ ${\displaystyle \Delta f_{\mathrm {grav} }<0}$ ${\displaystyle \Delta f_{\mathrm {grav} }>0}$ ${\displaystyle (4{,}2\pm 1{,}1)\cdot 10^{-15}}$ ${\displaystyle 4{,}92\cdot 10^{-15}}$ ${\displaystyle (-5{,}13\pm 0{,}51)\cdot 10^{-15}}$

Individual evidence

1. ^ RV Pound, GA Rebka Jr .: Gravitational Red-Shift in Nuclear Resonance . In: Physical Review Letters . 3, No. 9, November 1, 1959, pp. 439-441. doi : 10.1103 / PhysRevLett.3.439 . Retrieved September 23, 2006.
2. ↑ A. Einstein: About the influence of gravity on the spread of light. AdP 35, 898 (1911).
3. ^ RV Pound, Rebka Jr. GA: Apparent weight of photons . (abstract) In: Physical Review Letters . 4, No. 7, April 1, 1960, pp. 337-341. doi : 10.1103 / PhysRevLett.4.337 . Retrieved September 23, 2006.
4. ^ [[ Klaus Hentschel | Klaus Hentschel]]: Measurements of gravitational redshift between 1959 and 1971 . (article) In: Annals of Science . 53, No. 3, April 1, 1996, pp. 269-295. Retrieved June 14, 2020.