Ives Stilwell experiment

The relativistic Doppler effect was measured with the Ives-Stilwell experiment and similar experiments.

The Ives-Stilwell experiment was the first experiment with the transversal Doppler effect and thus from the special theory of relativity following time dilation could be detected directly. Together with the Michelson-Morley experiment and the Kennedy-Thorndike experiment , it is one of the fundamental experiments in special relativity from which the entire theory can be derived. Similar experiments to measure the relativistic Doppler effect are the Mössbauer rotor experiments and modern Ives-Stilwell experiments in storage rings . Another method is to measure the time dilation of moving particles . (see also tests of the special theory of relativity ).

Ives Stilwell experiment

history

Joseph Larmor (1900) and Hendrik Antoon Lorentz (1904) set up the Lorentz transformation to explain the undetectability of a dormant ether . Larmor noticed that the changed time co-ordinates can be understood in such a way that processes with moving objects in the ether run more slowly. Albert Einstein (1905) was able to show that this effect is a necessary consequence of the relativity of time, which is inferred from the principle of relativity and the constancy of the speed of light, and has nothing to do with an ether. According to Einstein, time dilation leads to a modification of the longitudinal Doppler effect, with an additional effect occurring in the transverse direction. In 1907 Einstein proposed an experiment using the light emitted by canal rays to demonstrate this effect.

It was not until 1938 that the related technical problems could be overcome by Herbert E. Ives and GR Stilwell. There was now a positive effect that corresponded to the prediction of the special theory of relativity. In 1941 they carried out the experiment again with greater accuracy. By the way, Ives himself was an opponent of the theory of relativity and referred to the confirmation of the " ether of Larmor and Lorentz ". However, compared to the special theory of relativity, this theory is conceptually outdated and is no longer taken into account. Experiments of this kind are repeated to this day, some in a different form. For example from Otting (1939), Mandelberg, et al. (1962),

While in this test the transversal Doppler effect was filtered out of the longitudinal, so to speak, a “purely transversal” test was also carried out in 1979.

execution

Ives-Stilwell experiment (1938), with which the Doppler effect of light, generated by canal rays , was evaluated.

Ives did without the transverse Doppler effect caused by time dilation

${\displaystyle f_{\rm {B}}=f_{\rm {S}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$,

observed at right angles to the direction of movement of the canal rays, since an influence of the longitudinal Doppler effect could hardly be ruled out. That is why he developed a method to observe the transverse Doppler effect in the longitudinal direction of propagation of the canal rays. Three light rays are compared, which originate from stationary, approaching and retreating canal rays.

According to the classic Doppler effect, the frequencies of light propagating in and against the direction of movement would have to be shifted by where c is the speed of light and v is the speed of the canal rays. If this is transferred to the wavelengths , the classic Doppler effect results in red- and blue-shifted wavelengths with the values and . If all three wavelengths (red-shifted, blue-shifted, unchanged) are marked on a linear scale, according to the classical theory, these wavelengths should be found at completely equal intervals. ${\displaystyle f'/f=c/(c\pm v)}$ ${\displaystyle 1+v/c}$ ${\displaystyle 1-v/c}$

However, if the time dilation is taken into account, the two outer markings (with respect to the stationary central mark) should be slightly shifted. This shift would have to correspond exactly to that which would also occur in the transverse direction. Ives and Stilwell actually found a significant shift in the center of gravity of the three markers, in agreement with the relativistic Doppler effect with a maximum deviation of 10 ⁻² .

Mössbauer rotor experiment

Relativistic Doppler effect

The Kündig Experiment (1963). A ⁵⁷ Fe Mössbauer absorber was placed 9.3 cm from the axis of an ultracentrifugal rotor, and a ⁵⁷ Co source was mounted in the center of the rotor on a piezoelectric transformer ( PZT ). During the rotation, the source and absorber lost their resonance. The source was also set in motion relative to the absorber, so that it alternately moved away and approached.

A more precise proof of the relativistic Doppler effect was achieved in the 1960s with the Mössbauer rotor experiments. From a source placed in the center of a rotating disc, gamma rays are sent to a receiver on the edge (variations of which are also reversed), with a stationary counter positioned behind the edge. Due to the rotation speed of the receiver, the characteristic absorption frequency decreases when there is a transverse Doppler effect, whereby the transmission of gamma rays through the absorber increases. In fact, such an effect could be demonstrated using the Mössbauer effect . The maximum deviation was 10 ⁻⁵ , while in the Ives-Stilwell experiments it was still 10 ⁻² . Such experiments were carried out by Hay et al. (1960), Champeney et al. (1963, 1965) and Kündig (1963).

Isotropy of the speed of light

Mössbauer rotor experiments were also used to determine a possible anisotropy of the speed of light or an ether wind in the sense of the Michelson-Morley experiment . This is based on the fact that the ether wind would have to have a disturbing influence on the absorption frequency. As in all other ether drift experiments, there was a negative result, whereby the accuracy allowed a maximum ether drift of 3–4 m / s. These include the experiments by Champeney and Moon (1961), Champeney et al. (1963) and Turner & Hill (1964).

Modern experiments

Fast moving clocks

With modern experimental arrangements, which have a certain similarity to the Ives-Stilwell experiments, a far greater accuracy is achieved. For example, lithium ions , whose emitted frequencies can be precisely determined and thus function as optical atomic clocks , are accelerated to 3–6% of the speed of light in heavy ion storage rings such as the test storage ring at the Max Planck Institute for Nuclear Physics (MPIK). The Doppler effect that occurs is evaluated, for which saturation spectroscopy is used.

author	year	maximum deviation from time dilation
Grieser et al.	1994	${\displaystyle \leq 1\times 10^{-6}}$
Saathoff et al.	2003	${\displaystyle \leq 2{,}2\times 10^{-7}}$
Reinhardt et al.	2007	${\displaystyle \leq 8{,}4\times 10^{-8}}$

Slow moving clocks

In the meantime it has been possible to prove the time dilation of optical atomic clocks even at everyday speeds. Chou et al. (2010) used aluminum ions , which were moved back and forth in a 75 m long, phase-stabilized fiber optic cable and transmitted signals of a certain frequency, the accuracy of these clocks being ∼10 ⁻¹⁷ . As a result, the shift of ∼10 ⁻¹⁶ occurring at speeds below 36 km / h (<10 m / s) according to the relativistic time dilation, could be measured by comparing the frequency of moving and resting ions.

See also

• History of the special theory of relativity

Individual evidence

1. ^ Robertson, HP : Postulates versus Observation in the Special Theory of Relativity . In: Reviews of Modern Physics . 21, No. 3, 1949, pp. 378-382. doi : 10.1103 / RevModPhys.21.378 .
2. ↑ Einstein, Albert: About the possibility of a new test of the principle of relativity . In: Annals of Physics . 328, No. 6, 1907, pp. 197-198.
3. ^ HE Ives, Stilwell, GR: An experimental study of the rate of a moving atomic clock . In: Journal of the Optical Society of America . 28, No. 7, 1938, p. 215. doi : 10.1364 / JOSA.28.000215 .
4. ^ HE Ives, Stilwell, GR: An experimental study of the rate of a moving atomic clock. II . In: Journal of the Optical Society of America . 31, No. 5, 1941, p. 369. doi : 10.1364 / JOSA.31.000369 .
5. ↑ Otting, G .: The quadratic Doppler effect . In: Physikalische Zeitschrift . 40, 1939, pp. 681-687.
6. ↑ Mandelberg, Hirsch I .; Witten, Louis : Experimental verification of the relativistic doppler effect . In: Journal of the Optical Society of America . 52, No. 5, 1962, p. 529. doi : 10.1364 / JOSA.52.000529 .
7. ↑ D. Hassel Kamp, E. Mondry, A. Scharmann : Direct observation of the transverse Doppler shift . In: Zeitschrift für Physik A; Hadrons and Nuclei . 289, No. 2, 1979, pp. 151-155. doi : 10.1007 / BF01435932 .
8. ↑ Hay, HJ; Schiffer, JP ; Cranshaw, TE; Egelstaff, PA: Measurement of the Red Shift in an Accelerated System Using the Mössbauer Effect in Fe ⁵⁷ . In: Physical Review Letters . 4, No. 4, 1960, pp. 165-166. doi : 10.1103 / PhysRevLett.4.165 .
9. ↑ Champeney, DC; Isaac, GR; Khan, AM: Measurement of Relativistic Time Dilatation using the Mössbauer Effect . In: Nature . 198, No. 4886, 1963, pp. 1186-1187. doi : 10.1038 / 1981186b0 .
10. ↑ Champeney, DC; Isaac, GR; Khan, AM: A time dilatation experiment based on the Mössbauer effect . In: Proceedings of the Physical Society . 85, No. 3, 1965, pp. 583-593. doi : 10.1088 / 0370-1328 / 85/3/317 .
11. ^ Kündig, Walter: Measurement of the Transverse Doppler Effect in an Accelerated System . In: Physical Review . 129, No. 6, 1963, pp. 2371-2375. doi : 10.1103 / PhysRev.129.2371 .
12. ↑ Champeney, DC; Moon, PB: Absence of Doppler Shift for Gamma Ray Source and Detector on Same Circular Orbit . In: Proceedings of the Physical Society . 77, No. 2, 1961, pp. 350-352. doi : 10.1088 / 0370-1328 / 77/2/318 .
13. ↑ Champeney, DC; Isaac, GR; Khan, AM: An 'aether drift' experiment based on the Mössbauer effect . In: Physics Letters . 7, No. 4, 1963, pp. 241-243. doi : 10.1016 / 0031-9163 (63) 90312-3 .
14. ↑ Turner, KC; Hill, HA: New Experimental Limit on Velocity-Dependent Interactions of Clocks and Distant Matter . In: Physical Review . 134, No. 1B, 1964, pp. 252-256. doi : 10.1103 / PhysRev.134.B252 .
15. ↑ Grieser, R .; Klein, R .; Huber, G .; Dickopf, S .; Klaft, I .; Knobloch, P .; Merz, P .; Albrecht, F .; Grieser, M .; Habs, D .; Schwalm, D .; Kühl, T .: A test of special relativity with stored lithium ions . In: Applied Physics B Lasers and Optics . 59, No. 2, 1994, pp. 127-133. doi : 10.1007 / BF01081163 .
16. ↑ Saathoff, G .; Karpuk, S .; Eisenbarth, U .; Huber, G .; Krohn, S .; Horta, R. Muñoz; Reinhardt, S .; Schwalm, D .; Wolf, A .; Gwinner, G .: Improved Test of Time Dilation in Special Relativity . In: Phys. Rev. Lett. . 91, No. 19, 2003, p. 190403. doi : 10.1103 / PhysRevLett.91.190403 .
17. ↑ Reinhardt, S .; Saathoff, G .; Buhr, H .; Carlson, LA; Wolf, A .; Schwalm, D .; Karpuk, S .; Novotny, C .; Huber, G .; Zimmermann, M .; Holzwarth, R .; Udem, T .; Hänsch, TW; Gwinner, G .: Test of relativistic time dilation with fast optical atomic clocks at different velocities . In: Nature Physics . 3, No. 12, 2007, pp. 861-864. doi : 10.1038 / nphys778 .
18. ↑ Chou, CW; Hume, DB; Rosenband, T .; Wineland, DJ: Optical Clocks and Relativity . In: Science . 329, No. 5999, 2010, pp. 1630-1633. bibcode : 2010Sci ... 329.1630C . doi : 10.1126 / science.1192720 .