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Ives–Stilwell experiment

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The Ives–Stilwell experiment exploits the transverse Doppler effect (TDE). This was the first direct, quantitative confirmation of the time dilation factor. Together with the Michelson–Morley and Kennedy–Thorndike experiments, it forms one of the fundamental tests of special relativity theory.[1] Other tests confirming the relativistic Doppler effect, are the Mössbauer rotor experiment and modern Ives–Stilwell experiments. For other time dilation experiments, see Time dilation of moving particles. For general overview, see Tests of special relativity.

Ives–Stilwell experiment

The TDE was described by Albert Einstein in his seminal 1905 paper.[2] Einstein subsequently suggested an experiment based on the measurement of the relative frequencies of light perceived as arriving from a light source in motion with respect to the observer. Herbert E. Ives and G. R. Stilwell (although they referred to time dilation as following from the "theory of Lorentz and Larmor") undertook the task of executing the experiment and they came up with a very clever way of separating the much smaller TDE from the much bigger longitudinal Doppler effect. The experiment was executed in 1938[3] and it was reprised multiple times (see, e.g.[4]). Similar experiments were conducted several times with increased precision, by Otting (1939),[5] Mandelberg et al. (1962),[6] Hasselkamp et al. (1979),[7]

Ives remarked, that it is nearly impossible to measure the transverse Doppler effect with respect to light rays emitted by canal rays, at right angles to the direction of motion of the canal rays (as it was considered earlier by Einstein), because the influence of the longitudinal effect can hardly be excluded. Therefore he developed a method, to observe the effect in the longitudinal direction of the canal rays' motion. If it is assumed that the speed of light is fixed with respect to the observer (“Classical Theory”), then the forward and rearward Doppler-shifted frequencies seen on a moving object will be f'/f = c/(c±v), where v is recession velocity. Under special relativity, the two frequencies will also include an additional “Lorentz factor” redshift correction.

When we invert these relationships so that they relate to wavelengths rather than frequencies, “Classical Theory” predicts redshifted and blueshifted wavelength values of 1+v/c and 1-v/c, so if all three wavelengths (redshifted, blueshifted and original) are marked on a linear scale, according to Classical Theory the three marks should be perfectly evenly spaced.

|.....|.....|

But if the light is shifted by special relativity's predictions, the additional Lorentz offset means that the two outer marks will be offset in the same direction with respect to the central mark.

|....|......|

Ives and Stilwell found that there was a significant offset of the centre of gravity of the three marks, and therefore the Doppler relationship was not that of "Classical Theory". This approach had two main advantages:

  1. didn't require us to commit to an exact value for the velocity involved (which might have been theory-dependent), and
  2. it didn't require an understanding or interpretation of angular aberration effects, as might have been required for the analysis of a "true" transverse test. A "true transverse test" has been run almost 40 years later, by Hasselkamp in 1979.[7]

Mössbauer rotor experiments

Relativistic Doppler effect

A more precise confirmation of the relativistic Doppler effect was achieved by the Mössbauer rotor experiments. From a source in the middle of a rotating disk, gamma rays are being sent to a receiver at the rim (in some variations this scheme was reversed). Due to the rotation velocity of the receiver, the absorption frequency decreases if the transverse Doppler effect exists. This effect was actually observed using the Mössbauer effect. The maximal deviation from time dilation was , thus the precision was much higher than that () of the Ives–Stilwell experiments. Such experiments were performed by Hay et al. (1960),[8] Champeney et al. (1963, 1965),[9][10] Kündig (1963).[11]

Isotropy of the speed of light

Moessbauer rotor experiments were also used to measure a possible anisotropy of the speed of light. That is, a possible aether wind should exert a disturbing influence on the absorption frequency. However, like in all other aether drift experiments (Michelson–Morley experiment), the result was negative, putting an upper limit to aether drift of 3–4 m/s. Experiments of that kind were performed by Champeney & Moon (1961),[12] Champeney et al. (1963)[13] and Turner & Hill (1964).[14]

Modern experiments

Further information: Modern searches for Lorentz violation

Fast moving clocks

A considerably higher precision has been achieved in modern variations of Ives–Stilwell experiments. In heavy ion storage rings, as the TSR at the MPIK, the Doppler shift of lithium ions traveling at high speeds is evaluated by using Saturated spectroscopy. Due to their frequencies emitted, these ions can be considered as optical atomic clocks of high precision.

Author Year Speed Maximum deviation
from time dilation
Grieser et al.[15] 1994 0,064c
Saathoff et al.[16] 2003 0,064c
Reinhardt et al.[17] 2007 0,064c
Novotny et al.[18] 2009 0,34c

Slow moving clocks

Meanwhile, the measurement of time dilation at every day's speeds has been accomplished as well. For that purpose, Chou et al. (2010) used aluminium ions, moving within a 75 m long, phase-stabilized optical fiber. These optical atomic clocks emitted frequencies of a certain frequency, and the sensitivity of this experiment was . Therefore, it was possible to measure a frequency shift due to time dilation of at speeds below 36 km/h (< 10 m/s), by comparison of the rates of moving and resting clocks.[19]

References

  1. ^ Robertson, H. P. (1949). "Postulate versus Observation in the Special Theory of Relativity". Reviews of Modern Physics. 21 (3): 378–382. Bibcode:1949RvMP...21..378R. doi:10.1103/RevModPhys.21.378.
  2. ^ Einstein, Albert (1905). "Zur Elektrodynamik bewegter Körper". Annalen der Physik. 322 (10): 891–921. Bibcode:1905AnP...322..891E. doi:10.1002/andp.19053221004. {{cite journal}}: Cite has empty unknown parameters: |month= and |coauthors= (help) English translation: ‘On the Electrodynamics of Moving Bodies’
  3. ^ Ives, H. E. (1938). "An experimental study of the rate of a moving atomic clock". Journal of the Optical Society of America. 28 (7): 215. Bibcode:1938JOSA...28..215I. doi:10.1364/JOSA.28.000215. {{cite journal}}: Cite has empty unknown parameter: |month= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  4. ^ Ives, H. E. (1941). "An experimental study of the rate of a moving atomic clock. II". Journal of the Optical Society of America. 31 (5): 369. Bibcode:1941JOSA...31..369I. doi:10.1364/JOSA.31.000369. {{cite journal}}: Cite has empty unknown parameter: |month= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  5. ^ Otting, G. (1939). "Der quadratische Dopplereffekt". Physikalische Zeitschrift. 40: 681–687.
  6. ^ Mandelberg, Hirsch I.; Witten, Louis (1962). "Experimental verification of the relativistic doppler effect". Journal of the Optical Society of America. 52 (5): 529. Bibcode:1962JOSA...52..529M.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  7. ^ a b Hasselkamp, D. (1979-06-01). "Direct observation of the transversal Doppler-shift". Zeitschrift für Physik A. 289 (2): 151–155. Bibcode:1979ZPhyA.289..151H. doi:10.1007/BF01435932. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  8. ^ Hay, H. J.; Schiffer, J. P.; Cranshaw, T. E.; Egelstaff, P. A. (1960). "Measurement of the Red Shift in an Accelerated System Using the Mössbauer Effect in Fe57". Physical Review Letters. 4 (4): 165–166. Bibcode:1960PhRvL...4..165H. doi:10.1103/PhysRevLett.4.165.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  9. ^ Champeney, D. C.; Isaak, G. R.; Khan, A. M. (1963). "Measurement of Relativistic Time Dilatation using the Mössbauer Effect". Nature. 198 (4886): 1186–1187. doi:10.1038/1981186b0.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  10. ^ Champeney, D. C.; Isaak, G. R.; Khan, A. M. (1965). "A time dilatation experiment based on the Mössbauer effect". Proceedings of the Physical Society. 85 (3): 583–593. doi:10.1088/0370-1328/85/3/317.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  11. ^ Kündig, Walter (1963). "Measurement of the Transverse Doppler Effect in an Accelerated System". Physical Review. 129 (6): 2371–2375. doi:10.1103/PhysRev.129.2371.
  12. ^ Champeney, D. C.; Moon, P. B. (1961). "Absence of Doppler Shift for Gamma Ray Source and Detector on Same Circular Orbit". Proceedings of the Physical Society. 77 (2): 350–352. doi:10.1088/0370-1328/77/2/318.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  13. ^ Champeney, D. C.; Isaak, G. R.; Khan, A. M. (1963). "An 'aether drift' experiment based on the Mössbauer effect". Physics Letters. 7 (4): 241–243. doi:10.1016/0031-9163(63)90312-3.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  14. ^ Turner, K. C.; Hill, H. A. (1964). "New Experimental Limit on Velocity-Dependent Interactions of Clocks and Distant Matter". Physical Review. 134 (1B): 252–256. doi:10.1103/PhysRev.134.B252.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  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. (1994). "A test of special relativity with stored lithium ions". Applied Physics B Lasers and Optics. 59 (2): 127–133. doi:10.1007/BF01081163.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  16. ^ Saathoff, G.; Karpuk, S.; Eisenbarth, U.; Huber, G.; Krohn, S.; Horta, R. Muñoz; Reinhardt, S.; Schwalm, D.; Wolf, A.; Gwinner, G. (2003). "Improved Test of Time Dilation in Special Relativity". Phys. Rev. Lett. 91 (19): 190403. Bibcode:2003PhRvL..91s0403S. doi:10.1103/PhysRevLett.91.190403.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  17. ^ Reinhardt, S.; Saathoff, G.; Buhr, H.; Carlson, L. A.; Wolf, A.; Schwalm, D.; Karpuk, S.; Novotny, C.; Huber, G.; Zimmermann, M.; Holzwarth, R.; Udem, T.; Hänsch, T. W.; Gwinner, G. (2007). "Test of relativistic time dilation with fast optical atomic clocks at different velocities". Nature Physics. 3 (12): 861–864. Bibcode:2007NatPh...3..861R. doi:10.1038/nphys778.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  18. ^ Novotny, C.; et al. (2009). "Sub-Doppler laser spectroscopy on relativistic beams and tests of Lorentz invariance". Physical Review A. 80 (2): 022107. doi:10.1103/PhysRevA.80.022107. {{cite journal}}: Explicit use of et al. in: |author= (help)
  19. ^ Chou, C. W.; Hume, D. B.; Rosenband, T.; Wineland, D. J. (2010). "Optical Clocks and Relativity". Science. 329 (5999): 1630–1633. Bibcode:2010Sci...329.1630C. doi:10.1126/science.1192720. PMID 20929843.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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