Ives–Stilwell experiment

In physics, the Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler shift of light.

[1][2] The result was in agreement with the formula for the transverse Doppler effect and was the first direct, quantitative confirmation of the time dilation factor.

Both time dilation and the relativistic Doppler effect were predicted by Albert Einstein in his seminal 1905 paper.

[4] Einstein subsequently (1907) suggested an experiment based on the measurement of the relative frequencies of light perceived as arriving from "canal rays" (positive ion beams created by certain types of gas-discharge tubes) in motion with respect to the observer, and he calculated the additional Doppler shift due to time dilation.

Eventually, Herbert E. Ives and G. R. Stilwell (referring to time dilation as following from the theory of Lorentz and Larmor) gave up the idea of measuring this effect at right angles.

For example, Stark's 1906 measurements showed systematic errors ten times the predicted effect.

[5] The maximum speed achievable in early gas-discharge tubes was about 0.005 c, which implied a transverse Doppler shift of only about 1.25×10−5.

The small TDE achievable was considerably less than the width of the emission lines, which were relatively diffuse due to the Doppler line-broadening resulting from non-uniformity of ion speeds.

[1] Even with these improvements, however, performing the experiment as usually imagined (with the observation being made at right angles to the beam) would be extremely difficult since small errors in the angle of observation would result in line-shifts of magnitude comparable to the magnitude of the anticipated effect.

[1] To avoid the issues associated with observing the beam at right angles, Ives and Stilwell used a small mirror within the canal ray tube (See Fig.

The TDE would manifest itself as a shift of the center of gravity of the simultaneously red- and blue-shifted spectral lines.

[1] In 1937, Ives performed a detailed analysis of the spectral shifts to be expected of particle beams observed at different angles following a "test theory" which was consistent with the Michelson–Morley experiment (MMX) and the Kennedy–Thorndike experiment (KTX), but which differed from special relativity (and the mathematically equivalent theory of Lorentz and Lamor) in including a parameter

The first few terms of the Taylor series expansion for the direct view of the particle beam is given by while the first few terms of the Taylor series expansion for the reflected view of the particle beam is given by The even power terms have the same sign for both views, meaning that both the direct and reflected rays will show an increase in wavelength over that predicted by the classical Doppler analysis.

Special relativity therefore predicts that the center of gravity of Doppler-shifted emission lines emitted by a source moving towards an observer and its reflected image moving away from the observer will be offset from unshifted emission lines by an amount equal to the transverse Doppler effect.

[11][12] In the experiment, Ives and Stilwell used hydrogen discharge tubes as the source of canal rays which consisted primarily of positive H2+ and H3+ ions.

These ions, after being accelerated to high speed in the canal ray tube, would interact with molecules of the fill gas (which sometimes included other gases than H2) to release excited atomic hydrogen atoms whose velocities were determined by the charge-to-mass ratios of the parent H2+ and H3+ ions.

The particle velocities, as measured by the first-order Doppler displacements, were consistently within 1% of the values computed by the theoretical relationship

where e is the charge on the hydrogen atom, E is the voltage between the electrode plates, and M is the mass of the observed particle.

The expected second order shift of the center of gravity of direct and reflected views of the emissions was only about 0.005 mm which corresponded to 0.05 Å, requiring measurement accuracies of several tenths of a micron.

The source of the unsystematic errors in measurement of the center of gravity of the displaced lines was found to be due to the complex molecular absorption spectrum of the fill gas.

[1] As a result of this issue, the number of voltages available yielding direct and reflected lines in clear spaces was relatively limited.

The advantage of this method over the other method presented in their paper (plotting center-of-gravity shifts against the computed velocity, based on voltage) is that it was independent of any errors of voltage measurement and did not require any assumptions of the voltage-velocity relationship.

[1] In terms of Ives's 1937 test theory,[10] the close agreement between the observed center-of-gravity displacements versus theoretical expectation support

The chief difficulty that Ives and Stilwell encountered in attempts to achieve larger shifts was that when they raised the electric potential between the accelerating electrodes to above 20,000 volts, breakdown and sparking would occur that could lead to destruction of the tube.

Using a four-electrode version of the canal ray tube with three gaps, a total potential difference of 43,000 volts could be achieved.

Under normal circumstances, this would be of no consequence, since this effect would only result in a slight apparent broadening of the direct and reflected images of the central line.

[2] A more precise confirmation of the relativistic Doppler effect was achieved by the Mössbauer rotor experiments.

In heavy-ion storage rings, as the TSR at the MPIK or ESR at the GSI Helmholtz Centre for Heavy Ion Research, the Doppler shift of lithium ions traveling at high speed [21] is evaluated by using saturated spectroscopy or optical–optical double resonance.

Due to their frequencies emitted, these ions can be considered as optical atomic clocks of high precision.

Chou et al. (2010) created two clocks each holding a single 27Al+ ion in a Paul trap.

Figure 1. Ives–Stilwell experiment (1938). " Canal rays " (a mixture of mostly H 2 + and H 3 + ions) were accelerated through perforated plates charged from 6,788 to 18,350 volts . The beam and its reflected image were simultaneously observed with the aid of a concave mirror offset 7° from the beam. [ 1 ]
Figure 2. The dispersing element of the spectrograph was a diffraction grating blazed to maximize the amount of the total light thrown into the first order. A high quality telescope lens of five foot focal length collimated the light from the slit into a parallel beam onto the grating, and the diffracted light was then focused by a similar lens onto a photographic plate. The entire apparatus was mounted on a stable platform and conducted in a constant temperature room regulated to 0.1 °C.
Figure 3. Why it is difficult to measure the transverse Doppler effect accurately using a transverse beam. The illustration shows the results of attempting to measure the 4861 ångström line emitted by a beam of "canal rays" as they recombine with electrons stripped from the dilute hydrogen gas used to fill the canal ray tube. With v = 0.005 c , the predicted result of the TDE would be a 4861.06 ångström line. On the left, conventional Doppler shift results in broadening the emission line to such an extent that the TDE cannot be observed. In the middle, we see that even if one narrows one's view to the exact center of the beam, very small deviations of the beam from an exact right angle introduce shifts comparable to the predicted effect. Ives and Stilwell used a concave mirror that allowed them to simultaneously observe a nearly longitudinal direct beam (blue) and its reflected image (red). Spectroscopically, three lines would be observed: An undisplaced emission line, and blueshifted and redshifted lines. The average of the redshifted and blueshifted lines was compared with the undisplaced line.
Figure 4. Doppler-shifted Balmer line from the Ives–Stilwell experiment
Figure 5. H β emission lines and H 2 molecular absorption lines in the Ives–Stilwell experiment
Figure 6. Computed and observed second-order shifts plotted against first-order Doppler shifts
The Kündig experiment (1963). An 57 Fe Mössbauer absorber was mounted 9.3 cm from the axis of an ultracentrifuge rotor. A 57 Co source was mounted on a piezoelectric transducer ( PZT ) at the rotor center. Spinning the rotor caused the source and absorber to fall out of resonance. A modulated voltage applied to the transducer set the source in radial motion relative to the absorber, so that the amount of conventional Doppler shift that would restore resonance could be measured. For example, withdrawing the source at 195 μm /s produced a conventional Doppler redshift equivalent to the TDE resulting from spinning the absorber at 35,000 rpm .
Schematic view of an optical optical double-resonance spectroscopy with the transition frequencies and of a moving ion and counter-propagating laser beams with the frequencies and .
Schematic view of saturation spectroscopy with the transition frequencies of a moving ion and counter-propagating laser beams with the frequencies and .