Ives–Stilwell experiment

In these experiments, the large relative velocities needed to exhibit relativistic effects are between the experimental apparatus (laboratory) and positive ions accelerated in a discharge tube, the streams of such ions being the canal rays. One observes the emission spectra of these ions, and in particular how the spectra change depending on the ion velocity, which can be varied via the voltage used to accelerate them. Experimental challenges Initial attempts to measure the second order transverse Doppler effect in canal rays completely failed. For example, Stark's 1906 measurements showed systematic errors ten times the predicted effect. Various values of n would correspond to various combinations of length contraction, width expansion, and time dilation, where n=1 would be the value predicted by special relativity. Ives proposed the optical experiment described in this article to determine the precise value of n. The experiment of 1938 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. (Free H+ ions were present in too small an amount to be usable, since they quickly combined with H2 molecules to form 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 excited atomic hydrogen atoms emitted bright emission lines. For their paper, Ives and Stilwell focused on the blue-green H_\beta line of the Balmer series. shows an example of the results that they obtained, with an undisplaced emission line in the center, and lines from Doppler-shifted atomic hydrogen released from H2+ and H3+ ions at three different voltages on either side of the center line. The particle velocities, as measured by the first-order Doppler displacements, were consistently within 1% of the values computed by the theoretical relationship eE = M(v^2/c^2)/2, 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 asymmetry of the Doppler-shifted lines with respect to the undisplaced central emission line is not evident to casual inspection, but requires extreme precision of measurement with careful attention to sources of systematic error. In their optical arrangement, illustrated in , the first order (classical Doppler) displacement of emissions from H2+ ions at 20,000 volts was about . The expected second order shift of the center of gravity of direct and reflected views of the emissions was only about which corresponded to , requiring measurement accuracies of several tenths of a micron. Initial measurements of the displacements were very erratic. 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. An emission line, passing adjacent to a molecular absorption line of the fill gas, would be differentially absorbed on one side or the other of its nominal center, and the measurement of its wavelength would thus be disturbed. illustrates the issue. illustrates an undisplaced H_\beta emission line. illustrates the molecular absorption spectrum of the fill gas, obtained by photographing the spectrum of the arc behind the electrode of the canal ray tube (see ). illustrates an undisplaced H_\beta emission line surrounded by displaced H_\beta emission lines from H2+ and H3+. At the particular voltage chosen, the lines from H2+ are clear of the molecular absorption lines (see arrows), but the lines from H3+ are not. As a result of this issue, the number of voltages available yielding direct and reflected lines in clear spaces was relatively limited. Ives and Stilwell compared their results against theoretical expectation using several approaches. compares theoretical versus measured center-of-gravity shifts \Delta\lambda_2 plotted against the emission lines' first-order Doppler shifts \Delta\lambda_1. 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. In terms of Ives's 1937 test theory, the close agreement between the observed center-of-gravity displacements versus theoretical expectation support n=1, which corresponds to length contraction by the Lorentz factor \lambda in the direction of motion, no length changes at right angles to the motion, and time dilation by the Lorentz factor. The results therefore validated a key prediction of the theory of relativity, although it might be noted that Ives himself preferred to interpret the results in terms of the obsolescent theory of Lorentz and Lamor. The experiment of 1941 In the 1938 experiment, the maximum TDE was limited to 0.047 Å. 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. This difficulty was overcome by using multiple electrodes. Using a four-electrode version of the canal ray tube with three gaps, a total potential difference of 43,000 volts could be achieved. A voltage drop of 5,000 volts was used across the first gap, while the remaining voltage drop was distributed between the second and third gaps. With this tube, a highest shift of 0.11 Å was achieved for H2+ ions. Other aspects of the experiment were also improved. Careful tests showed that the "undisplaced" particles yielding the central line actually acquired a small velocity imparted to them in the same direction of motion as the moving particles (no more than about 750 meters per second). 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. But if the mirror were tarnished, the central line might be expected to shift slightly, since the redshifted reflected view of the emission line would contribute less to the measured wavelength than the blueshifted direct view. Other controls were performed to address various objections of critics of the original experiment. The net result of all of this attention to detail was the complete verification of Ives and Stilwell's 1938 results and the extension of these results to higher speeds. ==Mössbauer rotor experiments==

(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. 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 sent to an absorber at the rim (in some variations this scheme was reversed), and a stationary counter was placed beyond the absorber. According to relativity, the characteristic resonance absorption frequency of the moving absorber at the rim should decrease due to time dilation, so the transmission of gamma rays through the absorber increases, which is subsequently measured by the stationary counter beyond the absorber. This effect was actually observed using the Mössbauer effect. The maximal deviation from time dilation was 10−5, thus the precision was much higher than that (10−2) of the Ives–Stilwell experiments. Such experiments were performed 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 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, as in all other aether drift experiments (Michelson–Morley experiment), the result was negative, putting an upper limit to aether drift of 2.0 cm/s. Experiments of that kind were performed by Champeney and Moon (1961), Champeney et al. (1963), Turner and Hill (1964), and Preikschat supervised by Isaak (1968). ==Modern experiments==

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 or ESR at the GSI Helmholtz Centre for Heavy Ion Research, the Doppler shift of lithium ions traveling at high speed 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. Using the framework of Mansouri–Sexl a possible deviation from special relativity can be quantified by : \frac{\nu_a\nu_p}{\nu_1\nu_2} = 1 + 2\hat{\alpha}\beta^2, with \nu_a as frequency of the laser beam propagating anti-parallel to the ion beam and \nu_p as frequency of the laser beam propagating parallel to the ion beam. \nu_1 and \nu_2 are the transition frequencies of the transitions in rest. \beta = v/c with v as ion velocity and c as speed of light. In the case of saturation spectroscopy the formula changes to : \frac{\nu_a\nu_p}{\nu_0^2} = 1 + 2\hat{\alpha}\beta^2, with \nu_0 as the transition frequency in rest. In the case that special relativity is valid \hat{\alpha} is equal to zero. Slow moving clocks Meanwhile, the measurement of time dilation at everyday speeds has been accomplished as well. Chou et al. (2010) created two clocks each holding a single 27Al+ ion in a Paul trap. In one clock, the Al+ ion was accompanied by a 9Be+ ion as a "logic" ion, while in the other, it was accompanied by a 25Mg+ ion. The two clocks were situated in separate laboratories and connected with a 75 m long, phase-stabilized optical fiber for exchange of clock signals. These optical atomic clocks emitted frequencies in the petahertz (1 PHz = 1015 Hz) range and had frequency uncertainties in the 10−17 range. With these clocks, it was possible to measure a frequency shift due to time dilation of ~10−16 at speeds below 36 km/h (< 10 m/s, the speed of a fast runner) by comparing the rates of moving and resting aluminum ions. It was also possible to detect gravitational time dilation from a difference in elevation between the two clocks of 33 cm. ==See also==