V.6 No 1

71

The problem of physical time in today physics

6.4.2.2. The generalised analysis of results of search of aethereal wind by interferometric methods

Well, possibly, speaking about organ, Einstein meant the experiments searching the aethereal wind with help of light beams? Maybe. Though, on the other hand, as it follows from the citations of Galilee and Einstein with the difference of three centuries between them, the cross of arguments and ways of substantiation makes very close the approaches of Einstein and Mach on one hand and of Aristotle’s adherents on the other. And if we can understand to a definite extent Aristotle and his adherents at times of Galilee, as the basis on which they could rely was too limited in absence of scientifically substantiated arguments proving the opposite, at times of Einstein the Earth’s orbiting was an experimentally established fact, as well as long time were known the effects that distinguish the orbital motion from that inertial. So it looks strange when relativists attempt to modify an old argumentation, disregarding the obviously changed level of knowledge. Additionally, should Einstein be speaking namely of experiments related to the search of aethereal wind, he could not misunderstand that at the level of feeling the difference is unrevealable, the more these effects cannot influence our feeling of organ’s sound. None the less, if Einstein meant such experiments, saying, “But with all the thorough of observations, we still could not reveal such anisotropy of terrestrial space, i.e. the physical equivalence of different directions”, he also was clearly incorrect, as on one hand these experiments more related to reveal the Earth’s motion relative to aether than to the orbital motion and related non-inertial effects.

On the other hand, undoubtedly, experiments revealing the aethereal wind were dramatic, and the first Michelson’s conclusion really was negative or nearly negative: “It follows from the said that if the relative motion of the Earth in aether exists, it has to be little, so little to be able to fully debunk Fresnel’s explanation of aberration … If now on the grounds of this work we could quite legally conclude that aether rests relative to the Earth’s surface, and according to Lorentz, the potential of speeds can be non-existent, the own theory of Lorentz appears bankrupt, too” [67, p. 25]. At the same time, even on the grounds of results processed by Michelson that were then multiply recalculated due to his incorrect technique of operations, we can see in Fig. 6.11 that the yielded results cannot be a statistic noise, though, really, the shift of fringes is well less than expected.

Fig. 6.12. “The results of observation of the ethereal wind. The angle of interferometer’s turn is taken as an abscissa and the values of fringes expressed in the wavelengths – as an ordinate. The theoretical curve is primed: the calculation is made in supposition that the ethereal wind has a direction opposite to the Earth’s motion in the ecliptics” [67, p. 25]

And S.I. Vavilov corroborated this result non-zero but little, in comparison with expected, when recalculated Michelson’s tables: “The utmost shift is about 0,05 of fringe, i.e. almost 10 times less than that theoretical” [68, p. 32].

It was Tom Roberts [69] who recalculated Michelson’s results last time, and namely with the target to substantiate the relativistic opinion of negative result. None the less, his calculation based on today level of spectral analysis of statistic data also showed the regular change of amplitude of shift of fringes in Michelson’s results (see Fig. 6.13).

Fig. 6.13. “The Michelson-Morley data, Noon (upper) and P.M. (lower), with errorbars (see text). These errorbars are under estimates” [69, Fig 12 of the original text].

Comparing the plots in Fig. 6.13 with Michelson’s Fig. 6.12, we see a general coincidence, with a little exception: the change of Michelson’s fringes shift correlates with a full period of device’s turn, while in Roberts’ calculation the scale is fixed to a half-period. We would think it to be Roberts’ blunder, should we did not see same change of period in his analysis of results of other experiments revealing the aethereal wind.

Thus, Miller in his work of 1933 [70] plots the regularities yielded on his experimental data processed with harmonic analysis; two of them are shown in Fig. 6.14.

Fig. 6.14. “The harmonic analysis of observations of ethereal wind. The angle of interferometer’s turn is taken as an abscissa; one degree relates to 1/16 of a turn” [70, p. 228, Fig. 21 of the original work]

“These charted ‘curves’ of the actual observations contain not only the second-order, half-period ether-drift effect, but also a first-order, full-period effect, any possible effects of higher orders, together with all instrumental and accidental errors of observation. The present ether-drift investigation is based entirely upon the second order effect, which is periodic in each half revolution of the interferometer. This second-order effect is completely represented by the second term of the Fourier harmonic analysis of the given curve. In order to evaluate precisely the ether-drift effect, each curve of observations has been analysed with the Henrici harmonic analyser for the first five terms of the Fourier series. The first-order effect in the observation is shown by the fundamental component, which is drawn under the corresponding curve of observations in Fig. 21; the second-order effect is shown by the curve next below; while the fourth curve in each instance shows the sum of the third, fourth and fifth components. It is evident that the observed curves contain very little trace of any effects of any higher orders. The residual curves are of very small amplitude and are evidence of the fact that the incidental and random errors are small” [70, p. 228].

In these plots we clearly see the coincidence of second harmonic (the third curve from the top) with the general period of experimental curve (the top curve), and the first harmonic and those following the second harmonic are small. While Roberts gives some other graph reduced, again, to the half-turn of interferometer (see Fig. 6.15).

Fig. 6.15. “The plot at the bottom of Fig. 1 (the table data from Miller’s paper [70, p. 204, Fig. 13] – Authors), with errorbars” [69, Fig. 4]

If we digress from the dimensions of abscissa, we clearly see in this graph the regularity of fringes shift. Its only fail is its smallness comparing with the expected result and errorbar in which Roberts, when calculated, ‘forgot’ to subtract from data the systematic shift and in this way too much overestimated its value: “The first thing to do is look at the data of Fig. 1 (the data from Miller’s table in the bottom of which he drew a curve, disregarding the systematic shift of fringes – Authors), plotted in Fig. 2, which shows the raw data with adjustments restored. There is huge variation about 100 times larger than the amplitude of the plot at the bottom of Fig. 1, and extracting any signal from such a large background is a challenge. Clearly the interferometer systematically drifted about 6 fringes during this run, as the large-scale changes cannot possibly be any real signal with a period of ? turn. From the way data were recorded and from Miller’s own estimates, the statistical errors in these data are on the order of 0.1 fringe. So both the size and the shape of the variations in Fig. 2 imply that this is a large systematic error” [69, p. 5].

The same strange approach we see when Roberts analyses the Illingworth’s results (Fig. 6.16).

Fig. 6.16. “The Illingworth data minus the assumed-linear systematic model” [69, Fig. 13]

This experiment is known to be one of most unsuccessful, so in their arguments with the adherents of aether theory, relativists like to refer to this experiment even more than to Michelson – Morley’s experiment. But even in this graph we can see: though the regularity well seen in the results of Michelson and Miller is distorted, they are not exactly zero.

Anyway, Roberts, basing on his clearly too high errorbar that much exceeds the sought result, thinks even unnecessary to analyse all three experiments, whether there is a non-negative result. In particular, Roberts writes about Michelson’s results so: “Unfortunately, their original data have been lost, and the only available data are the averages for six data runs in their 1887 paper. So while the modeling of their systematic drift is not possible, it is possible to estimate their errorbars using the same technique as above. Figure 12 (our Fig. 6.13 – Authors) displays their reported data, with errorbars computed from a histogram of the data after: a) subtracting the assumed-linear systematic for each run (and, as Roberts could not add the systematic shift here, the value of errorbar in Fig. 6.13 is well less, though in this case Roberts gives it much higher also – Authors), and b) subtracting the mean for the orientation of each data point. Subtracting the mean for each orientation removes any real signal from the histogram so that all orientations could be combined into a single histogram to improve the poor statistics (with the exception that the signal amplitude changes from run to run, because of change of device orientation in space together with the Earth, which, basically, disallows to join data in this way – Authors). Note this errorbar is an under estimate, because it comes from the variance of the per-run averages for the markers rather than from the variance of the raw data themselves. These data are dominated by the systematic drift, and the sigma of the histogram was used for the errorbars. While it is not possible to draw Fig. 3 for their raw data, one can compare the full-turn assumed-linear systematic for each data run to the marker in the middle: for 3 out of the 6 runs that difference is larger than the errorbars displayed in Fig. 12, so it is clear that their systematic drift is nonlinear by an amount considerably larger than the variations in their data. Just as for Miller’s data, it is inadequate to assume that the systematic drift is linear.

While it is not fruitful to attempt a more detailed analysis, it is clear from Fig. 12 that there is no statistically significant signal in their data (remember the errorbars are under estimates). Handschy (1982) comes to a similar conclusion via a different route.” [69, p. 15–16].

About Miller’s results: “Since Miller’s day our attitude toward experiments like this has changed, and we now use them to test theories, rather than to “determine the absolute motion of the earth”. And we do this quantitatively using ² fits (or similar). So the modern approach to interpreting these data in Miller’s theoretical context would be to start with Miller’s model of absolute motion as applied to his instrument, and test the class of theories “The earth is moving with absolute speed X in direction Y” where X and Y are determined by fitting to the data. The speed X is related to the amplitude of the signal, and the direction Y is related to its phase. Miller’s conversion from signal amplitude to absolute speed is given in Fig. 20 of (Miller, 1933) (Fig. 6.14 here – Authors), in which 0.7 fringe corresponds to 24 km/sec. Looking at Fig. 4 (Fig. 6.15 here – Authors), it is clear that this run will have a good ² for any sine wave with amplitude corresponding to speed X less than about 30 km/sec and phase corresponding to any direction Y whatsoever. So the errorbars on X and Y are huge. This is just one run out of hundreds, and some have smaller errorbars, some have larger errorbars. But all runs in the data sample have the property that the errorbars exceed the variation in the final ? turn plot, as in Fig. 4. That means that this analysis cannot really determine the direction of absolute motion at all, and cannot say very much about the speed other than that it is less than about 30 km/sec. (Miller, 1933) displays several plots of absolute speed and direction, but they are all without errorbars. Had he computed and plotted errorbars as above, they would be so large that in no case would they fit on the plot, and often would not even fit on the page. His “determination of the absolute motion of the earth” is not statistically significant. Because of the flaws in this data reduction algorithm (discussed next), there’s no point in actually performing a detailed statistical analysis of results from this analysis method” [69, p. 7].

And about Illingworth's results: “ Because of the under sampling it is not possible to perform useful Fourier transforms, nor is it possible to model the systematic drift. But it is worthwhile to examine the data, compute errorbars, and determine whether or not there is any significant variation in the data. Figure 13 (Fig. 6.16 here – Authors) displays the one run for which data are available from Table II in Illingworth (1927). Illingworth did not plot the data, but did perform averages and subtract an assumed-linear systematic (related to the full-turn effect – Authors) in his analysis, so in Fig. 13 the data points are the per-orientation averages of the ten turns minus the straight line between the average North measurements (N – Authors). The errorbar for each orientation came from the sigma of the histogram of its ten readings divided by v 10, because it is not clear if the errors are systematic or statistical; as there is likely some systematic component of the error, these errorbars are probably under estimates. The interferometer was adjusted to zero before the start of each turn, so the initial reading at North has a zero errorbar (this also makes determining the overall systematic drift impossible). Comparing the individual turns’ linear systematic to the value at the midpoint (as in Fig. 3) shows that four of the ten turns had a nonlinearity in the systematic that exceeds the errorbars displayed in Fig. 13, so the assumption that the systematic is linear is inadequate here, too. In any case, clearly there is no significant variation in these data.” [69, p. 16–17].

We intentionally gave Roberts’ conclusions for all three experiments, to see one important feature. Emphasising the smallness of values, he certainly refers to the systematic which he excludes from the analysed table data, as Michelson, Miller and Illingworth did. With it, he forgets to exclude this systematic from the values of errorbar and so yields as if untrustworthy values of fringe shift. But the systematic which all authors exclude is the so-called full-turn effect: in each full turn of the device, i.e. when the device returns to its initial state after a turn, relatively to the pole of Earth, the fringes regularly shifted, and Roberts just showed this regular shift in his Fig. 3 to which he permanently refers in the above citations. We show this his graph as Fig. 6.17.

Fig. 6.17. “The assumed-linear systematic drift from the data of Fig. 1. The lines are between successive Marker 1 values and the points are Marker 9. These markers are 180 degrees apart, so any real signal has the same value for every corner and every point.” [69, Fig. 3]