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A BRIEF REFLECTION ON THE USE OF LOGIC

IN ASTRONOMICAL THEORY

Walter van der Kamp

The following commentary was written by Walter van der Kamp as a paper for the Fifth International Conference on the Problems of Space, Time, Gravitation, which was held in St. Petersburg, Russia, in September 1998. It was intended to summarize and augment two earlier papers by him, “The Bradley-Airy-Einstein Syndrome” and “Relativity, a Broken Reed,” published respectively in the Proceedings of the Third and Fourth International Conferences on the Problems of Space, Time, Gravitation, in 1994 and 1996. The present short paper was almost complete at the time of Walter van der Kamp's death on January 26, 1998, and the manuscript was edited posthumously by C. van der Kamp. It was not sent to the Conference, but it serves as a brief summary of his thinking on these matters during the last years of his life for interested friends, correspondents, and family.

Among the many sciences, academic and applied, the astronomical disciplines seem the most prone to put their trust in theoretical constructs. Prudence, however, is essential here, particularly when two mutually exclusive explanations seem to “save the appearances” equally well. Neither of them should without more ado be taken as identical with truth.1 Yet logical thought, without which scientific enterprise cannot exist, requires one or the other to be adopted, at least provisionally, unless and until a third construct, comprising both of the former adequately, is developed.

In any case, “any physical theory is always provisional,” as Stephen W. Hawking warns his readers, “in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of the ex periments agree with some theory, you can never be sure that the next time the result will not contradict the theory.” What is more, after drawing attention to the vulnerability of a scientific method that puts its trust in such untrustworthy plausibilities, Hawking stresses that “you can disprove a theory by finding even a single observation that disagrees with [its] predictions.”2

In theory at least, therefore, philosophy of science recognizes the essential power of logic.3 If a hypothesis predicts A, but its opposite, B happens, the hypothesis is suspect. In practice, on the other hand, such prudence is quickly cast to the wind when the rejection of the hypothesis, necessitated by B is incompatible with prevailing opinion, with the Zeitgeist . Then ad hoc suppositions are quickly summoned to ward off danger.

In 1729, for instance, James Bradley (1692-1762) published his theory concerning stellar aberration.4 Telescopic observations had shown him that, in the heavens which seem to rotate daily, all stars also have another peculiar common small motion, all of them annually describing tiny ellipses of about the same size. Now Tycho Brahe (1546-1601), had these telescopic observations been available to him, in all likelihood would have considered those orbits real. It would have followed for him that all fixed stars must be at about the same distance from the observer. He would have arranged them in a Celestial Sphere, which Brahe's successor Kepler (1571-1630) still upheld against Giordano Bruno (1548- 1600). Additionally, Brahe would have surmised that this Stellatum was not, as in his 1588 diagram, centred on the Earth, but governed by our Great Light, with respect to which, in the Precession of the Equinoxes, it was also rotating very slowly.

Bradley, however, theorized that such aberration is only apparent, brought about by the Earth's 30km/sec velocity in its orbit about the Sun. That speed, he reasoned, compels astronomers to tilt their telescopes slightly forward to catch the stars' light rays, much as a man walking in a perpendicular rain would have to tilt a perpendicular stove pipe slightly forward to let the raindrops fall through. As it turned out, the angle of the required tilt fitted neatly with Roemer's 1675 determination of the speed of light. Since in any case Bradley and his contemporaries already ”knew” that the Earth was moving, his theory of the aberration of starlight could therefore easily be considered proven.5

Yet Bradley overlooked some vexing logical problems. To begin with, the proposition “If A, then B” does not entail that “If B then A.” It may be true that, if the Earth is moving, the telescope must be tilted, but that does not mean that, if the telescope must be tilted, it follows that the Earth is moving, however likely that seems. Additionally, if the Stellatum hypothesis “saves the appearances” as well as Bradley's own, his preferred conclusion is on even shakier ground. The logical principle of the excluded middle requires a verifying trial to assign such a preferred status, even if temporarily, to one or other of the contenders.

R. G. Boscovich (1711-1787) suggested such a trial. Lessen the velocity of star light traveling through the telescope, he suggested, by filling the instrument with water. If Bradley's theory is valid, an increased tilt will be measured. After such an affirming trial the aberration of starlight would more fully deserve the label of “the first proof that the earth has a yearly motion and that Copernicus was right”, as a 1961 textbook still blithely states.6

No one paid much attention to his suggestion. Bradley's stove pipe and raindrops were persuasive enough. Not until 1871 did recent advances in electromagnetic theory incite G.B. Airy (1802-1892) to make assurance doubly sure.7 The outcome, by then not wholly unexpected, overthrew the “proofs.” Water did not demand an increase in the telescopic tilt.

No one concluded that therefore the Earth might well be at rest. The result of the test was bizarre, to be sure, but fortunately a plausible theory of A.J. Fresnel (1788-1827), the recalled “Fresnel Drag,” lay at hand to hush up the awkward incident. Unhappily, however, sixteen years later the “Trial of the Century,” Michelson and Morley's experiment, again failed to verify what it was supposed to affirm, in the process becoming yet another experimental denial of post-Copernican theorizing. The negligible motion registered by the apparatus was, Michelson wrote, “quite small enough to refute Fresnel's explanation of stellar aberration.”8

Now what? The great mathematician J.H. Poincare (1854-1912) attempted an evasion of the dilemma. His 1904 “Principle of Relativity” stated that “the laws of physical phenomena are such that we do not have and cannot have any means of discovering whether or not we are carried along in a uniform motion of translation.”9 In a plane, at night, ten kilometers up, you cannot tell whether you are moving, even though you know you are.

Principles are not proofs, however; they are there to be believed as self evident. Or not, as the case may be. As the remaining mainstay for Galileo's “new science”, Poincare's suggestion was rather thin, though, applied to the solar system by itself, there is something to be said for his stopgap solution. For within the solar system the geocentric model “is in reality absolutely identical with the system of Copernicus, and all computations of the places of the planets are the same for the two systems.”10 As long as you overlook the stars.

About those stars later. In the meantime, notice that at each step so far the logically preferable conclusion, i.e. that we had better consider the possibility of an Earth at rest, was sidestepped in favour of some adhockery.

Soon enough the great Albert Einstein (1869-1955) shored up Poincare with his 1905 theory of relativity.11 That in the process far more than a change of scientific paradigm took place — an ontological shift with respect to the nature of being as such was accelerated by it — is not our concern in the present context. What matters here is that now “all optical problems for moving bodies [could] be solved,” because they were ”reduced to a series of problems for bodies at rest,” as Sir Fred Hoyle12 and the late Isaac Asimov13 reiterated in their commentaries, no doubt with some relief.

Well, not quite. The new paradigm, as these writers affirmed, allows us to take “any object within our system of objects … with equal validity as being at rest.”14 But what about those stars? If we have an Earth moving around the Sun, we have only an apparent stellar aberration. In reality the stars are scattered over (virtually) infinite distances, their own movements idiosyncratic. But if we have a stationary Earth, we have a problem. Now we have to bring those widely scattered stars back to Kepler's Stellatum, a “great, hollow, spherical shell”, the stars “embedded in it like tiny jewels.”15 Otherwise we can make no sense of the stellar aberration, which in this model describes real motion.

It turns out, then, that we cannot so blithely affirm that all motion is relative only, and every vantage point equally possible, all of them describing the same structure. Instead, we have vastly different structures resulting from different vantage points. Hence not all of them can be equally valid, not if we make use of that logic to which philosophy of science says it bows. In fact this single observation, to quote Hawking again, is enough to disprove the assertion that all motion is relative and can equally well be described from any vantage point.

It looks very much, then, although it seems preposterous, as if we are going to have to admit the possibility of a preferred frame of reference, even if such an admission undermines the work of Einstein and Poincare, and therewith, like dominoes falling backwards, Michelson and Morley, Fresnel, Boscovich, Bradley, yea the great Galileo himself. What is more, when it comes to selecting such a frame of reference, so far only Tycho Brahe's exposition, amended to have a Stellatum centered on the Sun, seems to account for all the data, however much that flies In the race of with century models based on the other paradigm.

What is to be done? Happily, there are already a number of individuals with geocentric leanings scattered through the world, and small but growing gatherings agreed on the cause here at hand. To them this reflection is addressed first and foremost, with two requests. First, if there are one or more flaws in the historical descriptions and the conclusion above, correction would be appreciated. Secondly, “a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation.”16 Two of such observations are recommended here. To begin with, the 1887 Michelson and Morley experiment could be performed in an airplane with a suitably sensitive refractometer.17 Also, the 1924 Michelson and Gale's trial, to demonstrate the daily rotation of space with respect to the Earth,18 could be improved by means of a temperature controlled version of the refractometer from stations high up North and & down South. Such a refractometer, “yielding a much higher sensitivity than the classical Michelson and Morley experiment” was already used in a simple first-order test of special relativity.19
In the end, of course, “being at rest” is a metaphysical concept. Although instinctively we imagine all motions of the cosmos against a background at rest, we cannot, I agree with Bertrand Russell (1872-1970),20 detect absolute rest with the use of empirical scientific observations from within that cosmos, however much we might want to. That is a yearning that can only be addressed by other means, and I can only point to what I have myself experienced, that trust in the God who has revealed himself in his Creation, in the Scriptures, and supremely in Jesus, stills that yearning.

And with that I rest my case.
 Walter van her Kamp
 Winter, '97

NOTES AND REFERENCES

1 Barfield, O., Saving the Appearances, New York, Harcourt Brace, p.51.

2 Hawking, S.W., A Brief History of Time, Bantam Books, p.10.

3 Hoyle, F., Astronomy and Cosmology, San Francisco, W.H. Freeman and Co, p.48.

4 This socalled aberration, of course, differs from parallax, the apparent secondary epicyclic circuits described by some stars so near to us that against the fixed background of the farther stars their distance from us can be calculated.

5 Abell, G., Exploration of the Universe, pp.40, 126.

6 Pannekoek, A., A History of Astronomy, 1961.

7 Airy, G.B., “On the supposed alteration in the amount of Astronomical Aberration of light, produced by the passage of light through a considerable thickness of Refracting medium”, Proceedings of the Royal Society, London, 1871, pp.35-39.

8 Michelson, A.A., and Morley, E.W., “On the Relative Motion of the Earth and the Luminiferous Ether”, American Journal of Science, Vol. 34, No. 203, Nov. 1887, p.341.

9 Poincare, J.H., “L'etat actuel et l'avenir de la physique mathematique”. Lecture given in St. Louis, USA, Sep.24, 1904.

10 Dreyer, J.L.E., A History of Astronomy from Thales to Kepler, pp. 363-364.

11 Einstein, A., “Zur Elektrodynamik Bewegter Korper,” Annalen der Physik, Vol. 17, 1905, p. 915.

12 Hoyle, F., Frontiers of Astronomy, p.304.

13 Asimov, I., Understanding Physics, Vol. II, p. 249.

14 Hoyle, F., Astronomy, p.416.

15 Abell, Exploration, p. 12.

16 Hawking, Brief History, p. 10.

17 Michelson and Morley, p.341.

18 Michelson, A.A., and Gale, H.G., “The Effect of the Earth Rotation on the Velocity of Light”, Astrophysical Journal, Vol. 61, April 1925.

19 Bijl, J., Sanderse, M., and van der Kamp, W., “Simple First Order Test of Special Relativity,” American Journal of Physics, 53:(1), Jan 1985.

20 Sciama, D.W., The Unity of the Universe, pp. l02, 163.



Quotes

An error in the first stages of deployment can never be made good.

 — Moltke
The Jesuits insisted that Galileo's advocacy of the Copernican system could have worse consequences on the established system of teaching ”than Luther and Calvin put together.”
 — Encyclopedia Brittanica
What no longer originates, we cannot conceive as originating. What has originated we do not comprehend.
 — Goethe
Duns Scotus has written very well … and has endeavoured to teach with good system and correctly. Occam was an intelligent and ingenious man … Thomas Aquinas is a gossiping old washerwoman.
 — Martin Luther, Table Talk
 Jena Edition, 1591, fol. 329

Translated on 11 February 2005 by ws2html