Relativity Since Einstein

Relativity-theory has always been a peculiarly philosophical branch of science: Einstein recognized a particular debt to Hume and Mach and current debates about the Rip-van-Winkle paradox are evidence that it is so still. The reasons are easily seen. Other scientists frame novel concepts to match newly-discovered facts, but the relativity-physicist has a more Socratic task—that of uncovering the presuppositions of our inherited ideas of space and time, and drawing fresh distinctions to cover situations in which those presuppositions fail us. So in thinking about relativity we are plunged into a world, not so much of costly apparatus and painstaking observations, as of suppressed premises and distinguos—into a conceptual, rather than an experimental argument. Nor is there anything unscientific about this fact: it is just in the nature of the case.

There is always scope, accordingly, for new philosophical critiques of our spatial and temporal concepts; and not only scope, but need. Since Einstein’s classic papers of 1905 and 1915, thousands of worthy articles on the subject have appeared, yet we have made surprisingly little progress beyond Einstein’s own analysis. In some respects, the level of the public debate has in fact dropped in the last forty years. Innocent-minded astronomers swept up into the heady stratosphere of cosmology now speculate about (e.g.) “an indefinite period when nothing changed, before time was,” with a logical abandon which causes the philosophical reader to gasp with unbelief. (Did Kant write in vain?) So one looks forward to a comprehensive re-analysis of our spatio-temporal ideas; this should make explicit the transition from everyday comparisons of distance and duration to progressively more abstract concepts, should bring the lessons of Kant’s “paralogisms” up-to-date, and should clarify the (now ambiguous) status of those “world-models” which cosmologists build on Einstein’s relativity-theory. Thus we find ourselves in a period of transition. Einstein was the founder of relativity as Aristotle was of mechanics; we at present have our Stratos and Buridans with us; and we are looking for our Galileo.

Alas, Adolf Grünbaum is not that Galileo—at any rate, not yet. In this book, which is one of the first in a new series of Borzoi Books in the philosophy of Science edited by Sidney Morgenbesser of Columbia University, he does no more than play Simplicius to Einstein’s Aristotle. His argument is, in effect, a series of commentaries on the founding-papers of relativity physics. Few of the issues he discusses are stated ab initio or pursued au fond, he takes for granted much prior knowledge, and the poor old average reader will be out of his depth very early. On top of this, his language is lumpish and ponderous, full of needless jargon-phrases like “remetrizational retainability,” mixed with academic waggery of a kind that is all very well in face-to-face debate, but which becomes mildly offensive in print. The trouble is that Grünbaum has built a reputation—a respected, even an intimidating reputation—in the sophisticated polemics of professional philosophy, and has not hitherto (to my knowledge) published anything longer than an extended monograph. Faced with the challenge of a book, he has done nothing to vary his style, his texture and his literary manners, and the result is hard on the jaw. (Dried octopus makes an excellent hors d’oeuvre, but …)

All this is a pity, for Grünbaum has a penetrating mind and is, within limits, a master of his material. His book is in three parts. The first deals with the “metric”—that complex of mathematical relations, measuring-procedures and reference-frames which defines what are to count, for the purposes of physical theory, as spatial and temporal magnitudes. In some 175 pages, he sets out to establish exactly how far the use of alternative metrics (a Euclidean “flat” metric, or one of the non-Euclidean “curved” metrics) is consistent with the same facts of observation, and to what extent, accordingly, there is room for an arbitrary, human choice between metrics. This question has been near the heart of relativity-theory from the beginning, and to state the answer precisely is a delicate task. Since Poincaré wrote in 1895, pronouncements about this topic have veered between a naive empiricism—putting the question “Is Space curved?” on a level with the question “Is my necktie straight?”—and the sophisticated extreme with Grünbaum entitles “trivial semantical conventionalism”—treating the choice of metric as little more than a verbal matter. Grünbaum himself steers a course between these extremes. In general, he follows the line laid down by Riemann, Einstein, and Reichenbach, and he comments acidly on those whom he takes to depart too radically from that line; but he ends by chiding Einstein for a weakness towards “conventionalism,” and argues that the facts of Nature limit our choice of geometry more severely than even Einstein recognized.

The second part of the book deals largely with the “direction” of time and and temporal change, notably with the concept of entropy, which is intimately involved with the irreversibility of physical changes. Once again, Grünbaum is careful to steer a middle way. He is not to be taken in by figurative language about “the flow of time”—it is not time that flows either forwards or backwards, but rather physical processes that occur reversibly or irreversibly. Nevertheless, to extend the ideas of classical thermodynamics, so as to provide a general account of the “anisotropy” of temporal change and the conditions for predictability, requires great circumspection. Finally, in the last part of the book, he explores philosophical issues arising directly out of Einstein’s Special Theory, and uses this examination to illuminate the historical development of Einstein’s ideas.

One can scarcely debate Grünbaum’s detailed conclusions here: he has in any case demonstrated adequately that this is no field for dogmatic judgments. Yet something needs saying about his methods of argument. These are essentially those of the scholastics: he does not deal in syllogisms, but he remains in general as committed to Einstein as Simplicius was to Aristotle, and this limits his sympathy for heretics. As a result, he makes heavy weather of his subject, often laboring through several pages at a point which could be stated in a single paragraph. His opponents, too, have not just to be answered: they must be belabored, put out of countenance, dismissed, with a vehemence greater than the force of his counter-arguments justifies. This violence of tone ends by alienating the impartial reader—especially since in several cases it is (on Grünbaum’s own admission) quite misplaced. Let me cite his attacks on E.A. Milne and A.N. Whitehead. He spends a whole chapter criticizing Milne’s theories, which he treats as though they represented an unsuccessful attack on Einstein, only to remark in the last paragraph—baldly and without apology:

It should be noted, however,….that if Milne’s construction is interpreted as applying not to special relativity Kinematics but to his [own] cosmological world model, then our criticisms are no longer pertinent.

Whitehead gets similar treatment. Grünbaum’s analysis (pp. 48-65) begins at sheer cross-purposes. but he ends up eventually by recognizing what Whitehead is driving at and, since his objections no longer apply, he grudgingly allows that “Whitehead’s important concession” is acceptable.

Behind this polemic there lie some profounder philosophical motives, notably Grünbaum’s distrust of all pragmatic or psychologistic elements and his fear of the genetic fallacy. He seems unwilling to acknowledge that our present science is the temporary product of a conceptual evolution which is forever incomplete: its validity must be preserved inviolate from the touch of time and the fallibility of our minds. In the passage under criticism, White head was in fact posing the question of how modern theoretical concepts of time and change relate back to earlier, pre-scientific notions, and how much carries over from these older notion even into relativity-theory. Grünbaum (I believe) would prefer to cut these historical threads entirely, and to justify relativistic physics by appeal to mathematical consistency and simple observation alone, disowning this older conceptual inheritance. Yet that separation cannot be completed. The most convincing part of his book is—significantly—the historical section, in which he examines the intellectual ancestry of Einstein’s ideas, and shows how exactly they improved on the so-nearly-relativistic theories of Poincaré and Lorenz. Discussing his own heroes, Grünbaum is sufficiently relaxed to drop his guard. He does not feel the need to lace Einstein’s theories into the same epistemological corset that he fastens onto rival systems. Can he not return now to these other theories in that wiser and more generous mood? If so, he could yet produce for us that magisterial analysis which the evolution of our spatial and temporal concepts still requires.