Introduction: AS Eddington, Physics and Philosophy

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A. S. EDDINGTON, PHYSICS AND PHILOSOPHY By H.G. Callaway … we know that the theory of general relativity must be modified. Because the classical (i.e. non quantum-mechanical) version predicts points of infinite density—singularities—it prognosticates its own failure… —Stephen Hawking, A Briefer History of Time.

In his 1927 Gifford Lectures, delivered at the University of Edinburgh, and subsequently expanded to their published form, the work of Arthur Stanley Eddington (1882-1944) displays a number of distinctive elements. First and foremost, Eddington explains the new physics of special relativity, general relativity and quantum mechanics. This task dominates the present volume. The reader learns of the scientific achievements of Albert Einstein, and Hermann Minkowski, and further, the developments of the “old quantum theory” and the “new quantum theory,” connected with the names of Max Planck, Einstein, Niels Bohr, Werner Heisenberg, Erwin Schr„dinger, Paul Dirac, and others. Eddington deploys the prior Newtonian physics for background and contrast, and most of the present book is devoted to introducing readers to the great, and still unfolding story of the revolutions in physics which took place in the opening decades of the twentieth century. Eddington, an English astronomer and physicist, did distinguished scientific work in astrophysics, and he was also the first major expositor of Einstein’s work in the English language. 1 Partly because The Nature of the Physical World (1928) did so much to introduce innovations in physics to the general, educated readers of the English-speaking world, the present book repays critical attention. In some degree, Eddington has entered into our ways of thought. His writings entered philosophical discussions and debates of his own time and have left an influence on subsequent philosophy. The emphasis in the present edition will be to understand and critically evaluate Eddington’s philosophy. There will be much history of physics and astronomy along the way. Eddington was concerned with more than physics, mathematics and astronomy. Particularly in his popular, expository books—the present volume is the most famous of them—he sketches a philosophy of science and of religion and makes suggestions for epistemology which have engaged the popular mind, and many in philosophy as well, over generations. His philosophical themes in the present book were developed further in subsequent writings, including New Pathways of Science (1935) and The Philosophy of Physical Science (1939) and they reach into his later scientific work. Part of what is going on in this more philosophical story turns on Eddington’s critical attention to philosophical themes of the past—chiefly themes developed under the influence of Isaac Newton and Newtonian physics—from the early modern period down to the nineteenth century. He disputes common sense, nineteenth-century mechanistic philosophy and notions of “substance;” and he defends his own alternatives—chiefly cast in terms of abstract “structure.” Eddington also reveals in the present book something of his Quaker religious background, and this enters into the philosophical themes of the book—Eddington’s philosophy of mind and religion. In his 1929 Swarthmore lecture given at Britain’s Quaker Yearly Meeting, and published with the title 

This is the Introduction to my 2014, annotated edition of Arthur S. Eddington, The Nature of the Physical World. Newcastle: Cambridge Scholars Publishing, pp. xi-xlix. Some reference is made in the following footnotes to pages in the printed text. 1. See, especially A.S. Eddington (1924) The Mathematical Theory of Relativity. Second ed. Cambridge: Cambridge University Press.

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Science and the Unseen World (1929), he declared that the significance of the world could not be uncovered in science; instead, “we have to build the spiritual world out of symbols taken from our own personality, as we build the scientific world out of the symbols of the mathematician.”2 He sponsors too, in the present book, his thesis of “selective subjectivism,” which will be a subject of criticism below. That thesis, in turn, is closely related to Eddington’s theme of “structure;” and scientific structuralisms have been highly esteemed.

1. Scientific career Eddington was a much honored British astrophysicist of the first half of the twentieth century. He has been called “the most distinguished astrophysicist of his time”3—not without good reason. Following his education at Owens College, Manchester, and Trinity College, Cambridge, where he received high honors and demonstrated very considerable mathematical talent and ability, he became chief assistant at the Royal Observatory at Greenwich (1906-1913). At Greenwich, he gained practical experience in astronomy and studied stellar motions and the structure of the Milky Way. In his early book, Stellar Movements and the Structure of the Universe (1914) he suggested the hypothesis that the spiral nebulae, long known, though conflated with glowing clouds of gas and dust, are galaxies, “island universes,” in the phrase of those times—stellar structures of the magnitude and character of the Milky Way.4 In 1913 Eddington was appointed Plumian Professor of Astronomy at Cambridge, and in 1914 he became Director of the Cambridge Observatory. By the end of his career, he was widely esteemed and had received honorary degrees from many universities. He was elected president of the Royal Astronomical Society (1921-1923), and subsequently elected President of the Physical Society (1930-1932), the Mathematical Association (1932), and the International Astronomical Union (1938-1944). Eddington was knighted in 1930 and received the Order of Merit in 1938. During the 1930s, his popular and more philosophical books made him a well known figure to the general public.5 When war broke out in 1914, Eddington declared himself a pacifist on grounds of religious conscience. This eventually caused him serious complications with the authorities, but did not inhibit development of his career. He claimed the status of a conscientious objector to war—at considerable personal and professional risk—but in contrast with many others objecting to the war, he was substantially protected, first by Cambridge University and later by the intervention of his Greenwich colleague, Frank W. Dyson, the Astronomer Royal of England.6 Though German publications were not generally available in Great Britain during the 1914-1918 war, Eddington was able to keep in touch with developments in Germany through the Netherlands, which remained neutral; and it is believed that he received a copy of Einstein’s 1916 paper on general relativity from the Dutch physicist Willem de Sitter. De Sitter published on relativity, Einstein and astronomy in Great Britain, during the war, while Eddington was Secretary of the Royal Astronomical Society. 7 Einstein’s famous paper,8 and his new physics, would change the direction and character of Eddington’s work in fundamental ways. 2. Eddington (1929) Science and the Unseen World, reprinted in Volker Heine ed. (2013) A.S. Eddington and the Unity of Knowledge, p. 28.

3. See Subrahmanyan Chandrasekhar (1983) Eddington. 4. See Eddington, below, p. 169. 5. An account of Eddington’s life is available in Allie Vibert Douglas (1956) The Life of Arthur Stanley Eddington. See also Matthew Stanley (2007) Practical Mystic: Religion, Science and A.S. Eddington, which focuses on the relationship between Eddington’s scientific work and his Quaker religious background. 6. Frank Watson Dyson (1868-1939), son of a Baptist Minister and life-long non-conformist, was appointed Astronomer Royal of Scotland in 1905 and afterward Astronomer Royal of England (1910-1933). Dyson arranged for Eddington’s participation in the 1919 eclipse expedition. See the account of Eddington’s pacifism and exemptions from conscription in Stanley (2007) Practical Mystic, pp. 124-152. 7. See McCrea (1979) “Einstein: Relations with the Royal Astronomical Society,” p. 253. 8. Albert Einstein (1916) “The Foundation of the General Theory of Relativity.”

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In 1918, Eddington published his Report on the Relativity Theory of Gravitation. This was followed by two further books devoted to relativity, culminating in The Mathematical Theory of Relativity (1923). In 1919 he led a famous expedition to the island of Pr†ncipe off the west-African coast, and made observations credited with confirming Einstein’s quantitative prediction of the gravitational curvature of the path of star-light in the vicinity of the sun during an eclipse. Eddington became a recognized expert on Einstein’s new physics, and Einstein himself became a world-wide scientific and popular celebrity. Eddington later emphasized the influence of Einstein on his philosophical thought as well. It was only with his book of 1926, The Internal Constitution of the Stars and 1927, Stars and Atoms, that Eddington more fully returned to focus on prior astrophysical themes and studies—and to threads of his work started before his encounter with Einstein and general relativity. His astrophysical work was now to be informed by Einstein’s physics. In his lecture, The Expanding Universe (1933) he came to terms with the work of Edwin Hubble. 9 Eddington did astrophysical work on the Cepheid variable stars early on—stars having regular, periodic patterns of variation in their brightness. Since the intrinsic brightness or luminosity (apparent brightness, corrected for distance) of the classic Cepheid variable stars correlates empirically with their periods of variation, and because it was possible to directly determine the distances of the closer Cepheids, by parallax, this provided a means of determining the distances of very faint Cepheids and associated objects—from observational data on their variations. The classical Cepheids exhibit a correlation between period and luminosity. The longer the period of variation in luminosity of the star, the greater its intrinsic brightness. Though it was later discovered that an important sub-class of Cepheids are not bound by this relationship, the Cepheids were of great interest because they provided a range of “standard candles,” allowing the observational determination of astronomical distances to remote stars and galaxies.10 Eddington’s work on the topic brought him to the general problem of explaining stellar luminosity in terms of internal processes. Direct observation of the interior processes of stars is not possible, but Eddington emphasized that it is possible to understand internal stellar processes based on two pillars of observational evidence— and established physical theory—, mass or gravitation and luminosity or output of radiation. Eddington starts from what is observable and uses the related results as crucial constraints on his development of theory. Both the mass and the luminosity of selected stars can be calculated from observational data. The theory of stellar interiors must provide predictions open to falsification or confirmation, but the available and accepted accounts of gravitation and radiation, together with details of stellar observations, provide a “structure” of constraint upon Eddington’s theoretical and indirect approach to internal stellar processes. The suspicion was afoot, even in the 1920s, that the enormous radiation output of stars depends on thermonuclear processes in the stellar interior, thought the relevant laws of nuclear physics were almost complete unknown at the time. 11 Familiar as he was with Einstein’s E = mc2, Eddington was favorable to the idea that hydrogen was being transmuted into heavier elements within the stars, in a process involving conversion of matter into energy. But this point remained speculative in his 1926 book. Eddington begins from the assumption that gas pressure, radiation and gravity typically establish a balance or equilibrium within the stars. Gravity, a function of mass, pulls everything toward the center, while gas and radiation pressure push outward. Eddington’s developed theory works with three variables of pressure, density and temperature, linked together by the perfect gas law. This law states that given a particular quantity of gas, the product of its volume v and pressure p is proportional to the 9. Cf. Eddington’s 1928 comments on Hubble below, p. 171n. 10.Henrietta Leavitt (1868-1921), American astronomer at the Harvard Observatory, had discovered the empirical period-luminosity relationship of the Cepheid variables in 1912.

11. James Chadwick’s discovery of the neutron, which facilitated probing of the atomic nucleus, would not come until 1932, four years subsequent to original publication of the present book; it was not until 1938 that the German-born, American physicist Hans Bethe (1906-2005) proposed the first detailed theory of stellar energy generation based on nuclear fusion.

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absolute temperature t; in the form of an equation, pv = kt, where k is an empirically estimated constant. The surface temperature of a star, in turn, is related to its luminosity. Eddington defended the applicability of the idealized gas law to stellar interiors, against considerable tradition and resistance; and this hypothesis gives his theory genuine predictive power. The overall effect is to explain correlations between stellar mass and luminosity by means of the idealized gas law. The scope of this generalization is limited, however, by extremely dense stars, including the white dwarfs12—which involve a degenerate state of matter. At very high densities, the atoms of these stars are stripped of their electrons, and the increase of density proceeds to the nuclear level. Resistance to further gravitational contraction is then no longer covered by the classical physics of the ideal gas law, and instead partly depends on quantum mechanical phenomenon related to the Pauli exclusion principle. 13 Though much of the relevant nuclear physics was unknown at the time of his work, Eddington’s theory of stellar interiors was successful and reasonably precise—and the basis for much subsequent work. In a 1924 paper, the American astrophysicist, Walter S. Adams,14 credited Eddington with predicting the displacement of the spectral lines of the white dwarf star, Sirius B, and thereby contributing to a new confirmation of Einstein’s theory of gravitation. Adams cited the quantitative prediction in Eddington’s 1924 paper, “On the Relations between Masses and Luminosities of the Stars,”15 and confirmed the prediction by his own observations. The general idea is that the white dwarfs have such high density that their intense gravitation produces a measurable red-shift of their emitted radiation— as though they were moving away from the observer at a relativistic velocity. Concluding his own paper, Adams wrote that “the results may be considered, … as affording direct evidence from stellar spectra for the validity of the third test of the theory of general relativity, and for the remarkable densities predicted by Eddington for the dwarf stars… .”16 In his discussion of the white dwarfs, Eddington had favored high densities, though these where anomalous at the time. Only a very few white dwarfs were known. He had written that the question concerning their density “could probably be settled by measuring the Einstein shift of the spectrum, which should amount to about 20 km. per second, if the high density is correct.”17 While Adams saw his own measurements of the red shift of Sirius B as confirming Einstein on gravitation, via Eddington’s calculated prediction of the red shift, Eddington was more inclined to take relativity for granted and use it to predict measurable consequences of his hypothesis concerning the density of the white dwarfs. The episode demonstrates Eddington’s high standing in his field and the close interrelations of theory and observation. It also demonstrates Eddington’s physical insight in deftly avoiding over generalization of his theory based on the perfect gas law. 18 An episode starting in the early 1930’s connected with the publication of the second edition of Eddington’s book, The Internal Constitution of the Stars, is closely connected with his long resistance to the idea of the final collapse of massive stars into black holes. When Eddington issued the second 12.Eddington (1926) The Internal Constitution of Stars, states, “I do not suppose that the white dwarfs behave like perfect gas.” See p. 174.

13.Electrons are theorized to form a separate “gas” above the degenerate nuclei, and resist further compression by their exclusion from occupying the same quantum state. The Fermi-Dirac statistics together with special relativity allow for precise prediction of the mass-radiation correlations of white dwarfs. See Eddington’s related discussion below, pp. 206-207. 14.Walter S. Adams (1876-1956) was Director of the Mount Wilson Observatory (1923-1946), and he is best known for his spectroscopic studies of stars. See Adams (1924) in the Proceedings of the National Academy of Science, vol. 11, pp. 382-332. 15.Eddington (1924) Monthly Notices of the Royal Astronomical Society, vol. 84, pp. 308-332. 16.Adams (1924), p. 387. 17.Eddington (1924), p. 322. 18.See Leon Mestel (2004) “Arthur Stanley Eddington: Pioneer of Stellar Structure Theory,” for a somewhat technical, contemporary astronomer’s appreciation of Eddington’s theory of stellar interiors and a brief discussion of the connected work of Adams. See also W.H. McCrea (1979) which disputes the validity of the 1924 measurements.

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edition, there was some updating, but he failed to mention Ralph Flower’s important 1926 paper on white dwarf equilibrium, based on the Pauli exclusion principle. But what developed out of the Flower paper was the proposal, by Chandrasekhar among others, that there is a limiting mass, beyond which no cold body (black dwarf, or burned-out white dwarf) could maintain itself against gravitational collapse—and the formation of what is now called a black hole. Just as increasingly dense white dwarfs would have their radiation output increasingly red-shifted, beyond a certain density, the radiation would be shifted completely off the spectrum, which is to say that light, and anything else, could not escape from it. During the 1930s, Eddington stubbornly rejected the idea of the Chandrasekhar limit and final gravitation collapse. The thesis of the inevitable collapse of stars with a mass beyond the limit of about 1.4 solar masses was supported by many famous physicists and astronomers and widely regarded as an implication of the Einstein’s gravitational curving of space-time—a thesis which Eddington himself had done so much to support. But Eddington was not convinced, and in sketching an alternative he held out the prospect of his own innovations in physics—connecting general relativity and quantum mechanics. Eddington was not entirely alone in rejecting the Chandrasekhar limit during the 1930s, and his professional standing and prestige were so great that many supporters of Chandrasekhar were unwilling to take a public stand, though, in the accepted outcome of the debates, Eddington’s arguments failed to sustain his position.19 He appears to have incorrectly favored his own physical speculations against Chandrasekhar’s rather firmer results in mathematical physics.20 Eddington’s later scientific work, from 1928 until his death in 1944, was of a highly theoretical and speculative character. It is continuous with his earlier work on relativity—including, for example, his generalization of Hermann Weyl’s theory of the electromagnetic and gravitational fields.21 Eddington had attempted a geometrical theory of electromagnetism, “so that a yet more comprehensive geometry can be found, in which gravitational and electric fields both have a place.”22 This element of Eddington’s thought lingers in the background of the present book. His emphasis on structure continued from early to late. In his 1921 paper, generalizing on Weyl, he wrote that “any conception of structure (as opposed to substance),” … must be analyzable into a complex of relations and relata, the relata having no structural significance except as the meeting point of several relations, and the relations having no significance except as connecting and ordering the relata.23

This statement of the contrast between “substance” and structure is directly comparable to his treatment of the topics in the present book. 24 The point of Eddington’s criticisms of the conception of “substance” is that he sees his own focus on relations, relata and structure as a needed improvement— one facilitating his own theoretical work. Employing his emphasis on “relation structure” in his later work, Eddington mounted a distinctive, theoretical approach to combining the physics of relativity and quantum mechanics. However, for many, the distance of this late work from experimental and observational results tends to render it excessively speculative.

19.For a detailed account of the issue, see Mestel (2004), pp. 70-71. 20.Chandrasekhar and Flower were awarded the 1983 Nobel Prize in physics for their related work. 21.The German-American mathematician, Hermann Weyl (1885-1955) had been a colleague of Einstein’s at Zurich, before Einstein moved to Berlin in April 1914, and Weyl produced the first attempt at a “unified field theory” uniting electromagnetism and gravitation. For his generalization see Eddington (1921) in the Proceedings of the Royal Society. 22.Eddington (1920) Space, Time and Gravitation, p. 167. Eddington’s early approach to a “unified field theory” will be found in chapter XI, of the 1920 book, pp. 167-179. 23.Eddington (1921), p. 121. 24.Regarding “structure” see Eddington, below, pp. 231-232ff.

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Introduction

In writing the present book, Eddington was following the latest developments in quantum mechanics closely and with considerable interest.25 He was aware of the developments starting from the early contributions of Max Planck, Einstein and Niels Bohr, through the “new quantum theory” of Heisenberg, Schr„dinger and Dirac—though there is no mention of Pauli.26 Max Planck introduced the concept of the quantum (the idea of discrete “atoms” or units of physical action) in 1900, in explanation of black-body radiation; and Einstein’s related work on the photoelectric effect, introducing the photon, appeared in 1905—the same year as his special theory of relativity. Bohr then developed his model of the atom, based in quantum mechanical concepts. In the mid-1920s, the pace of development in quantum mechanics intensified, including Heisenberg’s matrix mechanics, Schr„dinger’s wave mechanics, Paul’s exclusion principle, and culminating with Heisenberg’s uncertainty principle and later, Dirac’s prediction of the positron. Eddington provides below an engaging, and well informed account of the developments, up to the time of publication of the book, though he had been clearly more involved with Einstein and gravitation over the decade of the 1920s. He was sufficiently impressed by the uncertainty principle to reject the determinism of classical physics.27 Eddington came to believe, after publication of his Gifford lectures, that the time was ripe for a structural approach to the combination of relativity and quantum mechanics.28 In the present book, his structural approach aims to encompasses gravity and electromagnetism, but is not extended to quantum mechanics. The aim of encompassing both general relativity and quantum mechanics in a structural approach, however, is the distinctive theme of his late and most speculative writings. His philosophical ideas brought him to the hypothesis that such a theory would make it possible to calculate the values of the physical constants (including the fine-structure constant, the ratio of the gravitational force to the electromagnetic force, the ratio of the masses of the proton to the electron, and even the total number of protons in the universe). This undertaking culminates in Eddington’s Fundamental Theory (1946), published only after his death. His objectives in the final book are reflected, though, in earlier writings, including, Relativity theory of Protons and Electrons (1936) and The Combination of Relativity Theory and Quantum Mechanics (1943). The specifics of Eddington’s calculations of physical constants (those of particular interest are, at best, determined empirically) have generally been greeted with much criticism, skepticism, and even parody. 29 It is worth noting, though, that the editor of Eddington’s Fundamental Theory, the English mathematician, Edmund Whittaker (1873-1956) was an able and sympathetic expositor of Eddington’s late work.30 Overall, it is fair to say that Eddington’s late work has been closely read for its suggestiveness and his characteristic flashes of physical insight. Eddington was a pioneer of subsequent physical thought. The precise relationship of general relativity to quantum theory remains to the present a central, open question of contemporary theoretical physics; and it is now thought to require a theory of

25.See below Eddington’s chapter devoted to “The New Quantum Theory,” and p. 209, in particular: “My chief anxiety at the moment is lest another phase of reinterpretation [of QM] should be reached before the [Gifford] lecture can be delivered.” 26.Wolfgang Pauli was awarded Nobel Prize for Physics in 1945 for his discovery (1925) of the Pauli exclusion principle. 27.See Eddington, below, p. 292. 28.According to the account in C.W. Kilmister (1994) Eddington’s Search for a Fundamental Theory, this development was occasioned by Paul Dirac’s work, relating SR and QM. See Kilmister (1994), pp. 90-94; and Dirac (1928) “The Quantum Theory of the Electron,” Proceedings of the Royal Society London, A117, pp. 610-624. 29.For a contemporary criticism of Eddington’s attempt to calculate physical constants, see John D. Barrow (2002) The Constants of Nature. 30.See e.g., Edmund Whittaker (1951) “Eddington’s Principle in the Philosophy of Science,” reprinted in Heine (2013); but see also the Kilmister (1994) Eddington’s Search for a Fundamental Theory.

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“quantum gravity.”31 Though generally doubting the specifics of Eddington’s calculations, theoretical physics continues to wonder and speculate about the constants.32

2. Selective influence of mind In his concern with theory and the construction and reconstruction of theory, Eddington employs the idea of “world building” extensively.33 An entire chapter of the present book is devoted to the theme; and in his accounts of world building, Eddington places a very considerable emphasis on the selective influence of the mind. On one reading, Eddington’s conception of world building may be understood as a formal, mathematical exercise, or preparation, making explicit the particular language and interpretation of vocabulary to be used in a formalized physical theory. However, Eddington’s “world building” does not explicitly (i.e., meta-linguistically) address the language of physics. It lacks the rigor of later philosophical structuralisms and of formal semantics. Still, Eddington saw himself as close to Bertrand Russell’s theme of structure in The Analysis of Matter (1927).34 Again, in some contrast, his talk of world building might be viewed as a useful metaphor, taken up to facilitate his proposals in the popular presentation of physics. In that light, it unhappily contrasts, by its vagueness, with the alternative of explicitly addressing theory, interpretation and model construction. It is also possible to read Eddington literally, i.e., as an idealist, maintaining that the “world” of physics is literally a creation of the human mind.35 No doubt, human beings have designed and developed our theories in physics and the required concepts. We do so in pursuit of statable and even for debatable purposes. But there is no clear and plausible sense in which this might reasonably be considered a literal matter of “building” or construction of the physical world. Least of all is such a conclusion supported by results of physics alone. We have a task before us, according to Eddington: “We are going to build a World—a physical world which will give a shadow performance of the drama enacted in the world of experience.”36 The language of the “shadow performance,” here is so distinctively Eddington’s own that it is difficult not to take him at his word on the dependence of the physical world on the human mind. However that may be, there is a definite and distinctively nominalistic theme in Eddington’s notions of world building and the selective influence of mind. This nominalistic theme is intimately related to Eddington’s epistemology and his theory of mind. They are worth some examination in the present context. Eddington maintains, in the present volume that “…the laws which we have hitherto regarded as the most typical natural laws are of the nature of truisms, and the ultimate controlling laws of the basal structure (if there are any) are likely to be of a different type from any yet conceived.”37 The interpretation that is most natural here is that for Eddington, “the mind” selects particular systems of “relations and relata,” in the process of world building, so as to include particular laws of nature

31.See e.g., Carlo Rovelli (2001) “Quantum spacetime: What do we know?” and Rovelli (2008) for a brief overview of contemporary theoretical alternatives.

32.See e.g., Steven Weinberg (1993) The First Three Minuets, p. 187. 33.See Chapter XI, below, pp. 231-246. 34.See in particular, Bertrand Russell (1927), p. 226; and the discussion in Steven French (2003), p. 236. 35.See Eddington (1920) “The Meaning of Matter and the Laws of Nature According to the Theory of Relativity,” Mind, 29, 114, p. 145: “…it is the mind which from the crude substratum constructs the familiar picture of a substantial world around us;” p. 153: “According to this view matter can scarcely be said to exist apart from mind.” See also Eddington, below, e.g., p. 327, “…the world-stuff behind the pointer readings [of physics] is of nature continuous with the mind;” and p. 274, “The realistic matter and fields of force of former physical theory are altogether irrelevant—except in so far as the mind-stuff has itself spun these imaginings.” 36.Eddington, below, p. 231. 37.Eddington, below, p. 244.

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within the mathematical structure, so generated; and within the favored structure, the implicated laws are simply true by stipulation. 38 However, Eddington’s idea seems to conflict with attributing empirical status to the laws of nature; and this, no doubt, will strike many readers as strange. Einstein’s introduction of the principle of relativity into physics, after all (given the empirical finding of the constancy of the velocity of light, independent of the choice of frames of reference), is plausibly regarded as requiring that the laws of physics turn out the same independent of the particularities of frames of reference. My point is to emphasize the empirical motivation of the selection of a mathematical system for representation of the laws of nature—a kind of point which Eddington often fails to emphasize sufficiently. In his talk of world building, he appears to confuse the “analytical” selection of conceptual materials for theory construction with an imposition of concepts and laws on a neutral or indifferent world. There can be good judgment of better and worse in our related “world building,” i.e., the selection of elements for theory construction. This is not to say that available evidence completely determines choice of theoretical system and related concepts. That would be an absurdly strong anti-nominalism—leaving no prospect of further or conflicting empirical evidence. Still, what is today merely theorized and postulated may tomorrow be tested and confirmed or rejected. Eddington seems to conflate with his term “world building” the mathematical formalization of existing theory, or theoretical constraint on proposed theory, with the postulation (or the mind’s dictation) of constraints on theory and the future development of physical theory. This nominalism contributes significantly to the highly speculative character of Eddington’s later thought. According to Eddington, “the mind has by its selective power fitted the processes of Nature into a frame of law of a pattern largely of its own choosing; and in the discovery of this system of law the mind may be regarded as regaining from Nature that which the mind has put into Nature.”39 But this is to over-emphasize the role of theory and theorizing in relation to testing, experimentation and the accepted results of the scientific enterprise. Though scientists may reasonably select a prospective direction of the development of theory, new proposals are also bound by the past success of theory in accounting for empirical evidence. Even the most revolutionary theory has its conservative side. Surely, no one would have given Einstein’s new physics a second thought, if it had not adequately taken in the massive evidence supporting prior Newtonian physics—and had it not added new predictions as well. Science can freely choose a direction of development for theory, postulated law and concepts, only as hypothesis—or, rather, there is normally a diversity or pluralism of competing approaches; but the success of theory in testing depends on our inability to “put into nature,” that which is not confirm in continued testing. (Both the proponents of Einstein’s theory and those more skeptical can make the observations which confirmed Einstein’s theory.) In physics, as elsewhere in science, many theories and proposals are vetted and detailed, but only a few are continually confirmed and called into established and accepted status. Eddington will also be found below to emphasize values and the value of permanence in particular, in his arguments and in his conception of the selectivity of mind. “The element of permanence in the physical world,” he writes, “ … familiarly represented by the conception of substance, is essentially a contribution of the mind to the plan of building or selection.”40 But even here, the character of needed and reasonable replies is not essentially different. In his criticism of “substance,” Eddington chiefly has in mind the notion of impenetrable, “billiard-ball” atoms, and he tends to ignore the correlated cognitive function of categorical system. No one doubts that constellations of existing human values effect our relationships to nature and to other human beings, and this is not a matter to be settled without regard to those relationships. In particular, it seems completely unreasonable to suppose that arbitrary choice of values would be viable 38.Cf. Eddington, below, p. 148: “The whole thing is a vicious circle. The law of gravitation is—a put-up job.” 39.Eddington, below, p. 244. 40.Eddington, below, p. 242.

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in practice or suit human life and the purposes which human values serve. On the contrary, arbitrary choice of values, or over-emphasis on particular values, is the typical object of criticism when we consider the all too frequent, bad turns of human history. Something of crucial importance is typically ignored if values are selected arbitrarily. For, what does “arbitrary” choice mean, when employed in criticism, if not choice without sufficient grounds and consideration? This argument can be brought into contact with Eddington’s emphasis on the scientific value of “permanence” in theory choice, or the value which mind places upon the permanent. After we have noticed the scientific preference for concepts and laws which better stand the tests of time and further evidence, then the question remains as to better and worse in the cognitive selectivity of consciousness or mind. The mere fact of selective attention does not imply anything about the cognitive value of particular selections, though in nominalistic style, Eddington tends to equate selectivity of attention with arbitrary imposition. No doubt, selective attention can be as arbitrary and unfounded as any onesided human activity, but this does not show that all selectivity is arbitrary. Again, it does not show that preference for permanence can have no justification —as with the various conservation laws. Concern with permanence seems clearly an implication of the need and continued stress on confirmation by empirical tests; but this can not be plausibly understood as an imposition on, or dictation to nature.

3. Causation and indeterminacy Writing on cause and effect, Eddington emphasizes the directionality of time: Cause and effect are closely bound up with time’s arrow; the cause must precede the effect. The relativity of time has not obliterated this order. An event Here-Now can only cause events in the cone of absolute future; it can be caused by events in the cone of absolute past; … 41

In contrast to spatial dimensions, on this account, time has not only a measurable extension, it also has a direction: “time’s arrow”— pointing toward the future and away from the past. Part of the point of this short quoted passage, focused on the common-sense conception of cause and effect, is that the directionality of time is not disrupted by Einstein’s account of the interrelation of space and time. Though judgments of simultaneity may differ, depending on the relations of differing frames of reference, still, as the point is usually put in terms of “light cones” (which define the sphere of cause and effect for a particular event), the paths of light toward an event define the sphere of causal influences on it, and the paths of light, moving away from it define the sphere of its future causal influence— since it is generally conceded that no causal influence can propagate faster than the speed of light. Given Einstein, we can still make sense of the arrow of time. In a now classical chapter on “The Running-Down of the Universe,” Eddington emphasizes the relationship of time’s arrow to the second law of thermodynamics. The idea, simply put, is that in any physical process in a closed system (closed, so that new organization does not enter), entropy, a measure of disorder, tends to increase (it at best remains the same), and it never decreases. This fact may be regarded as indicating the direction of time. In a typical example, we are invited to consider a glass of water sitting on the edge of a table. The glass falls to the floor and shatters into enumerable shards, the water disperses across the floor. Such events are a common-place of human experience, though we never observe the exact opposite, where water and glass shards collect themselves together, assemble into a glass of water and ascend to sit on the edge of the table. We could film the fall of the glass and afterward run the film backward, but we would know that the film is running backward, if we see the glass of water self-assemble and ascent to the table. There is a very significant irreversibility of time in human experience; and our ordinary concept of cause and effect takes this into account. It is all the more interesting, therefore, that subsequent to the above quoted passage, and Eddington’s brief explanation of the concepts of cause and effect, he immediately turns to consider a scien-

41.Eddington, below, p. 293.

10

Introduction

tific alternative to the ordinary conception of cause and effect. “This elementary notion of cause and effect,” he says, “is quite inconsistent with a strictly causal scheme.” How can I cause an event in the absolute future, if the future was predetermined before I was born? The notion evidently implies that something may be born into the world at the instant Here-Now, which has an influence extending throughout the future cone but no corresponding linkage to the cone of absolute past. The primary laws of physics do not provide for any such one-way linkage; any alteration in a prescribed state of the world implies alterations in its past state symmetrical with the alterations in its future state. Thus in primary physics, which knows nothing of time’s arrow, there is no discrimination of cause and effect; but events are connected by a symmetrical causal relation which is the same viewed from either end.42

The crucial examples of what Eddington here calls “the primary laws of physics,” are Newtonian mechanics and gravity, and Einstein’s replacements for Newtonian mechanics—including his geometrical account of gravitation. While the ordinary concept of cause and effect is asymmetrical, observing time’s arrow, the relationships of events in “primary physical law,” are symmetrical, and equally applicable in either direction of time. For example, if we could determine the final positions and momentum of each shard of glass and atom of water from our broken glass, then the Newtonian laws would enable us to “retro-dict,” its original physical condition before the fall from the table. Much the same goes for Einstein’s revisions of Newton. Given the positions and momentum of the sun, moon and earth at the time of an eclipse, say, it would be possible to calculate the conditions at any earlier point in time. Eddington helps us pose the question of whether such an asymmetrical conception of causal relations will ultimately prove viable as a replacement for the ordinary concept of cause and effect. He ties the question to both the second law of thermodynamics and to the relationship between general relativity and quantum mechanics, since both quantum mechanics and the second law are statistical or probabilistic in character. A key element of what Eddington terms “secondary physics” is closely connected with entropy and the second law of thermodynamics. He explains the distinction as follows: Some things never happen in the physical world because they are impossible; others because they are too improbable. The laws which forbid the first are the primary laws; the laws which forbid the second are the secondary laws. It has been the conviction of nearly all physicists that at the root of everything there is a complete scheme of primary law governing the career of every particle or constituent of the world with an iron determinism. This primary scheme is all-sufficing, for, since it fixes the history of every constituent of the world, it fixes the whole world-history.43

But Eddington is not convinced of this “iron determinism,” of the “primary laws.” He is partly telling the story of nineteenth-century Newtonian physics—and this rigid determinism belongs to that history. “The question whether the second law of thermodynamics and other statistical laws are mathematical deductions from the primary laws, presenting their results in a conveniently usable form,” he writes, “is difficult to answer; but I think it is generally considered that there is an unbridgeable hiatus.”44 His deeper suspicion is that all the laws once regarded as primary are really statistical in character.45 “In recent times some of the greatest triumphs of physical prediction have been furnished by admittedly statistical laws,” he writes; “moreover the great laws hitherto accepted as causal appear on minuter examination to be of statistical character.”46 These “greatest triumphs of physical prediction” are the accomplishments of quantum theory, and in the present book, Eddington is much inclined to take quantum indeterminacy at face value. His argument for this is forceful and follows the pattern of argument in Heisenberg and Born.

42.Eddington, below, p. 293-294. 43.Eddington, below, p. 85. 44.Eddington, below, p. 86. 45.See Eddington, below, p. 105. 46.Eddington, below, p. 296.

A.S. Eddington, Physics and Philosophy

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He draws support for, and interprets, the Heisenberg uncertainty principle, by analogy with the rejection of the idea of (absolute) motion through the Maxwellian aether. Eddington is convinced of Bohr’s “correspondence principle”: “The classical laws are the limit to which the quantum laws tend when states of very high quantum number are concerned.”47 Similar points are sometimes put by the claim that classical laws “emerge” from quantum mechanical phenomena or, more recently, that a developed theory of quantum gravity will have to yield Einstein’s laws as a limit or special case—just as Newton’s laws can be regarded as a special, limit case of Einstein’s. Eddington had come to see Heisenberg’s uncertainty principle as an innovation equal in significance to the principle of relativity: The conditions of our exploration of the secrets of Nature are such that the more we bring to light the secret of position the more the secret of velocity is hidden. They are like the old man and woman in the weather-glass; as one comes out of one door, the other retires behind the other door. When we encounter unexpected obstacles in finding out something which we wish to know, there are two possible courses to take. It may be that the right course is to treat the obstacle as a spur to further efforts; but there is a second possibility—that we have been trying to find something which does not exist. You will remember that that was how the relativity theory accounted for the apparent concealment of our velocity through the aether.48

The passage shows the influence of Einstein on Eddington’s epistemological thought. What’s good for the goose of relativity is also good for the gander of QM. Just as Einstein’s theory accounts for the fact that the speed of light is constant, independent of frames of reference, by rejecting the Maxwellian aether, Eddington accounts for the uncertainty of specific measurements in quantum mechanics by postulation of physically objective randomness or indeterminacy. Looking for “hidden variables,” one might say, amounts to looking for something that is not there to find. Eddington’s interpretation on this point substantially anticipates the predominant, present-day view of the matter.49 Determinism (and its theological correlate of predestination) are very old ideas, and there has certainly been some tendency to hold them dogmatically. It is worth asking, then, what would count as evidence against the determinism of classical physics—and exactly what is meant by determinism. A fundamental concept in quantum mechanics is that of randomness, or indeterminacy. In general, the theory predicts only the probability of a certain result. The predicted statistical distributions of measured results over time support the generalizations of quantum mechanics with great precision, but there is no predicting the specifics of results in the overall distributions. The formalism of QM, or its up-dates in quantum field theory, cast in terms of the uniform evolution of the wave function, is deterministic, a deterministic formalism of the uniform evolution of probabilities, equally applicable backward or forward in time. Yet all the evidence consists of particular measurements, and the specifics of each such measurement are left without full prediction. Instead each represents, as it is sometimes put, “the collapse of the wave function.” Consider the QM account of radioactive decay. We have a collection of identical atoms with identical nuclei, the nuclei are somewhat unstable and subject to decay. When they do break down they emit a particle (say an α particle, identical to the nucleus of the helium atom). Over a specified period of time, a certain fraction of the atoms will breakdown. Quantum theory tells us, quite exactly, for a given unstable isotope, what that fraction will be; but it cannot predict the decay of a particular nucleus. All the nuclei are in an identical state at the start, but the sequence of decay of the nuclei is completely random and unpredictable. Are there some additional factors or conditions which would explain and predict the exact sequence of decay? That is the question of “hidden variables,” and the

47.Eddington, below, p. 197. 48.Eddington, below, p. 222. Compare the account of Heisenberg’s arguments with Einstein in A. Douglas Stone (2013) Einstein and the Quantum, pp. 277-278.

49.Cf. Max Born’s Nobel Prize lecture, (1954) “The Statistical Interpretation of Quantum Mechanics.” Writing of Heisenberg’s 1927 paper, he says, “It was through this paper that the revolutionary character of the new conception became clear. It showed that…the determinism of classical physics must be abandoned… ,” p. 262.

12

Introduction

attempts to “complete” quantum theory by the assumption of hidden variables have produced no compelling evidence. The indeterminism of quantum theory supports Eddington’s emphasis on time’s arrow, and consequently his emphasis on “becoming,”50 because it strongly suggest that deterministic or non-statistical theories in physics, those not keyed to the direction of time in some fashion, are approximations. “My intuition,” says Eddington, “is that the future is able to bring forth deciding factors which are not secretly hidden in the past.”51 Commenting on the status of such “intuition,” which may also be regarded as a matter of physical insight, or general hypothesis, Eddington says, “It is fair to assume the trustworthiness of this intuition in answering an argument which appeals to intuition;” though “the assumption would beg the question if we were urging the argument independently.” As against the intuition of an Einstein, say, favoring universal, symmetrical determinism, and that God “does not play dice,” in the present book Eddington takes his clue from quantum mechanics.

4. Mysticism, mind and values Eddington’s mysticism and his defense of it turn partly on a rejection of all-encompassing materialism. The rejection of all-encompassing materialism, I suppose, is supported by common sense and the pluralism of the sciences and scholarly disciplines. It is the same world we encounter in physics, and in biology or in our social discourse and interaction, though, in contrast to proposals for materialist reduction, we do not understand in all detail, the relationships of these various domains; the objects of biology are physical, we naturally suppose, though theory and explanation in biology are not part of the science of physics. The weakness of Eddington’s position, in contrast, is a reflection of the narrowness of the alternative to materialism he puts forward. There is a dualism, or quasi-Cartesian theme in Eddington’s thought which—though at one time fairly common—many, post Wittgenstein, will surely reject. Consider, for instance, his account of our awareness of space and time in Chapter III. He maintains that our knowledge of spatial relations is indirect, a matter of “inference and interpretation,” but knowledge of time is attributed a quite different status. Space is evident from sense experience, and “We have similar indirect knowledge of the time-relations existing between the events in the world outside us;” but in addition we have direct experience of the time-relations that we ourselves are traversing—a knowledge of time not coming through external sense-organs, but taking a short cut into our consciousness. When I close my eyes and retreat into my inner mind, I feel myself enduring. I do not feel myself extensive.52

Though Eddington does not, in the end, maintain a strict, Cartesian, mind-body dualism, the view here reflects a Cartesian or quasi-Cartesian conception of knowledge of the self or mind. It can surely be objected that we have just as much a “feeling” of our own spatial extension, say, if we close our eyes and focus on the arms or legs extended. What it would mean exactly, to insist on Eddington’s suggestion of retreating into the “inner mind” remains somewhat unclear, except that it calls on us to ignore the relevance of our intimate awareness of the positions of our limbs. Perhaps Eddington’s point just amounts to the claim that we are aware of temporal sequence and duration of our thoughts and reflections. Certainly, there is no reason to doubt that idea. But on the other hand, it remains plausible to insist that this awareness is not so “direct” as Eddington has it, but is instead, as with all knowledge—mediated through language—it involves an element of interpretation—since we express it as a matter of “time,” “sequence” and “duration.” It is, after all, possible to formulate alternative accounts of the meanings of these words and their proper application. The deeper problem, however, is not simply Eddington’s conception of the “direct” knowledge of mind, though 50.See Eddington, below, Chapter v. 51.Eddington, below, p. 299. 52.Eddington, below, p. 61.

A.S. Eddington, Physics and Philosophy

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this has its import; his contrasting conception of the “indirect and interpretive” character of physics is also problematic—involving, as it does, Eddington’s overly nominalistic themes and theses. The unhappy predominant tendency is to equate selectivity and interpretation with arbitrary selectivity and forced or imposed interpretation. “A defense of the mystic might run something like this,” says Eddington—in his most explicit treatment of the theme: We have acknowledged that the entities of physics can from their very nature form only a partial aspect of the reality. How are we to deal with the other part? It cannot be said that that other part concerns us less than the physical entities. Feelings, purpose, values, make up our consciousness as much as sense-impressions. We follow up the sense-impressions and find that they lead into an external world discussed by science; we follow up the other elements of our being and find that they lead—not into a world of space and time, but surely somewhere.53

If the “entities of physics” are said to form “only a partial aspect of reality,” then the reader might reasonably expect to find at this point some discussion of other, or additional aspects, e.g., those attended to by common sense, the other sciences, such as chemistry, biology, sociology, psychology, linguistics, etc.—and beyond to the concerns of the scholarly disciplines including history, literature, the arts and others. But the working assumption here is that there is only physics, “a world of space and time” and “the other part” of reality, “not a world of space and time.” This dualistic division of reality appears to be the very root of Eddington’s mysticism. The natural counter-position is to emphasize the factual pluralism of the sciences and scholarly disciplines and the wider realms of knowledge and discourse. No doubt, “Feelings, purpose, values, make up our consciousness as much as senseimpressions.” But feeling, purpose and values are not matters most productively pursued in an exclusively internal process of reflection. Eddington acknowledges that his two worlds or aspects of reality, the physical world and the world of consciousness, are not totally distinct. He cannot be accused of sponsoring a two substance conception, in the style of Descartes. A rejection of any concept of substance belongs to Eddington’s emphasis on structure—and to his frequent denigrations of common sense. Addressing philosophical materialism, he says, “If you take the view that the whole of consciousness is reflected in the dance of electrons in the brain, so that each emotion is a separate figure of the dance, then all features of consciousness alike lead into the external world of physics.”54 But I assume that you have followed me in rejecting this view, and that you agree that consciousness as a whole is greater than those quasi-metrical aspects of it which are abstracted to compose the physical brain.55

Eddington appears to avoid a more thorough-going dualism of the physical vs. consciousness by a hair, congruent with his long quotation from Bertrand Russell’s (1927) Analysis of Matter,56 since consciousness, “as a whole” does have “quasi-metrical aspects,” in our accounts of the brain. Again, the limitations of Eddington’s mysticism are not located in a dualism of substances, but in a poverty of his conception of consciousness or mind as the “other” aspect of reality beyond the physical. This is clear a sign of the inwardness of the man.57 A recent book provides a limited defense of Eddington’s mysticism and connects it with his Quaker background and with the late Victorian “Quaker Renaissance.”58 According to this view, we are to understand Eddington’s mysticism primarily in terms of a renewal of liberal Quaker emphasis on spiritual “seeking,” as this contrasts with adherence to dogmatic theology, and also in terms of the 53.Eddington, below, p. 319. 54.Eddington, below, pp.. 319-320. 55.Eddington, below, p. 320. 56.Eddington, below, pp. 2276-277. 57.Cf. James R. Newman (1961) “Arthur S. Eddington,” p. 285. Eddington was, Newman says, a “solitary, inward bachelor.” In McCrea (1979), Eddington is “the shyest of men.”

58.See Stanley (2007) Practical Mystic.

14

Introduction

Quaker doctrines of the “inner light” and “continuous revelation.” Eddington was, of course born into a Quaker background, and he was a devoted pacifist and life-long member of the denomination. The idea of being a religious “seeker,” as contrasted with confessions of dogmatic faith, is indeed, a common motif which appears repeatedly among the more liberal minded in many denominations deriving from the Reformation. The distinctively Quaker doctrines of the “inner light” and “continuous revelation” are also closely connected with Quaker practices. In its traditional form, the Quakers, calling themselves the “Society of Friends” come together at their Meeting House, and their services proceed without need of paid, professional clergy. They sit, facing one another on long benches and wait in silence. The idea is that the holy spirit may speak through anyone, on any occasion, so that “revelation” may be continuous, among those who attend sufficiently to the “inner light.” On occasion, a member will stand and speak, or the entire hour’s meeting will sometimes remain entirely silent. The argument, briefly put, is that Eddington was greatly influenced by the modernization of the Quaker denomination in the later Victorian period, when they gave up their traditional, distinctive denominational garb, and entered more fully into the modern world. This included the application of religious values to secular pursuits, which, according to this defense of Eddington’s mysticism, required interpretation of the ideals of the anti-dogmatic religious seeker in relation to the pursuit of truth in science. Eddington was a “seeker” both in religion and in physics and astrophysics. He will be found to say in the present volume that, In the mystic sense of the creation around us, in the expression of art, in a yearning towards God, the soul grows upward and finds the fulfillment of something implanted in its nature. The sanction for this development is within us, a striving born with our consciousness or an Inner Light proceeding from a greater power than ours. Science can scarcely question this sanction, for the pursuit of science springs from a striving which the mind is impelled to follow, a questioning that will not be suppressed.59

The problem of Eddington’s mysticism is not so much that he was a non-dogmatic seeker, but that his “seeking” was so narrowly focused as to suggest willful avoidance; and less narrow “seeking,” deployed amongst the pluralism of sciences, disciplines and forms of discourse, will not plausibly remain a variety of mysticism. It is as though Eddington would seek the “inner light” in the Quaker meeting, and among the astrophysicists, but not otherwise. Notice, too, that there are limits to Eddington’s seeking both in regard to values and in physics. The first is connected with the Quakers’ principled pacifism and the corollary of internationalism. My point is not to criticize these positions, but to emphasize their constancy. Regarding physics, Eddington’s limitation is illustrated in the present book, first by the theory of relativity and secondly by quantum mechanics. “You are seeking a frame of space which you call the right frame. In what does its rightness consist?”60 There is no correct answer to the question of which frame of reference is the correct frame—for physical questions and problems. The laws of physics turn out the same for all frames. Likewise, there is no correct answer concerning two arbitrarily selected events whether they take place at the same time or not, since Einstein’s work does away with the Newtonian concept of absolute simultaneity. We rightly stop asking common-sense questions which presuppose universal, simultaneous moments.61 Similarly, in discussion of the position and energy of a particle in quantum mechanics, Eddington says, In seeking to make the position of the particle more definite by reducing the area we make its energy more vague by dispersing the frequencies of the waves. So our particle can never have simultaneously a perfectly definite position and a perfectly definite energy; it always has a vagueness of one kind or the other unbefitting a classical particle.62

59.Eddington, below, pp. 323-324. 60.Eddington, below, p. 31. 61.See Eddington, below, p. 59. 62.Eddington, below, p. 219.

A.S. Eddington, Physics and Philosophy

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In Eddington’s account of physics, he rejects a variety of questions reasonably posed by common sense and prior theory. It may justly be said that part of the grounds of the acceptability of particular theories is that they promise fruitful extensions and an expanded basis for further research. Still, the promise of fruitfulness is a secondary element of established physics, in comparison to the capability of theory to encompass and explain the data—found in relation to empirical tests and experimentation. It is not that the positions Eddington adopts, allowing the exclusion of questions, and an end to seeking in respect to them, are intrinsically dogmatic. We rightly give up certain questions, say, according to quantum mechanics, those regarding the simultaneous position and energy of a subatomic particle. The point, in the rejection of dogmatism, is the need of emphasis on the difference between accepted theory and results, and further, connected speculations and possible hypotheses. Accepting particular theories often implies giving up questions posed by alternatives, but acceptability of particular theories remains undogmatic so long as this stance is open to further evidence. As a general point, though religious seeking may generalize to truth seeking, it seems clear that mysticism is no proper justification of scientific inquiry; and Eddington’s mysticism, as connected with his views of mind and consciousness, may reasonably be viewed, not as a result of the value he placed on inquiry, but instead as a consequence of artificial limitations he placed on his own inquiries. Eddington regularly engaged with his fellow Quakers and with his colleagues in astronomy and physics—though the example of Chandrasekhar is sometimes thought to suggest the opposite.63 His accounts of mind and spirit, however, seem bound to an excessively inward, or introspective practice and concept.

Limits of structure Concluding his discussion of the “Downfall of Classical Physics,” in the first chapter, Eddington puts considerable emphasis on the Fitzgerald contraction, posing the point that, “The FitzGerald contraction may seem a little thing to bring the whole structure of classical physics tumbling down.” But few indeed are the experiments contributing to our scientific knowledge which would not be invalidated if our methods of measuring lengths were fundamentally unsound. We now find that there is no guarantee that they are not subject to a systematic kind of error. Worse still we do not know if the error occurs or not, and there is every reason to presume that it is impossible to know.64

The argument is partly a matter of a gradual presentation of related material from recent physics, and the Lorentz transformations are in the offing. But Eddington suggests here something of his focus on “structure.” He does indeed want to say that it is basically the “whole structure of classical [Newtonian] physics” which has come tumbling down, and in the present book, he is concerned to sketch what he sees as an alternative or up-dated structure. The classical structure, according to Eddington, includes the Newtonian conceptions of space and time, and the idea that Nature has her own preferred frame of reference, naively identified with our own habitual standpoint in the universe. Of course, we cannot measure distances without assuming some frame of reference with its own zero point and scale for measurements, but it belongs to Eddington’s point about structure, that the specifics of our frames of reference are no more a part of nature than are our units of inches, feet or meters. We need to use some units in order to make measurements, but as long as the units are employed consistently, measurement is basically indifferent to the units selected. Some choice of units may be more convenient, in relation to a particular problem, say, because calculations are simplified, but in principle any other units could equally be used. Similarly, we need to use some frame of reference or other in order to measure distances and rates of

63.See Mestel (2004), p. 70. Writing of the famous 1935 meeting when Eddington replied to Chandrasekhar: “The Late William McCrea always resisted strongly the widespread judgment that Eddington had acted unethically on that occasion.” 64.Eddington, below, p. 29.

16

Introduction

motion, but in Einstein’s physics, the laws of physics turn out the same regardless of choice of frames of reference. Eddington treats the relativistic FitzGerald contraction as a crucial clue to the needed transformation of our concept of the structure of nature. The solution immediately at hand comes from Einstein. Regarding the diverse possible frames of reference, we come “… to accept them en bloc; so that distance, magnetic force, acceleration, etc., are relative quantities, comparable with other relative quantities already known to us such as direction or velocity.” However, … we must give up certain expectations as to the behavior of these quantities, and certain tacit assumptions which were based on the belief that they are absolute. In particular a law of Nature which seemed simple and appropriate for absolute quantities may be quite inapplicable to relative quantities and therefore require some tinkering. Whilst the structure of our physical knowledge is not much affected, the change in the underlying conceptions is radical.65

We find no problem in the idea that the direction to New York from Boston is different from the direction to New York from Chicago, say, since “direction to x from y” expresses a relation. In a somewhat similar way, Eddington’s point here is that we can also conceive of “distance, magnetic force, acceleration, etc” as things we must measure in relation to particular frames of reference, and that measurements employing different frames can quite reasonably yield different results. Knowing the relationships of differing frames of reference, we can then recover our prior “physical knowledge” but as Eddington puts the matter, “the change in the underlying conceptions is radical.” But notice that Eddington does not always seem to agree with this understanding of the matter, and this is connected with his conception or understanding of what relations are. “The writing-down of lengths for balance sheet purposes is the FitzGerald contraction,” he says, but this claim does not go without qualification: The shortening of the moving rod is true, but it is not really true. It is not a statement about reality (the absolute) but it is a true statement about appearances in our frame of reference.66

At best, this passage represents an extremely unhappy way to say anything which could possibly be true. It invites consideration of old confusions about relational predicates, as contrasted with monadic predicates and the idea, prevalent in early modern philosophy, that relations are somehow unreal, creations of the mind, or that they have a sort of second-class citizenship in the logical realm —in contrast to monadic predicates. The logic of monadic predicates is much older, more widely known and intuitively understood. The logic of relations, in contrast, is a comparatively recent advance,67 and Eddington appears subject to prevalent confusions which the modern logic of relations has alleviated. First off, then, the shortening of a rod in the FitzGerald contraction is not a matter of “appearances” in our frame of reference but instead a matter of measurements, possible measurements or calculations as provided for by special relativity. 68 Avoiding the invited contrast between reality as “the absolute” and some local, parochial appearances, it would be better to flatly say that the contraction is (physically) real in relation to a given frame of reference. This is to say that length, as conceived in special relativity, is not a monadic predicate of the rod, but instead expresses a relation of the rod to a given frame of reference, e.g., that from which or in terms of which the rod is measured. While some physical quantities are invariant, under the Lorentz transformations, length is not. Still, measurements of length are physical measurements, even those conducted in our local frame of reference—however parochial. These few quotations give the reader an opening to problems involved in Eddington’s conception of “structure” and “relation structure;” and he does go on to tell his readers, in some detail, what he means by structure in general terms. It is often helpful to think of this as a matter of constructing a formal mathematical model of a well established theory—though Eddington is not so meticulous. 65.Eddington, below, p. 45. 66.Eddington, below, p. 44. 67.The logic of monadic predicates is rooted in Aristotle. Development of the formal logic of relations is usually attributed to C.S. Peirce’s work in the late 1860s.

68.See Eddington, below, p. 43 and footnote 17.

A.S. Eddington, Physics and Philosophy

17

Again, contemporary concern with “structure” will often emphasize the systematic relations of formal distinctions, or place stress on formal, organizing or organizational aspects of a given topic or subjectmatter. Much of what Eddington says about structure and structures is consistent with this usage. 69 This ordinary usage involves a contrast, say, between “formal distinctions” and less formal distinction, or between “organizing aspects” and things organized. Such distinctions are contextually dependent upon specific applications, the systematic relations of levels of government, say, are one thing, while systematic relations of the structural elements of buildings are something else again. There is no general assurance, in the related usage, that a distinction between structural elements and other elements must be completely firm or that the distinctions are unchanging. Instead the distinctions may come to depend upon constitutional changes, say, or variations in styles of architecture. It is worth asking, then, whether he can really make out a firmer distinction between “structure” and “content”—the usual terms of contrast. There are some grounds to suspect that this kind of distinction is often ensnared in logical confusions.70 Not the least of these is to confuse a purely mathematical formalism with its exemplification by a physical theory. Putting excessive emphasis on structure, Eddington seems to neglect the oft argued point that the difference between abstract, mathematical structure (which many distinct theories might share) and exemplification of mathematical structure by a particular development of physical theory is not itself plausibly open to elucidation in structural terms. Talk of structure first arises in contrast to content, and if afterward the content seems to disappear into the structure, and most concern for empirical standing, too, then something has definitely gone amiss.71 Any excessive emphasis on purely formal aspects will tend toward the speculative, and the concept of a priori knowledge is the traditional home of dogmatism—regarded as intuitively obvious to all those having deeper understanding. Eddington’s concept of “world-structure” is keyed to the invariances of Einstein’s physics. For example, rejecting the Newtonian concept of world-wide instants or moments, we arrive at the alternative concept of light cones, and “we have had a glimpse of the absolute world-structure with its grain diverging and interlacing after the plan of the hour-glass figures.”72 But what is the difference between claiming that the light cones belong to Einstein’s physics and saying that they belong to the (absolute) “world-structure”? Is the “world-structure” something distinct from features of the world, which according to Einstein’s physics, are actually present in the world and which make up part of the content of his physical theory? Structure seems sometimes to be a matter of mathematics and formal theory construction and sometimes a matter of actual physical theory and results expressed in mathematical terms. Eddington can be found, below, to emphasize that though various abstract geometries can be explored by the mathematician, geometry proper, as most relevant to physics, is an experimental science: But it seems to be only in geometry that he [the pure mathematician] has forgotten that there ever was a physical subject of the same name, and even resents the application of the name to anything but his network of abstract mathematics. I do not think it can be disputed that, both etymologically and traditionally, geometry is the science of measurement of the space around us; and however much the mathematical superstructure may now overweigh the observational basis, it is properly speaking an experimental science.73

69.Compare Webster’s. “Structure”: the action of building; something arranged in a definite pattern of organization; manner of construction: makeup; the arrangement of particles or parts in a substance or body, organization of parts as dominated by the general character of the whole; the aggregate of elements of an entity in their relationships to each other. 70.The classical criticism of Eddington on structure can be found in the writings of the British philosopher R. B. Braithwaite (1900-1990). See Braithwaite’s reviews of Eddington in Mind, from 1929 and 1940. 71.This stands out like a sore thumb in Eddington’s late work, The Philosophy of Physical Science (1938), p. 57: “…all the laws of nature that are usually classed as fundamental can be foreseen wholly from epistemological considerations. They correspond to a priori knowledge, and are therefore wholly subjective.” 72.Eddington, below, p. 71. 73.Eddington, below, p. 164.

18

Introduction

Apparently, then, we must distinguish between the geometry of the mathematician, which merely explores the implications of particular axioms and postulates, be they Euclidean or non-Euclidean, and, following Einstein, the physical geometry of “the measurement of space around us.” Physical geometry, as we expect, exemplifies one of the mathematicians’ systems of geometry. If our Einsteinian, physical geometry is experimental and not purely mathematical, then it appears that the geometrical structures involved, such as the light cones mentioned just above, belong to the content of Einstein’s theory and are not purely mathematical-structural. It seems clear, then, that Eddington’s emphasis upon structure, “world building” and the “selective influence of mind,” tend to conflate the analytical process of the formalization of known, or empirically motivated, theory with an arbitrary imposition of mind upon nature. His frequently insightful discussions of the possible future direction of the development of physics are consequently often marred by an over-estimation of the role of theory. We may properly wonder at the constants of nature, for example, though doubtful in the extreme of Eddington’s late derivations of them.

Since the concept of “relation structure” in the present volume is intended to encompass general relativity and not quantum mechanics, the reader may wonder why this limited configuration alone did not bring Eddington to consider a less rigid conception of structure.74 Still, in amongst the philosophical problems of a scientist—a man not trained in philosophy— and temperamentally inclined to over reach his calling, there remain the flashes of insight, for which, and because of which, Eddington’s writings retain a broad interest.

74.The problem is formulated early on, e.g., in Eddington (1920) “The meaning of Matter and the Laws of Nature According to the Laws of Relativity,” in a discussion of “atomicity;” see pp. 156ff.

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