Abstract
The use of the material theory of induction to vindicate a scientist's claims of evidential warrant is illustrated with the cases of Einstein's thermodynamic argument for light quanta of 1905 and his recovery of the anomalous motion of Mercury from general relativity in 1915. In a survey of other accounts of inductive inference applied to these examples, I show that, if it is to succeed, each account must presume the same material facts as the material theory and, in addition, some general principle of inductive inference not invoked by the material theory. Hence these principles are superfluous and the material theory superior in being more parsimonious.
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Notes
For further discussion of this argument and a discussion of its relation to Einstein’s work in statistical physics from this period, see Norton (2006).
This transition is documented in Norton (1992, §16) in the case of Nordström’s theory of gravitation of 1912. In 1914, Nordström could proudly proclaim that “the laws derived [from his theory] for [free] fall and planetary motion are in the best agreement with experience.” In 1917, in an otherwise sympathetic review, Laue derived the same theory’s formula for perihelion motion and noted that it predicted a retardation, not an advance. The blow was severe enough for Laue not even to bother to compute the actual value predicted for Mercury’s perihelion motion, lamenting the “impossibility of explaining its perihelion motion.”
Einstein’s footnote here emphasized the importance of his achievement: “E. Freundlich has recently written a noteworthy paper on the impossibility of satisfactorily explaining the anomalies of Mercury’s motion on the basis of Newtoian theory (Astr. Nachr. 4803, Bd 201. Juni 1915).”
“ohne dass irgendwelche besondere Hypothese zugrunde gelegt werden müsste”
For then one orbit requires 360/(1-0.0000001574)1/2 = 360 + 0.000028332 degrees. Since the Mercurial year lasts 87.97 days, there are 100 x 365.25/87.97 = 415.198 Mercurial years in a century. Over this time the angular excess of 0.000028332 degrees accumulates to 0.000028332 × 3600 × 415 = 42.35 seconds of arc.
The examples are indeterministic physical systems whose complete physical specification fails to provide any physical chances for the different futures admitted by a given present state.
I am grateful to Thomas Kelly to directing my attention to this concern.
This experience stands in direct contradiction with the mythology in the underdetermination thesis literature that scientists are always awash in multiple theories, all fully adequate to the evidence. In practice theorists feel fortunate if they can find even one theory properly responsive to the evidence. For a critique, see Norton (2008a).
Here I share the hesitations of a referee for this journal who pointed out that the esthetics may incline us to acceptance but may not rationally justify the inclination.
The analysis can be recovered directly from Bayes’ theorem as given in (6) in Section 4.3 below. (M3) corresponds to P(H|E) being nearly one. It can fail to have that value in the two ways indicated above. First, (a), it can fail if P(~H) is very much greater than P(H). Second, (b), it can fail if P(E|H) is greater than P(E|~H). Neither loophole obtains in the cases at hand.
The difficulties are well known. If each of A, B, C, … are individually very likely, then, according to a common, tacit presumption, so is their conjunction. This presumption eventually must fail. While each, individual lottery ticket is very unlikely to win, at least one of all the tickets sold must win. Or while I may believe each individual assertion in my magnum opus very likely to be true, I am also convinced that very likely they cannot all be true. See Sorensen (2006, §§3–4).
Glymour (1980, pp. 288–89) balks at fitting the three classic tests of general relativity, one of which is Mercury’s perihelion motion, into his bootstrap framework. In Norton (2005) I included demonstrative induction within this first family as an extreme form. Its application to these two cases is sufficiently important to be reserved for a separate section below.
Another striking difference is that if we isothermally expand a cylinder filled with heat radiation, then more radiation is created to fill the new space. If that radiation consists of quanta, then the expansion creates new quanta. The isothermal expansion of an ideal gas certainly does not create new molecules.
Or perhaps we might construe explanation in the latter case of light quanta only as the revealing of an underlying constitution. It ends up to be pretty much the same, since, from the hypothesis of the constitution of radiation as light quanta, we still deduce the entropy formula (1).
Mayo’s notion of severe testing might also belong here, although her specification of just what counts as a severe test is ahistorical, so it can be applied without recounting the precise history of the test.
For example, the failure of nineteenth century ether drift experiments to detect an ether current is accommodated by the ad hoc hypothesis that we just happen to be at rest in the ether. I urge readers to resist the temptation of dismissing Einstein’s formulation of the light quantum hypothesis as a defective, ad hoc hypothesis, even though it was explicitly designed to accommodate the known entropy properties of heat radiation. The idea was too ingenious for such rude dismissal.
There is also a precedent in legal proceedings, in which the evidential record must be purged of improperly secured evidence.
The other way that P(H|E) can turn out close to one is if P(~H) is very small, that is P(H) is close to one. But that just asserts that we already think H very likely, so the displaying of a correspondingly large P(H|E) is no longer revealing the evidential import of E.
Another example is how Poincaré and Ehrenfest in 1911 and 1912 resolved the problem of assessing how much support the hypothesis of quantum discontinuity accrued from its success at entailing Planck’s distribution law for black body radiation. They showed that, with suitable auxiliaries, the deduction could be inverted. They deduced quantum discontinuity from the evidence of Planck’s distribution law. See Norton (1993).
We could try to mount a demonstrative induction for this case akin to Dorling’s for the case of the light quantum. One possibility is that we could deduce from the perihelion motion of Mercury relevant parameters of the PPN formalism. But these at best fix the weak field behavior of one class of gravitation theory. We are far from a demonstrative induction from Mercury’s perihelion motion to general relativity.
References
Dorling, J. (1971). Einstein’s introduction of photons: argument by analogy or deduction from the phenomena? The British Journal for the Philosophy of Science, 22, 1–8.
Earman, J. (1996). Bayes or bust. Cambridge: Bradford.
Earman, J., & Janssen, M. (1993). Einstein’s Explanation of the motion of mercury’s perihelion. In J. Earman, M. Janssen, & J. D. Norton (Eds.), The attraction of gravitation: New studies in the history of general relativity. Einstein Studies, volume 5 (pp. 129–172). Boston: Birkhäuser.
Einstein, A. (1905). Über einen die Erzeugung and Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik, 17, 132–148. Doc. 14.
Einstein, A. (1915). Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie. Königlich Preussische Akademie der Wissenschaften (Berlin). Sitzungsberichte 831–839.
Glymour, C. (1980). Theory and evidence. Princeton: Princeton University Press.
Howard, D. (1985). Einstein on locality and separability. Studies in History and Philosophy of Science, 16, 171–201.
Howson, C., & Urbach, P. (2006). Scientific reasoning: A Bayesian approach (3rd ed.). Chicago: Open Court.
Lakatos, I. (1970). History of science and its rational reconstruction. In I. Hacking (Ed.), Scientific revolutions (pp. 91–108). Oxford University Press, 1981.
Lewis, D. (1980). A subjectivist’s guide to objective chance. In R. C. Jeffrey (Ed.), Studies in inductive logic and probability (pp. 263–293). Berkeley: University of California Press.
Mayo, D. (1996). Error and the growth of knowledge. Chicago: University of Chicago Press.
Misner, C. W., Thonre, K. S., & Wheeler, J. A. (1973). Gravitation. San Francisco: Freeman.
Norton, J. D. (1984). How Einstein found his field equations: 1912–1915. Historical Studies in the Physical Sciences, 14, 253–315. Reprinted in D. Howard and J. Stachel (eds.), Einstein and the History of General Relativity: Einstein Studies Vol. I, Boston: Birkhäuser, pp. 101–159.
Norton, J. D. (1992). Einstein, Nordström and the early Demise of Lorentz-covariant, Scalar Theories of Gravitation. Archive for History of Exact Sciences, 45, 17–94. Reprinted in J. Renn and M. Schemmel (eds.), The Genesis of General Relativity Vol. 3: Theories of Gravitation in the Twilight of Classical Physics: Between Mechanics, Field Theory, and Astronomy. Springer, 2007, pp.413–87.
Norton, J. D. (1993). The determination of theory by evidence: the case of quantum discontinuity, 1900–1915. Synthese, 97, 1–31.
Norton, J. D. (2003). A material theory of induction. Philosophy of Science, 70(2003), 647–670.
Norton, J. D. (2005). A little survey of induction. In P. Achinstein (Ed.), Scientific evidence: Philosophical theories and applications (pp. 9–34). Johns Hopkins University Press, 2005.
Norton, J. D. (2006). Atoms entropy quanta: Einstein’s miraculous argument of 1905. Studies in History and Philosophy of Modern Physics, 37, 71–100.
Norton, J. D. (2007). Probability disassembled. British Journal for the Philosophy of Science, 58, 141–171.
Norton, J. D. (2008a). Must evidence underdetermine theory? In M. Carrier, D. Howard, & J. Kourany (Eds.), The challenge of the social and the pressure of practice: Science and values revisited (pp. 17–44). Pittsburgh: University of Pittsburgh Press.
Norton, J. D. (2008b). Ignorance and indifference. Philosophy of Science, 75, 45–68.
Norton, J. D. (2010a). There are no universal rules for induction. Philosophy of Science, 77.
Norton, J. D. (2010b). Cosmic confusions: Not supporting versus supporting not-. Philosophy of Science, 77, 501–523.
Popper, K. R. (1959). Logic of scientific discovery. London: Hutchinson.
Renn, J. (2007). (ed.), The genesis of general relativity. Vol. 2 Einstein’s Zurich Notebook: Commentary and Essays. Springer.
Sorensen, R. (2006). Epistemic Paradoxes. The Stanford encyclopedia of philosophy (Fall 2006 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2006/entries/epistemic-paradoxes/>.
Will, C. M. (2007). The confrontation between general relativity and experiment. Living Reviews in Relativity 9, (2006), 3. URL (cited on May 18, 2007): http://www.livingreviews.org/lrr-2006-3.
Zenneck, J. (1901). Gravitation. In A. Sommerfeld (Ed.), Encyklopädie der mathematischen Wissenschaften, Vol. 5: Physik (pp. 25–67). Leibzig: B. G. Teubner. Translated as “Gravitation”, pp. 77–112 in J. Renn, ed. The Genesis of General Relativity Vol. 3: Theories of Gravitation in the Twilight of Classical Physics: Between Mechanics, Field Theory, and Astronomy. Springer, 2007.
Acknowledgements
I am grateful for helpful discussion to Gerd Grasshoff, Kaerin Nickelsen and the participants in a block seminar, May 31–June 1, 2007, at the Institut für Philosophie, Wissenschaftstheorie und Wissenschaftsgeschichte, Universität Bern; and for helpful remarks from the referees and editor of this journal.
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Norton, J.D. History of science and the material theory of induction: Einstein’s quanta, mercury’s perihelion. Euro Jnl Phil Sci 1, 3–27 (2011). https://doi.org/10.1007/s13194-010-0001-7
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DOI: https://doi.org/10.1007/s13194-010-0001-7