Summary
The present paper constitutes an elaboration of a previous work by one of us which, among other things, proposed some modifications of Popper's tetradic schema. Here, in the first part, we consider critically and develop further these modifications and elaborate on methods which prove more satisfactory for the mapping of the problem solving processes in Physics. We also find the opportunity to make some comments on Physics and on its relation to Mathematics. In the second part, there is an attempt to test the above ideas on the genesis and development of the Special Relativity Theory. In doing this, we concentrate mainly on Einstein's 1905 paper and try to explicitate its relation with the situation Physics found itself in that period as well as to clarify the epistemological status of Einstein's two postulates.
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Literatur
K. Gavroglu, “Research Guiding Principles in Modern Physics: Case studies in Elementary Particle Physics”. Zeitschrift für allgemeine Wissenschaftstheorie,VII/2 1976, pp. 223–248.
P1→TT→P2. A tentative theory (TT) is proposed for the solution of a problem P1. Error elimination procedures (EE) lead to the falsification of TT and thus give rise to a new problem P2. See K. PopperObjective Knowledge, Oxford, 1975, p. 287 et seq.
K. Popper, op. cit., p. 106 et seq.
For a thorough and systematic “blowing up” of Popper's tetradic schema see G. Radnitzky, “Popperian Philosophy of Science as an Antidote against Relativism” in R. S. Cohen et al. (eds)Essays in Memory of Imre Lakatos, D. Reidel, 1976.
As it will become apparent in what follows, we qualify the term “problem situation” in a slightly different manner than Popper (Objective Knowledge, op. cit. p. 165). For us a problem situation comprises all right “a problem together with its background (and perhaps together with other third world objects)” but it is a situation which is itself “problematic” — no tentative solution seems to solve the problem and gain a satisfactory consensus. It is a crisis situation.
P. Feyerabend,Against Method, Verso, 1978, p. 274.
Popper's concept of the “third world” is indeed much larger than this. It includes “the objective contents of thought, especially of scientific and poetic thoughts and of works of art” (Objective Knowledge, op. cit., p. 106. See also K. Popper,Unended Quest, Fontana, 1977, pp. 180–187). One could perhaps go as far as to say that it includes all objectified and objectivable results of human practice which are not objects.
A. Lalande,Vocabulaire Technique et Critique de Philosophie, PUF, 1972, p. 1031.
K. Popper,Objective Knowledge, op. cit, p. 115.
See the article of J.-M. Lévy-Leblond, “Physique et Mathematiques” in Encyclopaedia Universalis, Vol. 13, p. 4 et seq. Lévy-Leblond goes as far as todefine the specificity of the science of Physics (as compared to that of Chemistry or Biology) through this constituting relation.
J. C. Maxwell,Collected Scientific Papers, ed. W. D. Niven, Dover, 1965, acticle titled “On Faraday's Lines of Force”.
A. Einstein,Mein Weltbild, as quoted by E. Zahar, “Why did Einstein's Programme supersede Lorentz's?” (II), The British Journal for the Philosophy of Science, 24 (3), 1973, p. 224–225.
R. Feynman,The Character of Physical Law, The M. I. T. Press, 1975, pp. 39 and 55. The chapter titled “The Relation of Mathematics to Physics” constitutes an elaboration of the above thesis.
The relations between mathematical branches are not static. The development of Mathematics continuously distorts their boundaries, opens new fields, questions hitherto “evident” premisses ets. See I. Lakatos,Proofs and Refutations, edited by J. Worral and E. Zahar, Cambridge University Press, 1977.
For an analysis of the status of Mathematics as a science, see P. Raymond,L'Histoire et les Sciences, Maspero, 1978, pp. 57–90.
Falsification, at least as it is accepted today, always refers to the experimental procedures that characterize thephysical sciences and which presuppose a reality that is “external” to the corresponding theoretical scheme. Even in the faillibilist and, in this sense, quasi-experimentalist, “proofs and refutations” conception of Mathematics (I. Lakatos, “Proofs and Refutations”, op. cit. See especially p. 127–128 for a succinct summary of this approach) there is no commensurate equivalent to Popper's falsification. Moreover, Popper himself considers Mathematics as an essentially deductivist enterprise. (K. Popper,The Logic of Scientific Discovery, Hutchinson, 1959, p. 31. See also I. Lakatos,Proofs and Refutations, op. cit., p. 139 n 1 and p. 143 n 1). In this respect, it is interesting to note that Popper always gives examples of what we termed the CIOS of Mathematics as scientific instances of his “world three” concept. This shows that Popper's W3 cannot be accomodated in Popper's initial tetradic schema which, indeed, is a mapping of his falsification procedure. This remark can serve as a mark of the content of our disagreement with Popper's initial schema and his “world three” concept as well as a mark of our agreement with Lakatos's conception of Mathematics.
T. S. Kuhn, “The Structure of Scientific Revolutions”, The University of Chicago Press, 1970, passim.
This “definition” of a physical theory constitutes a stronger statement than the just heuristic role in furthering physical discovery attributed by Zahar (E. Zahar, “Why did Einstein's ... (I)”, op. cit, p. 109–111) to the relation of Mathematics to Physics. Our “definition” does not imply, of course, that all mathematical quantities and operations should be given a physical interpretation but one way or another, we feel that as it stands, this “definition” is not sufficiently corroborated. A comprehensive definition should, at least, consider the relation of the particular physical theory with other theories that may serve as auxiliary premisses for the conduction of the relevant experiments (see P. Feyerabend, op. cit., p. 66 et seq.) and/or for the elucidation of the status of the eventually relevant parameters that are not accounted for by the initial theory. We are actually working on this. See also the quotations of Maxwell, Einstein and Feynman cited earlier in the text.
Our use of “ad hoc” is close to Zahar's “ad hoc 3” (E. Zahar, op. cit, p. 101, 105) and is consistent with our “definition” of a physical theory.
F. Lurcat, “Theory of Strong Interactions. I. Kinematics” Annals of Physics,106(2), 1977, p. 342.
See, for example, the discussion of Bohr's research programme and the successive steps for the construction of his model for the atom in I. Lakatos, “Falsification and the Methodology of Scientific Research Programmes”, in I. Lakatos and A. Musgrave eds,Criticism and the Growth of knowledge, Cambridge University Press, 1978, p. 140 et seq.
R. Feynman, op. cit., pp 57 and 39.
We have borrowed the term from G. Radnitzky, op. cit, p. 516.
G. Radnitzky, op. cit., p. 526.
For the use of this concept, introduced by Lenin, in epistemology see P. Feyerabend op. cit., p. 145 et seq.
P. Feyerabend, op. cit., p 66 et seq.
For the concept of “relative autonomy” and that of “in the last analysis” see L. Althusser, “Soutenance d' Amiens” inPositions, Editions Sociales, 1976, pp. 138–151.
The internal dynamics of Mathematics is magnificently depicted in I. Lakatos,Proofs and Refutations, op. cit.
A. Einstein, “On the Electrodynamics of Moving Bodies”, translated and reprinted inThe Principle of Relativity, Dover Publications.
I. Lakatos, “Falsification and the Methodology ...”, op. cit., p. 138.
I. Lakatos, ibid, p. 133. This use of “hard core” generalizes somewhat that of Lakatos. In his terminology, our use is practically a shorthand for the thesis that the hard core of practically all research programmes of the period had as a fundamental constituent the ether concept.
For a consice history of the ether concept see, Mary Hesse, “Ether”, article inThe Encyclopaedia of Philosophy, P. Edwards editor, Macmillan Publishing Co., 1967.
This dichotomy between influences that propagated materially with finite velocity and influences that propagated immaterially with infinite velocity, within the context of classical Physics, was not in fact a real dichotomy. There did not exist an upper velocity limit and one could in principle go up to as high velocities as wished. In this way, even “action at a distance” theories could not lightly do away with the ether concept. See M. Hesse, “Action at a Distance”, article in The Encyclopedia of Philosophy, op. cit.
See our “definition” of physical theory in Part I.
A very good summary of the different efforts deployed in this context can be found in the recent article of S. Bregia “Einstein and the Birth of Special Relativity”, in A. P. French editor,Einstein, A Centenary Volume, Heinemann, 1979.
A d'Abro, The Evolution of Scientific Thought, Dover, 1950, p. 134.
A. Einstein,The Principle of Relativity, op. cit. p. 38.
A. Einstein, ibid, p. 38.
A. Einstein, ibid, p. 37. This is the opening sentence of the 1905 paper.
For a similar situation in quite a different context see the comments of L. Althusser on Engels's comparison of Lavoisier's discovery of oxygen with Marx's formulation of the surplus value concept in L. Althusser et E. BalibarLire le Capital, Maspero (Petite Collection), Vol. II, p. 8 et seq. It seems that a general feature of such revolutionnary turnovers is the fact that the realization and explicit formulation of the problem is inseparable from the production of its solution. See Einstein's comments on how he arrived at the formulation of SRT in his autobiographical notes in P. A. Schilpp (editor), Albert EinsteinPhilosopher — Scientist, Open Court, 1969, p. 53.
K. Gavroglu, “Research Guiding ...”, op. cit., p. 37–38.
A definition of “intrascientific epistemological rupture” can be found in the introduction by E. Balibar of M. Fichant, M. Pêcheux,Sur l'Histoire des Sciences, Maspéro, 1971. In short, it denotes the radical changes of conceptual framework that intervence in the historical development of a particular science. It is to be distinguished from “epistemological break”, a term introduced by G. Bachelard to denote the “point of no return” from which a particular sciencebegins to exist. (For Physics this beginning can be situated in the work of Galileo.)
Einstein's procedure and the subsequent “clash of frameworks” could eventually be cast into the kuhnian terms of “gestalt switch” and “paradigm change”. We cannot enter here into an analytic exposition of our reasons for not using this terminology. We think it sufficient for what we are here trying to convey just to state that “gestalt switch”, by denoting the psychological aspect of a scientific breakthrough seems, correspondingly, to narrow down or even suppress itsobjective status. On the other hand, “paradigm and “paradigm change” seem relevant for contexts far wider than those involved in the development of science while they do not discriminate between features of scientific development such as those termed “epistemological rupture” and “epistemological break”. A general discussion of such matters can be found in I. Lakatos and A. Musgrave, eds.Criticism and ..., op. cit., passim.
This “lack of committement” may sound as a methodological prescription and, in an historical perspective, it may very well appear as one. (It seems that all scientific revolutions had as a prerequisite such a lack of committement). But inactual practice it really cannot be taken as an effective methodological policy. Every period in the development of science has its own “self-evident” prejudices or, as Bachelard puts it, “scientific knowledge is a sunlight that always projects shadows somewhere” (G. Bachelard,La Formation de l' Esprit Scietifique, Vrin, 1975, p. 1). And the “self evident” character attributed to such prejudices means exactly that these, as a rule, cannot be questioned. The effective questioning of such prejudices constitutes the revolutionary aspect of the development of science and there cannot exist a sufficient condition, a methodological quarantee for the breaking of a revolution.
A. Einstein,The Principle of Relativity, op. cit., p. 37–38.
The derivation of the implications of the RP, with all mathematical details, can be found in W. Rindler,Essential Relativity, Springer-Verlag, 1977, p. 51 et seq. See also M. Jammer, “Some Foundational Problems in the Special Theory of Relativity” in T. di Francia, editor, Proceeding of the International School of Physics “Enrico Fermi” — Course LXXII — Problems in the Foundations of Physics North Holland Publishing Co, 1979, pp. 213–223 and the references given there. A very interesting paper along those lines is that of W.V. Ignatowsky, Phys. Zeits.11, 972 (1910). See also W. Pauli,Theory of Relativity, Pergamon, 1967, p. 11.
See W. Rindler, op. cit. and especially M. Jammer, op. cit, who reviews thoroughly the status and the interelationship of such assumptions. These can be included in what Bunge (M. Bunge,Foundations of Physics, Springer-Verlag, 1967, p. 85 et seq.) calls “protophysics”. We consider that, as their naming intends to imply, the examination of such premisses may, in first approximation, be left out of the main argument.
A complete derivation of the linearity of this family of tranformations can be found in V. Fock,The Theory of Space, Time and Gravitation, Pergamon Press, 1976, Appendix A.
“... and also introduce another postulate, which is only apparently irreconciliable with the former ...” A. Einstein,The Principle of Relativity, op. cit., p. 38.
“... This shows that our two fundamental principles are compatible ...” A. Einstein, ibid. p. 46.
E. Zahar, “Why did Einstein's programme supersede Lorentz's” (I), Brit. J. Phil. Sci.24 (1973) p. 108.
E. Zahar, “Why did Einstein's ... (II)”, Brit. J. Phil. Sci.24 (1973), p. 23.
See the fundamental paper of Holton “Einstein, Michelson, and the “Crucial” Experiment” in G. Holton,Thematic Origins of Scientific Thought, Harvard University Press, 1974, pp. 261–352.
G. Holton, ibid, p. 302.
W. Pauli, op. cit., p. 16.
W. Rindler, op. cit., p. 53.
It is at this level that Einstein's heuristics as expressed by the paradox of the beam of light mentionned by him in his autobiographical notes (P. A. Schilpp editor,Albert Einstein Philosopher-Scientist, op. cit., p. 53) can best be evaluated. Moreover, the above remarks may have a pedagogical significance since it seems that it is intuitively more satisfactory to present SRT starting from the notion of a finite ultimate velocity (see, for example, the Landau-Lifchitz presentation).
This is what Einstein means when he says that this velocity “in our theory plays tho part physically of an infinitely great velocity”. (A. Einstein,The Principle of Relativity, op. cit., p. 48).
Among the reasons given for Poincarré's not formulating the SRT (see, for example, G. Holton, “Poicarré and Relativity” inThematic Origins ..., op. cit., p. 185–195) one could, perhaps somewhat naively, also add that such an insight concerning the relationship of a mathematical fact with everyday experience is usually of the realm of the physicist and not of the mathematician.
A. Einstein, ThePrinciple of Relativity, op. cit., p. 59–61.
A. Einstein,The Principle of Relativity, op. cit., p. 42, 48–50.
As Sommerfeld notes (A. Einstein, ibid, p. 63, footnote), Einstein's definition of force (which is equivalent to such a dynamical postulate) is not satisfactory. This was first shown by Planck (M. Planck, Verh. dtsch. Ges.,4 (1906), 136). Lewis and Tolman (G. N. Lewis and R. C. Tolman, Phil. Mag.,18 (1909), 510) postulated momentum and kinetic energy expressions such that the corresponding conservation laws are obtained. Moreover, they showed that the velocity dependence of these expressions is uniquely determined by the Lorentz invariance requirements of the conservation laws. See W. Pauli, op. cit., p. 118.
J. M. Lévy-Leblond, “The Importance of Being (a) Constant” in T. d. Francia, editor, Proceedings of the International School of Physics “Enrico Fermi ...,” op. cit., p. 253.
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Baltas, A., Gavroglu, K. A modification of Popper's tetradic schema and the special relativity theory. Zeitschrift für Allgemeine Wissenschaftstheorie 11, 213–237 (1980). https://doi.org/10.1007/BF01800907
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DOI: https://doi.org/10.1007/BF01800907