Abstract
In 1929, in the wake of the enormous success of nonrelativistic quantum mechanics in explaining atomic and molecular structure and interactions, Dirac, one of the main contributor to these developments, in a now famous quotation asserted that “The general theory of quantum mechanics is now almost complete.” Whatever imperfections still remained were connected with the synthesis of the theory with the special theory of relativity. But these were “... of no importance in the consideration of atomic and molecular structure and ordinary chemical reactions ... The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that exact application of these laws lead to equations much too complicated to be soluble ...”1
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Notes
Dirac, P. A. M., “Quantum mechanics of many-electron systems,” Proc. Royal Soc. (London) A 126 (1929), 714–723.
In fact, a year later Kenneth Wilson and Michael Fisher provided the missing link using renormalization group methods and 4-c expansions. See K. G. Wilson and J. Kogut, “The renormalization group and the e expansion,” Physics Reports C 12 (1974), 131–268; K. G. Wilson, “Problems in Physics with many scales of length,” Scientific American 241 (1979), 158–179; K. G. Wilson, “The renormalization group and critical phenomena,” Rev. Modern Physics 55 (1983), 583–600.
Van Hove’s speech is quoted in C. Domb, “Critical Phenomena: a brief historical survey,” Contemporary Physics 26/1 (1985), 49–72.
Among the theorists: Hans Bethe, Lev Landau, Robert Oppenheimer, Rudolf Peierls, John Slater, Edward Teller, Sin-Itiro Tomonaga, John van Vleck, Victor Weisskopf, Hideki Yukawa, Eugene Wigner; among the experimenters: Enrico Fermi, Ernest Lawrence, Isidore Rabi, Felix Bloch, Emilio Segre, Bruno Rossi.
E.g.: Robert Serber, John Wheeler, Julian Schwinger, Richard Feynman, Edward Purcell, Charles Lauritsen, William Fowler, Luis Alvarez, Norman Ramsey, Edwin MacMillan, Robert Wilson….
There exists by now an enormous literature on the physicists and World War II. This literature is quoted in M. Fortun and S. S. Schweber, “Scientists and the Legacy of World War II,” Social Studies of Science 23 (1993), 595–642.
In particular: symmetry breaking, renormalization group methods, decoupling, effective theories, etc. See T. Y. Cao and S. S. Schweber, “The conceptual foundations and philosophical aspects of renormalization theory,” Synthese 97 (1993), 33–108.
Russell MacCormmach and K. Jungnickel. The Intellectual Mastery of Nature ( Chicago: The University of Chicago Press, 1987 ).
See the suggestive article by Kurt Bayertz, “History of Science as a Natural Process?” Scientia 116 (1981), 285–293. See also the essays reprinted in Part I of E. P. Wigner, Symmetries and Reflections: Scientific Essays (Bloomington: Indiana University Press, 1967).
Thus already in 1928 J.C. Slater had a vision of a molecular engineering practice based on quantum mechanics. See S. S. Schweber,“ J. C. Slater and the development of quantum chemistry,” Historical Studies in the Physical and Biological Sciences 20/2 (1990), 339–406. For J. D. Bernal see his The World, the Devil and the Flesh.
According to Alexandre Koyré the most profound consequences of the scientific revolution of the 17th century stemmed from the fact it replaced the Aristotelian world picture - in which the cosmos was a finite, hierarchically ordered structure - by one in which the cosmos is an abstract, infinite, homogeneous and void space populated by isolated bodies built of mutually separated and immutable smallest particles. It provided the metaphysical framework within which could emerge the Newtonian concept of fundamental laws of nature that aimed at a unified, reductionist representation of the physical world. Alexandre Koyré, From the Closed World to the Infinite Universe (Baltimore: The Johns Hopkins Press, 1957).
Thus non-relativistic quantum mechanics came to be seen as correctly describing that domain of nature delineated by Planck’s constant h: Any system whose characteristic length (l),mass (m) and time (t) were such that the product ml 2/t was of the order of h,and such that lit was much smaller than c,the velocity of light, was to be described by the new non-relativistic quantum mechanics.
Einstein 1918, In his “Autobiographical Notes” Einstein was even more explicit: “I would like to state a principle, which cannot be based upon anything more than a faith in the simplicity, i.e., intelligibility, of nature; that is to say, nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally, completely determined constants occur (not constants, therefore, whose numerical values could be changed without destroying the theory).” (Einstein 1949).
Reductionism together with its atomistic component is what Ian Hacking has called a style of scientific reasoning. “A style of reasoning makes it possible to reason toward certain kinds of propositions, but does not of itself determine their truth value.” It determines what may be true or false and indicates what has the status of evidence. Similarly unification, the use of symmetry, the use of renormalization group methods, are examples styles of reasoning. Moreover, the fact these styles of reasoning are useful in both particle physics and in condensed matter physics — and in point of fact cross-fertilized these fields — illustrates the (nonlinear) additive properties of styles of reasoning. Styles of reasoning, as Hacking has noted, tend to be slow in evolution and are vastly more widespread than paradigms. They are not the exclusive property of a single disciplinary matrix [Hacking (1986)].
P. W. Anderson, “More is Different,” Science 177 (1972), 393–396.
Translated into the language of particle physicists, Anderson would say each level has its effective Lagrangian and its sets of (quasi-stable) particles.
Anderson would say that in each level the effective Lagrangians — the “fundamental” description at that level — are the best we can do. When particle theorists explore the consequences of the SU 3 × SU 2 × U1 standard model, their work is not more fundamental than what Anderson does exploring the consequences of the Schrodinger theory for condensed matter physics. Note in this case positivism leads to intellectual democracy.
The formulation of the strong interactions as a non-Abelian gauge theory can be considered a “fundamental” description. But to prove starting from QCD quark confinement in four dimensional space-time, or to go from that representation to an effective chiral Lagrangian to describe low energy pion-nucleon scattering, or to deduce from QCD the binding energy of the deuteron and explain why it is so small present enormous difficulties that have not as yet been overcome. Judging from the results obtained in the mathematical description of phase transitions in various dimensions, ascertaining the properties of the solutions of the “fundamental” equations — to say nothing of obtaining actual solutions — is an extremely difficult mathematical task involving delicate limiting procedures.
F. J. Dyson, Report to the Oldstone Conference held in April 1949.
Steven Weinberg, “Conceptual foundations of the unified theory of weak and electromagnetic interactions”, Rev. Mod. Physics 52 (1980), 515–524. See also S. Weinberg, “The search for unity: Notes for a history of quantum field theory,” Daedalus (Fall 1977), Vol. II of Discoveries and Interpretations in Contemporary Scholarship.
E. C. G. Stückelberg and A. Peterman, “La normalisation des constantes dans la theorie des quanta,” Heiv. Phys. Acta. 26 (1953), 499–520. M. Gell-Mann and F. Low, “Quantum Electrodynamics at Small Distances.” Phys. Rev. 95 (1954), 1300–12.
See also Steven Weinberg, “Why the Renormalization Group is a Good Thing,” in A. H. Guth, K. Huang, and R. L. Jaffe, eds., Asymptotic Realms of Physics: Essays in Honor of Francis E. Low ( Cambridge, Mass: MIT Press, 1983 ), pp. 1–19.
David Gross, “Beyond Quantum Field Theory,” in J. Ambjorn, B. J. Durhuus, and J. L. Petersen, eds., Recent Developments in Quantum Field Theory (New York: Elsevier Science Publishers, 1985). For an overview of Kenneth Wilson’s contributions see K. G. Wilson and J. Kogut, “The renormalization group and the e expansion,” Physics Reports C12 (1974), 131–264; K. G. Wilson, “The renormalization group: Critical phenomena and the Kondo problem,” Rev. Modern Physics 47 (1975), 773–840; K. G. Wilson, “Problems in Physics with many scales of length,” Scientific American 241 (1979), 158–179; K. G. Wilson, “The renormalization group and critical phenomena,” Rev. Modern Physics 55 (1983), 583–600.
Steven Weinberg, “Phenomenological Lagrangians”, Physica 96A (1979), 327–340. Howard Georgi, “Effective quantum field theories,” in Paul Davies, ed., The New Physics (Cambridge: Cambridge University Press, 1989) pp. 446–457.
Peter G. Lepage, “What is renormalization?” in T. DeGrand and T. Toussaint, eds., From Action to Answers (Singapore: World Scientific, 1990), pp. 483–504.
There is an interesting parallel to be made between Forman’s thesis about quantum mechanics and Weimar Germany, and the development of effective field theories. Forman claimed that the Weimar physicists and mathematicians accommodated themselves to a Spenglerian point of view and rejected causality — even though this could not be related to any internal developments of physics, and particularly quantum theory. He thus wants to correlate the acausal features of quantum mechanics with external factors. The thesis however is much less prone to being challenged if stated as referring to the reception of quantum mechanics. In the present situation the question to be answered is the following: Were there external factors that made the acceptance of the effective field theory point of view particularly attractive to large segment of the high energy theoretical physics community? Was it an accommodation with the Zeitgeist? How did the proposal for building the SSC and large collider facilities impact on the reception and adoption of this point of view? This revised version of the Forman thesis does not claim that context determines the physics — but rather it suggests that there always exists a range of possibilities of view points — and that the milieu helps select among these. Paul Forman, “Weimar culture, causality and quantum theory, 1918–1927: Adaptation by German physicists and mathematicians to a hostile intellectual environment,” Historical Studies of Phys. Sciences 3 (1971), 1–115; Paul Forman, “The reception of an Acausal Quantum Mechanics in Germany and Britain,” in Seymor Mauskopf, ed., The Reception of Unconventional Science,AAAS Selected Symposium 25 (Westview Press, 1979); Paul Forman, “Kausalität, Anschaulichkeit, and Individualität, or how cultural values prescribed the character and the lessons ascribed to quantum mechanics,” in Nico Stehr and Volker Meja, eds., Society and Knowledge (New Brunswick: Transaction Books, 1984).
Thus in 1984 David Gross explicitly embraced Einstein’s views regarding the possibility of ascertaining and formulating unique laws of nature and added that “It is a rather arrogant goal and a recent one in the history of physics.” He indicated that he found support for this view from the uniqueness of QCD, referring “not to the fact that it seems to be uniquely singled out by experiment but rather to the fact it contains essentially no adjustable parameters.” David Gross, “On the Uniqueness of Physical Theories,” in A Passion for Physics, C. DeTar, J. Finkelstein, and Chug-I Tan, eds. ( Singapore: World Scientific, 1985 ).
The parameters, such as density and viscosity, that enter the hydrodynamical level of description encapsulate the ignorance of the short distance behavior.
The differences between the non-relativistic (and essentially finite) field theoretic descriptions of condensed matter physics and the relativistic and divergent quantum field theories of high-energy physics ought not to be overlooked. The situation in the latter is clearly more ambiguous and more tentative — and the claims for the effective field theory methods ought to be tempered by that fact.
The effective Lagrangian for that level.
This point was made by Harvey Brooks already in 1973.
The date when “finalization” occurred for non-relativistic quantum mechanics can be taken to be when Bardeen, Cooper and Schrieffer explained superconductivity. Prior to that there was always the nagging possibility that quantum mechanics broke down at distances of the order of 100–200 Angstrom. Thus Feynman wrote Landau in 1954: “It is a remarkable achievement in less than 30 years after quantum theory was discovered we can say that, as far as we know, the qualitative explanation of all extra-nuclear phenomena are understood as a consequence of that theory with two exceptions. One is gravity, which we believe cannot be understood in terms of the simple Schrodinger equation. The other is superconductivity. There remains that one point still resisting siege! (I omit the phenomena of life because we don’t know enough about the atomic arrangement to know if quantum theory will hold up.)”
R. P. Feynman to L. Landau, November 22, 1954. Feynman Papers. Archives, C.I.T.
A few years later BCS removed that obstacle. BCS’s theory of superconductivity can indeed be taken as successfully completing the non-relativistic quantum mechanical agenda.
The notion of finalization and decoupling clearly have important ramifications for policy issues.
The concept of a quasi stable theory has some affinity with the notion of a “closed theory” that Heisenberg advanced in the late twenties and that he published in Dialectica in 1948. See “The Notion of a `Closed Theory’ in Modern Science” in Heisenberg (1974). For a historical account of the formulation of theses ideas see C. Chevalley (1991). The notion of a quasi-stable theory was also used in Schweber (1989). But the conceptualization there emphasizes the stability of the theory against small changes in the formalism. Thus it seems extremely difficult to make small changes in the formalism of quantum mechanics that maintain logical consistency, empirical validity and the usual notions of causality.
As is well known, dynamical symmetry breaking was brought into elementary particle physics from many-body physics. See L. M. Brown and Tian Yu Cao, “Spontaneous breakdown of symmetry: Its rediscovery and integration into quantum field theory,” Historical Studies in the Physical and Biological Sciences 21 (1991), 211–235.
D. A. Kirzhnitz and A. D. Linde, “Macroscopic consequences of the Weinberg model,” Phys. Letters 42B (1972), 471–4.
L. Dolan and R. Jackiw, “Symmetry behavior at finite temperature,” Phys. Rev. D9 (1974), 3320–41. S. Weinberg, “Gauge and global symmetries at high temperature,” Phys. Rev. D9 (1974), 3357–77.
See for example L. F. Abbott and So-Young Pi, eds., Inflationary Cosmology (Singapore: World Scientific, 1986); Adnrei Linde, Particle Physics and Inflationary Cosmology (New York: Harwood Academic Press, 1990) and Alan Guth and Paul Steinhardt, “The Inflationary Universe,” in Paul Davies, ed., The New Physics ( Cambridge: Cambridge University Press, 1989 ), pp. 34–60.
See for example Larry Abbott, “The Mystery of the Cosmological Constant,” Scientific American 256: 5 (1988), 106–113.
Note that the viewpoint posited does not exclude the possibility that there exists a “fundamental” unified theory, which can be represented at various energy scales by “effective” field theories.
The present situation with respect to symmetries may also be analogous to the relation between special and general relativity. In the special theory of relativity space-time is a rigid stage unaffected by the matter and energy present — as was the case in Newtonian physics. General relativity dynamicized space-time, with the geometry of space-time becoming a response to the energy-momentum density present. The analogy is the following: before the standard model, symmetries were likewise thought of as “rigid.” Gauge field theories have allowed the possibility to “dynamicize” the symmetries.
C. S. Peirce, “The architecture of theories”, in Chance, Love and Logic. Philosophical Essays (New York: Harcourt, Brace, 1923), p. 162. See also Henri Poincaré, “L’Évolution des Lois” in Dernières Pensées (Paris: Flammarion, 1913 ), pp. 48–67.
Interestingly, in the late 1960’s Cocconi had arrived at a somewhat similar position as a result of his confrontation with the diversity and complexity encountered in the world of elementary particles. G. Cocconi, “The Role of Complexity in Nature,” in M. Conversi, ed., Evolution of Particle Physics (New York: Academic Press, 1970), pp. 81–87.
The division between the various subfields of physics were sharpened during the eighties, partly because of shrinking budgets. The disparity in the time scales for constructing new accelerators and detectors and that for creating novel theories have brought a sense of crisis to the high energy community. There have essentially been no new experimental results since the early eighties when the electroweak theory was fully corroborated with the discovery of the W’s and the Z°. Particle physics theorists are divided into various camps — with string theorists representing the tradition of trying to seek unifying (unitary) theories and with many of them resonating to Dirac’s contention that theories ought to be “beautiful”. But, since their efforts thus far are so removed from experimental relevance, they are branded mathematicians by the more phenomenologically inclined theorists committed to effective field theory approaches.
And everyone seems to agree that some of the most exciting aspects of high energy physics are to be found in astrophysics.
Nor has the condensed matter physics community been immune to the sense of crisis. The excitement generated by the solution of the problem of phase transitions has abated. The problems of explaining high temperature superconductivity have proven more refractory than initially anticipated. Nor has the departure of a number of distinguished practitioners to such fields as biophysics and neural networks escaped notice.
The end of the cold war in the late eighties has exacerbated the sense of crisis. The New York Times reported that some 800 applicants had applied for a single tenure track position at Amherst College. Physics Today in March of 1992 reported on the sense of despair that characterizes the atmosphere at the meetings of the AIP. These suggest that the discipline is facing a situation as difficult as that during the early thirties at the height of the depression. Furthermore the demographics of the physics community has brought these issues to the nitty gritty of departmental politics precisely at a time when universities have to cut back and government funding is slackening. It is likely that the discipline will shrink sharply in size over the next decade or so.
I here draw on a paper I presented at the June 1992 SLAC conference on the “The Rise of the Standard Model” and on a draft for a workshop on the crisis in physics prepared by Tian Yu Cao and S.S. Schweber.
Fredric Jameson, Postmodernism, Or The Cultural Logic of Late Capitalism (Durham: Duke University Press, 1991). A list of ends was given by Jacques Derrida in an 1984 essay entitled “Of an Apocalyptic Tone Recently Adopted in Philosophy.”
See the fine sets of essays in Saul Friedlander, ed., Probing the Limits of Representation (Cambridge, MA: Harvard University Press, 1992). Also Zygmunt Bauman, Modernity and the Holocaust (Ithaca: Cornell University Press, 1989).
Everett Mendelsohn. Lechire, Harvard University, Fall 1989.
A. Pais, Bohr’s Times, in Physics, Philosophy and Polity ( New York: Oxford University Press, 1991 ), p. 227.
Perhaps monastery is an apter description of the Institute as long as Abraham Flexner was director. When Einstein first arrived at the Institute in Princeton in 1933, Flexner turned down an invitation to the White House that Einstein had received from Roosevelt, noting that Professor Einstein had come to Princeton “for the purpose of carrying out his scientific work in seclusion” and it was “absolutely impossible to make any exceptions.” Abraham Flexner to F.D. Roosevelt, 3 November 1933. In Science in America: A Documentary History, 1900–1939,Nathan Reingold and Ida Reingold, eds. (Chicago: The University of Chicago Press, 1981), p. 451. The Institute did become a Temple during the thirties when Flexner gave over the reins to Frank Aydelotte.
Recall the statement Einstein made in 1941. “Although it is true that it is the goal of science to discover rules which permit the association and foretelling of facts, this is not its only aim. It also seeks to reduce the connections to the smallest possible number of mutually independent conceptual elements. It is in this striving after the rational unification of the manifold that it encounters its greatest successes, even though it is precisely this attempt which causes it to run the greatest risk of falling prey to illusions…”; in Science, Philosophy and Religion. A symposium published by the Conference on Science, Philosophy and Religion in Their Relation to the Democratic Way of Life, Inc. New York, 1941. Reprinted in Ideas an Opinions.
J. Bronowski, Science and Human Values (New York: Harper Torchbook, 1959). See also, Alan G. Wasserstein, Scientific Optimism: A Progress Report, Raritan 9/1 (1989), 114–133.
I want to know how God created the world. I am not interested in this or that phenomenon, in the spectrum of this or that element; I want to know his thoughts; the rest are details.“ Albert Einstein. From ”A talk with Albert Einstein“ in The Listener. September 1955. Quoted in M. Sachs, Einstein versus Bohr (La Salle, Ill.: Open Court, 1988).
For Einstein’s views on God and religion see Ideas and Opinions.
The real then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you. Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of COMMUNITY, without definite limits and capable of a definite increase of knowledge.“ Elsewhere Peirce asserts that ”What anything really is, is what it may finally come to be known to be in the ideal state of complete information; so that reality depends on the ultimate decision of the community,“ and `But the reality of that which is real does depend on the real fact that investigation is destined to lead, at least, if continued long enough, to a belief in it.”
There is therefore some notion to convergence toward truth — but it requires an ideal society which has complete information.
In the final discourse at the centennial celebration of the NAS, Rabi pointed to this aspect of science as one of its greatest attraction. Rabi’s depiction of the community was as follows: “Members of this community possess an inner solidity which comes from a sense of achievement and an inner conviction that the advance of science is important and worthy of their greatest effort. This solidity comes in a context of fierce competition, strongly held conviction, and differing assessments as to the value of one achievement or another. Over and above all this too human confusion is the assurance that with further study will come order and beauty and a deeper understanding.” I.I. Rabi, “Science in the Satisfaction of Human Aspiration,” in The Scientific Endeavor. Centennial Celebration of the National Academy of Sciences (New York: The Rockefeller Institute Press, 1963), pp. 303–309, p. 308.
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Schweber, S.S. (1995). Physics, Community and the Crisis in Physical Theory. In: Gavroglu, K., Stachel, J., Wartofsky, M.W. (eds) Physics, Philosophy, and the Scientific Community. Boston Studies in the Philosophy of Science, vol 163. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2658-0_7
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