Racionalidade, consistência, reticulação e coerência: o caso da renormalização na teoria quântica do campo
DOI:
https://doi.org/10.1590/S1678-31662003000200003Palavras-chave:
Metodologia científica, Racionalidade científica, Modelo reticulado, Valores cognitivos, Teoria quântica do campo, Teoria de gauge, Renormalização, InconsistênciaResumo
Um exame do desenvolvimento da teoria quântica do campo, no período que vai de 1927 a 1971, evidencia o fato de que as técnicas de renormalização desempenharam um papel fundamental ao longo de todo o processo. Em particular, a renormalização reabilitou a eletrodinâmica quântica no final dos anos 40 e, depois, também reabilitou a teoria quântica do campo como um todo e ajudou a consolidar as teorias de gauge no início dos anos 70. O sucesso da renormalização foi tal que ela passou gradualmente de mero dispositivo teórico ad hoc à condição de critério para a construção e avaliação de teorias na física do campo. Um dos objetivos deste artigo é mostrar que essa transformação no estatuto metodológico da renormalização pode ser entendida no contexto do modelo reticulado de racionalidade de Larry Laudan. Apesar do extraordinário progresso teórico e empírico alcançado, porém, sempre houve polêmicas acerca do lugar que a renormalização deve ocupar dentro da estrutura conceitual da disciplina. Essas polêmicas giram em torno do fato de que a renormalização aparentemente vai contra um valor cognitivo considerado fundamental: a consistência. O segundo objetivo deste artigo é mostrar como o modelo reticulado também permite lançar luz sobre essa questão. Procuramos expor em que sentido foi racional adotar a renormalização na física de partículas e campos apesar de existir o problema da inconsistência. Para isso nos valemos das teses do modelo reticulado, complementadas por teses de Putnam, Quine e da teoria coerencial da justificação.Downloads
Referências
NOTA BIBLIOGRÁFICA. Estão disponíveis alguns volumes de reprints fotográficos que são muito convenientes por reunir vários artigos clássicos em um único lugar, no formato em que foram originalmente publicados (inclusive com a paginação original). Em Schwinger (ed., 1958) estão reproduzidos os seguintes artigos: Bethe, 1947; Dirac, 1927; Dyson, 1949a; 1949b; Feynman, 1949a; 1949b; Jordan & Wigner, 1928; Lamb & Retherford, 1947; Schwinger, 1949b; Tomonaga, 1946; 1948; Weisskopf, 1939; 1994b. Em Feynman (2000b) encontram-se reproduzidos os seguintes: Feynman, 1948a; 1948b; 1949a; 1949b; 1966; 2000a. Finalmente, em Salam (1994b), acham-se reproduzidos os seguintes artigos: Goldstone, Salam & Weinberg, 1962; Salam, 1994a; Salam & Ward, 1964.
ARNISON, G. et al. “Experimental observation of isolated large transverse energy electrons with associated missing energy at √s = 540 GeV.” In: Physics Letters, 122B, 1983a, p. 103-16.
ARNISON, G. “Experimental observation of lepton pairs of invariant mass around 95 GeV/c 2 at the CERN SPS collider.” In: Physics Letters, 126B, 1983b, p. 398-410.
BETHE, H. A. “The electromagnetic shift of energy levels.” In: Physical Review, 72, 1947, p. 339-41.
BEZERRA, V. A. Estruturas em busca do equilíbrio: o lugar da metametodologia e o papel da coerência no modelo reticulado de racionalidade científica. Tese de doutoramento. São Paulo, Departamento de Filosofia da Universidade de São Paulo, 1999.
BIRKHOFF, G. & VON NEUMANN, J. “The logic of quantum mechanics.” In: HOOKER, C. A. (ed.). The logico-algebraic approach to quantum mechanics. Volume I: historical evolution. Dordrecht, D. Reidel, 1975, p. 1-26.
BJORKEN, J. D. & DRELL, S. D. Relativistic quantum fields. Nova Iorque, McGraw-Hill, 1965.
BORN, M.; HEISENBERG, W. & JORDAN, P. “On quantum mechanics II.” In: VAN DER WAERDEN, B. L. (ed.). Sources of quantum mechanics. Nova Iorque, Dover, 1968, p. 321-85.
BROWN, L. M. & HODDESON, L. (eds.). The birth of particle physics. Cambridge, Cambridge University Press, 1983.
CAO, T. Y. Conceptual developments of 20th century field theories. Cambridge, Cambridge University Press, 1997.
CUSHING, J. T. “Models and methodologies in current theoretical high-energy physics.” In: Synthese, 50, 1982, p. 5-101.
DANCOFF, S. M. “On radiative corrections for electron scattering.” In: Physical Review, 55, 1939, p. 959-63.
DIRAC, P. A. M. “The quantum theory of the emission and absorption of radiation.” In: Proceedings of the Royal Society, A114, 1927, p. 243-65.
DIRAC, P. A. M. “The origin of quantum field theory.” In: BROWN, L. M. & HODDESON, L. (eds.). The birth of particle physics. Cambridge, Cambridge University Press, 1983, p. 39-55.
DIRAC, P. A. M. “Theory of the positron.” In: MILLER, A. I. (ed.). Early quantum electrodynamics: a source book. Cambridge, Cambridge University Press, 1994a, p. 136-44.
DIRAC, P. A. M. “Discussion of the infinite distribution of electrons in the theory of the positron.” In: MILLER, A. I. (ed.). Early quantum electrodynamics: a source book. Cambridge, Cambridge University Press, 1994b, p. 145-56.
DYSON, F. J. “The radiation theories of Tomonaga, Schwinger, and Feynman.” In: Physical Review, 75, 1949a, p. 486-502.
DYSON, F. J. “The S matrix in quantum electrodynamics.” In: Physical Review, 75, 1949b, p. 1736-55.
FEYNMAN, R. P. “A relativistic cut-off for classical electrodynamics.” In: Physical Review, 74, 1948a, p. 939-46.
FEYNMAN, R. P. “Relativistic cut-off for quantum electrodynamics.” In: Physical Review, 74, 1948b, p. 1430-8.
FEYNMAN, R. P. “Space-time approach to quantum electrodynamics.” In: Physical Review, 76, 1949a, p. 769-89.
FEYNMAN, R. P. “The theory of positrons.” In: Physical Review, 76, 1949b, p. 749-59.
FEYNMAN, R. P. “The development of the space-time view of quantum electrodynamics.” In: Science, 153, 3737, 1966, p. 699-708.
FEYNMAN, R. P. “The present status of quantum electrodynamics.” In: Selected papers of Richard Feynman (with commentary). Singapura, World Scientific, 2000a, p. 134-72.
FEYNMAN, R. P. Selected papers of Richard Feynman (with commentary). Ed. de L. M. Brown. Singapura, World Scientific, 2000b.
FURRY, W. & OPPENHEIMER, J. R. “On the theory of the electron and positive.” In: Physical Review, 45, 1934, p. 245-62.
GLASHOW, S. L. “Partial-symmetries of weak interactions.” In: Nuclear Physics, 22, 1961, p. 579-88.
GOLDSTONE, J. “Field theories with ‘superconductor’ solutions.” In: Nuovo Cimento (New series), 19, 1961, p. 154-64.
GOLDSTONE, J.; SALAM, A. & WEINBERG, S. “Broken symmetries.” In: Physical Review, 127, 1962, p. 965-70.
HASERT, F. J. et al. “Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment.” In: Physics Letters, 46B, 1973, p. 138-40.
HEISENBERG, W. “Remarks on the Dirac theory of the positron.” In: MILLER, A. I. (ed.). Early quantum electrodynamics: a source book. Cambridge, Cambridge University Press, 1994, p. 169-87.
HIGGS, P. W. “Broken symmetries, massless particles and gauge fields.” In: Physics Letters, 12, 1964a, p. 132-3.
HIGGS, P. W. “Broken symmetries and the masses of gauge bosons.” In: Physical Review Letters, 13, 1964b, p. 508-9.
HIGGS, P. W. “Spontaneous symmetry breakdown without massless bosons.” In: Physical Review, 145, 4, 1966, p. 1156-63.
HOOKER, C. A. (ed.). The logico-algebraic approach to quantum mechanics. Volume I: historical evolution. Dordrecht, D. Reidel, 1975.
ITZYKSON, C. & ZUBER, J.-B. Quantum field theory. Nova Iorque, McGraw-Hill, 1985.
JACKSON, J. D. & OKUN, L. B. “Historical roots of gauge invariance.” In: Reviews of Modern Physics, 73, 2001, p. 663-80.
JORDAN, P. & WIGNER, E. “Über das Paulische Äquivalenzverbot.” In: Zeitschrift für Physik, 47, 1928, p. 631-51.
JORDAN, P. & PAULI, W. “Zur Quantenelektrodynamik ladungsfreier Felder.” In: Zeitschrift für Physik, 47, 1928, p. 151-73.
KRAMERS, H. “Die Wechselwirkung zwischen geladenen Teilchen und Strahlungsfeld.” In: Nuovo Cimento (Série antiga), 15, 1938, p. 108-14.
LAKATOS, I. “Falsification and the methodology of scientific research programmes.” In: _______. The methodology of scientific research programmes. Cambridge, Cambridge University Press, 1978a, p. 8-101.
LAKATOS, I. The methodology of scientific research programmes. Ed. de J. Worrale & G. Currie. Cambridge, Cambridge University Press, 1978b.
LAMB, W. E. & RETHERFORD, R. C. “Fine structure of the hydrogen atom by a microwave method.” In: Physical Review, 72, 1947, p. 241-3.
LAUDAN, L. Progress and its problems: towards a theory of scientific growth. Londres, Routledge & Kegan Paul, 1977.
LAUDAN, L. Science and values: the aims of science and their role in scientific debate. Berkeley, University of California Press, 1984.
LAUDAN, L. “Progress or rationality? The prospects for normative naturalism.” In: American Philosophical Quarterly, 24, 1987, p. 19-31.
MANDL, F. & SHAW, G. Quantum field theory (Revised edition). Chichester, John Wiley & Sons, 1993.
MILLER, A. I. (ed.). Early quantum electrodynamics: a source book. Cambridge, Cambridge University Press, 1994.
OPPENHEIMER, J. R. “Note on the theory of the interaction of field and matter.” In: Physical Review, 35, 1930a, p. 461-77.
OPPENHEIMER, J. R. “On the theory of electrons and protons.” In: Physical Review, 35, 1930b, p. 562-3.
O’RAIFEARTAIGH, L. (ed.). The dawning of gauge theory. Princeton, Princeton University Press, 1997.
O’RAIFEARTAIGH, L. & STRAUMANN, N. “Gauge theory: historical origins and some modern developments.” In: Reviews of Modern Physics, 72, 1, 2000, p. 1-23.
PAULI, W. & FIERZ, M. “Theory of the emission of long-wave light quanta.” In: MILLER, A. I. (ed.). Early quantum electrodynamics: a source book. Cambridge, Cambridge University Press, 1994, p. 227-43.
PICKERING, A. Constructing quarks: a sociological history of particle physics. Chicago, University of Chicago Press, 1984.
PUTNAM, H. “The logic of quantum mechanics.” In: PUTNAM, H. Mathematics, matter and method: philosophical papers, volume I (Second edition). Cambridge, Cambridge University Press, 1979a, p. 174-97.
PUTNAM, H. Mathematics, matter and method: philosophical papers, volume I (Second edition). Cambridge, Cambridge University Press, 1979b.
QUINE, W. v. O. “Two dogmas of empiricism.” In: QUINE, W. v. O. From a logical point of view: nine logico-philosophical essays (Second, revised edition). Cambridge (Massachusetts), Harvard University Press, 1980a, p. 20-46.
QUINE, W. v. O. From a logical point of view: nine logico-philosophical essays (Second, revised edition). Cambridge (Massachusetts), Harvard University Press, 1980b.
SALAM, A. “Weak and electromagnetic interactions.” In: SALAM, A. Selected papers of Abdus Salam (with commentary). Singapura, World Scientific, 1994a, p. 244-54.
SALAM, A. Selected papers of Abdus Salam (with commentary). Ed. de A. Ali; C. Isham; T. Kibble & Riazuddin. Singapura, World Scientific, 1994b.
SALAM, A. & WARD, J. C. “Electromagnetic and weak interactions.” Physics Letters, 13, 1964, p. 168-71.
SCHWEBER, S. S. QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga . Princeton, Princeton University Press, 1994.
SCHWINGER, J. “Quantum electrodynamics. I. A covariant formulation.” In: Physical Review, 74, 1948, p. 1439-61.
SCHWINGER, J. “Quantum electrodynamics. II. Vacuum polarization and self energy.” In: Physical Review, 75, 1949a, p. 651-79.
SCHWINGER, J. “Quantum electrodynamics. III. The electromagnetic properties of the electron – Radiative corrections to scattering.” In: Physical Review, 76, 1949b, p. 790-817.
SCHWINGER, J. “Preface.” In: SCHWINGER, J. (ed.). Selected papers on quantum electrodynamics. Nova Iorque, Dover, 1958, p. vii-xvii.
SCHWINGER, J. (ed.). Selected papers on quantum electrodynamics. Nova Iorque, Dover, 1958.
SHAW, R. “Invariance under general isotopic spin transformations.” In: O’RAIFEARTAIGH, L. (ed.). The dawning of gauge theory. Princeton, Princeton University Press, 1997, p. 200-7.
SOPCZAK, A. “Higgs physics at LEP-1.” In: Physics Reports, 359, 2002, p. 169-282.
SOUZA, E. G. “Multideductive logic and the theoretic-formal unification of physical theories.” In: Synthese, 125, 2000, p. 253-62.
’tHOOFT, G. “Renormalization of massless Yang-Mills fields.” In: Nuclear Physics, B33, 1971a, p. 173-99.
’tHOOFT, G. “Renormalizable lagrangians for massive Yang-Mills fields.” In: Nuclear Physics, B35, 1971b, p. 167-88.
’tHOOFT, G. & VELTMAN, M. “Regularization and renormalization of gauge fields.” In: Nuclear Physics, B44, 1972a, p. 189-213.
’tHOOFT, G. & VELTMAN, M. “Combinatorics of gauge fields.” In: Nuclear Physics, B50, 1972b, p. 318-53.
TOMONAGA, S. “On a relativistically invariant formulation of the quantum theory of wave fields.” In: Progress of Theoretical Physics, 1, 2, 1946, p. 27-42.
TOMONAGA, S. “On infinite field reactions in quantum field theory.” In: Physical Review, 74, 1948, p. 224.
UTIYAMA, R. “Invariant theoretical interpretation of interaction.” In: O’RAIFEARTAIGH, L. (ed.). The dawning of gauge theory. Princeton, Princeton University Press, 1997, p. 213-39.
VAN DER WAERDEN, B. L. (ed.). Sources of quantum mechanics. Nova Iorque, Dover, 1968.
WEINBERG, S. “A model of leptons.” In: Physical Review Letters, 19, 21, 1967, p. 1264-66.
WEINBERG, S. “The search for unity: notes for a history of quantum field theory.” In: Daedalus, 106, 2, 1977, p. 17-35.
WEINBERG, S. The quantum theory of fields. Volume I: foundations. Cambridge, Cambridge University Press, 1995.
WEINBERG, S. The quantum theory of fields. Volume II: modern applications. Cambridge, Cambridge University Press, 1996.
WEISSKOPF, V. “On the self-energy and the electromagnetic field of the electron.” In: Physical Review, 56, 1939, p. 72-85.
WEISSKOPF, V. “The self-energy of the electron.” In: MILLER, A. I. (ed.). Early quantum electrodynamics: a source book. Cambridge, Cambridge University Press, 1994a, p. 157-68.
WEISSKOPF, V. “The electrodynamics of the vacuum based on the quantum theory of the electron.” In: MILLER, A. I. (ed.). Early quantum electrodynamics: a source book. Cambridge, Cambridge University Press, 1994b, p. 206-26.
WEYL, H. “Gravitation and electricity.” In: O’RAIFEARTAIGH, L. (ed.). The dawning of gauge theory. Princeton, Princeton University Press, 1997a, p. 24-37.
WEYL, H. “Electron and gravitation.” In: O’RAIFEARTAIGH, L. (ed.). The dawning of gauge theory. Princeton, Princeton University Press, 1997b, p. 121-44.
YANG, C. N. & MILLS, R. L. “Conservation of isotopic spin and isotopic gauge invariance.” In: O’RAIFEARTAIGH, L. (ed.). The dawning of gauge theory. Princeton, Princeton University Press, 1997, p. 186-96
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