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Searching for a response: the intriguing mystery of Feynman’s theoretical reference amplifier

  • Vincenzo d’Alessandro
  • Santolo Daliento
  • Marco Di Mauro
  • Salvatore EspositoEmail author
  • Adele Naddeo
Article
  • 11 Downloads

Abstract

We analyze Feynman’s work on the response of an amplifier performed at Los Alamos and described in a technical report of 1946, as well as lectured on at the Cornell University in 1946–47 during his course on Mathematical Methods. The motivation for such a work was Feynman’s involvement in the Manhattan Project, for which the necessity emerged of feeding the output pulses of counters into amplifiers or several other circuits, with the risk of introducing distortion at each step. In order to deal with such a problem, Feynman designed a theoretical “reference amplifier”, thus enabling a characterization of the distortion by means of a benchmark relationship between phase and amplification for each frequency, and providing a standard tool for comparing the operation of real devices. A general theory was elaborated, from which he was able to deduce the basic features of an amplifier just from its response to a pulse or to a sine wave of definite frequency. Moreover, in order to apply such a theory to practical problems, a couple of remarkable examples were worked out, both for high-frequency cutoff amplifiers and for low-frequency ones. A special consideration deserves a mysteriously exceptional amplifier with best stability behavior introduced by Feynman, for which different physical interpretations are here envisaged. Feynman’s earlier work then later flowed in the Hughes lectures on Mathematical Methods in Physics and Engineering of 1970–71, where he also remarked on causality properties of an amplifier, that is on certain relations between frequency and phase shift that a real amplifier has to satisfy in order not to allow output signals to appear before input ones. Quite interestingly, dispersion relations to be satisfied by the response function were introduced.

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References

  1. 1.
    P. Galison. Stud. Hist. Phil. Mod. Phys. 29, 391 (1998). MathSciNetCrossRefGoogle Scholar
  2. 2.
    L. Hoddeson, P.W. Henriksen, R.A. Meade, C. Westfall. Critical Assembly – A Critical History of Los Alamos during the Oppenheimer Years, 1943–1945. Cambridge University Press, Cambridge, 1993. Google Scholar
  3. 3.
    R.P. Feynman. Surely You’re Joking, Mr. Feynman! Adventures of a curious character. W.W. Norton & Co., New York, 1985. Google Scholar
  4. 4.
    T. Snyder. Absolute Measurement of γ − 25 with Long counter. Report LAMS-8. 6 September 1943. Summary of meeting of R.P. Feynman, J. McKibben and T. Snyder. Google Scholar
  5. 5.
    F. de Hoffmann. Intensity Fluctuations in of a Neutron Chain Reactor. Report LA-256, 27 June 1944. Work done by R.P. Feynman, F. de Hoffmann and R. Serber. Google Scholar
  6. 6.
    R.P. Feynman. Statistical Behavior of Neutron Chains. Report LA-591, 26 July 1946. Work done by R.P. Feynman. Google Scholar
  7. 7.
    R.P. Feynman, F. de Hoffmann and R. Serber. J. Nucl. Energy 3, 64 (1956). Google Scholar
  8. 8.
    R.P. Feynman. Report on the conference on Critical Concentrations of Material. Report A-83-0002, 7-3, 25 April 1944. Google Scholar
  9. 9.
    R.P. Feynman. A New Approximate Method for Rapid Calculation of Critical Amounts of X. Report A-83-002, 7-3, 12 September 1945. Google Scholar
  10. 10.
    R.P. Feynman. A Theorem and its Application to Finite Tampers. Report LA-608nSeries B, 15 August 1946. Work done by R.P. Feynman. Google Scholar
  11. 11.
    R.P. Feynman. IBM Calculations of Implosion Hydrodynamics (Problem 8 - Solid Gadget). Report LA-317, 21 June 1945. Work done by R.R. Davis et al. Google Scholar
  12. 12.
    R.P. Feynman, J. Ashkin and R. Ehrlich. First Report on the Hydride. Report LAMS-45 (classified SRD), 31 January 1944. Google Scholar
  13. 13.
    R.P. Feynman, J. Ashkin and R. Ehrlich. Second Report on the Hydride. Report LAMS-45 (classified SRD), 22 February 1944. Google Scholar
  14. 14.
    R.P. Feynman, J. Ashkin, R. Ehrlich and F. Reines. Third Report on the Hydride. Report LAMS-71 (classified SRD), 5 April 1944. Google Scholar
  15. 15.
    R.P. Feynman and T.A. Welton. The Calculation of Critical Masses Including the Effects of the Distribution of Neutron Energies. Report LA-524, 21 January 1947. Work done by J. Ashkin, R. Ehrlich, R.P. Feynman, M. Peshkin, F. Reines and T.A. Welton. Google Scholar
  16. 16.
    R.P. Feynman. Amplifier Response. Report LA-593, 2 August 1946. Work done by R.P. Feynman. Google Scholar
  17. 17.
    R.P. Feynman. Class notes from the course on Mathematical Methods at Cornell University. Notes taken by James C. Keck, 1946. http://james-keck-memorial-collection.unibs.it/classnotesFeynman.htm.
  18. 18.
    R.P. Feynman. Hughes Lectures on the Mathematical Methods of Physics. Notes taken and transcribed by John Neer, 1971. http://www.thehugheslectures.info/the-lectures.
  19. 19.
    M. Di Mauro, S. Esposito and A. Naddeo. Transversal Int. J. Historiography Sci. 4, 163 (2018). CrossRefGoogle Scholar
  20. 20.
    J.S. Toll. Phys. Rev. 104, 1760 (1956). ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    A. Lipson, S.G. Lipson and H. Lipson. Optical Physics. Cambridge University Press, Cambridge, 2010. Google Scholar
  22. 22.
    H.W. Bode. Network Analysis and Feedback Amplifier Design. Van Nostrand, New York, 1945. Google Scholar
  23. 23.
    J.A. Wheeler letter to R.P. Feynman, 10 November 1949; R.P. Feynman letter to J.A. Wheeler, 8 December 1949; in Feynman Papers, Caltech archive, Box 3, Folder 10. Cited in Ref. [1], p. 401. Google Scholar
  24. 24.
    H.N. Nussenzveig. Causality and dispersion relations. Academic Press, New York, 1972. Google Scholar
  25. 25.
    A. Sommerfeld. Ann. Physik 44, 177 (1914). ADSCrossRefGoogle Scholar
  26. 26.
    L. Brillouin. Ann. Physik 44, 203 (1914). ADSCrossRefGoogle Scholar
  27. 27.
    H.A. Kramers. La diffusion de la lumière par des atomes, in Atti del Congresso Internazionale di Fisica, Como, 2, 545 (1927). Google Scholar
  28. 28.
    R. de L. Kronig. J. Opt. Soc. Am. 12, 547 (1926). ADSCrossRefGoogle Scholar
  29. 29.
    W. Schutzer and J. Tiomno. Phys. Rev. 83, 349 (1951). ADSCrossRefGoogle Scholar
  30. 30.
    N.G. van Kampen. Phys. Rev. 91, 1267 (1953). ADSCrossRefGoogle Scholar
  31. 31.
    N.G. van Kampen. Phys. Rev. 89, 1072 (1953). ADSCrossRefGoogle Scholar
  32. 32.
    J. Bechhoefer. Am. J. Phys. 79, 1053 (2011). ADSCrossRefGoogle Scholar
  33. 33.
    H.W. Bode. U.S. patent 2123178 (23 June 1937). Bell Sys. Tech. J. 19, 421 (1940). CrossRefGoogle Scholar
  34. 34.
    M. Gell-Mann, M.L. Goldberger and W.E. Thirring. Phys. Rev. 95, 1612 (1954). ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    A. Pickering, in L.M. Brown et al. (eds), Pions to Quarks. Particle Physics in the 1950s, Cambridge University Press, Cambridge, 1989. Google Scholar
  36. 36.
    J.T. Cushing. Theory construction and selection in modern physics: The S matrix. Cambridge University Press, Cambridge, 1990. Google Scholar
  37. 37.
    E.P. Wigner (ed.). Dispersion relations and their relation with causality, Proceedings of the International School of Physics “Enrico Fermi”, course 29, held 15th July to 3rd August 1963. Academic Press, New York, 1964. Google Scholar
  38. 38.
    R.P. Feynman. Lectures on Physics (mainly mechanics, radiation and heat). Vol. I. http://www.feynmanlectures.caltech.edu/I-31.html.
  39. 39.
    M. Mézard, G. Parisi and M.A. Virasoro. Spin Glass Theory and Beyond. World Scientific, Singapore, 1987. Google Scholar
  40. 40.
    M.E. van Valkenburg. Network Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1974. Google Scholar
  41. 41.
    H.A. Wheeler. Wide-band amplifiers for television, in Proceedings of the I.R.E., July 1939, pp. 429. Google Scholar
  42. 42.
    R.P. Feynman. Lectures on Physics (mainly electromagnetism and matter). Vol. II. http://www.feynmanlectures.caltech.edu/II-22.html.
  43. 43.
    PSPICE User’s manual, cadence OrCAD 16.5. 2011. Google Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Elettrica e delle Tecnologie dell’Informazione, Universitá di Napoli “Federico II”NaplesItaly
  2. 2.Dipartimento di Fisica “E.R. Caianiello”, Universitá di SalernoFiscianoItaly
  3. 3.INFN Sezione di Napoli, Via CinthiaNaplesItaly

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