GOLDHABER AND NIETO Limits on the Photon Mass 295 through a superconducting loop.This condition is "remote"of all,measurement of velocity dispersion for derived from the fact that the line integral of the low frequency radiation in intergalactic space-which vector potential around the loop is equal to the flux means taking some spaceships a long,long way from through the loop.?8 That fact is not changed by finite u. home.29 What is changed is the equality between the line integral ACKNOWLEDGMENTS of H around a loop,and the total current through the loop.Thus,"current quantization"conditions,if ever In composing this paper,we have been inspired and enunciated,could be modified byμ≠O. instructed by a large number of people,both through published articles and private conversations.Among 3.Prospects for u Hunters publications of the last few years,the works of Bartlett We have seen that improvements of more than an Goldhagen and Phillips (1970);Feinberg (1969) Kobzarev and Okun'(1968);and Williams and Park order of magnitude in static photon mass limits may be (1971)have been most helpful. achieved by known methods.The theorem expressed in Eg.(6.19)demonstrates that such experiments require We have received valued comments from D.F not only low field frequency,but also large dimensions Bartlett,R.Y.Chiao,E.R.Cohen,J.E.Faller,G. of the "experimental region,"with the sole exception of Feinberg,D.Z.Freedman,P.A.M.Gram,J.L. the phenomenally accurate null test for deviations from Heilbron,R.W.P.King,N.M.Kroll,B.Lautrup, Coulomb's law.Chances for improvement in dynamic B.W.Lee,L.B.Okun',S.J.Peale,E.A.Phillips, mass limits are less clear.For both types of limit, J.M.Rankin,K.Riegel,A.E.Sanderson,L.Van terrestrial and extraterrestrial observations are com- Hove,C.N.Yang and D.Yennie. petitive with each other,although completed terrestrial A.S.G.wishes to thank Drs.Louis Rosen and B.Zumino for hospitality at Los Alamos Scientific measurements are about an order of magnitude worse than their extraterrestrial counterparts. Laboratory and CERN,respectively,while this work reached final form. There remains a class of promising extraterrestial M.M.N.wishes to thank Prof.Aage Bohr for static "experiments"with no competition from the laboratory.As Yamaguchi (1959)and Williams and hospitality at the Niels Bohr Institute,during the Park (1971)have noted,observations of magnetic period of a challenging transAtlantic collaboration. fields over galactic dimensions could lead to a far REFERENCES better limit on u,conceivably ten orders of magnitude below the geomagnetic value. 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J.Geophys.Res.70,3647. portant in quantum mechanics.Namely,one may replace the and S.J.Hendricks,1968,N.A.S.A.Tech.Note No electromagnetic current in Proca's Equation by Ja=Ja+A and have the new condition=A Only the combina D-4527 (unpublished). tion (A.-A)enters in any classical measurable quantity,but Ending on this wistful note,as we must in discussing a still this trick permits one to introduce a formal gauge invariance unfinished search,we find it cheering to recall an amusing anecdote that is helpful in a Lagrangian formulation of quantum electro by R.P.Feynman (1962-1963)in his Lecture Notes on Gravita- dynamics.It is equivalent to an explicit separation of spin-one tion.Feynman tells the story of a cocktail party in Paris,where, longitudinal photons from spin-zero photons.Gauge invariance challenged by a French professor,he managed in a short time to or current conservation,is equivalent to the statement that derive at least crude mass limits in almost all the ways indicated this separation has no physical significance,even for finite photon here.One can only regret the discussion was not longer,for a mass. new method might have been unearthed