Contains research objectives and project status

Weiss, Rainer

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VII. GRAVITATION RESEARCHProf. R. WeissE. P. JacobsR. A. SramekRESEARCH OBJECTIVES AND PROJECT STATUSResearch in this group is concerned with investigating the nature of the gravitationalinteraction, in particular, with performing experiments that might distinguish betweendifferent theories of gravitation and cosmology. These aims are admittedly grandiose,especially in view of the inadequacy of present techniques which preclude performingmany of the experiments that one can think of. The subject is, however, of such funda-mental importance that even marginal experiments appear to be justified.Our present intention is to perform an experiment to determine the constancy of G,the Newtonian gravitational constant. Interest in this has been motivated by a conjectureof Dirac that G may have a secular variation of ~10-10 year because of the expansionof the universe. Jordan 2 and Dicke 3 have formulated scalar theories of gravitation withinthe framework of general relativity which have been tailored to fit Dirac's conjecture.Dicke's theory not only predicts a secular change in G but also an annual periodic vari--10ation of ~3 X 10 because of the Earth's eccentric motion around the sun.Table VII-1. Limits on G variations.Gravitational Force versus Inertial Reaction -/yearMoon period versus earth rotation periodcoupled with theory of tidal torques for -9200 years of observations and a check 10point against ancient eclipse data 4Pendulum and Absolute Measurements of g 10 - 75made at Potsdam over 50 yearsGravitational Force versus Electric ForceSpring gravimeters 10-7Cavendish experiment 6  10-3Table VII-1 lists the limits that can be put on G variations from present knowledge.A distinction is made between limits set by measurements of a gravitational force againstan inertial reaction and the gravitational force against another force field, as, forexample, electromagnetic forces. It is conceivable that G variations would not beQPR No. 77(VII. GRAVITATION RESEARCH)observed in the first class of observations. The table is not exhaustive, studies of Gvariations as they might affect stellar evolution and the chronology of the Earth'shistory made by Dicke 7 and Jordan 8 do not offer smaller limits than those given inTable VII- 1.Proposed ExperimentThe experiment that we propose is to measure variations in g, the Earth's gravita-tional attraction at the surface, with a stable gravimeter of a new design. Although theproposed method has the advantage that it measures a gravitational force against an elec-tric force, it introduces the serious problem of the Earth's stability which will be dis-cussed presently. All previous gravimeters employ Hooke's law forces in solids or gaspressure to balance the gravitational force on a mass. Measurements of g made withgas gravimeters fall in the first class, and are extremely temperature-sensitive. Springgravimeters are troubled by temperature dependence of the Young's modulus of the springAg -6material (the best give a temperature dependence -10 /oC), and in a much moreg -8sinister manner by random material creeps of the springs (Ag/g ~ 10 - 8 month). In theproposed gravimeter (shown in Fig. VII-1) the spring is replaced by a measurable elec-tric force and is fundamentally an inverted Kelvin absolute electrometer. Plate 1 is theI 2 IMOLECULARBEAMI I T 1dc rf dc rf3 1mgdc3Fig. VII-1. Proposed gravimeter.gravitating mass, which is supported vertically by the electric field DC and maintainedhorizontally by the fringing field between the guard plate 3 and the gravitating plate. Theposition of plate 1 is established interferometrically; the interferometer is incorporatedin a null-seeking servomechanism which controls 6DC to maintain plate 1 co-planar withthe guard plates. The servo maintains the relationmg= F = 2 A,e  8r DC pwhere DCp is the average of the square of the electric field over the surface, A,DCpQPR No. 77(VII. GRAVITATION RESEARCH)of plate 1. In order to measure DCp the gravimeter plates are incorporated in thetransition region of a molecular beam electric resonance apparatus. AJ = 0, Dm = +lStark transitions in a polar molecule are induced in separated regions of 6RF betweenplates 1 and 2. If the Stark energies are small compared with the rotational energy ofthe molecule, the Stark transition frequency is given by vSTARK k ' DC>B' wherek is a function of the molecular constants and quantum numbers and 2> B is theaverage of the square of the electric field at the location of the molecular beam betweenthe regions of 6 RF Assuming that PL B = DCp (which is not strictly sobecause of the fringing field and, for only one molecular beam, because of nonparallelismof the plates) we can save the force equation and get8kVSTARK A mg.If m and A are constant, the g measurement becomes a frequency measurementAg =_ Ag vThis rudimentary description of the gravimeter only alludes to a host of problemswhich must be investigated first. Among these are:1. Constancy of the gravitating mass and temperature dependence of the plate area.2. Constancy of the relation between Fe and 2>B. In particular, how does therelation vary with plate separation, tilt, and co-planarity of the gravitating plate and theguard plates? An experiment is now in progress to study these effects for various plategeometries and potential distributions.3. Field homogeneity conditions necessary to see a resonance. Inhomogeneiticscan arise from nonparallelism of the plates and the time dependence of ground noise.For example, it may be necessary to have a fast AC servo to hold the plate, and henceDC, steady over the integration time of the servo that scans the resonance.Stability of the EarthAlthough no measurements have been reported of changes in g at a fixed point onthe Earth (besides calculable and known effects such as the tides), it is likely that theyexist, especially within the precision demanded for this experiment. In principle, theonly multipole moment of the Earth's gravitational potential whose changes are notamenable to averaging over distributed gravimeter sites is the monopole. A catalogueof the mass changes that one can think of would yield as the largest contributionAg/g ~ 10-16/year from meteor influx. Estimates of changes in the Earth's radius arefar more influential. Again, there are no measurements, and some theories predictexpansion, and others, contraction. Jeffreys,9 and MacDonald 1 0 are exponents ofQPR No. 77(VII. GRAVITATION RESEARCH)contraction caused by cooling which would result in changes in radius producingA~ +10 - 0 -1013 per year. Egyed calculates for an expansion, together with con-g Ag 0 -10tinental drift, a change in radius that could result in a g -10 per year. To empha-gsize this sensitivity, one need only observe that a change of 0. 3 mm in the radial positionAg -10of the gravimeter corresponds to a ~ g 10gOne change in the quadrupole moment can already be anticipated. The melting of theAg -i0polar ice caps results in a - 10 per year at 45 0 latitude; however, it is zero atg300 latitude. Variations in the Earth's rotation rate are monitored to the precisionnecessary for the experiment.Besides the Earth's radius, the other major unknowns are the magnitudes of localdistortions and mass redistributions in the vicinity of a given site (the very high ordermultipole moments). Knowledge of this will set a limit on the number of sites necessaryto establish a statistical estimate of the global g variation. We would endeavor, ofcourse, to pick seismically inactive rock shields with small gravity anomalies. To ourknowledge, the only measurements of secular earth distortion (except in regions of post-glacial uplift) have been made by the Benioff Strain seismometer at the Lamont Geo-At -8physical Laboratory site, in Ogdensberg, New Jersey, where a limit of < 10 /month12over a 200-ft length has been set. It appears, however, that the limit is instrumental.In order to have a handle on radius changes and to correlate local distortions withchanges in g, it would be useful to have a stable strain seismometer associated with thegravimeter. We are, at present, engaged in the design and construction of a stabilizedlaser strain seismometer. Another necessary instrument is a stable tiltmeter, sincethe gravimeter is quadratically dependent on the angle between the plumb and the normalto the gravitating plate. This instrument is being constructed as part of senior thesisresearch.Our first effort will be to build one gravimeter and search for the annual periodicchange in g predicted by Dicke's scalar theory.R. WeissReferences1. P. A. M. Dirac, Proc.Roy. Soc. (London) A165, 199 (1938).2. P. Jordan, Schwerkraft und Weltall (Friedrich Vieweg und Sohn, Braunschweig,1955).3. C. Grans and R. H. Dicke, Phys. Rev. 124, 1925 (1961).4. W. H. Munk and G. J. F. MacDonald, The Rotation of the Earth (CambridgeUniversity Press, London, 1960).5. G. P. Woollard, Advances in Geophysics, Vol. 1, p. 281, 1952.6. F. H. Newman and V. H. L. Searle, The General Properties of Matter(Edward Arnold Ltd., London, 5th edition, 1957).7. R. H. Dicke, Rev. Modern Phys. 34, 110 (1962).QPR No. 77(VII. GRAVITATION RESEARCH)8. P. Jordan, Naturwiss. 48, 417 (1961).9. H. Jeffreys, The Earth (Cambridge University Press, London, 4th edition,1962).10. G. J. F. MacDonald, Revs. Geophys. 1, 587 (1963).11. L. Egyed, Nature 178, 534 (1956).12. M. W. Major, G. H. Sutton, U. Oliver, and R. Metsger, Bull. Seismol. Soc.Am. 54, 295 (1964).QPR No. 77

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