1mZ2hsN

Is a Graviton Detectable?Freeman Dyson (Institute for Advanced Study, Princeton, USA)Freeman Dyson (Institute for Advanced Study, Princeton, USA)Feature1 IntroductionI am enormously grateful to Dr. K. K. Phua, and to everyoneelse who had a hand in organizing this conference, for invitingme to visit Singapore. I am also grateful to my old and newfriends who came to Singapore to help me celebrate my birthday.As a former Brit, I am delighted to see this sparkling newcountry, which has prospered by giving free play to Chineseenterprise while still driving on the left side of the road.Now I come to the technical substance of my talk. It isgenerally agreed that a gravitational field exists, satisfyingEinstein’s equations of general relativity, and that gravitationalwaves traveling at the speed of light also exist. The observedorbital shrinkage of the double pulsar [1] provides directevidence that the pulsar is emitting gravitational waves atthe rate predicted by the theory. The LIGO experiment now inoperation is designed to detect kilohertz gravitational wavesfrom astronomical sources. Nobody doubts that gravitationalwaves are in principle detectable.This talk is concerned with a different question, whetherit is in principle possible to detect individual gravitons, orin other words, whether it is possible to detect the quantizationof the gravitational field. The words “in principle” areambiguous. The meaning of “in principle” depends on therules of the game that we are playing. If we assert that detectionof a graviton is in principle impossible, this may havethree meanings. Meaning (a): We can prove a theorem assertingthat detection of a graviton would contradict the laws ofphysics. Meaning (b): We have examined a class of possiblegraviton detectors and demonstrated that they cannot work.Meaning (c): We have examined a class of graviton detectorsand demonstrated that they cannot work in the environmentprovided by the real universe. We do not claim to have answeredthe question of “in principle” detectability accordingto meaning (a). In Sec. 3 we look at detectors with the LIGOdesign, detecting gravitational waves by measuring their effectson the geometry of space–time, and conclude that theycannot detect gravitons according to meaning (b). In Secs. 4and 5 we look at a different class of detectors, observing theinteractions of gravitons with individual atoms, and concludethat they cannot detect gravitons according to meaning (c). InSecs. 6 and 7 we look at a third class of detectors, observingthe coherent transitions between graviton and photon statesinduced by an extended classical magnetic field, and find thatthey also fail according to meaning (c).In Sec. 2 we look at a historic argument used by NielsBohr and Leon Rosenfeld to demonstrate the quantum behaviorof the electromagnetic field, and explain why this argumentdoes not apply to the gravitational field. In Sec. 8 webriefly examine the possibility of observing primordial gravitonsat the beginning of the universe by measuring the polarizationof the cosmic background radiation today. No definiteconclusions are reached. This talk is a report of workin progress, not a finished product. It raises the question ofthe observability of gravitons but does not answer it. There ismuch work still to do.2 The Bohr–Rosenfeld ArgumentBefore looking in detail at graviton detectors, I want to discussa general theoretical question. In 1933 a famous paperby Niels Bohr and Leon Rosenfeld, [2] was published in theproceedings of the Danish Academy of Sciences with the title,“On the Question of the Measurability of the ElectromagneticField Strengths.” An English translation by Brycede Witt, dated 1960, is in the Institute library in Princeton,bound in an elegant hard cover. This paper was a historic displayof Bohr’s way of thinking, expounded in long and convolutedGerman sentences. Rosenfeld was almost driven crazy,writing and rewriting 14 drafts before Bohr was finally satisfiedwith it. The paper demonstrates, by a careful and detailedstudy of imaginary experiments, that the electric andmagnetic fields must be quantum fields with the commutationrelations dictated by the theory of quantum electrodynamics.The field-strengths are assumed to be measured by observingthe motion of massive objects carrying charges and currentswith which the fields interact. The massive objects are subjectto the rules of ordinary quantum mechanics which setlimits to the accuracy of simultaneous measurement of positionsand velocities of the objects. Bohr and Rosenfeld showthat the quantum-mechanical limitation of measurement ofthe motion of the masses implies precisely the limitation ofmeasurement of the field-strengths imposed by quantum electrodynamics.In other words, it is mathematically inconsistentto have a classical electromagnetic field interacting witha quantum-mechanical measuring apparatus.A typical result of the Bohr–Rosenfeld analysis is theirequation (58),∆E x (1)∆E x (2) ∼ |A(1, 2) − A(2, 1)| . (1)Here the left side is the product of the uncertainties of measurementof two averages of the x-component of the electricfield, averaged over two space–time regions (1) and (2). Onthe right side, A(1, 2) is the double average over regions (1)and (2) of the retarded electric field produced in (2) by aunit dipole charge in (1). They deduce (1) from the standardHeisenberg uncertainty relation obeyed by the measuring apparatus.The result (1) is precisely the uncertainty relation impliedby the commutation rules of quantum electrodynamics.Similar results are found for other components of the electricand magnetic fields.The question that I am asking is whether the argument ofBohr and Rosenfeld applies also to the gravitational field. Ifthe same argument applies, then the gravitational field mustbe a quantum field and its quantum nature is in principle observable.However, a close inspection of the Bohr–Rosenfeldargument reveals a crucial feature of their measurement apparatusthat makes it inapplicable to gravitational fields. In theEMS Newsletter June 2014 29