effect of earth's rotation in neutron interferometry

VOLUME 35, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S 25 AUGUST 1975

COMMENTS

Effect of Earth's Rotation in Neutron Interferometry

L o m e A. Page Physics Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

(Received 16 June 1975)

In a neutron interferometer experiment which can successfully demonstrate a quan­titative fringe shift due to the different gravitational potential for the neutron in the two legs of the apparatus, an adjunctive consideration must be the nonzero angular velocity of Earth and the lab. As in the classic Michelson-Gale-Pearson experiment done with light, and offset in the fringe pattern is predicted. Such a shift may not be subliminal at present precision levels.

Recently Colella, Overhause r , and Werne r 1

have p re t t i ly demons t ra ted that a slow neutron in a two-beam in t e r f e rome te r adapted f rom the Bonse and Har t type2 indeed s e n s e s a control led difference in gravi ta t ional potential between two legs of the sys t em, the control being effected by manipulat ing n *g, where h i s the n o r m a l to the plane of the appara tus and g is the nadi r .

The purpose of this note is to draw attention to the fact that in the cour se of this kind of e x p e r i ­ment the main loop (the pa ra l l e l og ram in the e x ­per iment ) n e c e s s a r i l y p r e s e n t s i ts no rma l h s o as to fo rm genera l ly a nonzero, and l ikewise con­t ro l lab le , dot product with the angular -ve loc i ty vec tor Qe of the E a r t h - l a b - i n t e r f e r o m e t e r s y s ­t em. An offset propor t iona l to Qe in the fringe pa t te rn for a given or ientat ion should be produced jus t as in the optical exper iment of Michelson, Gale, and P e a r s o n . 3

The s i ze of th is anc i l l a ry effect can be c o m ­pared to the s i ze of the g effect a s follows. C o ­lel la , Overhause r , and Werner 1 have a re la t ive phase f$g in rad ians due to gravi ty of

pg /sin<£ = 2M2gAXH ~2 (1)

where ft -g equals c o s ^ , A is the a r e a of the loop, M is the pa r t i c l e m a s s , and ft. is i ts deBrogl ie wavelength. A rud imenta ry calculation4 of the additional re la t ive phase jSfi gives for a nonre l a -

t iv is t ic pa r t i c l e

pQ/cosil)=2MAtteH-\ (2)

to f i r s t o r d e r in the angular velocity £le. Here cos^ i s n • Cle.

Numer ica l ly the r ight -hand s ide of (1) for the recen t exper iment is a lmos t 60 r a d p e r quadrant , whereas the r ight-hand s ide of (2) is about 2.3 rad pe r quadran t—thus down about \\ o r d e r s of magnitude from the gravi ta t ional effect. How­ever at lati tude ~45° the observed difference in dflm /dipcirca <p=0 between an Eas tward incident beam and a Westward incident beam might p o s ­sibly show the rotat ional effect, to the exclusion of any bending effects plus the main gravi ta t ional effect.

1R. Colella, A. W. Overhauser, and S. A. Werner, Phys0 Rev. Lett. 34, 1472 (1975).

2U. Bonse and M„ Hart, Appl. Phys. Lett. 6, 155 (1965).

3A. A. Michelson, Astrophys. J, j61, 137 (1925); A. A. Michelson, H. G. Gale, and F0 Pearson, Astrophys0

J. 61, 140 (1925). ^n neither expression has c been set equal to 1; the

speed of light does not enter. The expression (2) is just half the similar Michelson-Gale-Pearson expres­sion of Ref. 3, because the neutron goes only halfway around the loop to suffer interference, in contrast to their setup. Their result, divided by 2, could be stated as relative phase equals 2AH~i(Hcjj/c2)tie .

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