Evidence of “Terronium”: Spinning Earth Splits Atomic Levels

Background to the “News Report”

In 1988 and 1989 my papers “Rotational Degeneracy Breaking of Atomic Substates…” and “Rotationally Induced Optical Activity in Atoms” were published respectively in General Relativity & Gravitation and Europhysics Letters. The work caught the attention of a number of research labs, in particular that of Prof Geoffrey Stedman of the University of Canterbury in Christchurch, New Zealand. Dr Stedman’s group were at the time constructing what was hoped to become the world’s most sensitive ring laser, and I was invited to Canterbury to give the 1990 Erskine Lectures and remain afterward to interact with Geoff and his group. The ring laser was to be located deep underground in the Cashmere Caverns, and preliminary estimates seemed to indicate that the Canterbury Ring Laser might have the sensitivity to detect the very weak atomic optical activity predicted in my papers. Construction of the ring laser facility continued after I left New Zealand, and more refined analysis yielded a less optimistic outcome of the detection of optical activity induced by the Earth’s rotation.

In October and November of 1997, Physics Today, the flagship publication of the American Institute of Physics, in celebration of its 50th year invited readers to become “Search and Discovery reporters of the future” by submitting “an imagined story about an exciting discovery, an advance in physics, or a new technology.” I responded to that invitation by submitting on 28 November 1997 the following essay, describing in a “report” published in 2048—i.e. 50 years after 1998—the new technology that permitted detection of the ultra-small effects I predicted in 1988 and 1989.

Whereas Physics Today solicited the Physics Tomorrow essays to celebrate its 50th anniversary, I offer this “tomorrow essay” again in 2025 on the occasion of the 100th anniversary of the creation of quantum mechanics, marked as the International Year of Quantum Science and Technology (IYQ). Advances in QM since its inception in 1925 have been so rapid and remarkable in both theory and experiment, that—who knows?—it may well be possible by 2048 to detect the effects of the Earth’s rotation on atomic energy levels.

Although no sane person doubts that the Earth rotates on its axis, for all practical purposes virtually every table-top atomic physics experiment to date has been performed on an effectively flat, stationary planet. And why think otherwise? The Earth, after all, rotates at the leisurely rate of 7.3 x 10 ^-5 radians per second, giving rise to noninertial effects that are hardly perceptible except over very large distances. Throw a baseball to your friend; unless your aim is poor or there is a stiff wind blowing, the ball does not swerve to the right or left.

The size of an atom is some twelve orders of magnitude smaller than a baseball field, and even today, over a hundred and twenty years after the creation of quantum mechanics, the Coriolis effect of the Earth on a bound electron is not likely to be mentioned in any quantum mechanics textbook. But it will be in the next edition. Working independently and employing two quite different experimental methods, two collaborative efforts, one of the European Commonwealth, and the other of the US-Canadian Confederation each observed characteristic features of the system referred to as “Terronium”, the coupling of the spin of the Earth and the angular momentum of an atom. This is the first time that the dynamics of a quantum system has been observed lo be affected by the motion of a planet.

Quantum Coriolis Effect

To an observer in a rotating reference frame, the effective force on a classical object comprises, in addition to the actual force, two “pseudo” forces: a centrifugal force proportional to the square of the rotation frequency and a Coriolis force that depends linearly on both the rotation rate of the frame and the velocity of the object relative to the rotating frame. At the slow rate of the earth’s rotation and the high speed of electron motion about an earth-bound atomic nucleus (on the order of one-hundredth the speed of light), the Coriolis force on an atomic electron greatly exceeds the earth’s centrifugal force.

In the quantum description of the dynamics of bound particles, however, concepts such as force, orbit, and velocity are less relevant than that of potential or energy. Expressed as a potential, the rotation of the Earth contributes to the energy operator (Hamiltonian) of an atom a term proportional to the frame angular velocity and the total electron angular momentum. The added energy term, which resembles a magnetic interaction, splits the magnetic substates of each energy level. The resemblance to the Zeeman effect is not coincidental, but is a quantum manifestation of Larmor's theorem denoting the equivalence (for low magnetic fields) between a field-free rotating reference frame of angular frequency ω and an inertial reference frame with static magnetic field of strength B = 2mω/e, where e/m is the charge/mass ratio of the moving particle.

It is the diverse consequences of this level splitting that the two groups observed.

Birefringent Atoms

Since the Coriolis interaction depends on the sense of rotation of the frame (just like the Zeeman interaction depends on the orientation of a magnetic field), the refractive indices of a rotating transparent sample will differ slightly for left and right circularly polarized light. This difference, or circular birefringence, of magnitude Δn ~ 20 × 10 ^-18 for the earth's rotation, has long been beyond the capacity of any instrument to measure. No longer. Using the Super Large Ring-Laser Facility (SLARF) recently constructed at the University of Heidelberg, Fritz Lädbach and his associates, in collaboration with H. M. Fennapore and her group at Oxford University, directly observed the circular birefringence in optically inactive silicon pertusside glass induced by the diurnal motion of the Earth. ¹

In a continuous-wave single-mode ring laser the light beam entering the ring is divided into two components that circulate in opposite senses. The countercirculating beams, with identical frequencies in a stationary laser, are Doppler shifted by an amount proportional to the rate at which the laser rotates and thereby gives rise to a beat frequency. If, in addition, the beams pass through a circularly birefringent sample in the laser cavity, the beat frequency will shift by an amount Δ𝑣 linearly proportional to Δn. This is precisely what Lädbach, Fennepore, and their colleagues observed.

According to Lädbach, the successful outcome of the experiment is largely attributable to "the size, maneuverability, and mirror coatings at SLARF." All things being equal, the larger the perimeter of the ring, the smaller is the detectable birefringence. Square, with 7 m to a side, and located 30 m underground at the bottom of the Hilfmiraus mine outside Heidelberg, SLARF is presently the largest and most stable ring laser on earth. In preliminary geophysical investigations of the laser's sensitivity, researchers at SLARF picked up seismic disturbances on the other side of the globe that were so weak as to be barely detectable by locally placed conventional seismometers. "It is like hearing a hiccough at 18,000 km," remarked Fennepore.

Size is not everything, however. Unlike any other currently operating ring laser, SLARF is mounted on a maneuveable optical platform whose orientation and rotation rate are coarsely controllable by precision motors and finely adjustable by "angleworm" micro-roto-positioners. The angleworms—an extension to angular motion of the piezoelectric "inchworm" micropositioners developed in the 1990s for scanning-tunneling and atomic-force microscopes-permit the SLARF researchers quite literatally to "turn off" the earth's rotation in order to study and compensate for spurious effects unrelated to noninertial motion.

One such effect is the intrinsic circular birefringence of atoms resulting from weak neutral currents (WNC), in effect the exchange of Z ⁰ particles between the bound electrons and the nucleus. First observed nearly seventy years ago in heavy metal vapors of bismuth, thallium, and lead², this purely quantum interaction is in fact considerably larger than the essentially classical atomic-scale Coriolis effect of the earth. The SLARF researchers can detect WNC in atoms very easily, Lädbach claims, and routinely take these interactions into account. Although larger than atomic-scale noninertial ellects of the earth, the WNC manifest different symmetry properties. They are truly chiral, being odd under space-inversion and even under time-reversal, in contrast to the Coriolis effect which, again analogous to a magnetic interaction, is even under space-inversion and odd under time-reversal.

Another feature unique to the SLARF experiment is the "electroflex" coated mirrors which, in response to a small potential difference across the mirror surface, selectively reflect light in an ultra-narrow band of wavelengths. Thus, observed the dispersion in An over a spectral range from the near IR to the near UV, obtaining results in nearly perlect accord with theory.

World's best-known frequency

Although the splitting of magnetic substates is ultimately responsible for the inequivalent refractive indices for left- and right-circularly polarized light, this splitting is not seen explicitly in the measurement of circular birefringence, which is a nonresonant experiment.

In an entirely different approach, teams led by O. G. Willikers of Harvard University and Pierre J. Menfiche of Laval University, working at the Cambridge Superconducting Superfluid Supermaser Lab [SU(3)], directly observed the Coriolis splitting of the hyperfine transition 1²S_1/2(1,±1) – 1 ²S_1/2(0,0) in atomic hydrogen.³ Long the most precisely determined atomic level separation, the hydrogen hyperfine splitting ~1420 MHz) had been known until this year to an uncertainty of 1 part in 10¹³.⁴ Not until the satisfactory implementation several years ago of all-optical computers employing quantum-bit (qubit) logic elements was it possible for theorists to predict this frequency to the same extent that experimentalists were able to measure it. By reducing the uncertainty of the hyperfine line by two more orders of magnitude, the Harvard-Laval team were able to observe the 2.314 × 10 ^-5 Hz splitting induced by the Coriolis effect of the Earth.

Several unique features of the SU(3) Lab enabled the researchers to achieve this tour de force. Perhaps the most visually striking is the instrument's large size. Occupying one half the basement level of the Ramsey Physics Building at Harvard, the maser is the largest in the world. But, as with SLARF, size is not the whole story. Coating the inside surfaces of the maser is a layer of a metallofullerene sheeting in its high-temperature superfluid state which virtually eliminates all uncontrollable interactions between the hydrogen atoms and the walls of the container. In addition, to suppress the Zeeman effect and motional elecuic fields arising from the magnetic field of the earth, the maser is wrapped in room-temperature superconducting plastic ribbon (which expells magnetic fields by means of the Meissner effect), and the whole apparatus is surrounded by a shell of G-mu-nu metal, the alloy of highest known permeability.

A particularly interesting feature of the hydrogen hyperfine measurement is that it tests a nonclassical extension of the Coriolis effect. Within the framework of classical mechanics, the Coriolis effect involves the coupling of the angular velocity of the frame to the orbital angular momentum of the moving particle, whereas quantum theory predicts that the angular velocity is coupled to the total angular momentum. In the hydrogen ground state this distinction is important, for the electron orbital angular momentum is zero. Thus, the observation of Coriolis splitting of the field-free hydrogen hyperfine line confirms the coupling of the spin of the Earth to the (nonclassical) spins of the electron and proton.

"It was a helluva way to show the Earth turns," concluded Menfiche, "but we learned a lot."

References

1. F. Lädbach et al., EuroComm. J. Phys. 39, 125 (2048)
2. M.-A. Bouchiat and L. Pottier, Science 234, 1204 (1986)
3 O. G. Willikers et al., N. Am. Fed. Phys. Lett. 14, 87 (2048)
4. U. R Gonne and I. C. Farenwyde, J. UltraPrec. 32, 13 (2031)