A measurement of G with a cryogenic torsion pendulum

A cryogenic torsion balance using a liquid-cryogen free, ultra-low vibration cryostat

We describe a liquid-cryogen free cryostat with ultra-low vibration levels, which allows for continuous operation of a torsion balance at cryogenic temperatures. The apparatus uses a commercially available two-stage pulse-tube cooler and passive vibration isolation. The torsion balance exhibits torque noise levels lower than room temperature thermal noise by a factor of about four in the frequency range of 3-10 mHz, limited by residual seismic motion and by radiative heating of the pendulum body. In addition to lowering thermal noise below room-temperature limits, the low-temperature environment enables novel torsion balance experiments. Currently, the maximum duration of a continuous measurement run is limited by accumulation of cryogenic surface contamination on the optical elements inside the cryostat.

Additional Solar System Gravitational Anomalies

This article is motivated by uncertainty in experimental determinations of the gravitational constant, G, and numerous anomalies of up to 0.5 percent in Newtonian gravitational force on bodies within the solar system. The analysis sheds new light through six natural experiments within the solar system, which draw on published reports and astrophysical databases, and involve laboratory determinations of G, orbital dynamics of the planets and the moons of Earth and Mars, and non-gravitational acceleration (NGA) of ‘Oumuamua and comets. In each case, values are known for all variables in Newton’s Law F=G·M·mR2, except for the gravitational constant, G. Analyses determine the gravitational constant’s observed value, G^, which—across the six settings—varies with the mass of the smaller, moving body, m, so that G^=G×0.998+0.00016×lnm. While further work is required, this examination shows a scale-related Newtonian gravity effect at scales from benchtop to Solar System, which contributes to the understanding of symmetry in gravity and has possible implications for Newton’s Laws, dark matter, and formation of structure in the universe.

CODATA Recommended Values of the Fundamental Physical Constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

A dual-magneto-optical-trap atom gravity gradiometer for determining the Newtonian gravitational constant

As part of a program to determine the gravitational constant G using multiple independent methods in the same laboratory, an atom gravity gradiometer is being developed. The gradiometer is designed with two magneto-optical traps to ensure both the fast simultaneous launch of two atomic clouds and an optimized configuration of source masses. Here, the design of the G measurement by atom interferometry is detailed, and the experimental setup of the atom gravity gradiometer is reported. A preliminary sensitivity of 3 × 10^-9 g/Hz to differential gravity acceleration is obtained, which corresponds to 99 E/Hz (1 E = 10^-9 s^-2) for the gradiometer with a baseline of 0.3 m. This provides access to measuring G at the level of less than 200 parts per million in the first experimental stage.

CODATA recommended values of the fundamental physical constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council (CODATA). The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

On-chip torsion balances with femtonewton force resolution at room temperature enabled by carbon nanotube and graphene

The torsion balance, consisting of a rigid balance beam suspended by a fine thread, is an ancient scientific instrument, yet it is still a very sensitive force sensor to date. As the force sensitivity is proportional to the lengths of the beam and thread, but inversely proportional to the fourth power of the diameter of the thread, nanomaterials should be ideal building blocks for torsion balances. Here, we report a torsional balance array on a chip with the highest sensitivity level enabled by using a carbon nanotube as the thread and a monolayer graphene coated with Al nanofilms as the beam and mirror. It is demonstrated that the femtonewton force exerted by a weak laser can be easily measured. The balances on the chip should serve as an ideal platform for investigating fundamental interactions up to zeptonewton in accuracy in the near future.

Precision measurement of the Newtonian gravitational constant

The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10-11 m3 kg-1 s-2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.

High-Q Milligram-Scale Monolithic Pendulum for Quantum-Limited Gravity Measurements

We present the development of a high-Q monolithic silica pendulum weighing 7 milligram. The measured Q value for the pendulum mode at 2.2 Hz was 2.0×10^{6}. To the best of our knowledge this is the lowest dissipative milligram-scale mechanical oscillator to date. By employing this suspension system, the optomechanical displacement sensor for gravity measurements we recently reported in Matsumoto et al. [Phys. Rev. Lett. 122, 071101 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.071101] can be improved to realize quantum-noise-limited sensing at several hundred hertz. In combination with the optical spring effect, the amount of intrinsic dissipation measured in the pendulum mode is enough to satisfy requirements for measurement-based quantum control of a massive pendulum confined in an optical potential. This paves the way for not only testing dark matter via quantum-limited force sensors, but also Newtonian interaction in quantum regimes, namely, between two milligram-scale oscillators in quantum states, as well as improving the sensitivity of gravitational-wave detectors.

Measurements of the gravitational constant using two independent methods

The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way to resolve this issue is to measure G using a number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10^-11 and 6.674484 × 10^-11 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

Invited Review Article: Measurements of the Newtonian constant of gravitation, G

By many accounts, the Newtonian constant of gravitation G is the fundamental constant that is most difficult to measure accurately. Over the past three decades, more than a dozen precision measurements of this constant have been performed. However, the scatter of the data points is much larger than the uncertainties assigned to each individual measurement, yielding a Birge ratio of about five. Today, G is known with a relative standard uncertainty of 4.7 × 10-5, which is several orders of magnitudes greater than the relative uncertainties of other fundamental constants. In this article, various methods to measure G are discussed. A large array of different instruments ranging from the simple torsion balance to the sophisticated atom interferometer can be used to determine G. Some instruments, such as the torsion balance can be used in several different ways. In this article, the advantages and disadvantages of different instruments as well as different methods are discussed. A narrative arc from the historical beginnings of the different methods to their modern implementation is given. Finally, the article ends with a brief overview of the current state of the art and an outlook.

Why is it so easy to underestimate systematic errors when measuring G?

Before this Theo Murphy Meeting, my working hypothesis was that human activity during the measurement of G significantly affects the measurement itself. Noise caused by the gravity gradient of humans was indeed the reason why in one experiment the apparatus was raised 3 m above the floor. The meeting convinced me that all experimenters took adequate precautions against gravity gradients caused by human activity. During the meeting, another concern arose: was the cycle time between two states of the experiment so long that the environment changed significantly in the meantime? Once again, it appears that the experimenters were appropriately cautious. After the meeting, it became clear that ageing effects in thin, stressed wires could be an issue. I conclude with a speculation about a future 'atomic' value of G.