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.

A low-frequency torsion pendulum with interferometric readout.

We describe a torsion pendulum with a large mass-quadrupole moment and a resonant frequency of 2.8 mHz, whose angle is measured using a Michelson interferometer. The system achieved noise levels of ∼200prad/Hz between 0.2 and 30 Hz and ∼10prad/Hz above 100 Hz. Such a system can be applied to a broad range of fields from the study of rotational seismic motion and elastogravity signals to gravitational wave observation and tests of gravity.

Subangstrom Measurements of Enzyme Function Using a Biological Nanopore, SPRNT.

Nanopores are emerging as new single-molecule tools in the study of enzymes. Based on the progress in nanopore sequencing of DNA, a tool called Single-molecule Picometer Resolution Nanopore Tweezers (SPRNT) was developed to measure the movement of enzymes along DNA in real time. In this new method, an enzyme is loaded onto a DNA (or RNA) molecule. A single-stranded DNA end of this complex is drawn into a nanopore by an electrostatic potential that is applied across the pore. The single-stranded DNA passes through the pore's constriction until the enzyme comes into contact with the pore. Further progression of the DNA through the pore is then controlled by the enzyme. An ion current that flows through the pore's constriction is modulated by the DNA in the constriction. Analysis of ion current changes reveals the advance of the DNA with high spatiotemporal precision, thereby providing a real-time record of the enzyme's activity. Using an engineered version of the protein nanopore MspA, SPRNT has spatial resolution as small as 40pm at millisecond timescales, while simultaneously providing the DNA's sequence within the enzyme. In this chapter, SPRNT is introduced and its extraordinary potential is exemplified using the helicase Hel308. Two distinct substates are observed for each one-nucleotide advance; one of these about half-nucleotide long steps is ATP dependent and the other is ATP independent. The spatiotemporal resolution of this low-cost single-molecule technique lifts the study of enzymes to a new level of precision, enabling exploration of hitherto unobservable enzyme dynamics in real time.

A reference-beam autocollimator with nanoradian sensitivity from mHz to kHz and dynamic range of 10(7).

We describe an autocollimating optical angle sensor with a dynamic range of 9 mrad and nrad/√Hz sensitivity at frequencies from 5 mHz to 3 kHz. This work improves the standard multi-slit autocollimator design by adding two optical components, a reference mirror and a condensing lens. This autocollimator makes a differential measurement between a reference mirror and a target mirror, suppressing common-mode noise sources. The condensing lens reduces optical aberrations, increases intensity, and improves image quality. To further improve the stability of the device at low frequencies the body of the autocollimator is designed to reduce temperature variations and their effects. A new data processing technique was developed in order to suppress the effects of imperfections in the CCD.

Temporal extent of surface potentials between closely spaced metals.

Variations in the electrostatic surface potential between the proof mass and electrode housing in the space-based gravitational wave mission Laser Interferometer Space Antenna (LISA) is one of the largest contributors of noise at frequencies below a few mHz. Torsion balances provide an ideal test bed for investigating these effects in conditions emulative of LISA. Our apparatus consists of a Au coated Cu plate brought near a Au coated Si plate pendulum suspended from a thin W wire. We have measured a white noise level of 30 microV/sqrt Hz above approximately 0.1 mHz, rising at lower frequencies, for the surface potential variations between these two closely spaced metals.

Test of the equivalence principle using a rotating torsion balance.

We used a continuously rotating torsion balance instrument to measure the acceleration difference of beryllium and titanium test bodies towards sources at a variety of distances. Our result Deltaa(N),(Be-Ti)=(0.6+/-3.1)x10(-15) m/s2 improves limits on equivalence-principle violations with ranges from 1 m to infinity by an order of magnitude. The Eötvös parameter is eta(Earth,Be-Ti)=(0.3+/-1.8)x10(-13). By analyzing our data for accelerations towards the center of the Milky Way we find equal attractions of Be and Ti towards galactic dark matter, yielding eta(DM,Be-Ti)=(-4+/-7)x10(-5). Space-fixed differential accelerations in any direction are limited to less than 8.8x10(-15) m/s2 with 95% confidence.

Tests of the gravitational inverse-square law below the dark-energy length scale.

We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 microm, probing distances less than the dark-energy length scale lambda(d)=[4 -root](variant Planck's over 2pic/rho(d) approximately 85 microm. We find with 95% confidence that the inverse-square law holds (|alpha|

Laboratory test of Newton's second law for small accelerations.

We have tested the proportionality of force and acceleration in Newton's second law, F=ma, in the limit of small forces and accelerations. Our tests reach well below the acceleration scales relevant to understanding several current astrophysical puzzles such as the flatness of galactic rotation curves, the Pioneer anomaly, and the Hubble acceleration. We find good agreement with Newton's second law at accelerations as small as 5 x 10(-14) m/s(2).

Divorce and sex.

Studies on the sex lives of the divorced are relatively few and somewhat dated. Although they give a rather optimistic view of the subject, this research is flawed by high respondent refusal rates and poor representativeness of samples. Further, a major gap in this literature is that the possible predictors of sexual activity of the divorced remain largely unexplored. The present study, using national data on 340 divorced people, indicates a much lower level of sexual activity than found in past research. Regression analyses find that both number of partners and sex frequency are related to religiosity, education, and political liberality. Future research can explore the impact of low sexual activity among the divorced on indicators of emotional well-being.

Measurement of Newton's constant using a torsion balance with angular acceleration feedback.

We measured Newton's gravitational constant G using a new torsion balance method. Our technique greatly reduces several sources of uncertainty compared to previous measurements: (1) It is insensitive to anelastic torsion fiber properties; (2) a flat plate pendulum minimizes the sensitivity due to the pendulum density distribution; (3) continuous attractor rotation reduces background noise. We obtain G = (6.674215+/-0.000092) x 10(-11) m3 kg(-1) s(-2); the Earth's mass is, therefore, M = (5.972245+/-0.000082) x 10(24) kg and the Sun's mass is M = (1.988435+/-0.000027) x 10(30) kg.

Submillimeter test of the gravitational inverse-square law: a search for "large" extra dimensions.

Motivated by higher-dimensional theories that predict new effects, we tested the gravitational 1/r(2) law at separations ranging down to 218 microm using a 10-fold symmetric torsion pendulum and a rotating 10-fold symmetric attractor. We improved previous short-range constraints by up to a factor of 1000 and find no deviations from Newtonian physics.