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Luo et al. Reply: In the Comment [1] on our recent Letter [2], which reported a new limit on the product of the photon mass squared and the ambient cosmic vector potential 2 A e by a rotating torsion balance, the authors raised the problem that the laboratory limit on 2 A e would give no constraint on the photon mass m due to the possibility of an accidental-zero potential A e at our experimental location. The authors claimed that the plasma current method could overcome this problem, and the result is superior quantitatively to that of the torsion balance method [2,3] at current accuracy.We acknowledge that the plasma current method [4,5], applying a large scale current density supported by the plasma to cancel the pseudocurrent 2 A e = 0 induced by the photon mass, is indeed efficacious to overcome the accidental-zero potential in a particular measurement region. However, the physical properties of the interstellar medium (ISM), such as the mean electron density, temperature, and electron drift velocity, are different between in a spiral galaxy and in clusters of galaxies [6]. As for even a larger scale, comparatively little is known about intergalactic medium (IGM) at present [6]. When quoting the astrophysical data to place a limit on plasma currents everywhere in a large region, one would find it difficult to determine the systematic uncertainty. What we like to point out here is that our Letter deals mainly with the direct laboratory measurement of 2 A e with a rotating torsion balance. So far, as the limit on 2 A e is concerned, it is hard to say that the plasma current method is superior to the torsion balance method even though its generous limit on 2 A e is surely about a factor of 200 smaller than that in [2], since the incomplete knowledge about ISM and IGM [6,7] makes the plasma method hard to quote a definite result for the current density J, hence 2 A e . Because an accurate and comprehensive map of magnetic field on large distance is not available, the deduced limit on m from 2 A e would be solidly dependent on the available value A e , which may become unusually small or accidental zero at a particular location. The torque method indeed opens up this possibility while the plasma current method is completely immune to this accidentalzero problem because it is based on large scale. Thus, the real problem is to what extent the validity of deduced limit on the photon mass could be reliable by choosing the typical value of A e in a given region. In [2], we assumed A e 10 12 T m due to cluster level fields and obtained a limit on photon mass of 1:2 10 ÿ51 g. Although the accurate mapping of magnetic field on large distance such as in the Coma galactic cluster is not available, the structure of the regular magnetic field in the Galaxy is available [8,9]. The direct numerical calculation based on the 3D magnetic field structure in the Galaxy and the concentric-ring model [8,9] shows that the magnitude of A e is about 2 10 9 T m near the positions of the Sun. Hence, the torque method in our work will give...

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 and 6.674484 × 10 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.

We report a test of the universality of free fall by comparing the gravity acceleration of the ^{87}Rb atoms in m_{F}=+1 versus those in m_{F}=-1, of which the corresponding spin orientations are opposite. A Mach-Zehnder-type atom interferometer is exploited to alternately measure the free fall acceleration of the atoms in these two magnetic sublevels, and the resultant Eötvös ratio is η_{S}=(0.2±1.2)×10^{-7}. This also gives an upper limit of 5.4×10^{-6}  m^{-2} for a possible gradient field of the spacetime torsion. The interferometer using atoms in m_{F}=±1 is highly sensitive to the magnetic field inhomogeneity. A double differential measurement method is developed to alleviate the inhomogeneity influence, of which the effectiveness is validated by a magnetic field modulating experiment.

A rotating torsion balance method is used to detect the product of the photon mass squared and the ambient cosmic vector potential A(e). The signal is modulated by rotating the torsion balance to ensure the effectiveness of detection for all possible orientations of the vector potential. The influences of sidereal disturbances of environment are also removed by virtue of this modulation method. The experimental result shows micro (2)(gamma)A(e)<1.1 x 10(-11) T m/m(2), with micro (-1)(gamma) as the characteristic length associated with photon mass. If the ambient cosmic vector potential A(e) is 10(12) T m due to cluster level fields, we obtain a new upper limit on photon mass of 1.2 x 10(-51) g.