Quantum theory predicts the existence of the Casimir force between macroscopic bodies, due to the zero-point energy of electromagnetic field modes around them. This quantum fluctuation-induced force has been experimentally observed for metallic and semiconducting bodies, although the measurements to date have been unable to clearly settle the question of the correct low-frequency form of the dielectric constant dispersion (the Drude model or the plasma model) to be used for calculating the Casimir forces. At finite temperature a thermal Casimir force, due to thermal, rather than quantum, fluctuations of the electromagnetic field, has been theoretically predicted long ago. Here we report the experimental observation of the thermal Casimir force between two gold plates. We measured the attractive force between a flat and a spherical plate for separations between 0.7 $\mu$m and 7 $\mu$m. An electrostatic force caused by potential patches on the plates' surfaces is included in the analysis. The experimental results are in excellent agreement (reduced $\chi^2$ of 1.04) with the Casimir force calculated using the Drude model, including the T=300 K thermal force, which dominates over the quantum fluctuation-induced force at separations greater than 3 $\mu$m. The plasma model result is excluded in the measured separation range.Comment: 6 page

We report measurements of the short-range forces between two macroscopic gold-coated plates using a torsion pendulum. The force is measured for separations between 0.7 and 7 μm and is well described by a combination of the Casimir force, including the finite-temperature correction, and an electrostatic force due to patch potentials on the plate surfaces. We use our data to place constraints on the Yukawa-type "new" forces predicted by theories with extra dimensions. We establish a new best bound for force ranges 0.4-4 μm and, for forces mediated by gauge bosons propagating in (4+n) dimensions and coupling to the baryon number, extract a (4+n)-dimensional Planck scale lower limit of M(*)>70 TeV.

Copper Tubing-Flexible 1/4-inch cooper tubing used to form the transmitting and receiving coils can be found at most hardware stores. The cost is approximately $1 per foot. The 55-gallon industrial plastic drums that the copper tubing was wrapped around can also be found at many hardware stores and costs approximately $70. Miscellaneous-The WPT experiments also required 18-AWG magnet wire to form the transmitting and receiving loops, capacitors to set the resonant frequency of the loops, coaxial cables, and various rf connector adapters. All of these components can be purchased from Digi-Key Electronics (https://www.digikey.com/).

We present a simple autocollimator with sub-microradian sensitivity. To demonstrate the capabilities of our autocollimator, we study the simple harmonic motion of a cantilever beam and apply an external force to affect the cantilever's resonant frequency in the context of dynamic force microscopy. Our setup is ideal for the advanced undergraduate instructional laboratory and allows a variety of high-precision, tabletop experiments.