A water wave analog of the Casimir effect
Apparatus for demonstrating a water wave analog of the Casimir effect. (a) Support arrangement for the plates with thread and pendulum clamps. The thread length is 80 cm. (b) Parallel plates partially but deeply submerged in ethyl alcohol with the fluorescein dye. The dish has the diameter of 19 cm and is attached to a vertical shake table. (c) Shaker produces waves that cause a substantial attraction of the plates. There is very little wave motion between the plates.
Wavelength as a function of frequency according to the dispersion relation (1) for deep gravity-capillary waves on ethyl alcohol (solid curve) and water (dashed curve), and for pure deep gravity waves (dotted line).
Representation of a small-amplitude deep gravity wave traveling in the positive direction. The particle motion is circular; the bold arrows represent instantaneous particle velocity. The net momentum over one wavelength is the positive amount in the hatched region.
Diagram of a probe system that measures the vertical displacement of waves on ethyl alcohol with fluorescein dye. Calibration is done statically by vertically incrementing the position of the probe wires. Waves are measured by feeding the output of the lock-in amplifier into a signal analyzer.
Typical surface wave spectrum from the two-wire probe in Fig. 4. The root-mean-square surface wave vertical displacement is , which corresponds to the midrange of the experiment (see Fig. 6).
Equivalent mass of the radiation force on a plate as a function of the mean-square vertical displacement of the surface waves. The points are experimental, and the solid line is the gravity wave theory. The dashed line is a rough approximation for gravity-capillary waves. The theory lines have no adjustable parameters.
Article metrics loading...
Full text loading...