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The recent discovery that silicon nitride membranes can be used as extremelyhigh Q mechanical resonators makes possible a number of novel experiments,which include improved long range vacuum Casimir force measurements, andmeasurments of the properties of liquid helium below the lambda point. It isnoted that in the thermal correction to the Casimir force, the phase velocityof the excitations does not enter, with the force per unit area betweenparallel plates depending only on the temperature and distance between theplates. Thus it appears as possible to measure the phonon analog of the finitetemperature Casimir force in liquid helium.

Precision and Casimir Force Measurements in Superfluid and Vacuum with Silicon Nitride Membranes