Text: Acoustic analogs to electromagnetic effects According to quantum field theory, the vacuum state of the electromagnetic field has zero expectation value because it is a state of no real photons. However, the square fluctuations of the electromagnetic field are infinite because each classical normal mode of frequency w has an associated quantum zero-point energy *h w. Thus, the vacuum state is a state where the electromagnetic energy is infinity but no electromagnetic fields are present. Although the electromagnetic zero-point field (ZPF) cannot be measured directly, its effects are manifested in a variety of phenomena, including the Casimir force, the van der Waals force between polarizable matter, spontaneous emission of radiation and the Lamb shift, among others. Our research is motivated by the notion that acoustic noise can test, by analogy, predictions due to stochastic electrodynamics and to quantum electrodynamic ZPF effects which are difficult or impossible to directly verify by experiments. We have successfully measured the force law between two rigid, parallel plates due to the radiation pressure of broadband acoustic noise. This measurement constitutes an acoustic analog to the Casimir effect which is the force of attraction between two closely spaced uncharged parallel conducting plates due to the ZPF. However, in contrast to the ZPF Casimir effect, band-limited acoustic noise can cause the force to be attractive or repulsive as a function of separation between the plates. This acoustic analog to the Casimir effect can be readily demonstrated. We have recently conducted preliminary experiments to determine if the drag on a bubble can be modified by the presence of isotropic, homogeneous broadband acoustic noise, when the band overlaps the bubble's resonance width. This constitutes an acoustic analog to the Einstein-Hopf drag on an electromagnetic dipole oscillator in the presence of isotropic and homogeneous electromagnetic fluctuations. Our theoretical analysis shows that small-amplitude oscillations of a bubble in an acoustic field are described by an equation of motion that is analogous to the Abraham-Lorentz equation for an oscillating dipole. In the derivation of the velocity-dependent Einstein-Hopf drag force, the spectrum of radiation loses its isotropy when viewed from a moving particle. The fields experienced by the particle are Lorentz-transformed to a frame moving with the particle, and hence there arises a velocity-dependent force. On the other hand, the fields experienced by the bubble are Galilean-transformed to a frame moving with the bubble yielding a drag similar to Einstein-Hopf's. As in the case of the acoustic analog to the Casimir effect, band-limited acoustic noise can cause effects not considered in the electromagnetic Einstein-Hopf drag. For some spectral shapes in which the lower frequency of the spectrum coincides with the resonant frequency of the bubble, there is surprisingly an increase in the terminal velocity of a bubble. That is, the noise exerts a negative drag on the bubble in this case. Besides providing the acoustic analogs mentioned above, our investigations can thus also probe, by analogy, mechanisms for stochastic acceleration of charged particles that are used to explain cosmic rays. Email: larraza@physics.nps.navy.mil Back to Andrés Larraza Home Page

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