Gravitational Waves

In addition to telescopes for photons in the γ-ray, X-ray, UV, visible, IR, μ-wave, and radio parts of the electromagnetic spectrum, new windows to the universe are opening up with neutrino and gravitational wave observatories. Gravitational waves are expected to be produced by a changing mass quadrupole for example, two masses revolving about their common barycenter, such as the two stars in a binary star system. They would emit gravitational waves with wavelengths of many kilometers that interact with all objects that is, they exhibit most wave phenomena such as scattering, reflection, and transmission through objects in ways similar to other types of waves. The classical scattering cross section of gravitational waves by a mass pair in a detector was worked out by physicist J. Weber about 50 years ago.

For simplicity, assume that each pair of identical atoms in a material is a mass pair quadrupole scatterer of gravitational waves. We would like to know whether gravitational waves can scatter coherently in the detector that is, whether a gravitational wave can simultaneously scatter from many mass pairs in the detector )such as an aluminum bar) or whether a gravitational wave must scatter from a single mass pair at a time. What is the physics here?

Answer

Yes, the coherent scattering of gravitational waves is expected to occur, with the scatterers being mass quadrupoles that is, mass pairs in the antenna. J. Weber, the same physicist who first calculated the classical cross section for gravitational wave scattering in 1959, proposed in 1981 that the coherent scattering of gravitational waves would enhance the scattering cross section for certain detectors by a factor of 106 or more. The larger cross section might explain the large responses of his two independent one-ton cylindrical aluminum bar gravitational wave detectors every time either end faced the nucleus of the Milky Way galaxy, approximately twice per day. If his proposal for a coherent scattering response is correct, then solid bar antennas would be much more sensitive to gravitational waves than large interferometers with their small masses at the mirrors such as LIGO and VIRGO.

The QM calculation can be outlined as follows. With wavelengths in the kilometer range being much longer than the size of the Al bar antenna in the lab, all the mass pair quadrupoles in the antenna are within this one wavelength. Hence, their responses are approximately in phase, and each mass pair offers an equivalent alternative scattering path. By QM rule 2, Ψ = ψ₁ + ψ₂ + ψ₃ + . . . , and Ψ ~ N ψ₁ with probability P = N² |ψ1|², giving us coherent scattering proportional to N2, where N is the total number of mass pairs in the bar, about 1024. However, the bar is actually composed of many micro crystallites, so one really sums the QM amplitudes over the number of mass pairs within each micro crystallite, then sums the probabilities over all the micro crystallites. The coherent scattering probability is still more than 10 million times larger (after accounting for the crystalline defects) than the classical non-coherent scattering response that Weber first calculated in 1959.

Whether any bar antenna for gravitational waves behaves as a coherent scatterer has not been unambiguously demonstrated. Instead of the classical result with the bar oscillating at its resonant frequency and its harmonics when hit by a pulse of gravitational waves, the coherent scattering bar would essentially have an almost equal response to a wide range of frequencies. The actual experimental bar responses are complicated and require elaborate methods to find gravitational wave scattering signals buried in background noise.

If the Weber bars were really detecting gravitational waves from the galactic nucleus, there is an enigma when the original classical response cross section is used. The rate of conversion of mass to energy at the galactic nucleus should have devoured the whole galaxy by now! I suppose that we must wait for LIGO and VIRGO to detect and calibrate gravitational waves before we truly know whether gravitational waves can scatter coherently in Weber bar antennas.