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L.R. Doyle (SETI Institute), D.P. Carico (California Polytechnic University)
It is well known that a minimum exposure time required by the Heisenberg Uncertainty Principle for detection of photons within a frequency range \Delta \nu is {\Delta \tau} \approx {{1} / {\Delta \nu}}. If the twin images from a gravitational lens system are superimposed and observed at a frequency bandpass \Delta \nu < c / {\Delta L}, where \Delta L is the difference in path length between the two images, then the Uncertainty Principle will render the two paths indistinguishable to the observer and interference can occur. Hence, \Delta L should be directly measurable by a step-wise broadening of the bandpass \Delta \nu until interference fringes disappear; (current radio astronomy technology limiting bandpasses to about 10-4 Hz). While the gravitational lensing will effect the brightness and phase somewhat, the lensing effect itself is independent of wavelength. But theories of quantum gravity predict a small wavelength dependence at short wavelengths. Any wavelength dependent difference in \Delta L using this technique, therefore, may sometime provide constraints on the quantization of spacetime.