| Summary: | The effect of Planck scale quantum geometrical effects on measurements with interferometers is estimated with standard physics, and with a variety of proposed extensions. It is shown that effects are negligible in standard field theory with canonically quantized gravity. Statistical noise levels are estimated in a variety of proposals for non-standard metric fluctuations, and these alternatives are constrained using upper bounds on stochastic metric fluctuations from LIGO.
Idealized models of several interferometer system architectures are used to predict signal noise spectra in a quantum geometry that cannot be described by a fluctuating metric, in which position noise arises from Planck scale holographic bounds on directional information. Specific models of holographic spatial position states are adopted to predict mathematical characteristics of a possible quantum geometric departure from perfect coherence of a classical spacetime. Predictions in this case are shown to be close to current experimental bounds from GEO-600 and projected future sensitivity for the Fermilab Holometer.
A model-independent statistical framework is also presented. This serves as a generalized method of data interpretation in systems such as the Fermilab Holometer, where the mean time derivative of positional cross correlation between world lines, a measure of geometrical quantum decoherence, is measured with a precision smaller than the Planck time. A parameterized candidate set of possible time domain correlation functions caused by holographic decoherence is shown to be consistent with the known causal structure of the classical geometry measured by an apparatus, and the holographic scaling of information suggested by gravity. Corresponding predicted frequency-domain power spectra are derived, and simple projections of sensitivity for specific interferometric set-ups show that measurements will directly yield constraints on a universal time derivative of the correlation function, and thereby confirm or rule out this class of Planck scale decoherence, for particular arrangements of world lines.
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