Planck Fluctuations, Measurement Uncertainties and the Holographic Principle

Arguments based on general principles of quantum mechanics suggest that a minimum length or time associated with Planck-scale unification may entail a new kind of observable uncertainty in the transverse position of macroscopically separated bodies. Transverse positions vary randomly about classical geodesics in space and time by about the geometric mean of the Planck scale and separation, on a timescale corresponding to their separation. An effective theory based on a Planck...

A particular form for the quantum indeterminacy of relative spacetime position of events is derived from the limits of measurement possible with Planck wavelength radiation. The indeterminacy predicts fluctuations from a classically defined geometry in the form of ``holographic noise'' whose spatial character, absolute normalization, and spectrum are predicted with no parameters. The noise has a distinctive transverse spatial shear signature, and a flat power spectral density...

A new kind of quantum indeterminacy of transverse position is shown to arise from quantum degrees of freedom of spacetime, based on the assumption that classical trajectories can be defined no better than the diffraction limit of Planck scale waves. Indeterminacy of the angular orientation of particle trajectories due to wave/particle duality at the Planck scale leads to indeterminacy of a nearly-flat spacetime metric, described as a small nonvanishing quantum commutation rel...

A possible discrepancy has been found between the results of a neutron interferometry experiment and Quantum Mechanics. This experiment suggests that the weak equivalence principle is violated at small length scales, which quantum mechanics cannot explain. In this paper, we investigated whether the Generalized Uncertainty Principle (GUP), proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity Theories (DSR), can explain the violatio...

We point out that aspects of quantum mechanics can be derived from the holographic principle, using only a perturbative limit of classical general relativity. In flat space, the covariant entropy bound reduces to the Bekenstein bound. The latter does not contain Newton's constant and cannot operate via gravitational backreaction. Instead, it is protected by - and in this sense, predicts - the Heisenberg uncertainty principle.

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. Id...

We discuss a limit for sensitivity of length measurements which is due to the effect of vacuum fluctuations of gravitational field. This limit is associated with irreducible quantum fluctuations of geodesic distances and it is characterized by a noise spectrum with an order of magnitude mainly determined by Planck length. The gravitational vacuum fluctuations may (in an analysis restricted to questions of principle and when the measurement strategy is optimized) dominate fluc...

Exact conditions on the clock parameters corresponding to the minimal uncertainty in distance measurement are derived in uniform manner for any number of space time dimensions. The result espouses the holography principle no matter what the number of space time dimensions is. In this context the ADD braneworld model is considered. Some remarks are made on deviation of holography as well as of special relativity at the scales provided by the cosmological constant. We also comm...

An effective theory based on wave optics is used to describe indeterminacy of position in holographic spacetime with a UV cutoff at the Planck scale. Wavefunctions describing spacetime positions are modeled as complex disturbances of quasi-monochromatic radiation. It is shown that the product of standard deviations of two position wavefunctions in the plane of a holographic light sheet is equal to the product of their normal separation and the Planck length. For macroscopical...

We consider the uncertainty in the arm length of an interferometer due to metric fluctuations from the quantum nature of gravity, proposing a concrete microscopic model of energy fluctuations in holographic degrees of freedom on the surface bounding a causally connected region of spacetime. In our model, fluctuations longitudinal to the beam direction accumulate in the infrared and feature strong long distance correlation in the transverse direction. This leads to a signal th...