Planck Fluctuations, Measurement Uncertainties and the Holographic Principle

We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as the Planck time, length, mass and energy become larger by a factor of order 10-10^{4} compared to those quantities which result from the Heisenberg Uncertainty Principle. However, we prove that the dimensionless entropy enclosed in the cosm...

Arguments based on general principles of quantum mechanics have suggested that a minimum length associated with Planck-scale unification may in the context of the holographic principle entail a new kind of observable uncertainty in the transverse position of macroscopically separated objects. Here, we address potential implications of such a position uncertainty for establishing an additional threshold between quantum and classical behavior.

It is argued that holographic bounds on the information content of spacetime might be directly measurable. A new uncertainty principle is conjectured to arise from quantum indeterminacy of nearly flat spacetime: Angular orientations of null trajectories of spatial length L are uncertain, with standard deviation in each transverse direction \Delta \theta> \sqrt{l_P/L}, where l_p denotes the Planck length. It is shown that this angular uncertainty corresponds to the information...

A theory is developed to describe the nonlocal effect of spacetime quantization on position measurements transverse to macroscopic separations. Spacetime quantum states close to a classical null trajectory are approximated by plane wavefunctions of Planck wavelength (l_P) reference beams; these are used to connect transverse position operators at macroscopically separated events. Transverse positions of events with null spacetime separation, but separated by macroscopic spati...

We review a few topics in Planck-scale physics, with emphasis on possible manifestations in relatively low energy. The selected topics include quantum fluctuations of spacetime, their cumulative effects, uncertainties in energy-momentum measurements, and low energy quantum-gravity phenomenology. The focus is on quantum-gravity-induced uncertainties in some observable quantities. We consider four possible ways to probe Planck-scale physics experimentally: 1. looking for energy...

We argue in the following that the entropy-area law of black-hole physics and the various holographic bounds are the consequences of the microscopic dynamics of elementary degrees of freedom living on or near the Planck scale. We locate them both in the interior and on the boundary of, for example, the black hole with the strange area-behavior of various quantities being the result of a long-range bulk-boundary dependence among these degrees of freedom. In contrast to other a...

A model-independent statistical framework is presented to interpret data from systems where the mean time derivative of positional cross correlation between world lines, a measure of spreading in a quantum geometrical wave function, is measured with a precision smaller than the Planck time. The framework provides a general way to constrain possible departures from perfect independence of classical world lines, associated with Planck scale bounds on positional information. A p...

A basic inconsistency arises when the Theory of Special Relativity meets with quantum phenomena at the Planck scale. Specifically, the Planck length is Lorentz invariant and should not be affected by a Lorentz boost. We argue that Planckian relativity must necessarily involve the effect of black hole formation. Recent proposals for resolving the noted inconsistency seem unsatisfactory in that they ignore the crucial role of gravity in the saturation of Lorentz boosts. Further...

The Karolyhazy uncertainty relation is the statement that if a device is used to measure a length $l$, there will be a minimum uncertainty $\delta l$ in the measurement, given by $(\delta l)^3 \sim L_P^2\; l$. This is a consequence of combining the principles of quantum mechanics and general relativity. In this note we show how this relation arises in our approach to quantum gravity, in a bottom-up fashion, from the matrix dynamics of atoms of space-time-matter. We use this r...

After a pedagogical overview of the present status of High-Energy Physics, some problems concerning physics at the Planck scale are formulated, and an introduction is given to a notion that became known as ``the holographic principle" in Planck scale physics, which is arrived at by studying quantum mechanical features of black holes.