Planck Fluctuations, Measurement Uncertainties and the Holographic Principle

A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck's constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\lang...

Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard quantum field theory with general relativity on macroscopic scales can be reconciled by nonstandard, nonlocal entanglement of field states with quantum states of geometry. Wave functions of particle world lines are used to estimate scales of g...

It is shown that nearly-flat 3+1D spacetime emerging from a dual quantum field theory in 2+1D displays quantum fluctuations from classical Euclidean geometry on macroscopic scales. A covariant holographic mapping is assumed, where plane wave states with wavevector k on a 2D surface map onto classical null trajectories in the emergent third dimension at an angle \theta=l_P k relative to the surface element normal, where l_P denotes the Planck length. Null trajectories in the 3...

The Planck or the quantum gravity scale, being $16$ orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors that quantum gravity effects via the Generalized Uncertainty Principle affects the time required for free wavepackets to double their size, and this difference in time is at or near current experimental accuracies [1, 2]. In this work, we mak...

It is conjectured that the spatial structure of quantum field states is influenced by a new kind of directional indeterminacy of quantum geometry set by the Planck length, $l_P$, that does not occur in a classical background geometry. Entanglement of fields with geometry modifies the transverse phase of field states at wavelength $\lambda$ and propagation distance $c\tau$ by about $ \Delta \phi\approx \sqrt{l_P\tau}/\lambda$. The new effect is not detectable in measurements o...

The space-time metric is widely believed to be subject to stochastic fluctuations induced by quantum gravity at the Planck scale. This work is based on two different phenomenological approaches being currently made to this topic, and theoretical models which describe this phenomenon are not dealt with here. By using the idea developed in one of these two approaches in the framework of the other one, it is shown that the constraints on the nature of Planck scale space-time flu...

A theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, $t_P$. Departures from classical world lines in flat spacetime are described by Planckian noncommuting operators for position in different directions, as defined by interactions with null waves. The resulting evolution of position wavefunctions in two dimensions displays a new kind of directionally-coherent quantum noise of transverse position. Th...

We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We outline the definition of free fields and interactions over QST and take the first steps to adapting the usual perturbation theory. The quantum nature of the underlying spacetime repla...

Using Matrix Theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic noise, with phenomenology similar to that previously derived on the basis of a quasi-monochromatic wave theory. Traces of matrix operators on a light sheet with a compact dimension of size $R$ are interpreted as transverse position operator...

It is shown that quantum uncertainty of motion in systems controlled mainly by gravity generally grows with orbital timescale $H^{-1}$, and dominates classical motion for trajectories separated by distances less than $\approx H^{-3/5}$ in Planck units. For example, the cosmological metric today becomes indeterminate at macroscopic separations, $H_0^{-3/5}\approx 60$ meters. Estimates suggest that entangled non-localized quantum states of geometry and matter may significantly ...