Related papers: Comment on "Uncertainty in measurements of distanc…
Ng and van Dam have argued that quantum theory and general relativity give a lower bound of L^{1/3} L_P^{2/3} on the uncertainty of any distance, where L is the distance to be measured and L_P is the Planck length. Their idea is roughly…
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the…
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…
We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the…
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…
We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By "measuring a distance less than the Planck length" we mean, technically, resolve the eigenvalues of the position operator to…
We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$.…
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…
We discuss time measurement in quantum gravity. Using general relativity for large distances and the uncertainty principle we find a minimum time interval of the order of the Planck time, therefore the uncertainty in time measurment is…
We discuss a Gedanken experiment for the measurement of the area of the apparent horizon of a black hole in quantum gravity. Using rather general and model-independent considerations we find a generalized uncertainty principle which agrees…
First principles do imply a non-zero minimal distance between events in spacetime, but no positive lower bound to the precision of the measurement of a single coordinate.
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…
We show that an unification of quantum mechanics and general relativity implies that there is a fundamental length in Nature in the sense that no operational procedure would be able to measure distances shorter than the Planck length.…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg…
Starting from a critical analysis of recently reported surprisingly large uncertainties in length and position measurements deduced within the framework of quantum gravity, we embark on an investigation both of the correlation structure of…
Standard Quantum Physics states that the outcome of measurements for some distant entangled subsystems are instantaneously statistically correlated, whatever their mutual distance. This correlation presents itself as if there were a…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
For quantum particles in a Boltzmann state, we derive an inequality between momentum uncertainty $\Delta p$ and thermal de Broglie wavelength $\lambda_{\rm th}$, expressed as $\Delta p \geq \sqrt{2\pi}\hbar/\lambda_{\rm th}$, as a corollary…
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…