Related papers: Minimum Length from Quantum Mechanics and Classica…
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 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 generalized uncertainty principle and a minimum measurable length arise in various theories of gravity and predict Planck-scale modifications of the canonical position-momentum commutation relation. Postulating a similar modified…
A critical length has recently been identified that appears to provide a fundamental limit distinguishing quantum behavior from classical behavior. Because of the unique association between critical length and mass, it appears that we can…
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…
We show that the precision of an angular measurement or rotation (e.g., on the orientation of a qubit or spin state) is limited by fundamental constraints arising from quantum mechanics and general relativity (gravitational collapse). The…
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…
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…
We have argued that quantum mechanics and general relativity give a lower bound $\delta l \gtrsim l^{1/3} l_P^{2/3}$ on the measurement uncertainty of any distance $l$ much greater than the Planck length $l_P$. Recently Baez and Olson have…
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.…
The extreme smallness of both the Planck length, on the one side, and the ratio of the gravitational to the electrical forces between, say, two electrons, on the other side has led to a widespread belief that the realm of quantum gravity is…
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…
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients…
We address estimation of the minimum length arising from gravitational theories. In particular, we provide bounds on precision and assess the use of quantum probes to enhance the estimation performances. At first, we review the concept of…
Kempf et al. in Ref. [1] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles' momentum…
We present a hitherto unknown fundamental limitation to a basic measurement: that of the position of a quantum object when the total momentum of the object and apparatus is conserved. This result extends the famous Wigner-Araki-Yanase (WAY)…
The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated…
Quantum information theory is closely related to quantum measurement theory because one must perform measurement to obtain information on a quantum system. Among many possible limits of quantum measurement, the simplest ones were derived…
This essay argues that when measurement processes involve energies of the order of the Planck scale, the fundamental assumption of locality may no longer be a good approximation. Idealized position measurements of two distinguishable…
We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize…