Related papers: Another look through Heisenberg's microscope
We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit",…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between…
It is well known that the problem of divergence in the physical interpretation of quantum mechanics originating from the uncertainty principle has not yet been resolved. Attempting to clear the constraints and confusion of this situation…
The uncertainty relation formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable so that their product should be no less than…
Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of…
The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous…
In this paper we critically analyse W. Heisenberg's arguments against the ontology of point particles following trajectories in quantum theory, presented in his famous 1927 paper and in his Chicago lectures (1929). Along the way, we will…
The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)]. An…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Uncertainty relation for photons that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in…