Heisenberg Uncertainty Relation (Indeterminacy Relations) (original) (raw)

Heisenberg's Uncertainty Relation (Indeterminacy Relations) (Compendium entry)

Compendium of Quantum Physics, Concepts, Experiments, History and Philosophy (eds. D. Greenberger, K. Hentschel, F. Weinert), pp. 281-283, 2009

The term Heisenberg uncertainty relation is a name for not one but three distinct trade-off relations which are all formulated in a more or less intuitive and vague way in Heisenberg's seminal paper of 1927 [1]. These relations are expressions and quantifications of three fundamental limitations of the operational possibilities of preparing and measuring quantum mechanical systems which are stated here informally with reference to position and momentum as a paradigmatic example of canonically conjugate pairs of quantities: It is impossible to prepare states in which position and momentum are simultaneously arbitrarily well localized. In every state, the probability distributions of these ► observables have widths that obey an uncertainty relation. It is impossible to make joint measurements of position and momentum. But it is possible to make approximate joint measurements of these observables, with inaccuracies that obey an uncertainty relation. It is impossible to measure position without disturbing momentum, and vice versa. The inaccuracy of the position measurement and the disturbance of the momentum distribution obey an uncertainty relation.

Heisenberg's Uncertainty Relation (Compendium entry)

2008

The term Heisenberg uncertainty relation is a name for not one but three distinct trade-off relations which are all formulated in a more or less intuitive and vague way in Heisenberg's seminal paper of 1927 [1]. These relations are expressions and quantifications of three fundamental limitations of the operational possibilities of preparing and measuring quantum mechanical systems which are stated here informally with reference to position and momentum as a paradigmatic example of canonically conjugate pairs of quantities: ... (A) It is impossible to prepare states in ...

The uncertainty relations in quantum mechanics

Current science

The notion of uncertainty in the description of a physical system has assumed prodigious importance in the development of quantum theory. Overcoming the early misunderstanding and confusion, the concept grew continuously and still remains an active and fertile research field. Curious new insights and correlations are gained and developed in the process with the introduction of new `measures' of uncertainty or indeterminacy and the development of quantum measurement theory. In this article we intend to reach a fairly up to date status report of this yet unfurling concept and its interrelation with some distinctive quantum features like nonlocality, steering and entanglement/ inseparability. Some recent controversies are discussed and the grey areas are mentioned.

The Theory of Quantum Uncertainties and Quantum Measurements

  1. We shall discuss what modern interpretations say about the Heisenberg's uncertainties. These interpretations explain that a quantity begins to 'lose' meaning when a conjugate property begins to 'acquire' definite meaning. We know that a quantity losing meaning means that it has no fixed value and has an uncertainty . In this paper we look deeper into this interpretation and the outcome reveals more evidence of the quantity losing meaning. Newer insights appear. 2) We consider two extreme cases of hypothetical processes nature undergoes, without interference by a measurement: One, a system collapses to an energy eigenstate under the influence of a Hamiltonian instantaneously at a time ttt. This is thus what would happen if we would measure the system's energy. Next, when a particle becomes localised to a point at a time t_0t_0t_0 under the influence of a Hamiltonian. This is thus what would happen if we would measure the system's position. We shall prove th...

One unorthodox view of the Heisenberg uncertainty principle (english)

It has long been clear, that human's ideas about the structure of surrounds him world are correspond to its world only partly. This truth is banal, but only recognition of this fact today is not sufficient. It appears that it's time to make the next step in scientific knowledge and to try to create (once again!) The New Model of the World which is to near understanding of the World as it is.

Technology Heisenberg Form of Uncertainty Relations

2016

This paper, deals with the uncertainty relation for photons. In [Phys.Rev.Let.108, 140401 (2012)], and [1] the uncertainty relation was obtained as a sharp inequality by using the energy distribution on space. The relation we obtain here is an alternative to the one given in [Phys.Rev.Let.108, 140401 (2012)] by the use of the position of the center of the energy operator. The fact that the components of the center is non commutative affected the right hand side of the Heisenberg inequality. But this resolved by the increase of the photon energy. Furthermore we study the uncertainty of Heisenberg with respect to angular momentum and Foureir. We end the paper by giving some examples.

Heisenberg Form of Uncertainty Relations

American Journal of Applied Mathematics, 2015

This paper, deals with the uncertainty relation for photons. In [Phys.Rev.Let.108, 140401 (2012)], and 1 the uncertainty relation was obtained as a sharp inequality by using the energy distribution on space. The relation we obtain here is an alternative to the one given in [Phys.Rev.Let.108, 140401 (2012)] by the use of the position of the center of the energy operator. The fact that the components of the center is non commutative affected the right hand side of the Heisenberg inequality. But this resolved by the increase of the photon energy. Furthermore we study the uncertainty of Heisenberg with respect to angular momentum and Foureir. We end the paper by giving some examples.

Indeterminacy and the Limits of Classical Concepts: The Transformation of Heisenberg's Thought

Perspectives on Science, 2007

This paper examines the transformation which occurs in Heisenberg's understanding of indeterminacy in quantum mechanics between 1926 and 1928. After his initial but unsuccessful attempt to construct new quantum concepts of space and time, in 1927 Heisenberg presented an operational deªnition of concepts such as 'position' and 'velocity'. Yet, after discussions with Bohr, he came to the realisation that classical concepts such as position and momentum are indispensable in quantum mechanics in spite of their limited applicability. This transformation in Heisenberg's thought, which centres on his theory of meaning, marks the critical turning point in his interpretation of quantum mechanics.

A simple experimental checking of Heisenberg's uncertainty relations

2006

We show that the quantum mechanical interpretation of the diffraction of light on a slit, when a wave function is assigned to a photon, can be used for a direct experimental study of Heisenberg’s position-momentum and equivalent positionwave vector uncertainty relation for the photon. Results of an experimental test of the position-wave vector uncertainty relation, where the wavelength is used as the input parameter, are given and they very well confirm our approach. The same experimental results can also be used for a test of the position-momentum uncertainty relation when the momentum p0 of a photon is known as the input parameter. We show that a measurement of p0, independent of the knowledge of the value of the Planck’s constant, is possible. Using that value of p0, a test of the position-momentum uncertainty relation could be regarded as a method for a direct measurement of the Planck’s constant. This is discussed, since the diffraction pattern is also well described by classic...