General Uncertainty Relation

Zhengli Chen, Lili Liang, Haojing Li +1 more

Fang Wan

From heisenberg’s uncertainty relation, generalized uncertainty relation of quantum system under Planck scale is given and thus minimum uncertainty of position is obtained. The significance of generalized uncertainty relation is elaborated further.

Harris Varghese, M. Ravendranadhan

The Robertson's formulation of the uncertainty relation is the most widely accepted form of the Heisenberg uncertainty relation (HUR). It gets modified when we consider it for entangled particles. But this formulation does not consider the measurement process itself. There are reformulation of the uncertainty relations called the generalized uncertainty relations by including the measurement process into the uncertainty relation. HUR gets modified for the case of entangled particles. Here it is shown that the limit of the Generalized Uncertainty Relation (GUR) also reduces for entangled particles. So, GUR also shows similar trend as that of the HUR for entangled particles. Also as entanglement increases, the uncertainty reduces and measurement becomes more precise.

Willi-Hans Steeb

Gary E. Bowman

Commutators and uncertainty relations have sparked much debate and confusion as to their physical meaning. As such, this chapter focuses partly on historical and interpretational aspects. Because it is central to the uncertainty relations, the commutator — including its manifestation in matrix mechanics — is introduced first. It is emphasized that the commutator of two operators is generally another operator. The general form of the uncertainty relations is then introduced. These relations reflect the fact that probability distributions for different observables are generally not independent. Moreover, application of the uncertainty relations generally requires knowledge of the quantum state — a fact that is obscured by the well known position-momentum uncertainty relation. Various proposed physical interpretations of the uncertainty relations are then discussed. The chapter concludes with a brief reflection on the significance of the uncertainty relations.

Burcu Elif Akten