Heisenberg Uncertainty Relations as Statistical Invariants

Román Ingarden

Luca Nanni

In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for propagating statistical errors, we prove that the uncertainty relations between the moduli of conjugate observables are not relativistically invariant. The new relationships show that, in experiments involving relativistic particles, limitations of the precision of a quantity obtained by indirect calculations may affect the final result.

Людвиг Дмитриевич Фаддеев, O. Yakubovskiĭ

R. Shankar

Kin-ya Oda, Juntaro Wada

Abstract We define a set of fully Lorentz-invariant wave packets and show that it spans the corresponding one-particle Hilbert subspace, and hence the whole Fock space as well, with a manifestly Lorentz-invariant completeness relation (resolution of identity). The position–momentum uncertainty relation for this Lorentz-invariant wave packet deviates from the ordinary Heisenberg uncertainty principle, and reduces to it in the non-relativistic limit.

A. K. Rajagopal, V.K. Gupta

It is shown that the complete form of the Heisenberg Uncertainty Relation (HUR) must be employed in introducing the concepts of squeezing and coherent state in q-quantum mechanics. An important feature of this form of the HUR is that it is invariant under unitary transformation of the operators appearing in it and consequences of this are pointed out.