Kennard’s 1927 demonstration of the uncertainty relation, cited by Heisenberg as the earliest derivation using the formalism of quantum theory, invokes a trial function that severely limits the class of wave functions for which the uncertainty relation is shown to be valid.
Heisenberg’s uncertainty principle is a milestone of twentieth-century physics. We sketch the history that led to the formulation of the principle, and we recall the objections of Grete Hermann and Niels Bohr. Then we explain that there are in fact two uncertainty principles. One was published by Heisenberg in the Zeitschrift für Physik of March 1927 and subsequently targeted by Bohr and Hermann. The other one was introduced by Earle Kennard in the same journal a couple of months later. While Kennard’s principle remains untarnished, the principle of Heisenberg has recently been criticized in a way that is very different from the objections by Bohr and Hermann: there are reasons to believe that Heisenberg’s formula is not valid. Experimental results seem to support this claim.
Abstract How certain is Heisenberg’s uncertainty principle? Heisenberg’s uncertainty principle is at the heart of the orthodox or Copenhagen interpretation of quantum mechanics. We first sketch the history that led up to the formulation of the principle. Then we recall that there are in fact two uncertainty principles, both dating from 1927, one by Werner Heisenberg and one by Earle Kennard. Finally, we explain that recent work in physics gives reason to believe that the principle of Heisenberg is invalid, while that of Kennard still stands.
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise–disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulae for the noise and disturbance of measurements given by measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise–disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals , and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise–disturbance relation.
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise-disturbance uncertainty principle in the model independent approach based on measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulas for noise and disturbance of measurements given by measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise-disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals to the square root of 2, and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise-disturbance relation.