Interaction-free quantum measurements: A paradox?

Abstract

In Heisenberg’s famous discussion of the measurement of a particle’s position using a microscope, the momentum transferred to the particle by the scattered photon makes the particle’s momentum uncertain. It is shown that momentum is also transferred when the lack of a scattered photon is used to discover that the particle is absent from the field of view of the microscope (i.e., located outside the light beam). This apparent paradox, a transfer of momentum and/or energy to a missing particle by a light beam (without the scattering of a photon), is discussed and ’’resolved’’ using quantum measurement theory.