When one quantum object is measured by another: a new class of quantum paradoxes

Nearly all quantum experiments involve a classical object (a macroscopic apparatus) measuring a quantum mechanical one (a particle). In the Elitzur-Vaidman bomb-testing experiment the roles have been reversed, and a surprising result ensued. Later, Hardy expanded this method and allowed two and three particles to measure one another before the macroscopic apparatus made the final measurement, obtaining even more intriguing results. Recently, we elaborated this experimental paradigm further, increasing the number of particles that measure one another. The results seem to violate basic notions of space and time. In one experiment, the wave function appears to proceed in space non-sequentially. In the other experiment, entanglement ensues between particles that seem to have never interacted, giving the impression of an inconsistent history. We survey this family of experiments and discuss its implications.