Same difference

Teiko Heinonen, PEKKA J. LAHTI, Juha-Pekka Pellonpää

Covariant phase difference observables are determined in two different ways, by a direct computation and by a group theoretical method. A characterization of phase difference observables which can be expressed as the difference of two phase observables is given. The classical limits of such phase difference observables are determined and the Pegg-Barnett phase difference distribution is obtained from the phase difference representation. The relation of Ban’s theory to the covariant phase theories is exhibited.

Gunnar G. Bjork, Jonas Söderholm

We discuss phase-difference measurements of two bosonic modes and propose an experimental realization of the phase-difference operator by Luis and S?nchez-Soto (1993 Phys. Rev. A 48 4702). We show that a measurement of a two-mode state will collapse any state into a phase-difference eigenstate. We also show that the phase-difference number-difference commutator can be expressed in the phase-difference distribution. Finally, we discuss the associated minimum uncertainty states.

Stefan Hillmich, Robert Wille

Jeffrey Gray

This chapter shows that the Hameroff–Penrose theory of how different quantum superpositions in microtubules in different brain areas give rise to different qualia must rely for the origin of these differences on arguments taken from neuroanatomy and neurophysiology. And, despite its intricate Gothic architecture, the theory is incomplete. It offers no account of how differences at the Planck scale might relate to differences between qualia; nor of how differences in space/time in one brain might relate to differences in another brain observing the same scene at the same time. Nonetheless, the theory does offer an account in principle of the origin of differences in qualia. Whether even this is testable in practice is another matter. But quantum mechanics has a habit of taking the absurd, putting it into a laboratory experiment and showing the absurd to be reality. So we should not write the Penrose—Hameroff position off too lightly. And even an account in principle of how qualia might arise is better than no account at all.