`As an exercise I've been trying to pinpoint exactly what is wrong with`

`Plaga's paper. For anyone who doubts that it *is* wrong, note that it`

`proposed 10 years ago an experiment which he said was feasible with what`

`was then state-of-the-art equipment. This technology has now massively`

`advanced. The experiment would guarantee a Nobel prize for anyone who`

`performed it successfully. In that time the paper has been cited in the`

`published literature only 3 times, and never by an experimental physicist.`

`And this is not because the paper was unnoticed by the community at the`

`time, e.g. it was publicised by John Baez, whose writings are widely read.`

`On careful reading, the paper is just littered with confusions and errors.`

`I guess this explains why no-one bothered to publish a rebuttal; this`

`falls in the class of "not even wrong". Probably the root problem is a`

`confusion about the true nature of decoherence. Decoherence is often`

`presented using the maths of density matrices, so I better explain`

`this briefly:`

`Density matrices allow you to handle the case when you don't know the`

`exact quantum state. The procedure is to divide your description into a`

`measurable "system" and a complex, not-measurable-in-detail "environment".`

`One can then define the density matrix of the combined system, and "trace`

`out" the uncertain state of the environment, giving a density matrix for`

`the system alone in the absence of information about the environment. A`

`test to see if the system has been decohered by its interaction with the`

`environment is that the off-diagonal terms in the system-only density`

`matrix go to zero. Plaga clearly accepts the usual position that`

`irreversible branching in MWI occurs when decoherence is (FAPP) total.`

`If you follow this through in Plaga's example, you do indeed find that the`

`density matrix for the states of his trapped ion, |A1> and |A2>, is`

`diagonal, confirming the obvious that once a macroscopic measurement has`

`taken place, we have total decoherence. But what Plaga does in his Eq 8`

`is to reverse the roles of system and environment (he actually does the`

`algebra wrong but the numerical answer is unaffected). Because at this`

`stage the ion knows nothing about the rest of the lab, he gets a density`

`matrix *for the lab* with large off-diagonal terms, corresponding to a`

`"pure" state:`

(|W1> + |W2>) / sqrt(2). So far, so correct (after all, in MWI the state is *always* pure).

`But he now concludes that decoherence has not yet occurred. *WRONG*. The`

`condition "off-diagonal terms go to zero" is just a sufficient condition`

`for decoherence. It is only necessary if the "system" itself is so simple`

`that it could not decohere without the help of the environment. But Plaga`

`is treating the complex, macroscopic lab as the "system" and that`

`certainly can decohere without the help one more ion. The more basic`

`definition is that decoherence has occured once the states are permanently`

`orthogonal, so you cannot demonstrate quantum interference. Plaga`

`correctly states that |W1> and |W2> *are* permanently orthogonal, but does`

`not realise that this means that decoherence *is* complete, contrary to`

`what he says. Another way to put this is that the observer "Silvia"`

`doesn't need the density matrix in Eq. (8) because she knows for sure`

`already whether she detected the original photon or not, hence whether she`

`is in branch |W1> or |W2>.`

`Given this, the rest of Plaga's argument is just irrelevant. But he should`

`have noticed that his process blatantly violates the linearity of time`

`evolution, which is one of the fundamental assumptions of MWI QM. This is`

`manifest in his Eq. 6 which associates an excited ion with the |P2> term`

`in which no excitation took place (if you start with a photon in state`

`|P2>, when the photon is guaranteed not to be detected, the ion is never`

`excited). Hence Eq 6 is not a linear superposition of the two possible`

`histories. Hence, if we saw what he predicted, we would actually`

`*disprove* MWI QM, not confirm it as he thinks.`

Paddy Leahy ====================================================== Dr J. P. Leahy, University of Manchester, Jodrell Bank Observatory, School of Physics & Astronomy, Macclesfield, Cheshire SK11 9DL, UK Tel - +44 1477 572636, Fax - +44 1477 571618