my paper on the Born rule...

Proponents of the Everett interpretation of Quantum Theory have made efforts to show that to an observer in a branch, everything happens as if the projection postulate were true without postulating it. In this paper, we will indicate that it is only possible to deduce this rule if one introduces another postulate that is logically equivalent to introducing the projection postulate as an extra assumption. We do this by examining the consequences of changing the projection postulate into an alternative one, while keeping the unitary part of quantum theory, and indicate that this is a consistent (although strange) physical theory.

The paper critically assesses the attempt (Proc Roy Soc Lond 1999) by David Deutsch (followed up by various authors in later work) to derive the Born rule within the Everett interpretation via considerations of decision theory.
The author interprets Deutsch as claiming that QM - whether or not the Everett interpretation is assumed - may be decomposed into a unitary part and a "projection postulate" part. He then proposes an "alternative projection postulate" (APP) which, he argues, is compatible with the unitary part of QM but which does not entail the Born rule. He claims that, since his APP is a counterexample, Deutsch's proposal and any variants of it must be rejected.
A very similar project was undertaken by Barnum et al in a paper in Proc Roy Soc Lond in 2000. The author's APP has some mild technical advantages over Barnum et al's proposal, but these do not (in my view) merit a separate paper, especially since neither Barnum et al nor the author are proposing a viable alternative to the PP but simply making a logical point.
More importantly, the post-2000 literature on Deutsch's argument has not attempted to criticise the details of Barnum et al's counterexample. Rather, it has claimed that Barnum et al, treating measurement as a black-box process, misread Deutsch. Deutsch sets out to analyse measurement as one more physical process (realised within unitary dynamics - as such, any rival proposal to the Born rule which is couched (as is the author's) in terms of measurement observables taken as primitive will not be relevant within the context of the Everett interpretation.
It is fair to say that this point was somewhat obscure in Deutsch's 1999 paper, but it has been made explicitly in subsequent discussions, including some (by Wallace and Greaves) which the author cites. However, the author does not engage with this issue but continues to work in the Barnum et al tradition without further discussion.
In conclusion: if the Barnum et al framework is valid then the author's paper does not seem to add sufficiently to their existing criticisms of Deutsch to justify publication. And if it is not valid, then it is at best unclear how the author's paper relates to Deutsch.

The paper reviews an alternative projection postulate (APP) and contrasts it with the standard projection postulate (PP). Under the APP probabilities are uniform, instead of being proportional to the relative measure of vector components. APP is shown to be consistent with unitary symmetry and with measurements being defined in terms of projection operators, and it agrees with PP regarding results predicted with certainty. The paper also does a decent job of describing some of the strange empirical results that APP predicts. The main point, that we must rely on empirical data to favor PP over APP, is worth making.
The paper, however, purports to do more than this. The abstract and introduction claim to deal a blow to the Everett programme, by showing that "there is no hope of deriving the PP directly from the rest of the machinery of quantum theory." Beyond the review of APP described above, however, the paper itself says very little about this subject. The introduction ends by promising "we will then examine where exactly it is in disagreement with Deutsch's `reasonable assumptions,' or with Gleason's theorem." But the section at the end of the paper that is supposed to make good on this promise consists of only thirteen lines -- far too little to provide much exact examination.
Worse, the paper does not mention or discuss any of the many other approaches that have been suggested for deriving the PP from the rest of quantum theory, within the Everett programme. The paper claims "APP is in fact the most natural probability rule that goes with the Everett interpretation: on each `branching' of an observer due to a measurement, all of its alternative `worlds' receive and equal probability." However, many authors do not accept that equal probability per world is the most natural. Furthermore, many other authors do accept an equal probability rule, but then try to derive the PP from it, instead of the APP. For example, the review article at http://plato.stanford.edu/entries/qm-manyworlds/ says
"Another idea for obtaining a probability law out of the formalism is to state, by analogy to the frequency interpretation of classical probability, that the probability of an outcome is proportional to the number of worlds with this outcome. This proposal immediately yields predictions that are different from what we observe in experiments. Some authors, arguing that counting is the only sensible way to introduce probability, consider this to be a fatal difficulty for the MWI, e.g., Belifante 1975. Graham 1973 suggested that the counting of worlds does yield correct probabilities if one takes into account detailed splitting of the worlds in realistic experiments, but other authors have criticized the MWI because of the failure of Graham's claim. Weissman 1999 has proposed a modification of quantum theory with additional non-linear decoherence (and hence even more worlds than standard MWI), which can lead asymptotically to worlds of equal mean measure for different outcomes."
(Hanson 2003, which you incorrectly cite as discussing the Deutsch proof, is another such attempt.)
I cannot recommend the paper for publication as it is, but I can hold out hope that the author could make an acceptable revision. Such a revision could simply be a review of the APP, including its implications. Such a review should mention many of the previous authors who have considered such a posulate. Alternatively, a revision could critique some of the attempts to derive PP from quantum theory.
To accomplish this second goal, the author must first choose a set of previous papers that it is responding to. (It may not be feasible to respond to all previous papers on this topic.) Second, the author must explain exactly where there purported demonstration is claimed to fail. That is, at what point does a key assumption of theirs go beyond the basic machinery of quantum theory. Third, the author must explain why this key assumption is no more plausible than simply assuming the PP directly. This is what it would take to successfully show that such attempts to derive the PP from the machinery of quantum theory has failed.
Here are two minor comments. The paper switches its notation from from APP to AQT and PP to SQT, for no apparent reason. It would make more sense to stick with one notation. Also, as there may be other alternatives proposed someday, it might be better to call APP a "uniform projection postulate" (UPP). Finally, the title should more specifically refer to this alternative projection posulate, however named.

Hi,
A while ago I discussed here about a paper I wrote, which you can find on the arxiv: quant-ph/0505059
I submitted it to the Royal Society, and I received a notification of rejection, with the following comments from the referees, might be of interest for those who participated in the discussion. The emphasis is mine.
First referee:
The second referee:
On a personal note, although this paper was a bit outside of my field and thus "for fun", in my field too, I had several rejections of similar kind, which always make me think that the referee has missed the point I was trying to make (which must be due to the way I wrote it up, somehow).
The only point I tried to make was a logical one, as seems to be recognized by the first referee only, but then he seems to miss the point that in the end of the day, we want a theory that spits out results that are given by the PP, whether or not we take that "as primitive". So I don't see why considering the PP "as primitive" makes the reasoning "not relevant". The second referee seems to have understood this (that we have to rely on empirical data to endorse the PP), but he seems to have missed the point I was making a logical claim, and seems to concentrate on the minor remark when I said that "this APP seems to be the most natural probability rule going with MWI".
The very argument that some have tried to MODIFY QM introducing non-linear decoherence is *exactly what I claim*: that you need an extra hypothesis with unitary QM if you want to derive the PP. Finally, the proposition of revision, namely to limit myself to the consequences of the APP, take away the essential point of the paper which simply stated: since two different probability rules, the APP, and the PP, are both compatible with unitary QM, you cannot derive the PP logically from unitary QM without introducing an extra hypothesis.
The only truely valid critique I find here, is the one of the first referee who finds that my paper is not sufficiently different from Barnum's paper (something I ignored) - which is of course a valid reason of rejection (which I emphasised in red).
Most other points seem to miss the issue of the paper, I have the impression, and focus on details which are not relevant to the main point made. This often happens to me when I receive referee reports. Do others also have this impression, or am I such a terrible author ?

I always find that I have to ask an "outsider" to read my manuscript before I submit it. This is because what I find to be rather obvious, is really isn't. Authors have a clear idea in their heads what they're writing. Other people don't. So we tend to write things as if the reader already has an insight into our punch line.

This reminds me of a simple paper I wrote once with a student, about how the signal generating process should be included in a reliable simulation of the behaviour of the front end electronics of a neutron detector, because assuming that the detector just "sent out a delta-pulse" was giving results which deviated by a factor of 2 from observations, while including the signal formation did predict this factor 2. I found this maybe worth publishing - even though not big news - because other papers omitted exactly that: they only took into account the electronics, and supposed a deltafunction for the signal coming from the detector (which might have been justified in their application, no matter - but it was not mentioned in their papers).
So I carefully described the setup, and gave an explicit calculation of how the signal was generated in the detector, to show that this was the relevant part which allowed us to explain the discrepancy of a factor of 2. My point being that it was necessary to include this part in the description.
I got a rather nasty referee report, in which he explained me that I must be pretty naive to think that I was the first one explaining how signals were generated in radiation detectors

I don't know what you submitted that paper to, but honestly, where you send your manuscript is almost as important as what you wrote.
Zz.

It was Nuclear Instruments and Methods, quite appropriate, I'd think

Well, I'm not sure about that.
NIM is supposed to be a journal on new techniques, or an improvement of a technique. Your paper, from your description, is simply clarifying the missing piece that isn't commonly mentioned. In other words, there's nothing new or a new extension on an existing technique.

This is an interesting comment ! Nobody ever made that, and it explains several other problems I had with NIM ; indeed, each time I erred more on the explanatory part than the "here's a new method" part, I got rebiffed (or one asked me to remove or reduce the explanatory part and to emphasize the practical application). It is true that amongst my collegues, I'm by far the most "explanation" oriented.

Hi,
A while ago I discussed here about a paper I wrote, which you can find on the arxiv: quant-ph/0505059
I submitted it to the Royal Society, and I received a notification of rejection ...

... In fact, I should probably make it at least evident that I'm aware of Weissman, Deutsch, Barnum, Hanson, and all the other authors mentioned in the reviews.
So Patrick, do you think you're going to resubmit? I hope you do - I think (obviously) that it is a very important topic.

BTW, does it normally take that long for review? Hasn't it been, what, 5 months?
David

First I'll check out the Barnum paper. If (according to referee 1) my paper contains the same argument as his, well I conclude that 1) I'm in not a bad company (just 5 years late ) and 2) I won't resubmit.

If not, well, I wouldn't really know where to submit. Maybe foundations of physics.

A very similar project was undertaken by Barnum et al in a paper in Proc Roy Soc Lond in 2000. The author's APP has some mild technical advantages over Barnum et al's proposal, but these do not (in my view) merit a separate paper, especially since neither Barnum et al nor the author are proposing a viable alternative to the PP but simply making a logical point.

More importantly, the post-2000 literature on Deutsch's argument has not attempted to criticise the details of Barnum et al's counterexample. Rather, it has claimed that Barnum et al, treating measurement as a black-box process, misread Deutsch. Deutsch sets out to analyse measurement as one more physical process (realised within unitary dynamics - as such, any rival proposal to the Born rule which is couched (as is the author's) in terms of measurement observables taken as primitive will not be relevant within the context of the Everett interpretation.

It is fair to say that this point was somewhat obscure in Deutsch's 1999 paper, but it has been made explicitly in subsequent discussions, including some (by Wallace and Greaves) which the author cites.

which is "the assumption that a rational agent should be indifferent between any two quantum games that agree on the state |phi> to be measured, measurement operator X and payoff function P, regardless of how X is to me measured on |phi>."

In sec 5.2, Greaves very clearly argues that measurement neutrality automatically *excludes* the APP (where the APP = egalitarianism) as a possible probability rule. Therefore, measurement neutrality, as innocuous as it may appear at first glance, is not so innocuous at all.

All attempt to derive the PP from unitary theory is condemed to failure.

Juan wrote:
I cannot agree with that statement, altough I recognize a conceptual difficulty there.
For me, this problem is similar to the problem of irreversibility seen from the classical mechanics point of view.

Non-unitary evolution might be a good approximation (maybe even *exact*!) when an interaction with a huge system (huge freedom) is involved.

My favorite example is the decay of atomic states: clearly the interaction of the discrete atomic system with the continuum system of electromagnetic radiation brings the decay. This decay is very conveniently represented by a "non hermitian" hamiltonian: this allows modeling of an atom (for the Stark effect e.g.) without including the whole field. This represents correctly the reality, altough the fundamental laws are unitary.

For many people, the interaction with a 'classical' or 'macroscopic' system is all that is needed to derive the PP. I think this is the most probable explanation for the PP. Landau considered this so obvious that it comes in the first chapters in his QM book.