Hello all,

I figured I'd give an update on the paper I posted about in December.
Like I said, I took the good advice from the reviewer's comments,
answered some other issues that I think he misunderstood, resubmitted,
and got it accepted! This is my first peer-reviewed physics paper to
be accepted; a modest start, but a start nonetheless.

In the meantime, I submitted a much more serious paper to a journal
that is one or two tiers higher up: Studies in History and Philosophy
of Modern Physics. They have their act together and gave me their
response within 3 months. Unfortunately, a flat out rejection :( --
thankfully, one of the two reviewers wrote a lengthy and thoughtful
(though harsh) review that effectively pointed out to me a few ways in
which I was misusing terminology, and will help me rewrite it into a
better paper (which I'll probably submit to a different journal).

The rejection letter and reviewer comments are below.

David



Ms. Ref. No.: SHPMP-D-08-00021
Title: Egalitarianism offers a coherent alternative to decision theory
as a solution to the problem of probability of the many worlds
interpretation
Studies in History and Philosophy of Modern Physics

Dear David,

We have received two referee reports on your submission
"Egalitarianism offers a coherent alternative to decision theory as a
solution to the problem of probability of the many worlds
interpretation" to Studies in History and Philosophy of Modern
Physics. You will find them below.

I regret to inform you that based on these reports the editors have
decided that we cannot accept the present manuscript for publication.

We hope the comments of the referees are useful.

Sincerely,

Geurt Sengers

Managing Editor
On behalf of the editors of
Studies in History and Philosophy of Modern Physics

Reviewers' comments:

Reviewer #1: I am recommending that this paper be rejected, for two
reasons: (i) It fails to present a clear, coherent stance on the
foundations of classical statistical mechanics, on which it seeks to
build, and (ii) it boils down simply to a promissory note to the
effect that the Born rule could probably be derived in a
hidden-variable theory (which means both (a) that the research program
suggested in the paper cannot possibly achieve its stated aim, viz. of
solving the problem of probability *for the Everett interpretation*,
and (b) that it is merely a far inferior cousin to significant amounts
of existing detailed discussion as to how exactly one might derive a
probability rule in a hidden-variable theory (or, for that matter, in
any other deterministic theory)). These criticisms are spelled out
further in points (1) and (3) below. (Point (2) is included more as a
side-remark; in particular, I should highlight that it is to some
extent based on views that may not be
generally accepted among participants in the debate over Everettian
probability.)

1. The author claims that the basic idea of Egalitarianism is
central to the development of classical statistical mechanics. I
assume that he intends to claim that the Liouville measure can be
derived from the statement that he calls the "fundamental postulate of
classical statistical mechanics", viz. that "an isolated system in
equilibrium is found with equal probability in each of its accessible
microstates." But this is incorrect. All macrostates of interest
contain uncountably many microstates; to say that these microstates
have "equal probability" is only to say that they each have
probability zero; this does not suffice to pick out any particular
measure on the macrostate.

This very basic point is - and, I think, is generally acknowledged to
be - a stake through the heart of attempts to derive the Liouville
measure from "equiprobability" assumptions. The author clearly thinks
otherwise, but his attempts to justify this claim lead to nothing, and
eventually peter out without having borne fruit. We are told (page 3)
that "the solution involves measure theory". On page 13, we discover
that this measure-theoretic solution begins by distributing
representative points *uniformly* through some region of phase space
(emphasis added). It is then acknowledged (still p.13) that talk of
"uniform" presupposes a privileged measure, so that we have so far got
nowhere. (Actually, this isn't quite what the author says. He writes
that "the question *becomes*: how do we know which measure is the
"correct" measure?" (emphasis added) - But that has always been the
question!) There is then a brief allusion to the possibility of
justifications via ergodic theory, or (very differently!) a simple
appeal to experience. The discussion of the classical case concludes
with the defeatist remark "This [i.e. the assessment of the suggestion
that the assignment of equal probabilities to particular subsets of
state space can only be made a posteriori] remains an outstanding
philosophical problem in the understanding of classical (non-quantum)
probability, a solution to which is not sought in this paper." But
this is to give up the game: in the absence of an assessment of, or at
least an assumption about the outcome of further assessment of, this
suggestion, it is not reasonable to claim (as the paper does) that the
classical case is settled, and that we have only to ask whether and
how 'the same strategy' might be implemented in the quantum case.

(On page 2, the author mentions the need for a mechanical theory to
"tell us... how to place microstates in groups that are physically
relevant". This could be supposed to be part of the story if the
starting postulate made reference to these physically relevant groups,
rather than directly to the microstates themselves, but it is clear
that the stated "fundamental postulate" can have no use for it. This,
too, is therefore nothing more than a vague promissory note and, of
course, all the work will be involved in elaborating a notion of
"physical relevance" of microstate-groups that is supposed to connect
dynamics and probability.)

This is important for the following two reasons. First: If, as the
author supposes (but, as far as I can see, contrary to fact), the
Egalitarian strategy had worked well in classical contexts, the fact
that no adequate application of it in the quantum context has yet been
found would indeed cry out for investigation. If, on the other hand
(as I take it), such strategies have always been non-starters, there
is little prima facie reason to expect things to be otherwise in QM.
The issue is therefore important to the author's motivation for his
present project. Second: The author's main thesis is that in the
quantum context, a particular probability measure can be derived by a
process analogous to classical microstate-counting. Since there is
(contrary to the author's claims) no generally accepted account of
just how the usual classical measure might be reached by
microstate-counting, clarity requires that the author state exactly
how the classical derivation is supposed to go;
otherwise, the reader cannot know what the author intends to claim for
the quantum case, when he claims analogy.

2. My second point is more of a side-remark: I feel that the author
isn't setting things up in the most perspicuous way, but this is
somewhat tangential the main point of his paper.

The author describes the decision-theoretic approach to probability as
being an alternative to Egalitarianism. (Thus he writes, on page 4,
that the success of Egalitarianism "would obviate the need for DW
decision theory".) Whether this is true depends, of course, how much
one takes to be packed into the essence of "DW decision theory". But
the author's remarks seem to me to be based on an unhelpful conflation
of two quite distinct issues in the debate over Everettian
probability. As has become fairly standard in the literature, let's
distinguish between the incoherence problem (how, if all Everettian
branches are real, can it even make sense to talk of probabilities for
outcomes of future measurements?) and the quantitative problem (why
the Born rule, rather than some other way of assigning numbers summing
to unity to Everettian branches?). *The appeal to decision theory is
supposed, in the first instance, to solve the incoherence problem*.
The particular principle within
the Deutsch-Wallace approach that is supposed to address the
quantitative issue is that of "Equivalence" (or, in some of Wallace's
presentations, "Measurement Neutrality").

In that case, the relationship between the two projects would be
better captured as follows: Those working in the decision-theoretic
tradition (as a matter of contingent fact) usually argue that
counting-based solutions to the quantitative problem cannot succeed,
and are thus led either to give some non-counting-based argument for
Equivalence or to despair of finding any substantive argument for that
principle. In contrast, the author holds that counting-based solutions
are very promising. The need that would be "obviated" by the success
of the latter is that for Wallace's attempts to justify Equivalence
(or pessimism at the prospect of finding any justification), not the
need for decision theory.

My suspicion is that the author is not particularly interested in the
incoherence problem (and, perhaps, would not agree that it is even a
prima facie problem - I notice that he replaces the words
'quantitative problem' with 'problem of probability' in the first
quote on p.5!), and that he takes himself to be providing an
alternative solution to the quantitative problem (alternative to the
Equivalence-based arguments usually offered by those working in the
decision-theoretic tradition). But this simply means that he takes it
there has never been a need for an appeal to decision theory. Anyone
who ever thought that that need existed, and who (further) accepts a
counting-based derivation of the Born rule, will continue to think
that it is necessary to appeal to decision theory with a counting
principle, as they used to appeal to decision theory with (say) a
future-indifference principle, in order to have a solution to both
aspects of "the" Everettian probability problem.

3. The Egalitarian derivation of the Born rule offered so far is,
as the author acknowledges (on p.7), circular. As the author
succinctly puts it: "The Born rule measure is justified
as a probability because its value is proportional to the number of
microstates
associated with an experimental result; but conversely, the number of
microstates associated with a result is defined as its Born rule
measure." The author goes on to suggest that this is not to be
regarded as a permanent state of affairs, but rather the state of
affairs partway through the completion of a research program. In the
completed program (he continues), we will "augment the [present
account] by a [fundamental dynamical theory] in such a manner that it
becomes an independent Egalitarian account of the quantum probability
rule, i.e. the Born rule, in the same manner that Newton's laws
provide an independent Egalitarian account of the kinetic theory of
gases."

This isn't an unreasonable research program, *but it isn't an
Everettian program*. The author's suggestion is, in effect, that we
augment the ontology of Everettian QM, adding 'hidden variables' with
their own dynamics (T), and then derive the Born rule in this
hidden-variable theory much as we derive the Liouville measure in
classical statistical mechanics [however that may be]. (It seems clear
that hidden variables will be essential to any breaking of the
circularity. As long as we have only the quantum state in our
ontology, the only difference between (say) |psi> and 1⁄2 |psi> is
quantum amplitude, and so there cannot be possibly be any grounds for
saying that those vectors correspond to different "numbers of
microstates" other than by a (circularity-inducing) appeal to amplitude.)

But this program has already been much discussed: such a
hidden-variable theory is provided by, e.g., the de Broglie-Bohm
theory. Attempts to derive the Born rule within that theory have been
discussed by, e.g., Durr et al, "Quantum Equilibrium and the Origin of
Absolute Uncertainty," Journal of Statistical Physics 67: 843-907;
Callender, "The emergence and interpretation of probability in Bohmian
mechanics", Studies in the History and Philosophy of Modern Physics
38, 351-370; Maudlin, "What could be objective about probabilities?",
Studies in the History and Philosophy of Modern Physics 38, 275-91.




Reviewer #2: I think the author misunderstands the issue concerning
Egalitarianism in the context of Everett and the DW argument. As I
understand it, the issue is whether Egalitarianism provides an
alternative to the Born rule (as a basis for the credence-like weights
of a rational agent), *assuming* the Everett view. Hence I think it is
irrelevant to point out, as the author does on p. 20 and in the
following discussion, that Egalitarianism might have a place in the
context of "a deeper underlying classical model T". So far as the DW
argument is concerned, the issue is whether Egalitarianism can be made
to work in the context of the Everett picture, with no other ontology.