**Report on:**

**Rubin's response to report of Feb. 23, 2006 from referee #2**

Mar. 3, 2006

Rubin writes:

There seem to be two partly-interconnected sorts of misconception that
the reviewer has about my model:

1)  Some things which are criticized are actually not present in the
    model.

2)  The reviewer has in mind a particular interpretational framework,
    points out

> difficulties encountered in the context of that framework, and then
> objects that
>
> I do not "solve" these difficulties\-\--difficulties that simply do
> not arise
>
> within the interpretational framework, different from the reviewer's,
> which I
>
> employ.

REVIEWER: I shall go into more detail below, but I shall first summarize
my conclusions, which are closely connected to the two above points. The
author, both in the Abstract and in Section 1 claims to resolve (even
without invoking environmental decoherence) the "core basis problem"
spelled out in detail in a cited paper of Stapp's. So the basic question
about the paper is, of course, whether that claim is substantiated by
the arguments given in the paper being reviewed. The specific issue is
whether the property that Rubin calls "outcome determination" is
satisfied or not. This required property is,

in Rubin's words, "The formalism must unambiguously determine which
specific outcomes occur in a measurement situation, as well the
respective probabilities for these outcomes".

REV:Actually, the crux of the difficulty my be right here, in the
author's conception of what the problem is! This formulation may tend to
mix up two very different processes: One is, in Dirac's words, the
"choice on the part of Nature" that determines *in a specified
measurement situation* which of the pre-specified possible outcomes
actually occurs, and the probabilities associated with these various
pre-specified possibilities. The other process, called Process 1 by von
Neumann, specifies what the alternative possible outcomes are. The core
basis problem described in Stapp's paper was explicitly about this
"Process 1" action, which is not in general specified by the quantum
laws of motion, and which Bohr calls "a free choice on the part of the
experimenter."

REV: Suppose we have an observing system and an observed system, each
with a translational degree of freedom, and an interaction between them
that causes the posing of question: "Is the observed system in region R,
relative to me:Yes or No?" to make the state of the observer to end up
in one or the other of two disjoint regions of his space of internal
variables. The Process 1 choice is the choice of the region R: i.e., the
choice of which of the continuum of possibilities for the size, shape,
and location of R will be picked out. Because of the effects of the
uncertainty principle, acting since the birth of the universe, the state
of the observer at the moment of measurement will be a smear of
possibilities corresponding to a smear of possible regions R that might
have been chosen.

The author evades this problem, which *is* Stapp's core basis problem,
by simply, in his own words considering a model in which the observing
system does not have any internal degrees of freedom corresponding to
different possible choices of what the measurement

will be. He notes that an atom in its ground state has no internal
degrees of freedom. But why should a warm human experimenter capable of
performing many possible measurement actions be similar to a molecule in
its unique ground state?

REV: When the author points out that the problems raised by this
reviewer do not apply to his very restrictive model, he is completely
correct, but the point is that that simple model is too simple to
confront the "core basis problem" that the author's paper claims to
resolve. An adequate model must accommodate the smear of alternative
possible choices of which measurement will be performed, or explain how
a model that has, by fiat, no degrees of freedom corresponding to the
seeming free choices made by experimenters, really resolves the "core
basis problem.". The paper might be publishable if the author were to
scale back his claims, and presents his paper as a [step]{.underline}
toward a possible

resolution of the "core basis problem", rather than a resolution, and
made clear the nature of the remaining problems.

AUTHOR: Specifically:

\>Suppose we begin by imagining one single idealized state just prior to
the beginning of \>the measurement interaction. The observer and his
devices are a localized structure, and \>hence the state can be
expressed in terms of a discrete set of eigenstates. Let P(0) be a
\>projection operator that projects onto a subspace that corresponds to
some pertinent \>degree of freedom of the full observing system's being
in a "ready state". ...Both the \>"Observing System" and the "Observed
System" can be displaced arbitrarily with no \>difficulty. If the
interaction is a function of the difference of the coordinates of the
two \>systems then the observing system will register a location of the
observed system \>relative to itself...

Yes, let's begin here.

\>However, this single idealized initial states of the Observing System
is just one of a \>smear of states with continuously varying internal
structures. Each one has a slightly \>different Ready State, and, more
importantly, slightly different final P~i~ 's.

AUTH: What the reviewer describes in the above statement differs from
the model which I present in the paper under review, as described
explicitly in Sec. 3 of that paper. The internal structure, by
hypothesis, is not a function of the translational degree of freedom. It
would of course be a valid criticism to say that this feature of my
model is not to be found in any real physical system; but models which
are relevant for real physical systems which have this property abound.
The wavefunction of a hydrogen atom may be such that the probability
density for the center of mass is spread out over a region of space very
large compared to the Bohr radius, yet it may be certain that, wherever
it is, the atom is in, say, its ground state (i.e., the lowest
eigenstate of that part of the Hamiltonian corresponding to relative
position and motion of the atom's constituents.) The eigenstate's energy
is independent of the center-of-mass position, as is the functional
dependence of its Schrodinger-representation on the relative coordinate
(electron position -- proton position).

REV: As explained above, this model eliminates by simple fiat the "core
basis problem".

AUTHOR: Is the reviewer perhaps implicitly thinking of a situation in
which there are spatially- varying external fields present, or
interaction with swarms of other quantized particles in the environment?

REV: No! I am thinking about the internal degrees of freedom of the
observing system.

Classical external fields should not be employed in a completely quantum
theory of the type which Stapp considers in his paper, and which I
consider in mine. Interaction with the environment is of course of great
physical interest re: decoherence. But I wish to examine in this paper
the simpler case of isolated measurements. It is usually a good idea in
physics to analyze simpler situations before tackling more complicated
ones. A simple example of interaction with other objects is, in fact,
given in my paper, in Sec. 4, where several measuring devices interact
with a measured system and each other. The measuring devices split into
discrete sets of Everett copies as appropriate.

As for more complicated measuring devices, these too must have discrete
sets of distinguishable internal configurations. The rhodopsin molecule
in the human retina which changes its internal configuration upon
absorption of a photon comes to mind (see ref. 34) . The corresponding
operator would be one related to the relative spatial arrangement of the
constituent atoms, energy, etc. but not, e.g., to orientation w.r.t. the
external environment, in the same way that for an atom there is an
operator corresponding to the internal energy which is a scalar under
rotations and is (in the absence of external fields) unchanged upon
translation.

REV: The rhodopsin molecule can be located in a smear of possible
locations,

corresponding to different regions R.

AUTH: For something of the complexity of a computer or a brain, it is of
course not possible to describe the relevant type of internal-state
operator to anything like a comparable degree of specificity, except to
say that its eigenvalues/eigenstates too would correspond to
spatial-DOF-independent facts ("energy is such-and-such a value,"
"semiconductor junction is in 'on' state," etc.).

REV: But the discrete energy eigen states of an observing system cannot
be expected to map onto states of consciouness. The example (given
earlier) of the rotationally smeared Stern-Gerlach system, where the
eigen states are smeared out but the conscious states correspond to
fixed direction of the axis, is a simple counter-example.

AUTH: So: In the measurement model employed in this paper, there is
*one* internal ready state, and *one* set of projectors P~i~ projecting
out the ready state and other internal states corresponding to different
measurement results.

REV: But does this adequately confront the problem of the smear of
possible experiments?

\>But if the final P~i~ s (for each specified i) are slightly, for
different parts of the smear \>different \[Auth:which, as I've just
explained, in my model they are *not*\], are the final \>experiences for
each i *identical?*

AUTH: The reviewer wishes to interpret the results of measurement in
Everett quantum mechanics by examining the Schrodinger-picture
position-space wavefunction ("the smear") and somehow decomposing it
into pieces, each of which is in some sense a different Everett copy.
Admittedly, this is a very natural way to try to think about Everett QM
with spatial DOF's, probably particularly so if one is attempting to
construct models of measuring devices with "continuously varying
internal structures" (which, as I've just explained, is *not* what is
being done in the paper under review). But, natural though it may be, it
leads to some quite thorny questions, which Stapp and this reviewer both
point out:

\>If the different experiences (for each given i) are not identical, but
are parts of a \>continuum of experiences, then each experienced outcome
will have zero probability

\>

\>Since a continuum of different possible experiences seems problematic,
some sort of \>rule defining the (effective) identity of experiences
associated with different brain states \>seems required. The
Schroedinger equation by itself seems insufficient to resolve this
\>issue.

AUTH: I agree, there's quite a problem here. Therefore, I prefer to
employ interpretational rules that do not attempt to identify different
experiences with pieces of the Schrodinger-picture wavefunction. In this
paper, as in previous ones, I work in the Heisenberg picture.
Interpretation is based on the time evolution of operators with certain
forms and with certain actions on the HP state vector. The operators
have the properties of discreteness and independence from the
translation DOF's needed to fulfill their roles. Operators which do not
have the requisite properties are not interpreted as corresponding to
definite states of affairs, as pointed out in Sec. 1.3 of my paper
(revised version).

REV: But can doing the calculations in the Heisenberg rep. actually help
the

Problem, which is the overly-simple model that does not have the degrees
of freedom corresponding to the smear of possible experiments between
which the "observer" is free to choose. It is true that the question "Is
the other system in R? ,Yes or No", is discrete.

But there should be a smear of different initial operators P(R), for
different R.

Although it is fun to see measurement theory done in the Heisenberg
picture, the basic problem with the paper, namely that it "resolves" the
problem by a simplifying fiat that simply eliminates problem associated
with von Neumann's Process 1, and that problem is the "core basis
problem."

\>But the possibly different experiences need be distinguished only by
the question of \>whether or not they correspond to bin i (i in {1,2,
...M}. For each of the different parts \>of the smear of brain states
(observer states) this question "is it in bin i" might be \>associated
with a different projection operator. This seems to create problems for
a \>Heisenberg representation approach.

AUTH:What becomes of the SP "smear problem" in the HP can be seen, e.g.,
by looking at eq. (64) of the revised version of the paper. The
projectors which act on the continuous coordinates are defined in eqs
(43) and (55). We see that each operator acting in the internal space,
b~i~,\-\--note well, b~i~ , not b~i~ (z)\-\--is indeed associated with a
"smear" of projection operators acting on the continuous spatial
coordinates. But in the HP this is not a problem, merely an interesting
fact; interpretation of the formalism is through the interpretational
rules 1 and 2, and all that is relevant here is the (discrete)
decomposition in eq (64). (The uniqueness of this decomposition is shown
in the Appendix).

REV: Physically, there is the question of what fixes "a" to be one
unique number, in a world that has been evolving since the big bang with
no collapses? This is the core basis problem in the Heisenberg rep.
Going to the Heisenberg rep does not really help with *[this
problem,]{.underline}* though it may tend to slightly obscure the
problem.

\>However, in the Schroedinger representation one could introduce some
variable, say v, \>that identifies the different parts of the smear of
brain states, and then specify for each i \>and v the associated P~iv~
and then by breaking the smeared out brain states into its \>component
parts, v, and applying the associated P~iv~ to each part, specify the
part of the \>wave function associated with the experience associated
with each bin i.

AUTH: As I said above, that's a natural way to proceed. And it leads
straight to the question of what is the correct way to break the
continuous wavefunction into pieces. This is indeed a problem; Stapp has
raised an important issue which must be addressed in any Everett-type
interpretation. That this issue simply doesn't become a problem in the
HP, because the continuously-parameterized position--space projectors
are *automatically* grouped together correctly as in eq. (64), is a
reason to prefer the HP for Everett QM\-\--for other reasons to prefer
the HP, see refs. 16 (probability) and 20 (locality).

REV: We can examine this claim in more detail if the author chooses. But
I think the author will agree that the problem of the *technical need
for Process 1 reductions* is not fundamentally evaded by going to the
HP.

(Speaking of ref 16, an issue which may bear some relation to the "each
experienced outcome will have zero probability" problem which the
reviewer mentions in this email is resolved in that paper by going from
SP to HP. When trying to obtain the Born rule by examining
relative-frequency measurements in the infinite-ensemble limit, one is
faced with a proliferating number of "branches" of the SP wavefunction,
each of which has vanishingly small norm. In the SP, the question of how
one should group the branches together to obtain states of finite
probability is problematic. In the HP approach the grouping is
unambiguous. See ref. 16.)

\>But all of this is somewhat tangential to the real issue, which is the
"choice of basis",

\>not the choice of the outcome, once the basis has been selected.

\>

\>To focus on the real issue we can go to the simpler Yes/No question of
whether

\>the experience corresponds to i=1 or not. Then the real issue comes
into focus: what .\>decides the boundaries of the bin i=1. For this
simple Yes/No question this is the basis \>problem.. The simple question
"Where is the object?" becomes in quantum mechanics:

\>"Is the object in such-and-such a region \[relative to the observing
system\] at time t?" \>where the basis problem is to say how the
specification "such-and-such" is to be \>determined in a universe where
the observing system is a smear.

Indeed, my measuring device asks, and answers, this very question in
Sec. 3. "Such-and-such a region" is the region within distance a of the
observer. The second factor in the first term on the RHS of eq. (64) is
a sum of projectors onto states for which the measuring device and
measured system are farther apart than a. The probability for finding
that the particle is not in the radius-a "bin"\-\--i.e., for getting an
answer of "No"\-\--is given in eq. (80).

(One might be tempted to interpret eq. (64) as indicating, e.g., that
the Everett copy of the observer state-of-awareness DOF which got the
"No" answer is associated with a continuously-infinite set of Everett
copies of the observer location and observed-system location, each copy
of which is such that the observer and observed locations are separated
by more than distance a. But one cannot really justify this
interpretation, since there is no independent notion of either the
observed system or observing system being in a particular place. How
could there be? Only relative position info is obtainable in pure QM;
see comments in discussion section of revised paper. An analogous
interpretation *can* be made regarding a particular Everett copy of the
relative-frequency-measuring device being associated with all Everett
copies of experimental systems consistent with the relative frequency
specific to that particular Everett copy of the
relative-frequency-measuring device. See discussion section of Ref. 16
re: "Siamese n-tuplets.")

\>How is the very particular projection operator P to be specified. This
is the question of \>the choice of the projection operator P in von
Neumann's "process 1", and the issue that \>the Copenhagen precepts
resolve by saying "the experimenter freely chooses". This is \>the
problem that forced the founders of QM to the radical position of
bringing human \>beings, and their conscious choices, into the basic
fabric of quantum mechanics. The \>issues dealt with in the paper being
review are several levels of complexities and \>structure removed from
this issue. The paper deals with the *idealized* *case* mentioned
\>above, not, as has just been explained, with the basis problem.

The paper under review deals with ideal measurement\-\--as the term is
usually used in the literature, e.g., in d'Espagnat's 1976
book\-\--*extended* to include translational DOF's for both observing
apparatus and observed systems and localized measurement interactions,
as detailed in Sec. 3. All projection and other operators that play a
role in the measurement are part of the simple but quite reasonable
model Hamiltonian for localized measurements which is introduced. When
these measurements are analyzed using the Everett interpretation in the
Heisenberg picture, no "basis problems" or other ambiguities, or
problems with localization of measuring devices, are found.

Especially in light of the difficulties\-\--well-described in Stapp's
paper and the reviewer's emails\-\--encountered by Everett measurement
with translational degrees of freedom when analyzed using the kinds of
models and interpretational approaches which Stapp, the reviewer, and
many others employ, this result is interesting and important.

Sincerely,

Mark

REV: The bottom line is that attempts to deal with the "core basis
problem" may indeed be worth publishing, but I think the author needs to
say up front that the "solution"

described in his paper basically *assumes by fiat* that the key Process
1 choice of which measurements is to be performed by the observing
system, the apparent need for which is the origin of the "core basis
problem", is no problem. This is, I believe, an essential "begging of
the question." It may indeed be useful to nibble around the edges of the
problem, but I think it is seriously misleading to say that this paper
"solves" that problem.