a recent post by john baez
discussed a recent talk by jeffrey bub
where jeff gave arguments against mechanism in science

this was surprising to me
as jeff has done research in bohmian mechanics over the years
and so i was curious as to the nature of his arguments
and asked jeff some questions

he gave me a forward copy of a preprint he is completing
and i was intrigued by his arguments
and immediately decided usenet was the best place to turn

all misrepresentations are my fault and likely on purpose

..

i will not post any extended parts of the piece
as is proper
but i will try to give an outline of the idea

the paper is called "quantum probabilities as degrees of belief"

a recent paper by pitowski called "quantum mechanics as a theory of probability" is jeff's starting point

you may be thinking:
this sounds like what everyone thinks about quantum probabilities
it's stale news
old hat
i must insist that they have a much more seasoned view of these issues

you see
jeffrey bub has been a leading contributor to the modal logic school of quantum interpretation in recent times
and is quite familiar with much of the history of probabilistic interpretations of quantum mechanics

because he sees the field widely
his arguments are a bit more nuanced

pitowski's article mention two dogmas often debated in foundational studies
a) fundamental mechanics should have a dynamic mechanism for explanations; measurement should not be primitive
(j s bell)
b) quantum mechanics is a representation of reality

jeff asserts that these dogmas are called into question by information-theoretic results
known as "no-cloning" theorems

no cloning theorems proceed by showing
noncorrupting unitary transformations cannot clone all states
because any two states of the system would then be identical or orthogonal

http://en.wikipedia.org/wiki/No_cloning_theorem
http://arxiv.org/pdf/quant-ph/0012121

jeff argues that:
assume there is a device that can distinguish all states - ie. a universal measurer
it does this by itself transitioning to a distinguishable state upon measurement
then if we assume any known state can be prepared from a reference state
we have violated the no cloning theorem

if it is fundamentally impossible to copy a dynamic state
he argues
then information sources exist that have no knowable model
even if they have possible models
and so dynamical explanations are not useful to our information

what the bohmian models are really doing with their dynamical descriptions
are providing dynamics to explain why dynamical information cannot be extracted
they are explaining absences and lacks of information

..

instead
what is useful he argues
is the information received in the revision of beliefs due to observing an event

he interprets the projections P(H) as bayesian measures of partial belief
where the projection postulate for state change of a system (the von neumann projection collapse)
is just a noncommutative bayesian belief update

the projections are simply conditional probabilities
that bayesian update on information extraction

this has become a common interpretation that seems to be popping up from a number of directions and subfields
but i think this misses one of the most important points of bohmian models
they solve the observation problem and need no classical cut

the reason many bohmians are averse to taking measurements as fundamental
is because information exchange becomes relative
and information is local to an observer

but there is no clear quantum mechanical notion of observer
because of issues with wigner's friend and a need for classical correspondence as a fundamental principle

in my opinion
bub's objection mixes observables with beables
and then mistakes obstructions to duplicating observable information sources
as obstructions to meanings of existents in scientific models

he mentions this information-theoretic approach might be seen as a principled instrumentalism
which is important because bob coecke's quantum operationalism seems to make some of the same points
but without a position against mechanism

whereas the obstruction for observables is no-cloning theorems
obstructions for beables exist in kochen-specker

..

the kochen-specker theorem states that all observables cannot be given consistent values at all times
in a theory where the observables have values independent of the context of their measurement

http://plato.stanford.edu/entries/kochen-specker/

this result is foundational to categorial quantisation

isham and butterfield have shown

http://arxiv.org/pdf/quant-ph/9803055

given a collection W of boolean subalgebras
of the lattice P(H) of projection operators
on the hilbert space H of the system
it forms a poset under subalgebra inclusion and can be considered a category

a dual presheaf on W is the contravariant functor D:W -> Set suchThat
O e objects(W) <-> D(O) is the set Hom(O, {0,1})
i e morphisms(W) <-> D(i)(chi) := chi | range(i), the restriction of chi to the inclusion's range subalgebra

the kochen-specker theorem proves
for dim(H) > 2
the dual presheaf on W has no global section

thus there is no means for us to have a
continuous assignment of all observables
an unambiguous dynamic value at all times

indeed
abramsky and coecke
http://arxiv.org/pdf/quant-ph/0402130
have laid out a nice categorial description of
the cloning and teleportation information-theoretic results bub refers to

symmetric monoidal categories naturally derive no cloning results
but their view generalises to other mathematical models like what they call "reverse arithmetic"
where the validity of considering logical ontologies is not regularly questioned on bub's grounds
( though it raises the question of whether they should )

..

now bob clifton points out that
although bohmian mechanics is content with minimal beable sets to provide realist description
there in fact exist maximal collections of beables
http://arxiv.org/pdf/quant-ph/9711009
built from dispersion-free quasicommutative subalgebras of observables given ontological status

many of these maximal collections are bub-definite
ie. they are constructed from a modal description
building maximal beable collections of a system relative to a preferred observable

i keep refering back to grothendieck's "pursuing stacks"
where he has some existential constructions in groupoidification functors
that seem very similar to these beable constructions...

is there something here?