Evolution in Quantum Causal Histories

[marcus]

Baez recent paper "Quantum Quandaries" references one that Fotini Markopoulou wrote last year with Hanno Sahlmann and Eli Hawkins

"Evolution in Quantum Causal Histories"
http://arxiv.org/hep-th/0302111


I suspect I'm failing to get the point of this paper, so I mention it in case anyone can get some traction on it and wants to explain

 

[toloXXX]

What is that about ?
Why don't you explain first ? i think you can explain first and then I will try to give a comment.

Thanks

 

[selfAdjoint]

Just for reference, Baez refers to the Hawkins, Markopoulou, and Sahlmann (HMS) paper for a technical point, at the end of his section 2 (p. 8 in my copy) he says:

"There are some further technical complications arising from the fact that except in low dimensions, we need to use the C^*-algebraic approach to quantum theory instead of the Hilbert space approach [13]. Here the category Hilb should be replaced by one where the objects are C^*-algebras and the morphisms are completely positive maps between their duals [15]."

And reference 15 is the HMS paper. So what we are looking for in the HMS paper is this characterization of quantum theory in the algebraic context. Just at the beginning of the paper we see that they want to use the concept of causal quantum histories to get an abstract definition that will conver any quantization of gravity.

I will spend some time with the paper today and see if I can come up with anything cogent that can be applied to quantum quandries.

 

[selfAdjoint]

And now that I have been with the paper for a while I am more and more impressed with it. The aim is to provide a general theater in which quantum statements about spacetime can be discussed, regardless of the details of the quantum system that generates them. And it looks very general, and certainly should work. I can well see why Baez relied on it as a benchmark of careful quantumness.

One point. The authors use a lot of terms in their introductory section 1 that they don't define. If you are not already familiar with those terms you would do well to work back and forth between section 2, where they are defined, and section 1 to get a clear idea of what the authors mean.

 

[marcus]

for anyone who missed the beginning, we came across the Fotini paper in connection with Baez recent quantum gravity paper

http://arxiv.org/quant-ph/0404040

"quantum quandaries: a category theoretic perspective"

General relativity may seem very different from quantum theory, but work on quantum gravity has revealed a deep analogy between the two. General relativity makes heavy use of the category nCob, whose objects are (n-1)-dimensional manifolds representing "space" and whose morphisms are n-dimensional cobordisms representing "spacetime". Quantum theory makes heavy use of the category Hilb, whose objects are Hilbert spaces used to describe "states", and whose morphisms are bounded linear operators used to describe "processes". Moreover, the categories nCob and Hilb resemble each other far more than either resembles Set, the category whose objects are sets and whose morphisms are functions. In particular, both Hilb and nCob but not Set are *-categories with a noncartesian monoidal structure. We show how this accounts for many of the famously puzzling features of quantum theory: the failure of local realism, the impossibility of duplicating quantum information, and so on. We argue that these features only seem puzzling when we try to treat Hilb as analogous to Set rather than nCob, so that quantum theory will make more sense when regarded as part of a theory of spacetime."