Home > Uncategorized > Internal observers in causet-based algorithmic spacetime.

Internal observers in causet-based algorithmic spacetime.

(T.B. and Vincenzo Ciancia)

Notions of observation play a central role in Physics, but also in Theoretical Computer Science, notably in Process Algebra.  The importance in Physics of the mutual influences between observer and observed phenomena is well recognized, and yet the properties of the former are in general fuzzily specified, in spite (or because) of the fact that they may include sophisticated cognitive and operative skills.

Our purpose is to transpose the observer/observed interplay in a simple formal context that greatly facilitates their being treated on an equal footing.  We plan to identify observers and observed entities in the context of discrete models of spacetime – in particular, algorithmic causal sets (causets).  We shall define simple forms of observer, with associated synchronisation/observation mechanisms, and detect their emergence in dynamic causets.  The search can be automated by model checkers using spatial or spatio-temporal logics.

We shall focus on the internal (frog’s) view, as opposed to the external (bird’s) view, by assimilating frogs with simple causet substructures, e.g. fattened causal chains provided with some persistent identity (akin to ‘digital particles’ in cellular automata), that synchronise and communicate with their environment.  We shall investigate what ‘observation’ means to these entities and how they might ‘subjectively’ picture their neighborhood or remote environment.  These partial observations may be reminiscent, in spirit, of stroboscopic sampling or Poincaré maps.

The emergent features of various models of computation have been widely investigated, notably for the spatio-temporal diagrams of cellular automata, but always under an external viewpoint. Our aim is to restart this analysis under the radically different perspective of an internal (proto-)observer, with a focus on stochastic and deterministic, labelled or unlabelled causets.  Simply stated, our goal is to discover qualitative differences between the bird’s and the frog’s view. The issue becomes more challenging when considering different classes of observers of the same phenomena.  Identifying their different viewpoints leads to considerations on invariance, akin to Lorentz covariance.

Suitable notions of abstraction shall be considered, since an observer may be blind to the tiniest causet details but sensitive to a coarse-grained version of it.  Additionally, ‘smart’ observers may be required to tell apart regular from random-like causet regions.

In our investigation on observations within causets, we will adopt techniques that proved successful in theoretical computer science and process calculi, such as partially ordered Event Structures, and category-theoretical models. Coalgebras, in particular, provide flexibile notions of observation. Causality and locality are achieved using the emerging nominal computation model that endows observers with primitive forms of naming, whose power is balanced by a finite memory principle. We consider it an interesting additional research question to explore the impact of such basic computational constraints on algorithmic causal sets.

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