Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Are There Testable Discrete Poincar\'e Invariant Physical Theories?   In a model of physics taking place on a discrete set of points that
approximates Minkowski space, one might perhaps expect there to be an
empirically identifiable preferred frame. However, the work of Dowker,
Bombelli, Henson, and Sorkin might be taken to suggest that random sprinklings
of points in Minkowski space define a discrete model that is provably
Poincar\'e invariant in a natural sense. We examine this possibility here. We
argue that a genuinely Poincar\'e invariant model requires a probability
distribution on sprinklable sets -- Poincar\'e orbits of sprinklings -- rather
than individual sprinklings. The corresponding $\sigma$-algebra contains only
sets of measure zero or one. This makes testing the hypothesis of discrete
Poincar\'e invariance problematic, since any local violation of Poincar\'e
invariance, however gross and large scale, is possible, and cannot be said to
be improbable. We also note that the Bombelli-Henson-Sorkin argument, which
rules out constructions of preferred timelike directions for typical
sprinklings, is not sufficient to establish full Lorentz invariance. For
example, once a pair of timelike separated points is fixed, a preferred
spacelike direction {\it can} be defined for a typical sprinkling, breaking the
remaining rotational invariance.

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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph