25,769 research outputs found
Dependencies and Simultaneity in Membrane Systems
Membrane system computations proceed in a synchronous fashion: at each step
all the applicable rules are actually applied. Hence each step depends on the
previous one. This coarse view can be refined by looking at the dependencies
among rule occurrences, by recording, for an object, which was the a rule that
produced it and subsequently (in a later step), which was the a rule that
consumed it. In this paper we propose a way to look also at the other main
ingredient in membrane system computations, namely the simultaneity in the rule
applications. This is achieved using zero-safe nets that allows to synchronize
transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into
occurrence nets in a classical way, and to this unfolding an event structure
can be associated. The capability of capturing simultaneity of zero-safe nets
is transferred on the level of event structure by adding a way to express which
events occur simultaneously
Uniqueness of Simultaneity
We consider the problem of uniqueness of certain simultaneity structures in
flat spacetime. Absolute simultaneity is specified to be a non-trivial
equivalence relation which is invariant under the automorphism group Aut of
spacetime. Aut is taken to be the identity-component of either the
inhomogeneous Galilei group or the inhomogeneous Lorentz group. Uniqueness of
standard simultaneity in the first, and absence of any absolute simultaneity in
the second case are demonstrated and related to certain group theoretic
properties. Relative simultaneity with respect to an additional structure X on
spacetime is specified to be a non-trivial equivalence relation which is
invariant under the subgroup in Aut that stabilises X. Uniqueness of standard
Einstein simultaneity is proven in the Lorentzian case when X is an inertial
frame. We end by discussing the relation to previous work of others.Comment: LeTeX-2e, 18 pages, no figure
The fate of presentism in modern physics
There has been a recent spate of essays defending presentism, the view in the
metaphysics of time according to which all and only present events or entities
exist. What is particularly striking about this resurgence is that it takes
place on the background of the significant pressure exerted on the position by
the relativity of simultaneity asserted in special relativity, and yet in
several cases invokes modern physics for support. I classify the presentist
arguments into a two by two matrix depending on whether they take a
compatibilist or incompatibilist stance with respect to both special relativity
in particular and modern physics in general. I then review and evaluate what I
take to be some of the most forceful and intriguing presentist arguments
turning on modern physics. Although nothing of what I will say eventuates its
categorical demise, I hope to show that whatever presentism remains compatible
with empirical facts and our best physics is metaphysically repugnant.Comment: 23 pages, 4 figure
Time as an Empirical Concept in Special Relativity
According to a widespread view, Einsteinâs definition of time in his special relativity is founded on the positivist verification principle. The present paper challenges this received outlook. It shall be argued that Einsteinâs position on the concept of time, to wit, simultaneity, is best understood as a mitigated version of concept empiricism. He
contrasts his position to Newtonâs absolutist and Kantâs transcendental arguments, and in part sides with Humeâs and Machâs empiricist arguments. Nevertheless, Einstein worked out a concept empiricism that is considerably more moderate than what we find in the preceding empiricist tradition and early logical positivism. He did not think that the origin of concepts is in observations, but in conventions, and he also maintained a realist ontology of physical events, which he thought is necessary for his theory. Consequently, his philosophy of time in special relativity is not couched in terms of an anti-metaphysical verificationism
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