1,658 research outputs found
Simultaneity as an Invariant Equivalence Relation
This paper deals with the concept of simultaneity in classical and
relativistic physics as construed in terms of group-invariant equivalence
relations. A full examination of Newton, Galilei and Poincar\'e invariant
equivalence relations in is presented, which provides alternative
proofs, additions and occasionally corrections of results in the literature,
including Malament's theorem and some of its variants. It is argued that the
interpretation of simultaneity as an invariant equivalence relation, although
interesting for its own sake, does not cut in the debate concerning the
conventionality of simultaneity in special relativity.Comment: Some corrections, mostly of misprints. Keywords: special relativity,
simultaneity, invariant equivalence relations, Malament's theore
Rippling patterns in aggregates of myxobacteria arise from cell-cell collisions
Experiments with myxobacterial aggregates reveal standing waves called rippling patterns. Here, these structures are modelled with a simple discrete model based on the interplay between migration and collisions of cells. Head-to-head collisions of cells result in cell reversals. To correctly reproduce the rippling patterns, a refractory phase after each cell reversal has to be assumed, during which further reversal is prohibited. The duration of this phase determines the wavelength and period of the ripple patterns as well as the reversal frequency of single cells
Common Causes and The Direction of Causation
Is the common cause principle merely one of a set of useful heuristics for discovering causal relations, or is it rather a piece of heavy duty metaphysics, capable of grounding the direction of causation itself? Since the principle was introduced in Reichenbachâs groundbreaking work The Direction of Time (1956), there have been a series of attempts to pursue the latter programâto take the probabilistic relationships constitutive of the principle of the common cause and use them to ground the direction of causation. These attempts have not all explicitly appealed to the principle as originally formulated; it has also appeared in the guise of independence conditions, counterfactual overdetermination, and, in the causal modelling literature, as the causal markov condition. In this paper, I identify a set of difficulties for grounding the asymmetry of causation on the principle and its descendents. The first difficulty, concerning what I call the vertical placement of causation, consists of a tension between considerations that drive towards the macroscopic scale, and considerations that drive towards the microscopic scaleâthe worry is that these considerations cannot both be comfortably accommodated. The second difficulty consists of a novel potential counterexample to the principle based on the familiar Einstein Podolsky Rosen (EPR) cases in quantum mechanics
Effects and Propositions
The quantum logical and quantum information-theoretic traditions have exerted
an especially powerful influence on Bub's thinking about the conceptual
foundations of quantum mechanics. This paper discusses both the quantum logical
and information-theoretic traditions from the point of view of their
representational frameworks. I argue that it is at this level, at the level of
its framework, that the quantum logical tradition has retained its centrality
to Bub's thought. It is further argued that there is implicit in the quantum
information-theoretic tradition a set of ideas that mark a genuinely new
alternative to the framework of quantum logic. These ideas are of considerable
interest for the philosophy of quantum mechanics, a claim which I defend with
an extended discussion of their application to our understanding of the
philosophical significance of the no hidden variable theorem of Kochen and
Specker.Comment: Presented to the 2007 conference, New Directions in the Foundations
of Physic
Vienna Circle and Logical Analysis of Relativity Theory
In this paper we present some of our school's results in the area of building
up relativity theory (RT) as a hierarchy of theories in the sense of logic. We
use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and
we build on experience gained in FOM.
The main aims of our school are the following: We want to base the theory on
simple, unambiguous axioms with clear meanings. It should be absolutely
understandable for any reader what the axioms say and the reader can decide
about each axiom whether he likes it. The theory should be built up from these
axioms in a straightforward, logical manner. We want to provide an analysis of
the logical structure of the theory. We investigate which axioms are needed for
which predictions of RT. We want to make RT more transparent logically, easier
to understand, easier to change, modular, and easier to teach. We want to
obtain deeper understanding of RT.
Our work can be considered as a case-study showing that the Vienna Circle's
(VC) approach to doing science is workable and fruitful when performed with
using the insights and tools of mathematical logic acquired since its formation
years at the very time of the VC activity. We think that logical positivism was
based on the insight and anticipation of what mathematical logic is capable
when elaborated to some depth. Logical positivism, in great part represented by
VC, influenced and took part in the birth of modern mathematical logic. The
members of VC were brave forerunners and pioneers.Comment: 25 pages, 1 firgure
The Reconstruction Problem and Weak Quantum Values
Quantum Mechanical weak values are an interference effect measured by the
cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states,
leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase
space. We show that the knowledge of {\rho}_{{\phi},{\psi}}(z) and of one of
the two functions {\phi},{\psi} unambiguously determines the other, thus
generalizing a recent reconstruction result of Lundeen and his collaborators.Comment: To appear in J.Phys.: Math. Theo
Co-existence in the two-dimensional May-Leonard model with random rates
We employ Monte Carlo simulations to numerically study the temporal evolution
and transient oscillations of the population densities, the associated
frequency power spectra, and the spatial correlation functions in the
(quasi-)steady state in two-dimensional stochastic May--Leonard models of
mobile individuals, allowing for particle exchanges with nearest-neighbors and
hopping onto empty sites. We therefore consider a class of four-state
three-species cyclic predator-prey models whose total particle number is not
conserved. We demonstrate that quenched disorder in either the reaction or in
the mobility rates hardly impacts the dynamical evolution, the emergence and
structure of spiral patterns, or the mean extinction time in this system. We
also show that direct particle pair exchange processes promote the formation of
regular spiral structures. Moreover, upon increasing the rates of mobility, we
observe a remarkable change in the extinction properties in the May--Leonard
system (for small system sizes): (1) As the mobility rate exceeds a threshold
that separates a species coexistence (quasi-)steady state from an absorbing
state, the mean extinction time as function of system size N crosses over from
a functional form ~ e^{cN} / N (where c is a constant) to a linear dependence;
(2) the measured histogram of extinction times displays a corresponding
crossover from an (approximately) exponential to a Gaussian distribution. The
latter results are found to hold true also when the mobility rates are randomly
distributed.Comment: 9 pages, 4 figures; to appear in Eur. Phys. J. B (2011
Stochastic evolution of four species in cyclic competition
We study the stochastic evolution of four species in cyclic competition in a
well mixed environment. In systems composed of a finite number of particles
these simple interaction rules result in a rich variety of extinction
scenarios, from single species domination to coexistence between
non-interacting species. Using exact results and numerical simulations we
discuss the temporal evolution of the system for different values of , for
different values of the reaction rates, as well as for different initial
conditions. As expected, the stochastic evolution is found to closely follow
the mean-field result for large , with notable deviations appearing in
proximity of extinction events. Different ways of characterizing and predicting
extinction events are discussed.Comment: 19 pages, 6 figures, submitted to J. Stat. Mec
Reichenbach's Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom
In the paper it will be shown that Reichenbach's Weak Common Cause Principle
is not valid in algebraic quantum field theory with locally finite degrees of
freedom in general. Namely, for any pair of projections A and B supported in
spacelike separated double cones O(a) and O(b), respectively, a correlating
state can be given for which there is no nontrivial common cause (system)
located in the union of the backward light cones of O(a) and O(b) and commuting
with the both A and B. Since noncommuting common cause solutions are presented
in these states the abandonment of commutativity can modulate this result:
noncommutative Common Cause Principles might survive in these models
- âŚ