Proper time and Minkowski structure on causal graphs

For causal graphs we propose a definition of proper time which for small scales is based on the concept of volume, while for large scales the usual definition of length is applied. The scale where the change from "volume" to "length" occurs is related to the size of a dynamical clock and defines a natural cut-off for this type of clock. By changing the cut-off volume we may probe the geometry of the causal graph on different scales and therey define a continuum limit. This provides an alternative to the standard coarse graining procedures. For regular causal lattice (like e.g. the 2-dim. light-cone lattice) this concept can be proven to lead to a Minkowski structure. An illustrative example of this approach is provided by the breather solutions of the Sine-Gordon model on a 2-dimensional light-cone lattice.Comment: 15 pages, 4 figure

Shape in an Atom of Space: Exploring quantum geometry phenomenology

A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to develop a model of angular corrections to local, continuum flat-space 3-geometries. The physical effects involve neither breaking of local Lorentz invariance nor Planck scale suppression, but rather reply on only the combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example of how the effects might be observationally accessible.Comment: 14 pages, 7 figures; v2 references adde

Depth- and range-dependent variation in the performance of aquatic telemetry systems: Understanding and predicting the susceptibility of acoustic tag-receiver pairs to close proximity detection interference

BACKGROUND: Passive acoustic telemetry using coded transmitter tags and stationary receivers is a popular method for tracking movements of aquatic animals. Understanding the performance of these systems is important in array design and in analysis. Close proximity detection interference (CPDI) is a condition where receivers fail to reliably detect tag transmissions. CPDI generally occurs when the tag and receiver are near one another in acoustically reverberant settings. Here we confirm transmission multipaths reflected off the environment arriving at a receiver with sufficient delay relative to the direct signal cause CPDI. We propose a ray-propagation based model to estimate the arrival of energy via multipaths to predict CPDI occurrence, and we show how deeper deployments are particularly susceptible. METHODS: A series of experiments were designed to develop and validate our model. Deep (300 m) and shallow (25 m) ranging experiments were conducted using Vemco V13 acoustic tags and VR2-W receivers. Probabilistic modeling of hourly detections was used to estimate the average distance a tag could be detected. A mechanistic model for predicting the arrival time of multipaths was developed using parameters from these experiments to calculate the direct and multipath path lengths. This model was retroactively applied to the previous ranging experiments to validate CPDI observations. Two additional experiments were designed to validate predictions of CPDI with respect to combinations of deployment depth and distance. Playback of recorded tags in a tank environment was used to confirm multipaths arriving after the receiver\u27s blanking interval cause CPDI effects. RESULTS: Analysis of empirical data estimated the average maximum detection radius (AMDR), the farthest distance at which 95% of tag transmissions went undetected by receivers, was between 840 and 846 m for the deep ranging experiment across all factor permutations. From these results, CPDI was estimated within a 276.5 m radius of the receiver. These empirical estimations were consistent with mechanistic model predictions. CPDI affected detection at distances closer than 259-326 m from receivers. AMDR determined from the shallow ranging experiment was between 278 and 290 m with CPDI neither predicted nor observed. Results of validation experiments were consistent with mechanistic model predictions. Finally, we were able to predict detection/nondetection with 95.7% accuracy using the mechanistic model\u27s criterion when simulating transmissions with and without multipaths. DISCUSSION: Close proximity detection interference results from combinations of depth and distance that produce reflected signals arriving after a receiver\u27s blanking interval has ended. Deployment scenarios resulting in CPDI can be predicted with the proposed mechanistic model. For deeper deployments, sea-surface reflections can produce CPDI conditions, resulting in transmission rejection, regardless of the reflective properties of the seafloor

The structure of causal sets

More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case of a physical theory predestined to be interpreted in structuralist terms. It is shown how employing structuralism lends itself to a natural interpretation of the physical meaning of causal sets theory. Conversely, the conceptually exceptionally clear case of causal sets is used as a foil to illustrate how a mathematically informed rigorous conceptualization of structure serves to identify structures in physical theories. Furthermore, a number of technical issues infesting structuralist interpretations of physical theories such as difficulties with grounding the identity of the places of highly symmetrical physical structures in their relational profile and what may resolve these difficulties can be vividly illustrated with causal sets.Comment: 19 pages, 4 figure

Emergence of spatial structure from causal sets

There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying discreteness. The causal set approach, in which the fundamental relation is based upon causality, finds it easy to reproduce timelike distances, but has a more difficult time with spatial distance, due to the unique combination of Lorentz invariance and discreteness within that approach. We describe a method to deduce spatial distances from a causal set. In addition, we sketch how one might use an important ingredient in deducing spatial distance, the `$n$-link', to deduce whether a given causal set is likely to faithfully embed into a continuum spacetime.Comment: 21 pages, 21 figures; proceedings contribution for DICE 2008, to appear in Journal of Physics: Conference Serie

Semiclassical Mechanics of the Wigner 6j-Symbol

The semiclassical mechanics of the Wigner 6j-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the methods of Roberts and others for deriving the Ponzano-Regge formula are discussed, and a new approach, based on the recoupling of four angular momenta, is presented. A generalization of the Yutsis-type of spin network is developed for this purpose. Special attention is devoted to symplectic reduction, the reduced phase space of the 6j-symbol (the 2-sphere of Kapovich and Millson), and the reduction of Poisson bracket expressions for semiclassical amplitudes. General principles for the semiclassical study of arbitrary spin networks are laid down; some of these were used in our recent derivation of the asymptotic formula for the Wigner 9j-symbol.Comment: 64 pages, 50 figure

Spacelike distance from discrete causal order

Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly difficult to extract spacelike distances, because of the unique combination of discreteness with local Lorentz invariance in that approach. We propose a number of methods to overcome this difficulty, one of which reproduces the spatial distance between two points in a finite region of Minkowski space. We provide numerical evidence that this definition can be used to define a `spatial nearest neighbor' relation on a causal set, and conjecture that this can be exploited to define the length of `continuous curves' in causal sets which are approximated by curved spacetime. This provides evidence in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio

Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation

The properties of the Volume operator in Loop Quantum Gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater than four. The present analysis benefits from the general simplified formula for matrix elements of the Volume operator derived in gr-qc/0405060, making it feasible to implement it on a computer as a matrix which is then diagonalized numerically. The resulting eigenvalues serve as a database to investigate the spectral properties of the volume operator. Analytical results on the spectrum at 4-valent vertices are included. This is a companion paper to arXiv:0706.0469, providing details of the analysis presented there.Comment: Companion to arXiv:0706.0469. Version as published in CQG in 2008. More compact presentation. Sign factor combinatorics now much better understood in context of oriented matroids, see arXiv:1003.2348, where also important remarks given regarding sigma configurations. Subsequent computations revealed some minor errors, which do not change qualitative results but modify some numbers presented her

Simulating causal collapse models

We present simulations of causal dynamical collapse models of field theories on a 1+1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a procedure of coarse graining and renormalising the fundamental field can overcome its noisiness and argue that this coarse grained renormalised field will show interesting structure if the state vector does on the coarse grained scale.Comment: 18 pages, 8 fugures, LaTeX, Reference added, discussion of probability distribution of labellings correcte

Effect of and Acute Bout of Kettlebell Exercise on Glucose Tolerance in Sedentary Men: a Preliminary Study

International Journal of Exercise Science 9(4): 524-535, 2016. Impaired glucose tolerance can have significant health consequences. The purposes of this preliminary study were to examine whether a single session of kettlebell exercise improves acute post-exercise glucose tolerance in sedentary individuals, and whether it was as effective as high-intensity interval running. Six sedentary male subjects underwent a two-hour oral glucose tolerance test following three different conditions: 1) control (no exercise); 2) kettlebell exercise (2 sets of 7 exercises, 15 repetitions per exercise with 30 seconds rest between each exercise); or 3) high-intensity interval running (10 one-minute intervals at a workload corresponding to 90% VO2max interspersed with one-minute active recovery periods). Blood glucose and insulin levels were measured before (0 minutes), and 60 and 120 minutes after glucose ingestion. Both kettlebell and high-intensity interval running exercise significantly lowered blood glucose 60 minutes after glucose ingestion compared with control. However, there was no significant difference in blood glucose between the two exercise conditions at any time point. In addition, there were no significant differences in insulin concentration between high intensity interval running, kettlebell, and control conditions at all time points. Results indicate that an acute bout of kettlebell exercise is as effective as high intensity interval running at improving glucose tolerance in sedentary young men