Interacting vector fields in Relativity without Relativity

Barbour, Foster and \'{O} Murchadha have recently developed a new framework, called here {\it{the 3-space approach}}, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of 3-dimensional metric--matter configurations. In fact gravity, the universal light cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity -- and more -- without presupposing relativity. This paper completes the recovery of the presently known bosonic sector within the 3-space approach. We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang--Mills fields minimally coupled to gravity.Comment: Replaced with final version accepted by Classical and Quantum Gravity (14 pages, no figures

Strongly coupled lattice gauge theory with dynamical fermion mass generation in three dimensions

We investigate the critical behaviour of a three-dimensional lattice \chiU\phi_3 model in the chiral limit. The model consists of a staggered fermion field, a U(1) gauge field (with coupling parameter $\beta$) and a complex scalar field (with hopping parameter $\kappa$). Two different methods are used: 1) fits of the chiral condensate and the mass of the neutral unconfined composite fermion to an equation of state and 2) finite size scaling investigations of the Lee-Yang zeros of the partition function in the complex fermion mass plane. For strong gauge coupling ($\beta < 1$) the critical exponents for the chiral phase transition are determined. We find strong indications that the chiral phase transition is in one universality class in this $\beta$ interval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the \chiU\phi_3 model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small $\kappa$, we explore a region in which the mass in the neutral fermion channel is large but the chiral condensate on finite lattices very small. If it does not vanish in the infinite volume limit, then a continuum limit with massive unconfined fermion might be possible in this region, too.Comment: 27 pages, 16 figure

Scale-invariant gravity: Spacetime recovered

The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. Recently a manifestly 3-dimensional theory was constructed with conformal superspace as the configuration space. Here a fully 4-dimensional action is constructed so as to be invariant under conformal transformations of the 4-metric using general relativity as a guide. This action is then decomposed to a (3+1)-dimensional form and from this to its Jacobi form. The surprising thing is that the new theory turns out to be precisely the original 3-dimensional theory. The physical data is identified and used to find the physical representation of the theory. In this representation the theory is extremely similar to general relativity. The clarity of the 4-dimensional picture should prove very useful for comparing the theory with those aspects of general relativity which are usually treated in the 4-dimensional framework.Comment: Replaced with final version: minor changes to tex

Scale-Invariant Gravity: Geometrodynamics

We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's idea of a compensating field, our direct approach dispenses with this and is built by extension of the method of best matching w.r.t scaling developed in the parallel particle dynamics paper by one of the authors. In spatially-compact GR, there is an infinity of degrees of freedom that describe the shape of 3-space which interact with a single volume degree of freedom. In conformal gravity, the shape degrees of freedom remain, but the volume is no longer a dynamical variable. Further theories and formulations related to GR and conformal gravity are presented. Conformal gravity is successfully coupled to scalars and the gauge fields of nature. It should describe the solar system observations as well as GR does, but its cosmology and quantization will be completely different.Comment: 33 pages. Published version (has very minor style changes due to changes in companion paper

The geometry of the Barbour-Bertotti theories I. The reduction process

The dynamics of $N\geq 3$ interacting particles is investigated in the non-relativistic context of the Barbour-Bertotti theories. The reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element. The involved metric, degenerate in the flat configuration space, is the first fundamental form of the space of orbits of translations and rotations (the Leibniz group). The Riemann tensor and the scalar curvature are computed by a generalized Gauss formula in terms of the vorticity tensors of generators of the rotations. The curvature scalar is further given in terms of the principal moments of inertia of the system. Line configurations are singular for $N\neq 3$. A comparison with similar methods in molecular dynamics is traced.Comment: 15 pages, to appear in Classical and Quantum Gravit

Einstein gravity as a 3D conformally invariant theory

We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Horava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections

Relational interpretation of the wave function and a possible way around Bell's theorem

The famous ``spooky action at a distance'' in the EPR-szenario is shown to be a local interaction, once entanglement is interpreted as a kind of ``nearest neighbor'' relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the ``nearest neighbor'' relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, ``position'' becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the ``weird'' aspects, like the particle-wave duality, the non-locality of entanglement, or the ``mystery'' of the double-slit experiment, disappear. Furthermore, this picture cirumvents the restrictions set by Bell's inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics.Comment: Accepted for publication in "International Journal of Theoretical Physics

Relational Particle Models. II. Use as toy models for quantum geometrodynamics

Relational particle models are employed as toy models for the study of the Problem of Time in quantum geometrodynamics. These models' analogue of the thin sandwich is resolved. It is argued that the relative configuration space and shape space of these models are close analogues from various perspectives of superspace and conformal superspace respectively. The geometry of these spaces and quantization thereupon is presented. A quantity that is frozen in the scale invariant relational particle model is demonstrated to be an internal time in a certain portion of the relational particle reformulation of Newtonian mechanics. The semiclassical approach for these models is studied as an emergent time resolution for these models, as are consistent records approaches.Comment: Replaced with published version. Minor changes only; 1 reference correcte

New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split

I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding to cyclic coordinates. The latter treatment works through the physical meaninglessness of auxiliary variables' values applying also to the end points (or end spatial hypersurfaces) of the variation, so that these are free rather than fixed. [This is also known as variation with natural boundary conditions.] Further principles of dynamics workings such as Routhian reduction and the Dirac procedure are shown to have parallel counterparts for this new formalism. One advantage of the new scheme is that the corresponding actions are more manifestly relational. While the electric potential is usually regarded as a multiplier coordinate and Arnowitt, Deser and Misner have regarded the lapse and shift likewise, this paper's scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose corresponding velocities are, respectively, the abovementioned previously used variables. This paper's way of thinking about gauge theory furthermore admits interesting generalizations, which shall be provided in a second paper.Comment: 11 page

Assessing the usefulness of an online chat room in the integrated renal and cardiovascular courses

Background: Pharmacy students in their first professional year (P1) often struggle to adapt to the demands of the rigorous curriculum. The integrated renal and cardiovascular courses at the University of Rhode Island (URI) facilitate learning of renal and cardiovascular disorders and the medications used to treat them. The courses are challenging but important to the students’ future practice. There have been no studies assessing the impact or usefulness of using online chat rooms to supplement traditional teaching methods for pharmacy students. Objective: The objective of the online chat room was to provide an additional resource that students could use to clarify course material. We hypothesized that the chat room would serve as a useful supplemental learning tool for pharmacy students. Method: The online chat room function of the course management system at URI (Sakai) was offered throughout the spring semester to P1 students. During chat room settings, P1 students submitted questions in a real-time list format. The P3 students or professor then responded to the questions and posed questions to the students to encourage discussion. At the end of the semester, the students were asked to fill out a brief, electronic survey via Survey Monkey. The survey asked 12 questions about the chat room using a 5-point Likert scale, including asking if they attended the chat room and, if they did not, the reason(s) why, as well as the impact of the chat room on their learning. The survey was approved by the URI Institutional Review Board. Results: 63 students responded to the survey (response rate = 53%). Seventy percent attended the live chat and 95% viewed the archived transcript. The majority of students agreed that chat room sessions encouraged faculty-student interaction outside of the classroom, encouraged them to ask questions and helped them learn by asking questions and seeking answers. Students who attended the live session were more likely to agree that the chat room sessions were helpful and encouraged them to stay up to date in their work. Conclusion: Survey results showed supported the online chat room as a useful adjunct that P1 students can use to enhance their understanding of the renal and cardiovascular course material. Overall, the chat room encouraged students to stay up-to-date in their studying, encouraged student-faculty interaction outside of class, helped the students learn more by asking their own questions, and facilitated their learning. In addition, the chat room clarified material the students did not understand and encouraged them to ask questions about the material. The feedback provided by the students who participated will be used in the future to further improve the chat room