相关论文: Relational mechanics of shape and scale
Relational particle mechanics are models in which there is, overall, no time, position, orientation (nor, sometimes, scale). They are useful for whole-universe modelling - the setting for quantum cosmology. This note concerns 3 particles in…
Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1-d to include…
In scaled relational particle mechanics, only relative times, relative angles and relative separations are meaningful. It arose in the study of the absolute versus relative motion debate. It has then turned out to be a useful toy model of…
Relational particle models are of value in the absolute versus relative motion debate. They are also analogous to the dynamical formulation of general relativity, and as such are useful for investigating conceptual strategies proposed for…
I investigate useful shape quantities for the classical and quantum mechanics of the relational quadrilateral in 2-d. This is relational in the sense that only relative times, relative ratios of separations and relative angles are…
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex minisuperspace models. In this…
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…
Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as…
I investigate qualitatively significant regions of the configuration space for the classical and quantum mechanics of the relational quadrilateral in 2-d. This is relational in the sense that only relative ratios of separations, relative…
This paper considers passing from the usual $\mathbb{R}^d$ model of absolute space to $\mathbb{S}^d$ at the level of relational particle models. Both approaches' $d = 1$ cases are rather simpler than their $d \geq 2$ cases, with $N$…
In Euclidean relational particle mechanics (ERPM) only relative times, relative angles and relative separations are meaningful, while in similarity relational particle mechanics (SRPM) only relative times, relative angles and ratios of…
Relational particle mechanics models bolster the relational side of the absolute versus relational motion debate, and are additionally toy models for the dynamical formulation of General Relativity and its Problem of Time. They cover two…
It is argued that substantial portions of both Newtonian particle mechanics and general relativity can be viewed as relational (rather than absolute) theories. I furthermore use the relational particle models as toy models to investigate…
With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so…
This paper provides the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are $\mathbb{CP}^2$ and the cone over this, C($\mathbb{CP}^2$). We consider exact free and isotropic HO potential cases…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
This paper concerns the absolute versus relative motion debate. The Barbour and Bertotti 1982 work may be viewed as an indirectly set up relational formulation of a portion of Newtonian mechanics. I consider further direct formulations of…
The tomographic map of quantum state of a system with several degrees of freedom which depends on one random variable, analogous to center of mass considered in rotated and scaled reference frame in the phase space, is constructed. Time…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…