http://arxiv.org/abs/1406.4531
Renormalization of lattice-regularized quantum gravity models II. The case of causal dynamical triangulations
Joshua H. Cooperman
(Submitted on 17 Jun 2014)
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme--in concert with finite size scaling analysis--is essential to this aim. Formulating and implementing such a scheme in the present context raises novel and notable conceptual and technical problems. I explored these problems, and, building on standard techniques, suggested potential solutions in the first paper of this two-part series. As an application of these solutions, I now propose a renormalization group scheme for causal dynamical triangulations. This scheme differs significantly from that studied recently by Ambjorn, Gorlich, Jurkiewicz, Kreienbuehl, and Loll.
26 pages, 11 figures. The first paper in the two-part series will appear shortly. The second paper is sufficiently self-contained to be read on its own.
http://arxiv.org/abs/1406.4532
Renormalization for Philosophers
Jeremy Butterfield, Nazim Bouatta
(Submitted on 17 Jun 2014)
We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites (Sections 2 and 3). Our motivation is that renormalization is undoubtedly one of the great ideas, and great successes, of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction (Section 4).
One theme will be a contrast between two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization (from 1970 onwards) explains why the phenomena we see, at the energies we can access in our particle accelerators, are described by a renormalizable quantum field theory. For whatever non-renormalizable interactions may occur at yet higher energies, they are insignificant at accessible energies. Thus the new approach explains why our best fundamental theories have a feature, viz. renormalizability, which the old approach treated as a selection principle for theories.
We also maintain that universality, a concept stressed in renormalization theory, is essentially the familiar philosophical idea of multiple realizability; and that it causes no problems for reductions of a Nagelian kind.
Comments: 48 pages, 1 figure, Forthcoming in
Metaphysics in Contemporary Physics: a volume of Poznan Studies in Philosophy of Science, eds. T. Bigaj and C. Wuethrich; 2015.
briefly noted as possibly of side interest:
http://arxiv.org/abs/1406.4354
Reduction, Emergence and Renormalization
Jeremy Butterfield
(Submitted on 17 Jun 2014)
43 pages,
The Journal of Philosophy, volume 111 (2014), pp. 5-49
http://arxiv.org/abs/1406.4745
On Time in Quantum Physics
Jeremy Butterfield
(Submitted on 18 Jun 2014)
First, I briefly review the different conceptions of time held by three rival interpretations of quantum theory: the collapse of the wave-packet, the pilot-wave interpretation, and the Everett interpretation (Section 2).
Then I turn to a much less controversial task: to expound the recent understanding of the time-energy uncertainty principle, and indeed of uncertainty principles in general, that has been established by such authors as Busch, Hilgevoord and Uffink.
Although this may at first seem a narrow topic, I point out connections to other conceptual topics about time in quantum theory: for example, the question under what circumstances there is a time operator (Section 4.3).
26 pages, '
The Blackwell Companion to the Philosophy of Time', edited by A. Bardon and H. Dyke, Wiley-Blackwell, 2013; pp. 220-241
http://arxiv.org/abs/1406.4747
On Under-determination in cosmology
Jeremy Butterfield
(Submitted on 18 Jun 2014)
31 pages,
Studies in the History and Philosophy of Modern Physics, vol 46, (2014), pp. 57-69
http://arxiv.org/abs/1406.4732
Laws, Causation and Dynamics at Different Levels
Jeremy Butterfield
(Submitted on 18 Jun 2014)
29 pages, 3 figures