Is spacetime fundamentally discrete?
APA
Dittrich, B., Major, S., Oriti, D., Percacci, R. & Fritz, T. (2012). Is spacetime fundamentally discrete?. Perimeter Institute. https://pirsa.org/12100100
MLA
Dittrich, Bianca, et al. Is spacetime fundamentally discrete?. Perimeter Institute, Oct. 24, 2012, https://pirsa.org/12100100
BibTex
@misc{ pirsa_PIRSA:12100100, doi = {10.48660/12100100}, url = {https://pirsa.org/12100100}, author = {Dittrich, Bianca and Major, Seth and Oriti, Daniele and Percacci, Roberto and Fritz, Tobias}, keywords = {Mathematical physics}, language = {en}, title = {Is spacetime fundamentally discrete?}, publisher = {Perimeter Institute}, year = {2012}, month = {oct}, note = {PIRSA:12100100 see, \url{https://pirsa.org}} }

Perimeter Institute for Theoretical Physics

Hamilton College

LudwigMaximiliansUniversität München (LMU)

SISSA International School for Advanced Studies

Universität Innsbruck
Collection
Talk Type
Subject
Abstract
Modelling continuum dynamics on
discrete space time
We will discuss perfect discretizations which aim at mirroring exactly continuum physics on a given lattice. Such discretizations avoid typical artifacts like Lorentz violation, energy dissipation, particle doubling and in particular breaking of diffeomorphism symmetry. Thus the question arises how to distinguish such lattice dynamics from continuum physics.
____________________________
Turning Weyl’s tile argument into a mathematically rigorous nogo theorem
Weyl's tile argument notes that if space was fundamentally discrete then the set of allowed velocities of a classical particle would not be isotropic. I will generalize Weyl's heuristic argument to a nogo theorem applying to any discrete periodic structure. Since this theorem does not take quantum mechanics into account it should only be regarded as the first step of a program of understanding the phenomenology of discrete spacetimes in a mathematically rigorous way.See arXiv:1109.1963
____________________________
On the Observability of Discrete Spatial Geometry
If quantum geometry is an accurate model of microscopic spatial geometry then two related questions arise, one observational and one theoretical: How and at what scale is the discreteness manifest? And, how is the general relativistic limit achieved? These questions will be discussed in the context of studies of a single atom of geometry. It will be shown that the effective scale of the discreteness could be much larger than the Planck scale. Before this scale can be predicted, the relations between discrete geometry, coherent states, and the semiclassical limit need to be clarified. Work towards this goal, using coherent states in spin foams and the spin geometry theorem of Penrose and Moussouris will be described.
______________________________
Asymptotic safety and minimal length
Since asymptotic safety  if true  would make a quantum field theory of gavity consistent "up to arbitrarily high energy", it would seem that this notion is incompatible with the existence of a minimal length. I will argue that this is not necessarily the case, due to ambiguity in the notion of minimal length.
We will discuss perfect discretizations which aim at mirroring exactly continuum physics on a given lattice. Such discretizations avoid typical artifacts like Lorentz violation, energy dissipation, particle doubling and in particular breaking of diffeomorphism symmetry. Thus the question arises how to distinguish such lattice dynamics from continuum physics.
____________________________
Turning Weyl’s tile argument into a mathematically rigorous nogo theorem
Weyl's tile argument notes that if space was fundamentally discrete then the set of allowed velocities of a classical particle would not be isotropic. I will generalize Weyl's heuristic argument to a nogo theorem applying to any discrete periodic structure. Since this theorem does not take quantum mechanics into account it should only be regarded as the first step of a program of understanding the phenomenology of discrete spacetimes in a mathematically rigorous way.See arXiv:1109.1963
____________________________
On the Observability of Discrete Spatial Geometry
If quantum geometry is an accurate model of microscopic spatial geometry then two related questions arise, one observational and one theoretical: How and at what scale is the discreteness manifest? And, how is the general relativistic limit achieved? These questions will be discussed in the context of studies of a single atom of geometry. It will be shown that the effective scale of the discreteness could be much larger than the Planck scale. Before this scale can be predicted, the relations between discrete geometry, coherent states, and the semiclassical limit need to be clarified. Work towards this goal, using coherent states in spin foams and the spin geometry theorem of Penrose and Moussouris will be described.
______________________________
Asymptotic safety and minimal length
Since asymptotic safety  if true  would make a quantum field theory of gavity consistent "up to arbitrarily high energy", it would seem that this notion is incompatible with the existence of a minimal length. I will argue that this is not necessarily the case, due to ambiguity in the notion of minimal length.