Explanation of word foliation in quantum gravity?

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Discussion Overview

The discussion revolves around the term "foliation" as it pertains to quantum gravity and its relation to general relativity. Participants explore the concept of foliating spacetime, including its implications and interpretations within the context of physics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant defines foliation as a method for coordinating spacetime by establishing spacelike hypersurfaces and describing their evolution over time.
  • Another participant provides an analogy comparing spacetime to a book, where the pages represent hypersurfaces and page numbers indicate the transition between them.
  • A different participant notes that a foliation can be viewed as a way to create "time-slices" of spacetime, which can vary depending on the observer's perspective.
  • One participant asserts that foliation is applicable only to spacetimes with a global structure of R*M³, where M³ is a spacelike manifold.

Areas of Agreement / Disagreement

Participants express varying interpretations of the concept of foliation, with some agreeing on its definition and others highlighting its limitations and specific conditions for applicability. The discussion does not reach a consensus on the implications of foliation in quantum gravity.

Contextual Notes

There are unresolved aspects regarding the specific conditions under which foliation applies, particularly in relation to the global structure of spacetimes.

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explanation of word "foliation" in quantum gravity?

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A foliation is a prescription for coordinitizing spacetime. It is an aspect of general relativity, and is not specific to quantum gravity. When you 'foliate' a spacetime, you define spacelike hypersurfaces and give a prescription for how these hypersurfaces evolve in time. In short, you 'fill' the spacetime manifold with hypersurfaces such that for every point x in the manifold, there is a hypersurface that contains it. As a simple analogy, allow a book to represent a 3D spacetime. Then, the 2D pages of the book are your hypersurfaces, and the page numbers define how you go from one to the next: the pages and page numbers make up your foliation.
 


Good explanation!
Foliage means leaves.
A folio is a book.
A portfolio is a kind of flat box to keep pages or drawings, any kind of flat stuff, in.

A foliation of spacetime is a way of slicing it up. For example into "time-slices" which are sheets consisting of events that some observer considers to be simultaneous. Different observers will slice it differently.
 


Foliation does only apply to spacetimes with global structure R*M³, where M³ is a spacelike manifold.
 

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