Research – Colin MacLaurin

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My research area is general relativity. These papers are drafts not yet ready for arXiv, but exhibit my work prior to Europe conferences.  — Colin MacLaurin

  • 2017, “Distance in Schwarzschild spacetime” (draft). Observers with “energy per mass” e measure a radial distance |e|^{-1}dr. I overview four different tools to measure spatial distance — spatial projector, tetrads, adapted coordinates, and radar — which are locally equivalent. Though spatial distance is foundational, it remains underdeveloped. I clarify subtleties, and counteract the Newton-esque over-reliance on the static distance (1-2M/r)^{-1/2}dr.
  • 2017, “Cosmic cable” (draft). A cosmic-length cable could be used to mine energy from the expansion of the universe. Beyond sci-fi, this is instructive for relativity pedagogy. The dynamics include motion-dependent distance, and time-dilation which reduces the force, effects which are missed in most existing treatments.

2015 Master’s thesis

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Here is my Master of Science thesis, titled “Expanding space, redshifts, and rigidity: Conceptual issues in cosmology“. It was submitted in mid-2015 and supervised by Prof. Tamara Davis at the University of Queensland. I am working on several papers from this material, and also hope to submit the thesis itself to arXiv after polishing its language. I am expanding the material in §7 into a paper on “Measuring distances in Schwarzschild spacetime”. I am also expanding the kinematics of a moving rigid cable (§9, §11) to include force, tension, and power, in the de Sitter space case. Existing treatments of both topics typically have “Newtonian” misconceptions but my work properly includes the relativity of distance and simultaneity for instance.

It has a detailed introduction to distance measurement including the spatial projector and “proper metric” (aka “pullback” onto a material manifold) (§3), along with a defense of ruler distance (§6) where the Rindler quote says it best! There is also a detailed introduction to Rindler’s accelerated coordinates (§2.7, §3 etc), followed by a generalising procedure (§8). Also present is an overview of Newtonian cosmology and the Milne model (§4). Experts, please tell me if the interpretation of redshift material is worth publishing!

Relativity wiki

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I have decided to start a relativity “wiki”, which is closer to my aims than a blog. Besides, I have experience of making over 16,000 edits on Wikipedia itself. A wiki will allow for better structuring and linking of content, for instance of niche content such as: Black hole → Schwarzschild → Geodesics → “drips” → exact integral. The content is still being polished, and I have many notes which are not integrated yet.