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We do seem to spend an awful lot of time worrying about infinities when it appears the cosmological horizon is finite. But I guess if we find some way around th

We do seem to spend an awful lot of time worrying about infinities when it appears the cosmological horizon is finite. But I guess if we find some way around that we will be prepared.

raattgift 5y ago
In an accelerating expanding universe like the one we appear to occupy (and the one modelled by our current "concordance" standard model of comology), the comoving horizon is at constant comoving distance. Cast into more Earth-centric coordinates, it is at a finite spatial distance at all finite times. However, there is no reason to expect that a timelike worldline rooted at "here and now" (converting a chosen comoving coordinate into the origin of spherical coordinates for a Eulerian observer) cannot be extended into the infinite future, and at +infinite time the horizon will be at an infinite spatial distance in this system of coordinates. We don't even need to say anything about the matter content of the Hubble volume at any time, anything about -infinite time, or anything about how various measures of entropy fit in; all of these can generate infinities that defy easy (and possibly any) removal in a universe similar to the concordance model. A taste of this can be found at https://en.wikipedia.org/wiki/Cosmological_horizon#Future_horizon https://en.wikipedia.org/wiki/Cosmological_horizon#Future_ho... More deeply and technically, Baez's "Struggles with the Continuum" is great A smooth manifold tends to generate infinities and infinitesimals, and all our fundamental physical descriptions of the universe we inhabit are (at least at present) defined on a Lorentzian spacetime, which is a smooth manifold. He discusses practical reasons to [a] worry about infinities and [b] to work with them anywhere because they might not be removable. https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421 (§5 starting on p. 27 is directly relevant, and the concluding §6 is pithy).

We do seem to spend an awful lot of time worrying about infinities when it appears the cosmological horizon is finite. But I guess if we find some way around that we will be prepared.

raattgift 5y ago

In an accelerating expanding universe like the one we appear to occupy (and the one modelled by our current "concordance" standard model of comology), the comoving horizon is at constant comoving distance. Cast into more Earth-centric coordinates, it is at a finite spatial distance at all finite times. However, there is no reason to expect that a timelike worldline rooted at "here and now" (converting a chosen comoving coordinate into the origin of spherical coordinates for a Eulerian observer) cannot be extended into the infinite future, and at +infinite time the horizon will be at an infinite spatial distance in this system of coordinates. We don't even need to say anything about the matter content of the Hubble volume at any time, anything about -infinite time, or anything about how various measures of entropy fit in; all of these can generate infinities that defy easy (and possibly any) removal in a universe similar to the concordance model. A taste of this can be found at https://en.wikipedia.org/wiki/Cosmological_horizon#Future_horizon https://en.wikipedia.org/wiki/Cosmological_horizon#Future_ho... More deeply and technically, Baez's "Struggles with the Continuum" is great A smooth manifold tends to generate infinities and infinitesimals, and all our fundamental physical descriptions of the universe we inhabit are (at least at present) defined on a Lorentzian spacetime, which is a smooth manifold. He discusses practical reasons to [a] worry about infinities and [b] to work with them anywhere because they might not be removable. https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421 (§5 starting on p. 27 is directly relevant, and the concluding §6 is pithy).