PAllen's latest activity
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PPAllen replied to the thread Undergrad The quintessence as variable dark energy.While the FLRW metric, when used for a realistic universe, is purely an emergent approximation at large scales, there is one aspect of...
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PPAllen replied to the thread Undergrad The quintessence as variable dark energy.Yeah, but if you are talking about galaxies, you are outside the FLRW idealized model - that has only perfect fluid with different...
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PPAllen replied to the thread Undergrad The quintessence as variable dark energy.As far as I know, the common models of quintessence still use the FLRW equation metric, just with particular forms of ##a(t)##. In...
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POne thought that occurs to me is that virtually all learning is self-learning. If you enroll in a course and listen to the lectures but...
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PPAllen replied to the thread Some thoughts about self-education.I don’t think the difficulty is insurmountable. I have a counterexample from my own experience. I wanted to learn calculus before the...
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PPAllen replied to the thread Undergrad Differential Geometry with GNU/Linux.I like it and will probably play with it some. I'll ask if I have any questions. I appreciate your effort. I disagree with the decision...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.No, because its total surface area is finite. It is actually just a small piece of the hyperbolic plane, it just 'looks' big in...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.I can’t seem to let this go, partly because some have asked for how to make the embedding result (part of Euclidean plane in 3-sphere)...
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PPAllen replied to the thread Undergrad Is using r as a coordinate in Birkhoff's theorem a limitation?.I don't know if I can track it down from a long ago posts of mine, but I discussed a paper by a mathematician specializing GR that...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Radius of curvature = 1
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.When discussing isometric embeddings, there is a little more to it. The metric of the submanifold is taken to be induced from the...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.In the side discussion of embedding a piece of a plane smoothly, isometrically, in a 3-sphere (following is part of a response to...
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PPAllen replied to the thread Undergrad The Einstein Clock aka Light Clock.Well, you have claimed counterfactual things (e.g., that aberration does not apply) multiple times in this thread, so we do need to...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.But your argument was you can’t embed a plane in e.g. a 3 sphere because the plane has zero curvature and the sectional curvature in...
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PPAllen replied to the thread Undergrad About the notion of non-standard inertial frame.Ok. That would rule out e.g. the coordinate transform ##x'=log(x)## because an object with no proper acceleration moving in the x'...
