PAllen's latest activity
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PPAllen replied to the thread I Euclidean geometry and gravity.I assumed the beam was perpendicular to r, supported against gravity by external transverse force all along the bottom of the beam...
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PPAllen replied to the thread I Euclidean geometry and gravity.But I think the claim is simply that you can’t deduce balance opposing forces from proper acceleration; that doesn’t mean they don’t...
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PPAllen replied to the thread I Euclidean geometry and gravity.You can start here to look for references: https://en.wikipedia.org/wiki/Nash_embedding_theorems Also look at the Whitney embedding...
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PPAllen replied to the thread I Euclidean geometry and gravity.Yes, since you are looking for a cause of changed pressure. The final state by itself has no memory of how it originated.
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PPAllen replied to the thread I Euclidean geometry and gravity.Of course I meant number density and coordinate values. I note you haven’t commented on the second part of that post, which, to me...
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PPAllen replied to the thread I Euclidean geometry and gravity.Ok, here I forgot to add 'preserving local density'.
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PPAllen replied to the thread I Euclidean geometry and gravity.This isn't a good example. To see the issue, you need,e.g. a 'rectangle' bounded by some two value of ##\theta## and r, 'built' far...
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PPAllen replied to the thread I Euclidean geometry and gravity.Well, it depends on the material model (equivalently, considering e.g. EM fields as well as gravity). A given bound material at some...
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PPAllen replied to the thread I Euclidean geometry and gravity.Ok, sorry I misunderstood that. This is where I start to differ, and we may never agree. An object is a world tube, and all...
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PPAllen replied to the thread I Euclidean geometry and gravity.This can't be right. By that logic, you can't embed a 2-sphere in Euclidean 3-space since it has positive scalar curvature and every...
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PPAllen replied to the thread I Euclidean geometry and gravity.Look later in the paper. They show a wider class of possible born rigid objects when the slices are not flat. But, in any case...
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PPAllen replied to the thread I Euclidean geometry and gravity.Moving from near flat to more curved, e.g. radial motion SC spacetime.
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PPAllen replied to the thread I Euclidean geometry and gravity.I found a reference which, indeed claims to show that a rigid body cannot exist in FLRW spacetime with accelerated expansion...
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PPAllen replied to the thread I Euclidean geometry and gravity.Ok, maybe some sense, but conversely, there is an invariant sense in which you cannot - any such congruence must have changing mutual...
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PPAllen replied to the thread I Euclidean geometry and gravity.No. See the end of paragraph 2 in irrotational motion in the current Wikipedia article on born rigid motion. Hate to use this, but the...