PAllen's latest activity
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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'...
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PPAllen replied to the thread Undergrad Some confusion with the Binding Energy graph of atoms.I guess it is worth pointing out that if you have two nuclei with equal and opposite momentum collide perfectly and fuse, the initial...
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PJust think about that for a minute. You are standing by the road and a passing car turns on its turn indicator. How are you and the...
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PPAllen replied to the thread Undergrad The Einstein Clock aka Light Clock.Maybe it would help to imagine two flash bulbs, one in motion relative to the other. They both flash when one just passes the other. In...
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PPAllen replied to the thread Undergrad The Einstein Clock aka Light Clock.Let's stop right here. We will not get far by insisting that "we all must agree that 2 + 2 = 5". A given flash bulb (for example) has...
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PPAllen replied to the thread Undergrad The Einstein Clock aka Light Clock.I only have time for a quick reply now, just focusing on some issues with your first bullet: .. in the ship's inertial frame (assuming...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Well, arbitrarily close any horizon, irrespective of how mild the tidal forces are near the horizon of a supermassive BH, the...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.From the thesis I referenced earlier is a notion of what embeddings are 'hard' versus 'easy'. 'Hard' implies you are likely only to get...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.A smooth embedding is possible. Just try to think about a 2-sphere embedded in Euclidean 3-space. There is no curvature anywhere in the...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.I found something right on point, but it is a thesis, so I don’t swear to its accuracy (I have not studied it in detail). Its results...
