PAllen's latest activity
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PPAllen replied to the thread High School A question on the geometry of black holes.One can discuss the topology of limiting surfaces approaching a singularity. In that sense, the topology of the initial big bang...
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PPAllen replied to the thread High School A question on the geometry of black holes.Also, it should be noted that spherically symmetric nonrotating collapse to a BH per general relativity does predict unbounded density...
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PPAllen replied to the thread Undergrad Our Mathematical Universe book -- Since when does light contain voltage?.But that is part of the measuring device. In the continuum approximation, you can take the limit as charge approaches zero, voltage...
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PPAllen replied to the thread Undergrad Our Mathematical Universe book -- Since when does light contain voltage?.One other example is simply that if you charge metal ball or plate with static electricity, then you measure a potential difference...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.Yes, I agree with you.
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.I don’t think that works. I tried that. Remember f is a function (hidden within r) of all 4 coordinates. That means zeta must be as...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.My current view is back to the idea that you can have synchronous, but not diagonal. However, the trick used by Hiscock for...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.True, but if you switch to coordinates that manifest the orthogonality, then the Eulerian world lines do have constant spatial...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.good catch, I'll fix.
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.I would like to summarize conclusions scattered across this thread. The following are key references: The main document that...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.A curve orthogonal to all Eulerian world lines it touches must have zero t component. But one that is orthogonal to just one need not...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.This I don’t believe. One thing that is confusing about the notation in some of these papers is that f is a function of all 4 spacetime...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.There is always a geodesic orthogonal to any world line at any point. What happens is the spacetime geodesic and the slice geodesic are...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.Just to take up a detail discussed earlier: whether There is a difference between computing distance using a geodesic of a Euclidean...
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PPAllen replied to the thread Undergrad Does the Alcubierre drive shorten distances?.Before the full solution, I can put an upper bound on the odometer reading. It is easy to compute, using the full metric, rigorously...