![]() ![]() And yes there can be special cases where it remains a sphere, but it's not normal. A thing in one frame of reference looks now different in another equally valid frame of reference. Of course you can ask: "But what's about the sphere in 3D." Obviously it gets distorted. Your everyday physics problem has now length contraction (only in direction of the movement) and time dilation. A sphere with length 1 is now 4D and doesn't look like a conventional sphere anymore. Every phenomenon is now described with a new metric. Now extending to spacial relativity you need to combine space and time to a Minkowski spacetime. Now metrics are used as a tool that different reference frames can get the same answer. The core to measurements in Euclidean space is the 3D Pythagorean Theorem. Then let's get to it a little more physical. I can understand you want to try to measure things. I don't know what happens really in there. ![]() I appreciate your help so far.Īt this point you are putting stuff into a black hole. I'm not sure if this clarifies, but it's the best I can do off the top of my head. If I take one of those four sticks and move it inside the sphere, will it exactly occupy the sphere's diameter? Now, I have four straight, massless, inflexible, incompressible, perfectly narrow sticks which, when used to form the four sides of a square, fit exactly around the sphere with each of them tangent at one point each to the sphere's surface. So the rest of the space stays perfectly flat. We complete this interversal surgery without allowing the curvature from the point-particle to propagate beyond the transplanted sphere's radius. I'm imagining a taking a static slice of curved space (a sphere with a 1 m Schwarszchild radius which is empty except for a massive point-particle at its center) from an empty universe (no mass anywhere in it except the point particle) and then snipping it from that universe and embedding it instead into another space which is, prior to transfer, perfectly Euclidean and empty. Here's a shot at pinning down what I take myself to mean by that, exactly: Is there a known and meaningful answer to whether 1 m along the Schwarzchild radial coordinate corresponds to a layperson's understanding of "1 m in that direction in my reference frame"? I understand this is a newbie question, but any help is appreciated! If they do, then only (b) is correct and (a) is false. If they don’t, then both (a) and (b) above are correct. (b) 4-dimensional spacetime is rendered non-Euclidean by the presence of any mass which is not homogeneously distributed.Īnother way to put the question: If we exactly measured a sphere with a radius of 10k km around the earth’s center, would we find that the sphere’s volume and surface area do not stand toward one another in exactly the ratio that is predicted by Euclidean geometry? ![]() (a) 3-dimensional space is rendered non-Euclidean by the presence of any mass which is not homogeneously distributed. I’m wondering which of the following descriptions is correct, according to general relativity: But I’m finding it hard to get a clear answer as to whether mass warps 3D space as well. I understand that according to general relativity, mass ‘curves’ or ‘warps’ space-time (renders it non-Euclidean). ![]()
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