User talk:Ems57fcva/sandbox/Equivalence Principle
... inertial field" is nothing more than the geodesics of spacetime. The modern Principle of Inertia ... has changed is the characterstics of those geodesics. The metric you gave in the Sagnac ... interia is that objects will follow timelike geodesics unless they are acted on by a ... Similarly, light follows light-like (or null) geodesics (where $ds\; =\; 0$). The metric simply describes what those geodesics are. As you go from one ...
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Talk:Geodesic
... I agree; I reformulated a bit. Also, geodesics by definition really only give locally the ... since I studied that, but aren't geodesics straight with respect to the local curvature ... let someone else, who knows more about geodesics than I do, fix it. Anthony DiPierro ... elaboration of In more general spaces the geodesics can be more complicated, but one often ... to my mind when I think of geodesics, and "straight" is definitely not one ...
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Geodesic
... the space carries a natural metric then geodesics are defined to be (locally) the shortest ... shape of the band is a geodesic. Geodesics are commonly seen in the study of ... and more generally metric geometry. In physics, geodesics describe the motion of point particles; in ... a planetary orbit are all described by geodesics in the theory of general relativity. More ... defining, finding, and proving the existence of geodesics, in the case of Riemannian and ...
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Prime geodesic
... traces out its image exactly once. Such geodesics are called prime geodesics because, among other things, they obey an ... geometry which are helpful in understanding prime geodesics. Hyperbolic isometries Consider the Poincaré half-plane ... points of isometries for more details. Closed geodesics Now consider the quotient surface Γ\H ... gives a 1-1 correspondence between closed geodesics on Γ\H and hyperbolic conjugacy ...
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Talk:Gravity/Archive 2
... orbits are, because of extremal time, also geodesics in spacetime. But for 15 y.o ... fact that wordlines of the particles take geodesics in spacetime and therefore are imune to ... warping the spacetime" causes gravitational effects: through geodesics in spacetime; explaining Newtonian orbits and all ... about Riemann tensors, Christoffel symbols, and the geodesics equation ad infinitum? I think that I ... relativity the following is valid: objects follow geodesics. In order to make an object ...
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User talk:Ems57fcva
... and the dropped object are both following geodesics around the Sun. But remember, please, that ... verify) that massive objects also travel on geodesics. That issue led to a whole series ... on the surface of the earth follow geodesics in the Earth's gravity field - the ... bodies as being inertial motion along timelike geodesics of spacetime. Pdn's response Dear EMS ... too tiresome. About the massive bodies following geodesics I am still not sure I ...
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Geodesic (general relativity)
... relativity) In physics, and specifically general relativity, geodesics are the world lines of a particle ... in general relativity is a Lorentzian manifold. Geodesics on a Lorentzian manifold fall into three ... metric signature of ( −+++ ) being used, timelike geodesics have a tangent vector whose norm is negative, null geodesics have a tangent vector whose norm is zero, and spacelike geodesics have a tangent vector whose norm ...
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Gödel metric
... a given observer, we find that null geodesics moving orthogonally to $\backslash partial\_y$ spiral ... mutual twisting of our family of timelike geodesics, it is more or less inevitable that ... r_c is a null curve. Null geodesics If we examine the past light cone ... we find the following picture: The null geodesics spiral counterclockwise toward an observer on the ... each other. The fact that the null geodesics spiral inwards in the manner shown ...
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Talk:Hyperbolic geometry
... I am removing the parenthetical statement about geodesics in Escher's circle limit III. It ... In both one can clearly see the geodesics (in III they appear explicitly). the reason ... the white lines in CLIII are not geodesics. The angles on the triangles are slightly ... more than 60 degrees. If they were geodesics they would meet the "bounding circle" at ... don't. Do a google search on "geodesics in circle limit III" and the ...
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Jacobi field
... Take a smooth one parameter family of geodesics $\backslash gamma\_\backslash tau$ with $\backslash gamma\_0\; ...\; Jacobi\; field\; there\; is\; a\; family\; of$geodesics $\backslash gamma\_\backslash tau$ describing the field ... then corresponds to the same variation of geodesics as $J$, only with changed ... parametrizations. Motivating example On a sphere, the geodesics through the North pole are great circles. Consider two such geodesics $\backslash gamma\_0$ and $\backslash gamma\_\backslash \; ...$
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