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Natural Science Forum / Physics / General Physics / April 2008Straightforward question about the presence of PI in EFE.
Hi, Pi represents the ratio of any circle's circumference to its diameter in EUCLIDEAN geometry; in non-Euclidean geometry, the ratio of any circle's circumference to its diameter is not a constant. Pi appears routinely in equations describing fundamental principles of the Universe. The frequent occurrence of pi in these equations is supposed to be due in no small part to its relationship to the nature of the circle and, consequently, spherical coordinate systems. In particular I am thinking about Einstein's field equations. My question is, since the geometry of the universe is non-Euclidean, why doesn't the presence of pi in the formula cause errors in the calculation of the curvature of spacetime -- especially at cosmological distances, because spacetime is highly curved on cosmological scales? Thanks, Michael  SignatureThis message is brought to you by Androcles http://www.androcles01.pwp.blueyonder.co.uk/ | Hi, | [quoted text clipped - 9 lines] | | My question is, since the geometry of the universe is non-Euclidean, The answer is: you are a crank making an assumption. > Hi, > > Pi represents the ratio of any circle's circumference to its diameter > in EUCLIDEAN geometry; in non-Euclidean geometry, the ratio of any > circle's circumference to its diameter is not a constant. Can you show me an Example where "circle's circumference to its diameter is not PI"? What do you mean by non-Euclidean geometry What is it? Bye Sanny > > Hi, > > [quoted text clipped - 4 lines] > Can you show me an Example where "circle's circumference to its > diameter is not PI"? [snip crap] The arctic and antarctic circles, the equator; all lines of longitude and latitude; great circles and not great circles. The surface of the Earth is Bolyai-Lobechevsky not Euclid. Idiot. SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 > Hi, > > Pi represents the ratio of any circle's circumference to its diameter > in EUCLIDEAN geometry; in non-Euclidean geometry, the ratio of any > circle's circumference to its diameter is not a constant. Good so far. Pi remains the same value regardless. Pi is *not* defined as the ratio of an arbitrary circle's circumference to its diameter. There are eight fundamental geometries of 3-space (Thurston). > Pi appears routinely in equations describing fundamental principles of > the Universe. h/2(pi) Don't leave home without it. > The frequent occurrence of pi in these equations is > supposed to be due in no small part to its relationship to the nature > of the circle and, consequently, spherical coordinate systems. In > particular I am thinking about Einstein's field equations. GR is covariant - no coordinate background. > My question is, since the geometry of the universe is non-Euclidean, > why doesn't the presence of pi in the formula cause errors in the > calculation of the curvature of spacetime -- especially at > cosmological distances, because spacetime is highly curved on > cosmological scales? Pi is a mathetmatical constant not a measurement (observation). SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 > Hi, > [quoted text clipped - 7 lines] > of the circle and, consequently, spherical coordinate systems. In > particular I am thinking about Einstein's field equations. As explained - correctly - by Uncle Al, pi is a mathematical constant that is independent of specific geometries. It happens that certain things are proportional to pi in certain geometries, but that doesn't mean pi is dependent on them. As for the field equations, technically all that is known is that G_uv = k T_uv where k is some proportionality constant. The fixing of k = 8piG/c^4 is done by demanding equivalence between GR's weak field predictions and Newtonian gravitation. The pi in Newtonian gravitation comes from the divergence theorem when you integrate around a sphere of constant radius to obtain the point source gravitational field. > My question is, since the geometry of the universe is non-Euclidean, > why doesn't the presence of pi in the formula cause errors in the > calculation of the curvature of spacetime -- especially at > cosmological distances, because spacetime is highly curved on > cosmological scales? pi is a constant. > Thanks, > > Michael > > Hi, > [quoted text clipped - 31 lines] > > > Michael Thanks Eric and Uncle Al -- that explains it very well thanks. I thought pi was defined as the ratio C:D. Uncle Al, I will see if I can find out more about the fundamental geometries of 3-space. Can you give me the title of the book you are referring to (Thurston)? We're bound to have it in the library (I work at a university -- but not in the Physics department obviously). I wasn't going to suggest that Einstein got it wrong, or demand all the equations were re-written without pi ;-) As far a GR is concerned, I knew before I asked the mis-understanding was with me, and I hope that was clear from the way I asked the Q. Thanks again. Michael |
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