This predicts that if a giant triangle was to be constructed around the sun, the angles at its vertices would in fact add up to more than 180 o. This local curvature can be described in mathematical terms using tensor calculus, an incredibly elegant tool which provides consistent results, regardless of the chosen frame of reference. This is a central tenet of the General theory of Relativity. The sun, for instance warps spacetime, and it is this warping of geometry to which the planets react and not directly to the sun itself. He suggested that matter causes spacetime to curve positively. General Relativity and Spacetime Curvature Įinstein's brilliance was to suggest that although gravity manifests itself as a force, it is in fact a result of the geometry of spacetime itself. This has several intriguing implications (for example it implies that the total mass-energy of the universe is zero), some of which are covered later in this article. NASA's WMAP project showed to within 2% accuracy, by measuring angles between notable features in the Cosmic Microwave Background, that the universe is indeed flat (not in the pancake sense of the word, but meaning that it obeys the laws of Euclidean geometry). The 7-year data provide compelling evidence that the large-scale fluctuations are slightly more intense than the small-scales ones, a subtle prediction of many inflation models. Wmap data place tight constraints on the hypothesized burst of growth in the first trillionth of a second of the universe, called 'inflation', when ripples in the very fabric of space may have been created. WMAP has detected a key signature of inflation. WMAP now places 50% tighter limits on the standard model of cosmology (cold dark matter and a cosmological constant in a flat universe), and there is no compelling sign of deviations from this model. Latest Limits on anisotropy of background radiation from WMAP it is shaped like a so-called hypersaddle it is shaped as a hypersphere (3D spherical surface) If we extend these ideas to three dimensions, (do not be worried if you can't imagine a three-dimensional surface of a sphere, the human mind was never equipped to do so), we have three options to describe the geometry of the universe. For example, the angles of a triangle add up to less than 180 o. ![]() Negatively curved surfaces also exist - they are shaped somewhat like an infinitely extended saddle - and Euclidean geometry does not apply to these surfaces either. ![]() Such a surface is said to have a positive curvature. The angles of a triangle can add up to as much as 270 o, and flat-surface geometry no longer works. the surface of a sphere, these axioms no longer apply. the angles of a triangle add up to 180 o, and the area of concentric circles increases proportionally to the square of the radius. But the part of the universe we can observe appears to be fairly flat.The geometry taught in schools is Euclidean geometry the geometry of a flat surface. ![]() Of course, the observable universe may be many orders of magnitude smaller than the whole universe. Measurements from the Wilkinson Microwave Anisotropy Probe (WMAP) have shown the observable universe to have a density very close to the critical density (within a 0.4% margin of error). And if the universe’s density is less than the critical density, then the universe is open and has negative curvature, like the surface of a saddle. A universe with density greater than the critical density has positive curvature, creating a closed universe that can be imagined like the surface of a sphere. You can imagine a flat universe like a sheet of paper that extends infinitely in all directions. If the density is equal to the critical density, then the universe has zero curvature it is flat. The density of matter and energy in the universe determines whether the universe is open, closed, or flat. Mass also has an effect on the overall geometry of the universe. Overall Curvature of Space Closed universe (top), open universe (middle), and flat universe (bottom). So, locally, spacetime is curved around every object with mass. According to Einstein’s theory of general relativity, massive objects warp the spacetime around them, and the effect a warp has on objects is what we call gravity.
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