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	<div id="02004"></div>'''Problem 4.''' The main qualitative difference from the usual explosion lies in the fact that the explosive charge is usually surrounded by atmospheric air. The expansion is then caused by the difference between the huge pressure of the gaseous products of the explosion and comparatively small pressure of the surrounding air. But when considering the expanding Universe, one assumes that the pressure (according to the cosmological principle) is uniformly distributed too. Therefore there are neither pressure gradients nor forces that could cause or even affect the expansion. The expansion of the Universe itself is the result of initial velocity distribution.		<div id="02004"></div>'''Problem 4.''' The main qualitative difference from the usual explosion lies in the fact that the explosive charge is usually surrounded by atmospheric air. The expansion is then caused by the difference between the huge pressure of the gaseous products of the explosion and comparatively small pressure of the surrounding air. But when considering the expanding Universe, one assumes that the pressure (according to the cosmological principle) is uniformly distributed too. Therefore there are neither pressure gradients nor forces that could cause or even affect the expansion. The expansion of the Universe itself is the result of initial velocity distribution.
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Revision as of 21:39, 27 February 2012

Homogeneous and isotropic Universe, Hubble’s law

Problem 1. A system with constant magnetic field is homogeneous but not isotropic, because the direction along the field and perpendicular to it are not equivalent. On the contrary, a spherically symmetric distribution of electric charges is by construction isotropic, but not, in general, homogeneous.

Problem 2. Due to isotropy the distribution must coincide in any two points, because they can be transformed to each other by rotation by $180^\circ$ around the middle of the interval connecting them. The opposite is not true (see problem).

Problem 3. There are three cases: three-dimensional plane (zero curvature), sphere (positive curvature) and hyperboloid (negative curvature).

Problem 4. The main qualitative difference from the usual explosion lies in the fact that the explosive charge is usually surrounded by atmospheric air. The expansion is then caused by the difference between the huge pressure of the gaseous products of the explosion and comparatively small pressure of the surrounding air. But when considering the expanding Universe, one assumes that the pressure (according to the cosmological principle) is uniformly distributed too. Therefore there are neither pressure gradients nor forces that could cause or even affect the expansion. The expansion of the Universe itself is the result of initial velocity distribution.

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