Difference between revisions of "Homogeneous Universe"
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− | === 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 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. ==== |
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Revision as of 11:10, 15 May 2012
Contents
- 1 Homogeneous and isotropic Universe, Hubble’s law
- 1.1 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.
- 1.2 Problem 2.
- 1.3 Problem 3.
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.
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).
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 3.
There are three cases: three-dimensional plane (zero curvature), sphere (positive curvature) and hyperboloid (negative curvature).
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 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. |
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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. |