What is the meaning of homogenous and isotropic in Gallilean transformation?

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In the context of Galilean transformations, "homogeneous" refers to the uniformity of space, indicating that its properties remain consistent across different locations. "Isotropic" signifies that space exhibits the same characteristics in all directions, meaning it is unaffected by rotation. These concepts imply that the laws of physics apply equally regardless of where or how one observes them. The discussion clarifies that homogeneous allows for any choice of coordinate center, while isotropic ensures invariance in all axes. Understanding these terms is crucial for grasping the foundational principles of classical mechanics.
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in this kind of transformation , what is the meaning of homogenous and isotropic??
 
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In this case, we are referring to the statement that space is homogeneous and isotropic. Homogeneous means the properties of space are the same everywhere, that is, space is invariant under any translation. Isotropy means the properties of space are the same in all directions, that is, space is invariant under all rotations
 
okay now i got it because our profeesor said that homogenous means that the center of coordinates is chosen anywhere while isotropic means the direction for any axis is invarient . thank you
 

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