Homogeneity Definition and 59 Threads

Hi, can a homogeneous equation be homogeneous to the 5/2 degree? Must it be a integer degree?

If the assumptions of homogeneity and isotropy lead to the conservation laws of linear momentum, angular momentum, and energy, would a cosmology that drops either of those assumptions lead to violations of those conservation laws which in turn could be observed? My first guess would be yes, but...

...on the gauge-invariance of classical electrodynamics ? I'm thinking of flat Minkowski space-time of SR in which a charged particle moves and generates an electromagnetic field described by the well-known Lie/nard - Wiechert potential. In this situation can we say all spacetime is...

Let's consider the position x and momentum p of a free particle. \Delta\ x\Delta\ p\geq \hbar/2 so, if \Delta \ x is little enough, \Delta \ p is big enough. The fact \Delta \ p is big implies that we cannot say the momentum conservation law is valid anylonger. But: space is...

Landau's Mechanics and also a cranky book on waves & oscillation I read some time ago talks about space and time being homogeneous and isotropic. I assume that the homogeneous property of space means that it does not matter where the motion of a closed dynamical system unfolds, the result will...

We can probe the isotropy of the universe by observing the universe just from a single place. However, as I know, that is not true for homogeneity. What type of expriments we can carry out on ground or spcae, for probing the homogeneity of the universe.

Does homogeneity infer isotropism?

What do homogeneity and isotropy mean as properties of the universe? [skippable complaining]It seems like a pretty basic question, but I can only find analogies or short and sweet 'definitions' with no context to give them meaning (which aren't necessarily bad - just not helping me). To give...

I’m wondering if it’s mathematically permissible, if space is homogeneous and isotropic, for a moving rod to experience a uniform expansion or contraction during the time it’s not in its stationary frame of reference. What’s preventing a moving rod from returning to its point of origin smaller...