Isotropic and homogeneous of space

[sadegh4137]

we say the universe around us is isotropic and homogeneous.

it means that all direction and points are the same for some special class of reference.

if this is true why we say in large scale universe is isotropic and homogeneous?

it seems that the space, itself, to be isotropy and homogeneous.

 

[Drakkith]

I'm sorry I don't understand what you are asking. Could you try to make your specific question a little clearer?

 

[phinds]

we say the universe around us is isotropic and homogeneous.

yes we do

it means that all direction and points are the same for some special class of reference.

NO ... it means that for ALL frames of reference. There IS no "special class of reference" (which I take to be your way of saying frame of reference)

if this is true why we say in large scale universe is isotropic and homogeneous?

because it is, as far as we can tell. Why do you think otherwise?

it seems that the space, itself, to be isotropy and homogeneous.

I have no idea what you mean by "space itself". Space is just the volume that contains matter. It is the distribution of matter that is isotropic and homogeneous (on large scales)

 

[Chalnoth]

NO ... it means that for ALL frames of reference. There IS no "special class of reference" (which I take to be your way of saying frame of reference)

Well, actually, the universe only appears homogeneous and isotropic for a particular class of observers: comoving observers (that is, observers that are stationary with respect to the overall expansion).

It is still an interesting statement that such a class of observers exists (the universe could in principle be different such that no class of observers saw our universe as homogeneous or isotropic).

And to answer the OP's question, no, this isn't simply about the fundamental symmetry of space-time, because all observers see the same laws of physics: space itself is perfectly symmetric, for all observers, in all directions. But our universe is only homogeneous and isotropic for a particular class of observers. That fundamental symmetry, in other words, is broken by the fact that our universe is expanding. And that expansion makes the past look different from the future while also imposing a sensible meaning of simultaneity. The fundamental physics has neither an arrow of time nor a notion of simultaneity.

To expand a bit on what I mean by simultaneity, there is no way within General (or special) Relativity to say definitively that two events separated by some distance happened at the same time. On observer might observe two events as happening at the same time, but an observer moving relative to them in general will tend to interpret one as happening before the other. But because our universe has a reference frame in which it appears symmetric, we can set up a notion of simultaneity by picking out just those observers for whom this symmetry appears.