- #1

gionole

- 281

- 24

**I'd appreciate if you could read my exact questions and only try to answer them and if you don't understand the questions, you can say so and I will make it clearer if possible. This is really important as I believe, deviating from these questions is what's causing my confusion.**

After your help, I now understand that mathematically, active and passive transformations are the same, but this post will only be about active transformation and its usage in the subject of homogeneity. I've seen that people use active transformation as mathematical tool for the homogeneity detection and here is what I'm curious about.

Imagine you got a huge area that includes only 3 objects - earth, sun and ball - Let's call all of this to be "space" - i.e area that includes its objects in it.

Now, what one can do is move ONLY the ball somewhere else and observe its behaviours. If it's the same behaviour as it had before moving, then space can be said to be homogeneous. Nice and easy.

**My question though is this**: When would it be required to move two objects instead of one ? (i.e move the earth and ball both) - It seems to me that moving only the ball(i.e one object) is enough to show mathematically whether space can be said to be homogeneous or not. Just to repeat the question again - in terms of homogeneity, when would moving 2 objects be much more insightful than moving only one ? and please, let's use my example that I mentioned above.

I don't want to ask any other related questions yet on this not to confuse the discussion yet. I would understand as well if you don't want to participate in the discussion. Thank you everyone for your help so far.