
#1
Jul604, 09:44 PM

P: 3

How do the dimension, at least the first three we can observe, fit in the universe? We can monitor up/down, left/right, forward/backward on our planets, yes? But then how does this fit in with the idea that the universe has no center and shape, no true directions. Does this mean that the first three only pertain to planetary shapes, or is there something I am missing? Perhaps a great deal I am missing. Hopefully someone will be kind enough to answer and clear this up.
Thank you Blossom Morphine 



#2
Jul704, 11:13 AM

Emeritus
PF Gold
P: 8,147

So the general situation is that you don't have a single coordinate system of length, width, and height, but rather always a family of equivalent coordinate systems, any of which can be rotated into any of the others by a three dimensional rotation^{*}; an "equivalence class under SO(3)", to use mathspeak. All the physics theories and cosmology theories start from there. ^{*} The question of left and right, and "handedness" is more subtle. The group SO(3) takes care of this by including reflections along with rotations. 


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