Non-isolated universe and arrow of space Could you please help me to understand two statements in physics:
1) Universe by definition is an isolated system.
But universe expands, space pours into universe, space (vacuum) has zero-point energy, so does expansion means more energy in the universe? If yes, how can it be an isolated system?
2) There is time arrow, but no space arrow. 
If universe can only expand, isn't it that space goes only in one direction: from smaller to larger, that is the space arrow? Aren't time and space arrows similar?
 A: As John pointed out in his comment the concept of conservation of energy, which you are using to state that an expanding universe is not isolated, does not hold in General Relativity, but only in subspaces that are flat and governed by the Lorenz transformation. Space and time are not uniform in GR, the coordinates are curved.
The two dimensional example of the surface of an expanding balloon is a good analogue for the way all matter distances itself from all other matter. Two points drawn on the expanding balloon will recede from each other without an "arrow" for the direction of recession, so you cannot define an arrow of space, except by the statement : it is expanding. The same for the arrow of time , it just means "it is growing". It is not an arrow in the sense of a vector in any dimension. In this sense they are similar. 
Two dimensional people on the surface of the balloon would not be able to determine a center of expansion of the two dimensional surface. Conceptually as analogue to the Big Bang , the beginning of expansion would have all the balloon surface at one point. In a similar manner we are all at the center of the original expansion, because when the BB happened all spacetime points were at the singularity. Our astronomical observations are from the neighborhood of our original expansion, the way that two points on a balloon see each other receding if they were neighbors in the original point before the balloon is pressurized.
Hope this helps.
