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I am a first year and general student. I Am just curious about the vacuum or space. I just don't get what actually space is. Well, I know our scientists are still working on it but still I just want to know what is the accepted and best definition of space or a point in space that is the basic building block of this medium that allows matter to exist and its properties.

Is space accepted as absolute zero or we believe that space itself lies within another medium having higher dimension or something like this.

One more question when we say universe is expanding, in reference to what we are saying it is expanding? I mean is space itself stretching (which means space in between basic building blocks of matter is increasing, and if it is like this then how can we measure it as even our standard of measurement will be effected and hence net change will be zero) OR just heavenly bodies are going away from each other but then what is the reference ? Let us suppose it is Milkyway, but is Milkyway itself not moving and gaining velocity in the direction of the objective (the heavenly body which we say is going far from us)? Hence net change in velocity here should be zero?

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Your second question is a duplicate of physics.stackexchange.com/questions/2110/… and many other questions found by searching for "expanding is:question". –  John Rennie Jul 14 '13 at 16:54
    
Related: physics.stackexchange.com/a/69259/520 –  dmckee Jul 14 '13 at 22:34
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I'm going to take a whack at answering this. While these questions may seem naive, they are still the basis of research that cosmologists are doing today. But I'll try to keep my answer to a sub-grad student level.

Let's start with space and the vacuum.
First of all, space is not infinite in size. If it were, everything would have cooled to 0K a long time ago and the probability of finding another galaxy cluster (let alone multiple millions of them) within our visible horizon would shrink to very near zero unless there were also an infinite amount of matter (that would be bad).
Now that we've established that, space and the vacuum are not the same thing. A pure vacuum is a volume that contains nothing. While this includes an absence of EM radiation, usually we use the term to describe an absence of matter. There are no known natural or artificial pure vacuua. Every volume (within reason) has some matter in it. For instance, there is 100 times more air in a random volume from between the stars of our galaxy than there is in the same volume from between two galaxies. But this is just trivia. Space, on the other hand, is (as referred to in physics) the fabric of the 3 geometric dimensions. If you picture the x-, y-, and z-axes and you extend them over all the universe, that is space. Space is not, however, the basic building block that allows matter to exist nor is a point in space. A point in space has zero size. It is just a coordinate. You can no more ask what the point right next to it is than you can ask what number is right next to pi (if anyone says it's pi+1, I will slap them).

Moving on to your second paragraph: Space is not at absolute zero. The accepted temperature of space is around $2.7K$ ($-270.45^\circ C$). As for laying in another dimension, there are a number of cosmological theories surrounding this. Without going into far too much detail, I will just say that there are no higher geometric dimensions and to say more would be well above the scientific limit for this post.

Now the fun part. When we say the universe is expanding, that is usually in reference to itself. The universe is expanding within itself. There are again some cosmological theories that provide alternate media for it to expand into, but at this level of understanding, what I said will hold. Picture, if you will, an ant on the surface of a balloon and suppose that ant has no concept of anything but the surface of that balloon. Then imagine someone starts inflating the balloon. From the ant's perspective, the balloon has no boundaries; things are just getting further and further away from it and the amount of space to walk around in is growing. The ant, thus, knows that the balloon is expanding. The analogy doesn't completely work; we are believed to be the interior of the balloon, there isn't a 4th geometric dimension, and the universe isn't as curved as much as a sphere, but for explaining expansion, it works.

There is a rate of expansion. All points in space grow apart from each other. However, gravity works against that; it holds objects together. The result being that it looks very much like all heavenly bodies are moving away from us. However, because we have objects on all sides of us, we can use the milky way as the reference and see that things are moving away in all directions. We can also tell that objects farther from us are moving away faster. This is because there is more space in between and so, more expansion.

I may have misinterpreted some of your questions or comments. I hope this helps somewhat but let me know if I left anything out.

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"...and the probability of finding another galaxy cluster (let alone billions of them) within our visible horizon would shrink to very near zero..." Nitpicking a bit, but for typical definitions of "galaxy cluster", there aren't billions within our horizon. There are on the order of millions. Maaaaybe 10s or 100s of millions if you count things way down to $10^{13}M_\odot$ or so, but most people would call things of that size a group. –  Kyle Jul 15 '13 at 14:12
    
@Kyle ya wasn't sure on the number. My reasoning went like this: "let's see 100 billion galaxies, I'm guessing about 100 galaxies per cluster cause otherwise super-clusters would be massive, that gives a billion clusters" But I guess my guess was off. Thanks, fixing it. –  Jim Jul 15 '13 at 14:19
    
Thanks Mr. Jim ..but you said space is expanding like a balloon and we are like an ant ..but here the ant is not effected by balloons expansion .. distance between ants molecules is not increasing. The question is if space is stretching... then the space between particles of our measuring instruments is also increasing with same ratio .. that means our 'one metre' has changed with same ratio so instrument should measure the same distance (as before) between two super clusters everytime we measure the distance. Thank You –  Ankur Antil Jul 15 '13 at 16:27
    
Sorry, should have been more clear. Gravity and the other forces hold the particles of matter in relative positions. The space between our atoms is not growing. It also holds local space. The space between stars of our galaxy isn't growing because gravity keeps it bound. –  Jim Jul 15 '13 at 18:16
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