The dreaded invasion from another dimension

A quick, light thought.

Reading about the horrible things that are supposed to happen when the Large Hadron Collider is fully switched on, one of the scenarios is that we open a hole to another dimension, and invading aliens proceed to come in and conquer all the Earth, sending humanity into slavery.

Thinking back over the various Sci-Fi movies I've seen, and books that I've read, I find it interesting that anytime a hole is opened into another dimension we always seem to promptly have an invasion force streaming through it which humanity has to fight off.  Its almost like the other dimensions all either direct these tears in the space-time fabric to always-ready invasion forces, or they have invasion forces ready all over the place - just in case there is a dimension hole opened.

Is this really likely?  Isn't it more likely that the dimension hole will open into some totally random place - maybe a living room where the beings are casually watching their equivalent to 'The Love Boat', when this tear opens and ruins the ending of the show?  I'd expect that we're more likely to have beer cans thrown at us than a prompt invasion from highly trained armed forces.  Maybe we'd have the bad luck to open a dimension hole into their garbage dump...

Why not think of some great outcomes - we open a hole to an alternate dimension where Carbon Dioxide is the breath of life, and they are having trouble with global warming caused by Oxygen?  We could start up a great trade in gas swaps - send them the excess CO2 that we have, pick up the O2 that we need.  Maybe their garbage is pure energy which we can easily harness to provide electricity within this dimension - solving our looming energy crisis.

I say, let the collisions happen - we're much more likely to find the salvation of mankind in the other dimenstions that the LHC opens to us than our own doom.  (And, just in case we do happen to open into the middle of a highly trained and prepared group of alien commandos - I was all for opening the dimension gateway, I appreciate your mercy...)