Can you use a wormhole to travel through space not time? I want to know if you could theoretically travel from your house to work via a wormhole but stay in the present day...without changing time. Kind of like teleportation but harnessing the energy of a black hole or wormhole. My background is chemistry not physics so I'd prefer a mathematical explanation. Thanks.
 A: Any motion in "space" is between an entry and an exit point. If the wormhole is a handle linking two distant regions, you will enter at one point and emerge at another. The entry and exit events can have three possible relations:


*

*The exit is strictly past of the entry

*The exit is spacelike from the entry (you move in space to a distant location faster than light).

*The exit point is to the future of the entry point.


Possibility 1 allows you to kill your grandfather. Possibility 2, together with relativity, is tantamount to possibility 1, since you can boost the two exits of the wormhole and make another copy of the wormhole boosted in the other direction, and by traversing the two copies suitably, you can rearrange possibility 1. So the only sensible possibility is possibility 3.
But in this case, the two ends of the wormhole are always causally linked--- you can't separate the entry and exit so that they are spacelike to each other. This means that the wormhole is nothing more than a room--- it is equivalent to entering and exiting the same region later, and there is nothing mysterious at all going on.
Such wormholes are known to exist in the extremal continued Reissner Nordstrom solution (charged black hole) and the exactly analogous Kerr solution (rotating black hole). The maximal extension of rotating/charged (or rotating and charged) black holes are tunnels to other branches, and the only barrier to crossing the tunnel is a Cauchy horizon which is possibly singular.
The Cauchy horizon in exact solutions is not singular at all, you just cross it. But Penrose speculates that the full solution will become singular as matter piles up on the Cauchy horizon (which sees the entire future of the black hole). This picture has not been supported by detailed calculations, which show the Cauchy horizon is a little hard, perhaps like a potential step, but not singular enough to disallow matter from crossing.
The result is that crossing a charged/rotating black hole is entering and leaving a "wormhole" that just spits you out of the same black hole. It has to be in our universe, since there is no information loss. Nobody knows how this works in detail, because the actual process classically spits you out in another universe.
That the "other universe" or wormehole interpretation is nonsense can be seen by a simple physical argument--- if you have two ends of a wormhole, they have to have matching radius, since they are continuations of each other. If you throw an object in, it increases the horizon area as it crosses, and when it leaves the other side, it decreases the horizon area, so they no longer match. The only sensible resolution is that it leaves in the same patch it enters, which means that strictly speaking, in a Penrose diagram, it crosses its own past. But if the traversal time is always positive, the outgoing object will not be able to see its incoming version, since it will already be behind the "brick wall" when the object comes out.
This resolution is not believed by anyone except me. Other people believe something must be going on in the interior to make the Cauchy horizon singular, so that the black hole is a one-way surface.
A: I believe that space cannot be isolated from time once matter enters the wormhole. Time is bound to the third dimension, so time would enter from the same point of matter (the end assumes the nature of the entry, compromising the wormhole's integrity); kept open I believe it would behave as a tube as long as the wormhole (similar to last, post but less specific). I thought about having a wormhole inside of a wormhole to keep the integrity of the outer tube, but you are still compromising the inner tube and ignoring any effect from the outer tube. I believe that anything that enters physically brings space/time with itself by definition: either it doesn't enter, or it doesn't exit. 
A: According to current knowledge no wormhole allowing survival durning passage can exist, so - no. 
A: In fact that's the only way to use a wormhole. You won't stay exactly in the present time, you'll go a tiny bit into the future, since a wormhole takes some time to traverse as well. Then again, time is relative; but basically you won't go too far. Remember, wormholes are still hypothetical, and theory predicts their properties but not how they may be generated.
Any wormhole that can travel through time destroys itself, as a beam of vacuum fluctuations (virtual particles) will circulate through it, building upon itself till it reaches infinite intensity and destroys the wormhole.
A black hole would be a Very Bad Idea. Unless all black holes are wormholes (unknown; doubtful), you'd be spaghettified and reduced to a singularity. Not a good way to go. Not a good way to go to work, either :P.
I myself can't give a mathematical explanation; but I fail to see why a chemist would want one. All this stuff deals with tensors and whatnot, and gets pretty confusing to a non-physicist. I've come across statements like this: "consider a four-dimensional matrix of four dimensional matrices". Ouch. 
A: No, but not because of anything special about the wormhole itself. The problem is with the implicit idea of simultaneity you have invoked.
Travelling some distance will inherently mess up the idea of when 'now' is.
Depending on the observer's reference frame you will arrive before you left, after you left and simultaneously with when you left. And each observer would be "right" in some sense.
