What is the difference between an Einstein-Rosen Bridge (wormhole) and a tunnel through a mountain? Obviously, light that travelled around the mountain would take longer to reach other side so that light travelling through the tunnel. So, in principle, a relativistic particle travelling at 0.9c through the tunnel could beat the light that travelled around the mountain. This does not violate any known laws of physics (i.e. causality), does not permit time travel, and tunnels definitely exist.
However, many physicists express doubts about the existence of an Einstein-Rosen Bridge (from a theoretically standpoint), which, from what I understand, is simply just a tunnel through space. I had one physics professor who dismissed it as science fiction because he thought it was allowing faster-than light travel, violating special relativity (I was in his special relativity class at the time). A prior, I don't see why the Einstein-Rosen Bridge would violate either causality or special relativity and permit time travel. After all, it would just provide two paths for light to take, one of which would be shorter than the other. This may appear to permit faster than light travel because the beam of light travelling through the wormhole would beat the beam of light travelling around it. How is this different from light travelling through a mountain tunnel beating light travelling around the mountain?
If it is not possible (in principle) to construct such tunnel through space, why? Would some law of quantum mechanics or quantum field theory restrict the topology of empty space so that there can only be no tunnels or holes like there are through matter? In particular, do some physicists believe, under physical assumptions about the stress-energy tensor, that spatial slices of spacetime must be simply connected (fundamental group is trivial; no holes)?