This is more like a conceptual question. Wormholes are tunnels connecting two different parts of the same universe or connecting two parts in different universes. Taking the former one as an example; It makes sense to think about them if the two mouths are spacelike separated since this way it makes the interstellar travel shorter.
According to Wikipedia (even though it's not a perfectly reliable source)
What happens if the mouths are so close to each other like a few $mm$ even $nm$ ? If they are too close, I can't think of a configuration where it would take shorter period of time to travel a distance through a wormhole than travelling between the points. (Unfortunately, we have covered Einstein-Rosen bridges superficially so I don't have the right machinery to carry out the math)
This way of thinking leads to a conclusion that there might be a lower limit to the distance between two mouths of an Einstein-Rosen bridge, I wonder what this limit is and how to find it, to be more precise is there even a lower limit?
Possible Way To Resolve This Dilemma
- Einstein-Rosen bridges don't necessarily make the travel time shorter between two points hence the distances shorter so it's reasonable to have as short distances as $mm$, $nm$ between the two mouths.
Yet I'm not sure of whether this assumption would be correct or not.