[Firefoot]

While reading this chapter I had some musings on the Wraith-world similar to davem's.

Both Glorfindel & the wraiths live in both worlds - yet is it the same supernatural dimension that he & they inhabit?

I would argue that it is in fact the same spiritual dimension, albeit different parts of it. When Frodo puts on the Ring and enters into the wraith-world, he sees them as pale-shining white figures. Glorfindel is a brightly shining figure of white light. In this way they are similar. Maybe the difference in brightness has to do with the good and evil of the being. It would seem that the wraith-world is a dimension of dim shadows in which shapes are clear but there is very little coloration. This can be gotten from Aragorn, in chapter 11

"They themselves do not see the world of light as we do, but our shapes cast shadows in their minds, which only the noon sun destroys; and in the dark they perceive many signs and forms that are hidden from us: then they are most to be feared."

compared to Frodo here

Frodo's pain had redoubled, and during the day things about him faded to shadows of ghostly gray. He almost welcomed the coming of night, for then the world seemed less pale and empty.

and here

With his last failing senses Frodo heard cries, and it seemed to him that he saw, beyond the Riders that hesitated on the shore, a shining figure of white light; and behind it ran small shadowy forms waving flames, that flared red in the grey mist that was falling over the world.

Both of these examples are from later stages in the journey from Weathertop to Rivendell when Frodo is falling more and more into the wraith-world and seeing things like the Nazgûl. An interesting thing is that Frodo was able to see Glorfindel revealed in his full majesty while not wearing the Ring. This could be an indicator of how close he was coming to succombing to the Morgul blade and the Riders. The Riders too were able to perceive Glorfindel's light, according to Gandalf in the next chapter. This I would see as an argument that they are a part of the same spiritual dimension.

The first quote from Aragorn also touches on a point that I think is relevant to the Morgul blade: "they perceive many signs and forms that are hidden from us." Later Glorfindel says about the signs on the hilt: "maybe your eyes cannot see them." This would seem to indicate that only those with a connection to the spiritual realm can see/read the signs on the sword. The blade seems to have a very tight connection to the spirtual dimension; if it were just a regular sword I do not think the broken sliver would have continued to work its way inward. This is also a possible reason for why the blade disintegrated.