Being a man far from physics, I still got hold of several ideas, among which:
Observation does change the process observed.
What it has to do with prophecies:
Situation A Earnur tries to pursue Witch King, Glorfinded, judging from some data we are unaware of, warns him that 'man' can not kill him. It may be a prophecy/insight proper (like to opening of the window into another time and actually seeing 'how it happened/is going to happen'), it may be a wish to keep Earnur from foolish actions, it may be both. Glordfindel being what he is, his words are taken at face value and made somehow 'canon'. Start of the rumour: "Glorfindel said Witch King can not be killed by a man" (when all he actually said was 'Far off yet is his doom, and not by the hand of man will he fall' which may mean a lot of things. What exactly 'doom' and 'fall' may mean to be dealt with some other time, or in some other thread
)
Situation B Years pass, Witch King roams to and fro, is now and again challenged by 'living men' (Earnur included) who eventually all get killed not specifically because they are men but because Witch King is really hard to kill. The rumour grows the empirical bird - kind of confirmation of its 'truthfulness', conclusion drawn is as follows: 'See, Glorfindel said so, and indeed we see it happen - no man can kill him' (When all that happened was that noone yet killed him)
Situation C Witch King, who is aware of the situation, himself starts to believe the truth of the situation (BTW, on Wheathertop the truth of the statement was not tested - as we learn later on, wraiths withdrew of their own will, deeming their goal accomplished, waiting for Frodo to become a wraith himself). His belief also is confirmed all the time - he is not killed but kills himself
Situation D Belief on the part of Witch King mades him reckless - "I'm not going to be killed" motto makes him enter duels he would (probably) otherwise shy (encounter with Gandalf by the gate, per instance) away from or enter in with more caution. Such behavioral pattern ends him up headless - rushing in to be beheaded by a woman and a man (hobbits are men, whatever they themselves say)
Very elegant - Actually, Witch King is killed
as a result of the prophecy made by Glorfindel
. Or, back to physics - Glorfindel observing the future in fact conditiions it. (No knowing what would have happened if the prophecy haven't been made)
Conclusion: Witch King could have been killed by anyone of any race with enough guts and prowess to perform the act. His actual mode of death was at the same time a consequence of the prophecy and its confirmation.
(The situation is reminiscent to Sci-Fi 'Time-Loop Problem', when hero is sent on some mission into the future by himself returned from said future (Lem's Star Diaries, per instance, Diary #20), and it is inexplicable how the 'latter one' of himself who came back got into the future in the first place, and where (or when, rather) got he at the moment of becoming 'earlier' one, the one who was left behind when the former 'earlier' one become 'latter' one by traveling into the future in his stead. Stumbling sentences, I know, I've got lost myself)