On a recent flight from YYJ to SEA on Horizon the aircraft made a sudden upwards movement and I saw a small plane zip by underneath us. The pilot came on the PA and explained that while we were in no danger, the other aircraft had come within 1/4 mile and was too close for their comfort. He said he would be reporting this as a near miss. A 1/4 mile seems like a lot of distance but when you realize how fast space is eaten up with two planes flying torwads each other you have to wonder. Does anybody know what the FAA qualifies as a near miss?