The effect was that the shifted matter didn't exist in the normal universe.
"So why can we see the normal universe," Dax asked.
"The affairs, the wars, of the normal universe do not affect us."
Nothing crosses from this way to the normal universe.
When he returned to the normal universe, he still had the costume.
Perhaps it is a side effect of the drive, or simply an emotional reaction to isolation from the normal universe.
One moment we were in the normal universe, the next nowhere.
We don't notice the fact that it has no more contact with the normal universe.
Time itself stops when the subject is removed from the normal universe.
The normal universe had no use for an incorporeal being.