I have experienced slowing of time in improvised couples dancing. I may have to react to very complex situations in a time frame that feels impossible.
For example, at the same time my follower can be so tense that she cannot feel leading/following signals as well as if she was relaxed, and she mis-interprets my lead and goes where I was not expecting her to go, her clothing gets stuck, another couple comes into the space I have directed our dance and we are about to crash etc. All this while I am interpreting live music in an interesting way. (This is an extreme example, most of the time things go smoothly.)
It may be unbelievable that it is possible to be able to solve such problems in split second, but it happens all the time in improvised couples dancing. The analytical mind is way too slow for it, however. If I am experiencing time that has slowed down, there is ample time to do everything. It does not even feel I need to rush it, but I can stay relaxed, and continue improvising go the music.