I had read some stories (maybe in science fiction books, maybe in comics, probably both) in which time stops for everyone except one person or group of people.
The two standard approaches to this situation are:
1) Time flows normally for you and you can basically do whatever you do normally while everyone around you appears to be frozen. (So you can breathe, gravity appears to be normal, you can pick up and move around objects that you would normally be able to move, etc.)
2) You're unable to change anything, so you can just walk around and observe things. In extreme versions of this you can't even move air, so you are stuck in place and suffocate. (I think Borges had a story where a guy who is about to be executed is frozen in time, so that even his body is completely immobile, but his thoughts are able to continue.)
I decided that the second version was more reasonable for various reasons. One of the ideas I came up with (or borrowed from somewhere -- it isn't the most original idea, but then few if any of my ideas are) is the situation where instead of time stopping it slows down for you. At or near the extreme this has a similar effect to scenario (2) above, but there should be some point at which your muscles are able to handle the (to you) increased inertia of everything around you, so that you can breathe, move things, and so on. (See,
A=S/T2, so if 1 minute of your time = 2 minutes of the outside world's time, then you have to exert four times as much force [as far as you're concerned] to move the same amount of mass the same distance as if your times matched up, which to you feels like the object has four times as much mass. Right?)
Another thing that a sped-up person would notice would be that it was suddenly cooler. Air molecules would seem to be moving slower, and of course that corresponds to a lower temperature. If you were sped up enough you could be frozen to death at room temperature. [In my original post I got this backwards, because I am a dope.]
Of course, there's no particular reason that this time-speeding process should be restricted to living beings, so I next thought about what would happen if you modified a glass of water so that time for it passed twice as quickly as the outside world. How could you distinguish it from a normal glass of water? The previous discussion indicates that one method I thought of is that they would boil and freeze at different temperatures.
Then I started thinking of what would happen if you mixed sped-up water with normal water and eventually I realized that it was all more work than it was worth, even if it did let me pass the time at the old miniature golf course. There may be a way to make a nifty science fiction story out of this, but I don't know what it is.
[I thought about this whole thing again recently because this week's New Yorker contains an article by Oliver Sacks about people whose subjective senses of time differ from the norm. (Unfortunately it doesn't appear to be in the online edition.) The article doesn't have anything to do with any of the junk discussed above, of course.]